DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX A 

Dioxin Workshop Report 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
EPA/600/R-09/027 

May 2009 

Summary of U.S. EPA 

Dioxin Workshop 

February 18−20, 2009 

Cincinnati, Ohio 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 45268 
This document is a draft for review purposes only and does not constitute Agency policy. 

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DISCLAIMER 

This document summarizes the discussions presented at the Dioxin Workshop in 

February 2009, in Cincinnati, OH, as documented by the Session Co-Chairs. This document is 

not all inclusive or binding. Conclusions and recommendations to the U.S. EPA may not 

represent full consensus. The views expressed in this document are those of the Dioxin 

Workshop Panelists and do not necessarily reflect the views and policies of the U.S. 

Environmental Protection Agency. Mention of trade names or commercial products does not 

constitute endorsement or recommendation for use. 

Preferred Citation: 

U.S. Environmental Protection Agency (U.S. EPA). (2009) Summary of U.S. EPA Dioxin Workshop: 

February 18−20, 2009. U.S. Environmental Protection Agency, National Center for Environmental Assessment, 

Cincinnati, OH. EPA/600/R-09/027. 
This document is a draft for review purposes only and does not constitute Agency policy. 

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TABLE OF CONTENTS 

DIOXIN WORKSHOP TEAM ................................................................................................. A-iv 

ACKNOWLEDGMENTS ......................................................................................................... A-iv 

INTRODUCTION ...................................................................................................................... A-1 

REFERENCES ............................................................................................................... A-2 

SCIENTIFIC WORKSHOP TO INFORM THE TECHNICAL WORK PLAN FOR U.S. 

EPA’S RESPONSE TO NAS COMMENTS ON THE HEALTH EFFECTS OF 

DIOXIN PRESENTED IN U.S. EPA’S DIOXIN REASSESSMENT ................................ A-3 

SESSION 1: QUANTITATIVE DOSE-RESPONSE MODELING ISSUES................ A-3 

SESSION 2: IMMUNOTOXICITY ............................................................................... A-6 

SESSION 3A: DOSE-RESPONSE FOR NEUROTOXICITY AND 

NONREPRODUCTIVE ENDOCRINE EFFECTS............................................... A-8 

SESSION 3B: DOSE-RESPONSE FOR CARDIOVASCULAR TOXICITY 

AND HEPATOTOXICITY ................................................................................. A-11 

SESSION 4A: DOSE-RESPONSE FOR CANCER .................................................... A-13 

SESSION 4B: DOSE-RESPONSE FOR 

REPRODUCTIVE/DEVELOPMENTAL TOXICITY ....................................... A-16 

SESSION 5: QUANTITATIVE UNCERTAINTY ANALYSIS OF DOSERESPONSE.......................................................................................................... A-20 

APPENDIX A: 2009 U.S. EPA DIOXIN WORKSHOP AGENDA........................................ A-24 

APPENDIX B: 2009 U.S. EPA DIOXIN WORKSHOP QUESTIONS TO GUIDE 

PANEL DISCUSSIONS..................................................................................................... A-31 

APPENDIX C: 2009 U.S. EPA DIOXIN WORKSHOP DRAFT SELECTION 

CRITERIA TO IDENTIFY KEY IN VIVO MAMMALIAN STUDIES THAT 

INFORM DOSE-RESPONSE MODELING FOR 

2,3,7,8-TETRACHLORODIBENZO-p-DIOXIN (TCDD)................................................ A-34 
This document is a draft for review purposes only and does not constitute Agency policy. 

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DIOXIN WORKSHOP TEAM 

The Dioxin Workshop Team, under the leadership of Peter W. Preuss, Director, NCEA, 

comprised the following members: 

National Center for Environmental Assessment, Office of Research and Development, 

U.S. Environmental Protection Agency, Cincinnati, OH 45268 

 Belinda S. Hawkins 

 Janet Hess-Wilson 

 Glenn Rice 

 Jeff Swartout 

 Linda K. Teuschler 

 Bette Zwayer 

Argonne National Laboratory, Argonne, IL 60439 

 Maryka H. Bhattacharyya 

 Andrew Davidson 

 Mary E. Finster 

 Margaret M. MacDonell 

 David P. Peterson 

ACKNOWLEDGMENTS 

The Track Group, Alexandria, VA 22312 

 Kara Hennigan 

 Alan Minton 

 Brandy Quinn 

ECFlex, Inc., Fairborn, OH 45324 

 Dan Heing 

 Heidi Glick 

 Amy Prues 

 Lana Wood 

IntelliTech Systems, Inc., Fairborn, OH 45324 

 Cris Broyles 

 Luella Kessler 

 Stacey Lewis 

 Linda Tackett 
This document is a draft for review purposes only and does not constitute Agency policy. 

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INTRODUCTION 

This document provides a summary of the Scientific Workshop to Inform EPA’s 

Response to National Academy of Science Comments on the Health Effects of Dioxin in EPA’s 

2003 Dioxin Reassessment. The U.S. Environmental Protection Agency (U.S. EPA) and 

Argonne National Laboratories (ANL), through an inter-Agency agreement with the U.S. 

Department of Energy, convened this scientific workshop (“Dioxin Workshop”) on February 

18−20, 2009, in Cincinnati, Ohio. The goals of the Dioxin Workshop were to identify and 

address issues related to the dose-response assessment of 2,3,7,8-tetrachlorodibenzo-p-dioxin 

(TCDD). This report summarizes the discussions and conclusions from this workshop. 

Previously, at the request of the U.S. EPA, the National Academy of Sciences (NAS) prepared a 

report, Health Risks from Dioxin and Related Compounds: Evaluation of the EPA Reassessment

(NAS, 2006), which made a number of recommendations to improve the U.S. EPA’s risk 

assessment for TCDD (U.S. EPA, 2003). The 3-day Dioxin Workshop was convened 

specifically to ensure that the U.S. EPA’s response to the NAS recommendations focuses on the 

key issues and reflects the most meaningful science. 

The Dioxin Workshop included seven scientific sessions: 

(1) Session 1: Quantitative Dose-Response Modeling Issues 

(2) Session 2: Immunotoxicity 

(3) Session 3A: Dose-Response for Neurotoxicity and Nonreproductive Endocrine Effects 

(4) Session 3B: Dose-Response for Cardiovascular Toxicity and Hepatotoxicity 

(5) Session 4A: Dose-Response for Cancer 

(6) Session 4B: Dose-Response for Reproductive/Developmental Toxicity 

(7) Session 5: Quantitative Uncertainty Analysis of Dose-Response 

During each session, the U.S. EPA asked a panel of expert scientists to: 

• identify and discuss the technical challenges involved in addressing the key NAS 

comments on the TCDD dose-response assessment in the U.S. EPA Reassessment 

(U.S. EPA, 2003); 

• discuss approaches for addressing the key NAS comments; and 

• identify important published, independently peer-reviewed literature, particularly studies 

describing epidemiologic and in vivo mammalian bioassays, which are expected to be 

most useful for informing the U.S. EPA’s response. 

The sessions were followed by open comment periods during which members of the 

audience were invited to address the Panels. At the conclusion of the open comment periods, the 

Panel Co-Chairs were asked to summarize and present the results of the panel discussions. The 

summaries could include minority opinions stated by panelists. The main points derived from 

the session summaries were used to prepare this document. Additionally, this document includes 

a list of the session panelists and their affiliations and three appendices. Appendix A presents 

the Dioxin Workshop Agenda. Appendix B identifies the charge questions presented to the 

Panel. Appendix C describes draft study selection criteria proposed by the Dioxin Workshop 

Team for consideration by the workshop panelists. 
This document is a draft for review purposes only and does not constitute Agency policy. 

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REFERENCES 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

review draft, Volumes 1−3 (EPA/600/P-00/001Cb, Volume 1). U.S. Environmental Protection 

Agency, National Center for Environmental Assessment, Washington, DC (December). 

Available at http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 
This document is a draft for review purposes only and does not constitute Agency policy. 

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SCIENTIFIC WORKSHOP TO INFORM THE TECHNICAL WORK PLAN FOR U.S. 

EPA’S RESPONSE TO NAS COMMENTS ON THE HEALTH EFFECTS OF DIOXIN 

PRESENTED IN U.S. EPA’S DIOXIN REASSESSMENT 

Dioxin Workshop Co-Chairs: Peter W. Preuss and Glenn Rice 

The Dioxin Workshop session summaries were prepared by the session panel Co-Chairs 

with input from the panelists, as requested by the U.S. EPA prior to the workshop. The CoChairs subsequently presented these summaries to all of the workshop participants during 

designated periods at the workshop. In these summaries, the U.S. EPA asked that the Co-Chairs 

summarize the key issues from the panel discussions. Because the sessions were not designed to 

achieve consensus among the panelists, the summaries do not necessarily represent consensus 

opinions; rather, they reflect the essence of the panel discussions. Some of the specific points 

may represent the views of multiple panelists, while others only the views of a single panelist. 

Prior to the summarizations, there were opportunities for public comments on the discussion 

topics. Some Co-Chairs met with their sessions’ panelists after their sessions ended to develop 

these summaries, while others developed reports based on their personal notes. Because Session 

5 was the last session of the workshop—with little time provided to develop the summary—the 

Co-Chairs circulated a draft for comment by the Session 5 panelists after the workshop, prior to 

finalizing the session summary. The U.S. EPA collected the session summaries and then 

prepared this document. A draft of this document was distributed to all of the session Co-Chairs 

to provide them with a final opportunity to comment and make revisions. Finally, it should be 

noted that U.S. EPA was not prescriptive to the session Co-Chairs with respect to the format of 

the presentation materials and provided no specific instructions, resulting in unique formats 

among the session summaries. 

SESSION 1: QUANTITATIVE DOSE-RESPONSE MODELING ISSUES 

This session discussed the general dose-response modeling issues related to TCDD. 

Many of these issues were highlighted by NAS (2006). There was a general introductory 

presentation on TCDD kinetics, including information and uncertainties pertaining to the 

conversion of administered doses in animals to human body burden (BB) and additivity to 

background issues. This presentation was followed by a Panel discussion on the state of the 

science regarding dioxin dose-response modeling issues. 

Session 1 Panelists (Session Co-Chairs are identified by asterisk) 

• Bruce Allen, Bruce Allen Consulting 

• Lesa Aylward, Summit Toxicology 

• Roger Cooke, Resources for the Future 

• Kenny Crump, Louisiana Tech University 

• Mike DeVito, U.S. EPA 

• Dale Hattis, Clark University 

• Rick Hertzberg, Biomath Consulting 

• Rob McDowell, U.S. Department of Agriculture 

• Jim Olson, State University of New York, University at Buffalo 
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• *Lorenz Rhomberg, Gradient 

• Woody Setzer, U.S. EPA 

• *Jeff Swartout, U.S. EPA 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-Chair and 

represent a synopsis of the panel discussions. 

Key Study Selection Criteria 

 The Panel discussed the advantages and disadvantages of using key study criteria 

(Appendix C). They concluded that a priori criteria foster transparency and consistency, and 

could deflect a posteriori criticism. However, the Panel also acknowledged that having a priori

criteria could introduce the potential for excluding useful data. Although the key study criteria 

provided by the U.S. EPA listed studies using TCDD only as a criterion, the Panel posed the 

possibility of using closely related dioxin-like compounds (DLCs) as surrogates for TCDD. The 

criterion for use of data from mammalian studies only was one criterion that received generalized 

support due to the lack of extrapolation protocols for nonmammalian species. The Panel also 

discussed the specific exposure-duration criterion and asked if there should be a preference for 

longer-term rather than acute studies. The Panel made three suggestions to modify U.S. EPA’s 

key study selection criteria: 

(1) Define more relevant exposure-level (i.e., dose) cut points using tissue concentrations. 

(2) Reword statistical criteria to include do-it-yourself analysis. 

(3) Reword the response criteria to clarify “outside of normal range.” 

Dose Metrics 

 The Panel discussed the relative merits of various measures of dose for modeling TCDD 

dose response. One general conclusion was that tissue concentration (TC) is the preferred 

metric, especially lipid-adjusted TC, because this measure more closely approximates exposures 

close to the target tissue when compared to administered doses. However, the Panel 

acknowledged that these data are often unavailable. They further noted that BB, which is 

defined as the concentration of TCDD in the body (ng/kg body weight) (U.S. EPA, 2003), might 

be useful as a surrogate for TC provided the two measures were proportional. 

The Panel suggested that a linear approach to BB estimation, which was utilized by 

U.S. EPA (2003), is too simplistic because this approach does not take into account toxicokinetic 

issues related to TCDD—e.g., sequestration in the liver and fat, age-dependent elimination, and 

changing elimination rates over time. The Panel recommended the use of kinetic/mechanistic 

modeling to the extent possible to quantify tissue-based metrics. 

The Panel raised the issue of whether the preferred dose metric would be different for 

different endpoints and exposure durations. This led to the Panel’s comment that the peak 

exposure might be a more important metric than average BB for variable exposure scenarios. 

Given this discussion about different exposure durations being relevant to a specific endpoint, 

the Panel suggested that the U.S. EPA also consider peak measures in dose-response modeling. 
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The last point raised in this part of the discussion centered on the possibility of dose 

errors in experimental studies. The Panel highlighted the need for the U.S. EPA to consider dose 

error (i.e., uncertainty in the x-axis of the dose-response curve) when using dose surrogates. 

Dose-Response Modeling of Mammalian Bioassays 

 The Panel considered several issues related to dose-response modeling of mammalian 

bioassay data for TCDD: supralinearity and incomplete response data (“anchoring”), defining the 

benchmark response (BMR) level with respect to establishing the point of departure (POD), and 

the use of threshold modeling—as further explained below. 

 The Panel discussed the specific issues of supralinearity and anchoring raised by the 

U.S. EPA with respect to modeling noncancer endpoints. The panel recognized that, for many of 

the most sensitive endpoints, the response at the lowest dose is high (e.g., quantal responses 

above 25% and continuous endpoints differ substantially from the mean, often implying 100% 

incidence in the treated animals). This lack of response anchoring at the low end of the doseresponse curve (near the BMR) results in the higher responses determining the shape of the 

curve. 

The Panel asked whether new tools might be needed or whether the current tools could be 

applied differently. In the context of developing new tools, the Panel emphasized the need for 

collaboration between biologists and mathematicians. When discussing application, the Panel 

suggested that the problem with supralinearity might be overcome by simply dropping the 

requirement for using the lower bound on the Benchmark Dose. In addition, the Panel posed 

several more approaches for further consideration in dose-response modeling by the U.S. EPA: 

(1) Combine similar data sets to fill in data gaps. 

(2) Use mechanistic approaches to model the data gaps. 

(3) Dichotomize continuous data. 

Finally, the Panel acknowledged that, in certain situations, there simply may not be enough 

information to provide meaningful answers. 

 The Panel discussed the BMR level for establishing a POD in the context of deriving a 

Reference Dose (RfD). The Panel generally agreed that, while the effective dose level (ED01) 

used in the 2003 Reassessment may be useful for comparative analysis across endpoints, the 

ED01 estimates developed for all endpoints considered in the Reassessment were not appropriate 

for deriving an RfD because they were not based on the effect’s adversity. The panel noted that 

ED01 also is much lower than typical EPA BMR levels. The Panel recommended that the U.S. 

EPA work to define endpoint-specific BMRs based on the consideration of adversity. Given that 

the same uncertainty factor framework is applied to all PODs, the Panel emphasized the need for 

consistency in BMRs; numerical consistency is needed for quantal BMRs and consistency in the 

choice of biological relevance should be applied for continuous BMRs. 

 The Panel generally discouraged threshold modeling by stating that thresholds are very 

difficult to pin down and suggested that the lower bound may always be zero. 
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Dose-Response Modeling of Epidemiological Studies 

 The Panel noted that many studies have been published with measured concentrations of 

TCDD that could be used for dose reconstruction. In this discussion, the Panel acknowledged 

that use of these data would entail dealing with toxicity equivalence (TEQ) issues and 

pharmacokinetic (PK) modeling. Pertaining to the use of these data for quantitative risk 

assessment by the U.S. EPA, the Panel posed the question, “At what point does indirect or 

confounded human data supersede controlled animal bioassay data?”, or alternatively, “How 

much human data uncertainty can we tolerate?” The Panel suggested, at the least, that the 

epidemiologic data could be used to “ground-truth” the animal bioassay modeling results. 

Supporting Information 

The Panel acknowledged that Ah receptor (AhR) binding affinities are not necessarily 

tied to endpoint sensitivity, but they reiterated the need to consider mechanistic modeling to aid 

in developing appropriate dose metrics or filling in data gaps in the existing dose-response data. 

References 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

Review Draft (EPA/600/P-00/001Cb). U.S. Environmental Protection Agency, National Center 

for Environmental Assessment, Washington, DC. Available at 

http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

SESSION 2: IMMUNOTOXICITY 

The U.S. EPA plans to consider development of a quantitative dose-response assessment 

for the immunologic effects associated with TCDD exposure. Such an assessment would be 

based on information in U.S. EPA (2003), NAS (2006) and key studies identified in this 

workshop. The purpose of this session was to identify and discuss key issues pertaining to doseresponse assessment for dioxin-induced immunologic effects. 

Session 2 Panelists (Session Co-Chairs are identified by asterisk) 

• Roger Cooke, Resources for the Future 

• Rob Goble, Clark University 

• *Belinda Hawkins, U.S. EPA 

• Nancy Kerkvliet, Oregon State University 

• Manolis Kogevinas, Centre for Research in Environmental Epidemiology 

• Robert Luebke, U.S. EPA 

• Paolo Mocarelli, University of Milan 

• *Allen Silverstone, State University of New York, Upstate Medical University 
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• Courtney Sulentic, Wright State University 

• Nigel Walker, National Institute of Environmental Health Sciences 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-Chair and 

represent a synopsis of the panel discussions. 

Key Study Selection Criteria 

The Panel first addressed the Key Study Selection Criteria proposed by the U.S. EPA 

(Appendix C). The Panel raised the issue that the key study criteria do not apply to most studies 

designed to investigate immunotoxicity, including those used to calculate ED01s (U.S. EPA, 

2003). The Panel observed that most dioxin immunotoxicity studies are relatively high dose 

(>200 ng/kg-d) acute studies and/or use parenteral rather than oral administration. 

The Panel discussed several studies often considered important for assessing the 

immunotoxic effects of TCDD exposure. The Oughton et al. (1995) mouse bioassay was 

discussed and, although the study does meet the proposed criteria, it could not be considered a 

key study; specifically, the Panel contended that since there were no functional alterations 

observed or measured in this bioassay, the changes in cellular phenotypes are only “suggestive” 

of immune alterations and cannot be regarded as having immunopathologic significance. 

 The Panel discussed two additional studies for further consideration by the U.S. EPA: 

• Baccarelli et al. (2002). The Panel discussed this as a potentially key human 

epidemiological study that should be reviewed and considered further by the U.S. EPA. 

It measured the level of IgG, demonstrating a significant decline relative to dioxin body 

burdens. 

• Smialowicz et al. (2008). The Panel noted that this study identified the antibody response 

to sheep red blood cells (SRBCs) as the critical effect, labeling this protocol as a 

functional assay. The Panel stated that if modeled, the U.S. EPA could calculate the 

BMR for this endpoint as 1 standard deviation from the control mean. 

References 

Baccarelli, A., P. Mocarelli, D.G. Patterson et al. 2002. Immunologic effects of dioxin: New 

results from Seveso and comparison with other studies. Environ. Health Perspect. 

110(12):1169-1173. 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

Oughton, J.A., C.B. Pereira, G.K. Dekrey, J.M. Collier, A.A. Frank and N.I. Kerkvliet. 1995. 

Phenotypic analysis of spleen, thymus, and peripheral blood cells in aged C57BI/6 mice 

following long-term exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin. Toxicol. Sci. 25(1):60-69. 
This document is a draft for review purposes only and does not constitute Agency policy. 

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Smialowicz, R.J., M.J. DeVito, W.C. Williams and L.S. Birnbaum. 2008. Relative potency 

based on hepatic enzyme induction predicts immunosuppressive effects of a mixture of 

PCDDS/PCDFS and PCBS. Toxicol. Appl. Pharmacol. 227(3):477-484. 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

Review Draft (EPA/600/P-00/001Cb). U.S. Environmental Protection Agency, National Center 

for Environmental Assessment, Washington, DC. Available at 

http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

SESSION 3A: DOSE-RESPONSE FOR NEUROTOXICITY AND NONREPRODUCTIVE 

ENDOCRINE EFFECTS 

The U.S. EPA plans to consider development of a quantitative dose-response assessment 

for neurological and/or nonreproductive endocrine effects associated with TCDD exposure. 

Such an assessment would be based on information in U.S. EPA (2003), NAS (2006) and key 

studies identified in this workshop. The purpose of this session was to identify and discuss key 

issues pertaining to dose-response assessment for dioxin-induced neurological and/or 

nonreproductive endocrine effects. 

 

Session 3A Panelists (Session Co-Chairs are identified by asterisk) 

• *Maryka Bhattacharyya, Argonne National Laboratory 

• Mike DeVito, U.S. EPA 

• Mary Gilbert, U.S. EPA 

• Rob Goble, Clark University 

• Nancy Kerkvliet, Oregon State University 

• Fumio Matsumura, University of California-Davis 

• Paolo Mocarelli, University of Milan 

• Chris Portier, National Institute of Environmental Health Sciences 

• Lorenz Rhomberg, Gradient 

• Allen Silverstone, State University of New York, Upstate Medical University 

• Marie Sweeney, National Institute of Occupational Safety and Health 

• *Bernie Weiss, University of Rochester 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-Chair and 

represent a synopsis of the panel discussions. 

What Are the Key Questions Regarding These Endpoints? 

The Panel used the following question to initiate discussion: “Are there identifiable 

indices of neurotoxicity and nonreproductive endocrine effects in animal studies and human 

populations?” Under this discussion topic, the Panel discussed three endpoints: neurotoxicity 

(with focus on developmental exposures), thyroid dysfunction (e.g., thyroid hormone deficits), 

and diabetes. The Panel also addressed the relevance of windows of vulnerability to each 
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endpoint. The Panel acknowledged that, in some cases, the window of exposure may precede the 

window of expression of toxicity. 

Epidemiological Study Selection 

Developmental Neurotoxicity 

The Panel recognized that an unusual feature for this endpoint is that there are sufficient 

human data for dose-response modeling (e.g., Dutch children [Huisman et al., 1995; Patandin et 

al., 1999] and U.S. children [Jacobson and Jacobson, 1996]) and there is an internal dose metric 

(serum concentrations). Additionally, the Panel discussed recent studies that address this 

endpoint in humans (from Japan [reference not provided] and Holland [e.g., Koopman-Esseboom 

et al., 1996; Vreugdenhil et al., 2002]). For continued investigation into this endpoint, the Panel 

raised two issues to the U.S. EPA: 

• Conduct an evaluation of whether a modeled effect can be attributed to TCDD and not 

some other persistent organic pollutant (POP), although the Panel recognized that it is 

unlikely U.S. EPA will be able to distinguish among these exposures because other POPs 

are intrinsic confounders in the Dutch study. 

• Allow animal data to inform the dose-response modeling of epidemiological data.

Thyroid Dysfunction 

The Panel identified the availability of human data for this endpoint (e.g., Calvert et al., 

1999; Koopman-Esseboom et al., 1994). Much of the thyroid dysfunction literature has been 

published since the 2003 Reassessment (e.g., Wang et al., 2005; Baccarelli et al., 2008). The 

Panel also noted the availability of an internal dose metric (serum concentrations). Additionally, 

the Panel discussed the mechanistic studies in animals that link TCDD to thyroid dysfunction. 

For continued investigation into this endpoint, the Panel raised three issues for the U.S. EPA to 

consider: 

• Consider the newly available human data since the Reassessment. 

• Investigate and clarify of the role of TCDD-induced thyroid dysfunction in 

developmental neurotoxicity. 

• Evaluate and determine whether an effect can be attributed to TCDD or other 

contaminants. 

Diabetes 

The Panel discussed that data suggest that diabetes incidence in those under 55 years old 

may be associated with exposure to PCBs. They acknowledged that whether this is a dioxin-like 

compound (DLC) mediated effect or whether other POPs are responsible is still undetermined. 

The Panel also acknowledged that no animal model exists for the investigation of xenobioticinduced diabetes, and that separating the injury dose level from the current body burdens would 

depend on good pharmacokinetics in humans. For continued investigation into this endpoint, the 

Panel listed two issues for the U.S. EPA to consider: 

• Results from the Anniston study and the Great Lakes Fishermen study (references not 

provided) should be examined for dose metrics (both studies examine human PCB 

exposures). 
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• Changes of adipose tissue status need to be considered, given that dieting can cause 

release of lipid-soluble contaminants. 

References 

Baccarelli, A., S.M. Giacomini, C. Corbetta et al. 2008. Neonatal thyroid function in Seveso 25 

years after maternal exposure to dDioxin. PLoS Med. 5(7):e161.

doi:10.1371/journal.pmed.0050161. 

Calvert, G.M., M.H. Sweeney, J. Deddens and D.K. Wall. 1999. Evaluation of diabetes 

mellitus, serum glucose, and thyroid function among United States workers exposed to 

2,3,7,8-tetrachlorodibenzo-p-dioxin. Occ. Env. Med. 56:270-276. 

Huisman, M., C. Koopman-Esseboom, V. Fidler et al. 1995. Perinatal exposure to 

polychlorinated biphenyls and dioxins and its effect on neonatal neurological development. 

Early Hum. Devel. 41(2):111-127. 

Jacobson, J.L. and S.W. Jacobson. 1996. Intellectual impairment in children exposed to 

polychlorinated biphenyls in utero. N. Engl. J. Med. 335:783–789. 

Koopman-Esseboom, C., N. Weisglas-Kuperus, M.A.J. de Ridder, C.G. Van der Paauw, 

L.G.M.Th. Tuinstra and P.J.J. Sauer. 1996. Effects of polychlorinated biphenyl/dioxin exposure 

and feeding type on infants’ mental and psychomotor development. J. Pediatr. 97(5):700-706. 

Koopman-Esseboom, C., D.-C. Morse, N. Weisglas-Kuperus et al. 1994. Effects of dioxins and 

polychlorinated biphenyls on thyroid hormone status of pregnant women and their infants. 

Pediatr. Res. 36:468–473. 

Patandin, S., C.I. Lanting, P.G.H. Mulder, E.R. Boersma, P.J.J. Sauer and N. Weisglas-Kuperus. 

1999. Effects of environmental exposure to polychlorinated biphenyls and dioxins on cognitive 

abilities in Dutch children at 42 months of age. J. Pediatr. 134:33–41. 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

Review Draft (EPA/600/P-00/001Cb). U.S. Environmental Protection Agency, National Center 

for Environmental Assessment, Washington, DC. Available at 

http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

Vreugdenhil, H.J., C.I. Lanting, P.G. Mulder, E.R. Boersma and N. Weisglas-Kuperus. 2002. 

Effects of prenatal PCB and dioxin background exposure on cognitive and motor abilities in 

Dutch children at school age. J. Pediatr. 140:48–56. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-11 DRAFT—DO NOT CITE OR QUOTE 

Wang S.L., P.H. Su, S.B. Jong, Y.L. Guo, W.L. Chou and O. Päpke. 2005. In utero exposure to 

dioxins and polychlorinated biphenyls and its relations to thyroid function and growth hormone 

in newborns. Environ. Health Perspect. 113:1645–1650. 

SESSION 3B: DOSE-RESPONSE FOR CARDIOVASCULAR TOXICITY AND 

HEPATOTOXICITY 

The U.S. EPA plans to consider development of a quantitative dose-response assessment 

for cardiovascular and/or hepatic effects associated with TCDD exposure. Such an assessment 

would be based on information in U.S. EPA (2003), NAS (2006) and key studies identified in 

this workshop. The purpose of this session was to identify and discuss key issues pertaining to 

dose-response assessment for dioxin-induced cardiovascular and/or hepatic effects. 

Session 3B Panelists (Session Co-Chairs are identified by asterisk) 

• Bob Budinksy, Dow Chemical 

• Manolis Kogevinas, Centre for Research in Environmental Epidemiology 

• Rob McDowell, U.S. Department of Agriculture 

• Jim Olson, State University of New York, University at Buffalo 

• Marian Pavuk, Agency for Toxic Substances and Disease Registry 

• *Jeff Swartout, U.S. EPA 

• *Mary Walker, University of New Mexico 

• Nigel Walker, National Institute of Environmental Health Sciences 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-chair and 

represents a synopsis of the panel discussions. 

Key Study Selection Criteria 

 The Panel initially focused on the draft key study selection criteria offered by the 

U.S. EPA (Appendix C). The panel recommended that for cardiovascular effects, which are not 

usually observed in rodents, the use of knockout mouse models (ApoE KO and LDLR KO) be 

moved to the “primary” column because only these studies establish the cardiovascular toxicity 

model in mice. 

The panel also was concerned that the gavage procedure can increase mouse blood 

pressure. Consequently, the panel recommended that gavage studies not be used for the blood 

pressure endpoint (i.e., only dietary dosing studies should be considered). 

Human Health Endpoints 

 In relation to the hepatic endpoint, the Panel acknowledged the large body of dose 

response information on hepatic effects in rodents and that enzyme (mostly CYP1A1) induction 

was a sensitive effect. However, the Panel cited the lack of linkage of CYP1A1 to downstream 

events, which complicates the toxicological interpretation of this endpoint, and concluded that 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-12 DRAFT—DO NOT CITE OR QUOTE 

the more important liver effects in rodents are probably on the “road to cancer.” The Panel noted 

that hepatic effects were not seen in the epidemiological studies, but acknowledged that these 

studies were not designed to detect them. 

In relation to the cardiovascular endpoint, the Panel identified hypertension and ischemic 

heart disease (IHD) as two key endpoints from the epidemiological studies. The Panel 

recommended that the U.S. EPA perform a meta-analysis of these data. The Panel also 

commented that recent animal studies support the observations linking TCDD exposure to IHD 

and hypertension. In particular, the National Toxicology Program (NTP) study shows 

inflammatory and structural effects on resistant vascular arterioles (NTP, 2006). Additional 

evidence from the study suggests that the vascular effects may be CYP1A1-dependent. The 

Panel suggested that the NTP study data might be used as a surrogate for dose-response 

modeling of hypertension and that such an approach would be supported by data on the role of 

AhR in vascular function and remodeling. 

POD Issues 

The Panel was not supportive of 1% of maximal response (ED01), which was utilized in 

the 2003 Reassessment. The Panel concluded that the POD should depend on the specific 

endpoint and recommended the following to the U.S. EPA: 

• For continuous measures, base the BMR on difference from control. Consider the 

adversity level—at what point does the endpoint become adverse? 

• For incidence data, set the BMR to a fixed-risk level. 

Supporting Information 

The Panel posed several suggestions to the U.S. EPA for reducing uncertainty and 

improving the knowledge base for TCDD toxicity. 

• Use in vitro data to define uncertainties, such as the relative sensitivity between rodents 

and humans and around the definition of a POD. 

• Consider studies on dioxin-like compounds (DLCs). 

• Use PK modeling to define the dose metric for hepatic effects. 

• Use body burden or serum concentrations for cardiovascular endpoints. 

Finally, the Panel recommended that U.S. EPA finish the reassessment quickly and establish a 

definitive plan to review and incorporate new data as they become available. 

References 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-13 DRAFT—DO NOT CITE OR QUOTE 

NTP (National Toxicology Program). 2006. Toxicology and Carcinogenesis Studies of 

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) (CAS No. 1746-01-6) in Female Harlan SpragueDawley Rats (Gavage Studies). U.S. Department of Health and Human Services. NTP TR 521. 

Research Triangle Park, NC (April). 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

Review Draft (EPA/600/P-00/001Cb). U.S. Environmental Protection Agency, National Center 

for Environmental Assessment, Washington, DC. Available at 

http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

SESSION 4A: DOSE-RESPONSE FOR CANCER 

The U.S. EPA plans to consider development of a quantitative dose-response assessment 

for cancer associated with TCDD exposure. Such an assessment would be based on information 

in U.S. EPA (2003), NAS (2006) and key studies identified in this workshop. The purpose of 

this session was to identify and discuss key issues pertaining to dose-response assessment for 

dioxin-induced cancer. 

Session 4A Panelists (Session Co-Chairs are identified by asterisk) 

• Lesa Aylward, Summit Toxicology 

• Kenny Crump, Louisiana Tech University 

• Dale Hattis, Clark University 

• *Janet Hess-Wilson, U.S. EPA 

• Karen Hogan, U.S. EPA 

• Manolis Kogevinas, Centre for Research in Environmental Epidemiology 

• Marian Pavuk, Agency for Toxic Substances and Disease Registry 

• Chris Portier, National Institute of Environmental Health Sciences 

• Lorenz Rhomberg, Gradient 

• Jay Silkworth, General Electric 

• *Nigel Walker, National Institute of Environmental Health Sciences 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-chair and 

represent a synopsis of the panel discussions. 

Key Study Selection 

 The Panel discussed both human and rodent studies. In reviewing the epidemiological 

data, the Panel agreed the EPA should focus on four cohort studies (Dutch cohort, NIOSH 

cohort, BASF accident cohort, and Hamburg cohort) and pointed out that there are numerous 

updates and reevaluations of data now in the literature and others will be published soon. The 

Panel stated that it is appropriate for the U.S. EPA to consider the increase in total cancers for 

modeling human cancer data, however, Non-Hodgkin's lymphoma, and lung tumors are the main 

TCDD-related cancer types seen in humans exposed to TCDD. The Panel suggested the U.S. 

EPA focus the quantitative dose-response modeling on the human data. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-14 DRAFT—DO NOT CITE OR QUOTE 

In reviewing the rat data, the Panel identified four new NTP rodent cancer bioassays with 

liver and lungs as the main target organs. However, they suggested that dose-response modeling 

efforts should model “all cancers” from these NTP data sets as well and use tumor incidence—

not individual rats as measures. 

Key Study Selection Criteria 

The Panel discussed whether data for TCDD only should be used or if PCB126 could be 

used to develop a dose-response curve. From this discussion, the Panel reached a general 

agreement that limiting the dose-response modeling and cancer assessment to TCDD only would 

be the best approach. 

Regarding the oral dosing regimens, the Panel discussed the differences in results from 

different bioassays. They concluded that there were insufficient data to pick between oral feed 

(Kociba et al., 1978) and oral gavage (NTP, 2006) studies, but stated “If all aspects of studies 

were equal, an oral feed study is preferred.” However, given that current data sets are not equal, 

they agreed that U.S. EPA should consider both feed and gavage studies. 

The Panel put forth the recommendation that studies that include initiation-promotion 

model data and TgAC transgenic model data from oral exposure studies should be excluded from 

the primary category in the key study selection criteria (Appendix C lists the draft study selection 

criteria distributed prior to the meeting). Studies from both classifications should be moved to 

the second tier. 

The Panel was also unsupportive of the “response magnitude outside the range of normal 

variability” criterion, as they did not believe it was applicable to a cancer endpoint. 

Critical Endpoints to Consider 

 The Panel recognized that the MOA for TCDD includes cell growth/differentiation 

dysregulation, that different endpoints (tumor types) across species may be expected, and that 

there are differences in tumor sites across species. The Panel further acknowledged that there is 

insufficient information to determine if rodent tumor types observed are relevant to humans. 

Thus, the Panel suggests the following: 

• U.S. EPA should consider all the observed cancer endpoints in its evaluation. 

Nonlinear (aka threshold) Versus Linear Dose-Response Modeling 

 The Panel agreed that NTP bioassays appear to demonstrate nonlinear dose response, but 

they expressed concern about using animal data to infer slope and dose response for humans. 

The Panel pointed out that there are differences in slopes across different bioassays, and 

specifically, that some appear linear while others appear nonlinear. Given the observation of 

both nonlinear vs. linear, the Panel concluded that neither could be ruled out for extrapolation 

below the POD simply based on the available data. One panelist noted that U.S. EPA Cancer 

Guidelines (U.S. EPA, 2005) state that only if one can demonstrate that the MOA has a threshold 

dose-response shape, and can exclude all other potential linear MOAs, can one use a nonlinear 

model. Lastly, the Panel noted that there are data and rationales to support use of both linear and 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-15 DRAFT—DO NOT CITE OR QUOTE 

nonlinear response below POD. From this discussion, the Panel raised one possibility to the U.S. 

EPA: 

• Both linear and nonlinear model functions should be considered in the dose-response 

analysis. 

Dose Metrics 

 In considering human data, the Panel expressed a preference for lipid-adjusted serum 

levels over body burden (BB), and they expressed concerns over the assumptions used in the 

back calculation of the BB in the epidemiologic cohorts. In considering the rat data, the Panel 

supported the use of BB—especially lipid-adjusted BB. The Panel, however, did express 

concern over the sequestering of TCDD in liver and then the use of liver levels in BB 

calculations. 

Supporting Information—Biologically-Based Dose-Response (BBDR) Models and MOA 

The Panel discussed BBDR. Though once considered an attractive proposition, BBDR 

models may mask uncertainty within the models, necessitating them to be used with greater 

caution. The Panel suggested two issues for the U.S. EPA to consider: 

• If there is a published model, use it if it is valid—do not generate a new model. 

• Focus on the actual experimental data to drive the analysis. 

References 

Kociba, R.J., D.G. Keyes, J.E. Beyer et al. 1978. Results of a two-year chronic toxicity and 

oncogenicity study of 2,3,7,8-tetrachlorodibenzo-p-dioxin in rats. Toxicol. Appl. Pharmacol. 

46:279-303. 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

NTP (National Toxicology Program). 2006. Toxicology and Carcinogenesis Studies of 

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) (CAS No. 1746-01-6) in Female Harlan SpragueDawley Rats (Gavage Studies). U.S. Department of Health and Human Services. NTP TR 521. 

Research Triangle Park, NC (April). 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

Review Draft (EPA/600/P-00/001Cb). U.S. Environmental Protection Agency, National Center 

for Environmental Assessment, Washington, DC. Available at 

http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

U.S. EPA (U.S. Environmental Protection Agency). 2005. Guidelines for Carcinogen Risk 

Assessment. U.S. Environmental Protection Agency Risk Assessment Forum. 

EPA/630/P-03/001F. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-16 DRAFT—DO NOT CITE OR QUOTE 

SESSION 4B: DOSE-RESPONSE FOR REPRODUCTIVE/DEVELOPMENTAL 

TOXICITY 

The U.S. EPA plans to consider development of a quantitative dose-response assessment 

for reproductive and developmental effects associated with TCDD exposure. Such an 

assessment would be based on information in U.S. EPA (2003), NAS (2006) and key studies 

identified in this workshop. The purpose of this session was to identify and discuss key issues 

pertaining to dose-response assessment for dioxin-induced reproductive and developmental 

effects. 

Session 4B Panelists (Session Co-Chairs are identified by asterisk) 

• Barbara Abbott, U.S. EPA 

• Bruce Allen, Bruce Allen Consulting 

• Roger Cooke, Resources for the Future 

• George Daston, Procter & Gamble 

• Mike DeVito, U.S. EPA 

• Rob Goble, Clark University 

• *Fumio Matsumura, University of California-Davis 

• Paolo Mocarelli, University of Milan 

• Brian Petroff, University of Kansas 

• *Glenn Rice, U.S. EPA 

• Marie Sweeney, National Institute of Occupational Safety and Health 

• Mary Walker, University of New Mexico 

• Bernie Weiss, University of Rochester 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-Chair and 

represent a synopsis of the panel discussions. 

A Major Question Posed During this Workshop Session was “Are Human Embryos and 

Infants Less Sensitive to Dioxin Exposures Than Some Experimental Animals?” 

The Panel recognized that animal data show a wide range of species sensitivity to dioxin 

for a given developmental or reproductive endpoint. Presently, there are data for some endpoints 

that show that human sensitivity is comparable to experimental animals (e.g., semen quality), 

and for other endpoints the data demonstrate that humans are insensitive compared to other 

species (e.g., cleft palate). Lastly, the Panel recognized that there are some endpoints for which 

relative human sensitivity remains uncertain. 

Key Study Selection 

 The Panel reviewed the charge questions (Appendix B), discussed them, and listed two 

issues for the U.S. EPA to consider: 

• Concerning key study determination, use a stepwise approach that is dependent upon the 

information available and needed to address the question. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-17 DRAFT—DO NOT CITE OR QUOTE 

• Concerning the key studies informing the POD and the POD endpoint choice, use the 

POD to depart from what is certain and use a high-confidence study that has found 

effects at a low enough level at which other effects are protected. 

The Panel also developed Table 1, based on the information presented in this session. Table 1 

identifies specific reproductive and developmental effects of concern, listing whether an effect 

has been observed in test animals and epidemiologic cohorts. It also identifies the ED10

estimated by the U.S. EPA (2003) for health effects observed in rodent bioassays. If the U.S. 

EPA did not report an ED10 for an effect, the table identifies a study where the effect was 

reported and the lowest study dose where the effect was observed. Table 1 also identifies the 

epidemiologic cohort where the specific reproductive and developmental effects were observed. 

Epidemiological Study Utility 

The Panel reviewed the charge questions (Appendix B), discussed them, and made two 

suggestions to the U.S. EPA: 

• Concerning the ability of epidemiological studies to inform critical effects, start with 

concordance across species (including humans) for the spectrum of effects. 

• Concerning the ability of epidemiological studies to inform dose-response modeling, start 

with the epidemiology and then go to animal data if the dose response has not been well 

characterized for an endpoint of interest and compare to animal data as a reality check. 

Animal Model Utility 

The Panel reviewed and discussed the charge questions (Appendix B). Table 1, which 

identifies the effects that occur in animals and also have relevance to humans, summarizes much 

of this discussion. Regarding the influence of mode of action (MOA) on animal model choice, 

the Panel concluded that by evaluating concordance among health effects reported in 

epidemiologic and animal bioassay data, the U.S. EPA could identify a set of plausible 

reproductive and developmental effects to consider. Actual animal and human MOA 

information is helpful in that it creates comfort with the animal models and in defining the 

boundaries of possible effects. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-18 DRAFT—DO NOT CITE OR QUOTE 

TABLE 1 

Reproductive/Developmental Effects of Concern for Human Health 

Endpoint Rodent 

(ED10 ng/kg-d) Human Notes 

Sperm Count/Motility Yes (6.2−28; 

66−200) 

Yes ED10 bases Mabley et al. (1992a,b) caudal 

sperm count and daily sperm production 

range from 6.2−28; Gray et al. (1997) 

epididymal sperm count and total testis sperm 

counts range from 66−200. 

Sex Ratio No Yes, Seveso 

Delayed Puberty Males Yes (94) Yu-cheng ED10 basis rat male puberty delay Gray et al. 

(1997). Need to qualify epidemiology data 

because of cohort PCDD/PCDFs exposures. 

Delayed Puberty in Females Yes No in Seveso Gray and Ostby (2002) report delayed 

puberty in female offspring of pregnant rats 

receiving a single dose of 1 μg TCDD/kg on 

GD 15. 

Cleft Palate Yes (6300−6400) No ED10 basis Birnbaum et al. (1989). 

Premature Senescence Yes No, Seveso Franczak et al. (2006) report that rats 

prematurely entered reproductive senescence, 

after receiving cumulative TCDD doses as 

low as 1.7 μg TCDD/kg. They considered 

first occurrence of prolonged interestrous 

interval (>6 d) as evidence of onset of 

reproductive senescence. 

Hormones E2 Yes Yes, Males—

Seveso 

Li et al. (1995) report serum estradiol-17β

(E2) concentrations induced by equine 

Chorionic Gonadotropin injection were 

significantly elevated in female rats orally 

administered 10 μg/kg TCDD on PND 22. 

While E2 decreased dramatically in control 

animals during the preovulatory LH surge, it 

did not in TCDD-treated rats. 

Low Birth Weight Yes (190) Suggestive 

effect in Seveso 

in first 8 years 

after exposure 

ED10 basis Gray et al. (1997). 

Reproductive Cycling 

(prolongation) 

Yes Yes, Seveso 

Prepubertal 

exposure 

Franczak et al. (2006) report loss of normal 

cyclicity in female rats at 8 months of age

following a cumulative dose of 1.7 μg 

TCDD/kg.
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-19 DRAFT—DO NOT CITE OR QUOTE 

Supporting Information 

 The Panel reviewed the charge questions (Appendix B), discussed them, and made two 

suggestions to the U.S. EPA: 

• Concerning deviation from default approaches for noncancer endpoints, there needs to be 

a careful assessment of the POD and the application of uncertainty factors in light of 

PK/pharmacodynamics (PD), population characteristics and variability, and MOA 

information. 

• Concerning the MOA’s ability to clarify endpoint and the incorporation of a cascade of 

cellular event into dose-response for noncancer endpoint, any study that helps inform the 

dose response should be considered—including studies not specific to dioxins. 

Complicated mechanistic models need not be developed. Standard dose-response models 

can be applied. One can look at the cascade of events in a stepwise, simple way. 

References 

Birnbaum, L.S., M.W. Harris, L.M. Stocking et al. 1989. Retinoic acid and 2,3,7,8-

tetrachlorodibenzo-p-dioxin selectively enhance teratogenesis in C57BL/6N mice. Toxicol. 

Appl. Pharmacol. 98:487-500. 

Franczak, A., A. Nynca, K.E. Valdez, K.M. Mizinga and B.K. Petroff. 2006. Effects of acute 

and chronic exposure to the aryl hydrocarbon receptor agonist 2,3,7,8-tetrachlorodibenzop-dioxin on the transition to reproductive senescence in female Sprague-Dawley rats. Biol. 

Reprod. 74:125-130. 

Gray, L.E. and J.S. Ostby. 2002. In utero 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) alters 

reproductive morphology and function in female rat offspring. Toxicol. Appl. Pharmacol. 

133(2):285-294. 

Gray, L.E., J.S. Ostby and W.R. Kelce. 1997. A dose-response analysis of the reproductive 

effects of a single gestational dose of 2,3,7,8-tetrachlorodibenzo-p-dioxin in male Long Evans 

Hooded rat offspring. Toxicol. Appl. Pharmacol. 146:11-20. 

Li, X., D.C. Johnson and K.K. Rozman. 1995. Reproductive effects of 2,3,7,8-

tetrachlorodibenzo-p-dioxin (TCDD) in female rats: ovulation, hormonal regulation, and possible 

mechanism(s). Toxicol. Appl. Pharmacol. 133:321-327. 

Mably, T.A., D.L. Bjerke, R.W. Moore et al. 1992a. In utero and lactational exposure of male 

rats to 2,3,7,8-tetrachlorodibenzo-p-dioxin. 3. Effects on spermatogenesis and reproductive 

capability. Toxicol. Appl. Pharmacol. 114:118-126. 

Mably, T.A., R.W. Moore, R.W. Goy et al. 1992b. In utero and lactational exposure of male 

rats to 2,3,7,8-tetrachlorodibenzo-p-dioxin. 2. Effects on sexual behavior and the regulation of 

luteinizing hormone secretion in adulthood. Toxicol. Appl. Pharmacol. 114:108-117. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-20 DRAFT—DO NOT CITE OR QUOTE 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds. NAS 

Review Draft (EPA/600/P-00/001Cb). U.S. Environmental Protection Agency, National Center 

for Environmental Assessment, Washington, DC. Available at 

http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

SESSION 5: QUANTITATIVE UNCERTAINTY ANALYSIS OF DOSE-RESPONSE 

This session addressed the uncertainty analysis to be considered for the dose-response 

assessments. The session opened with a presentation on current estimates of dioxin exposure 

levels. Then it focused on the factors to include in the scope of an uncertainty analysis including 

dioxin kinetics. 

Session 5 Panelists (Session Co-Chairs are identified by asterisk) 

• Bruce Allen, Bruce Allen Consulting 

• Lesa Aylward, Summit Toxicology 

• Roger Cooke, Resources for the Future 

• Kenny Crump, Louisiana Tech University 

• Mike DeVito, U.S. EPA 

• Dale Hattis, Clark University 

• *Rick Hertzberg, Biomath Consulting 

• Nancy Kerkvliet, Oregon State University 

• Leonid Kopylev, U.S. EPA 

• Rob McDowell, U.S. Department of Agriculture 

• Lorenz Rhomberg, Gradient 

• Woody Setzer, U.S. EPA 

• Marie Sweeney, National Institute of Occupational Safety and Health 

• *Linda Teuschler, U.S. EPA 

Please note that the use of the term “concluded” or “recommended” in this summary does not mean that a consensus 

was reached. Session Summaries were written from the material prepared by the non-EPA/ANL Co-Chair and 

represent a synopsis of the panel discussions. 

The Panel summarized the NAS comments regarding uncertainty. Areas for improvement 

include: 

• Ensure “transparency, thoroughness, and clarity in quantitative uncertainty analysis.” 

• Describe and define (quantitatively to the extent possible) the variability and uncertainty 

for key assumptions used for each key endpoint-specific risk assessment, including 

choices of data set, point of departure, dose-response model, and dose metric. 

• Incorporate probabilistic models to represent the range of plausible values. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-21 DRAFT—DO NOT CITE OR QUOTE 

• Assess goodness-of-fit of dose-response models. 

• Provide upper and lower bounds on central tendency estimates for all statistical estimates. 

• When quantification is not possible, clearly state it, and explain what would be required 

to achieve quantification. 

Identification of Important Uncertainties 

 The Panel reviewed the charge questions (Appendix B), discussed them, and listed eight 

issues for consideration by the U.S. EPA: 

• Concerning species and strain differences in the U.S. EPA’s Response to NAS, current 

U.S. EPA procedures do not take this into account when selecting one data set for risk 

assessment. Issues include “Where are humans in the distribution of potencies that can 

be generated? How likely is it that human response is similar to the selected data? Can 

we infer inter-individual variability from these differences?” 

• Concerning the use of animal data for cross species extrapolation to humans (PK and PD 

uncertainties), issues to consider include differences in distribution and responses 

following bolus doses from those of subchronic and chronic protocols; uncertainty in 

liver doses due to sequestration; differences in receptor binding affinity among 

congeners; and age factors (e.g., assumption of a lifetime constant daily dose for a cancer 

extrapolation). 

• Concerning the description of AhR response, biochemical changes occur at lower doses 

than toxicological changes. There should be an effort to identify the biochemical changes 

that would mark Ah receptor binding to inform the BMR, and, thus, prevent toxicity. 

• Concerning model uncertainty, the mathematical model choice depends on endpoint. 

There should be an effort towards determining what is the most sensitive endpoint(s) for 

humans and conducting animal studies to model that endpoint(s). 

• Concerning exposure and dose response in human studies, ensure enough similarity to 

current human exposure profiles (mixture composition) so that a dose-response 

assessment can be done. Incorporate new epidemiological studies. Evaluate 

concordance with animal data and consistency across studies. Panel-acknowledged 

uncertainties include exposure estimates from person to person, shape of human doseresponse curve, healthy worker effect, and age dependence. 

• Concerning POD determination, uncertainty factors are inherently mathematically 

inconsistent and that should be conveyed in the discussion of uncertainties when 

interpreting the POD. 

• Concerning dose metric, tissue concentration is preferred. It should be evaluated against 

a background of variability in AhR-binding expression. There is uncertainty in what 

level of binding should be considered, in different cell types, tissues, life stage 

(development). The relationship between dose metric and causation of adverse effects 

should be examined. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-22 DRAFT—DO NOT CITE OR QUOTE 

Low-Dose Extrapolation 

 The Panel reviewed the charge questions and discussed them (Appendix B). The Panel 

concluded that curve-fitting uncertainty (for a given dataset, dose metric, and model) can be 

characterized and is useful, but, by itself, it is an incomplete characterization of uncertainty. The 

Panel acknowledged the difficulty of fully characterizing uncertainty, especially quantitatively. 

Some panelists argued that the problem is insurmountable and that no meaningful uncertainty 

analysis is likely to be performable. Other panelists contended that, the difficulties 

notwithstanding, “good-faith” efforts to do something practical and forthright to characterize 

uncertainty in low-dose extrapolation would be useful and important. The Panel clarified “good 

faith” as meaning a characterization that is useful and not misleading to decision makers and is 

inclusive of approaches that have meaningful support in the scientific community as a whole. 

Being in “good faith” is more important than being complete (i.e., addressing every uncertain 

element), especially since completeness is not a realistic goal. From this discussion, the Panel 

listed four issues for consideration by the U.S. EPA: 

• Review alternative data sets, dose metrics, and models to see where consequential 

uncertainties and impacts on low-dose implications arise. 

• Consider the impacts of choices among plausible alternative data sets, dose metrics, 

models, and other more qualitative choices—issues include how much difference the 

choices make and also how much relative credence should be put to each alternative as a 

way of gauging and describing the landscape of imperfect knowledge 

regarding possibilities for the true dose-response. 

 Hard to do quantitatively, since the factors are not readily expressed as statistical 

distributions, but can describe the rationale for believing/doubting each alternative in 

terms of available supporting evidence, contrary evidence, and needed assumptions. 

 Expert judgment methods may be helpful in characterizing the relative weights of 

scientific credibility among alternatives. The expert judgment process, when 

conducted systematically, can be thought of as adding data to the assessment of 

credibility of alternatives, rather than as just an opinion poll. 

 Information on plausibility of alternative low-dose extrapolation approaches can 

come from external considerations of mode of action, and not just from statistical 

success at fitting particular (high-dose) data sets. 

• Characterizing uncertainty through a variety of approaches could be tried, and their 

relative merits and shortcomings discussed, as a way forward. 

• Consider the sources of potential error, particularly in epidemiological data (e.g., TEF 

uncertainty and variation in congener mixtures) and if possible quantify their impact on 

the dose-response assessment. 

Considerations for Conducting Uncertainty Analysis 

Overall, the Panel was split on whether U.S. EPA should do quantitative uncertainty 

analyses. The Panel noted that if done on only some of the uncertainties, then results would be 

misleading and could be misused. Ultimately, the Panel listed seven issues for consideration by 

the U.S. EPA: 
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1/15/10 A-23 DRAFT—DO NOT CITE OR QUOTE 

• The Panel recapped what some consider as being the first integrated risk assessment, with 

structured expert judgment and uncertainty analysis, i.e., the Rasmussen Report 

(WASH-1400; U.S. Nuclear Regulatory Commission, 1975). In their discussion of the 

report, the Panel noted that in addition to standard event tree/fault tree modeling, this 

report also tackled difficult model uncertainty issues involved in accident progression, 

dispersion of released pollutants in the atmosphere, environmental transport, exposure, 

health, and economic impacts. And though the Panel also recognized that this method 

was no longer state-of-the-art, the Panel contended that it represents a good example of a 

structured approach and methodology that could be built upon. 

• The Panel also discussed TEQs used in epidemiological studies, based on intake, and 

recognized that the key uncertainty in what was measured was not just intake but also 

involved PK/PD issues. The Panel acknowledged that the TEQ system is regularly used 

on a concentration basis, but they expressed concern that the qualification becomes lost. 

TEQs ignore pharmacokinetics and the common practice of rounding to orders of 

magnitude introduces more error. 

• Structure the risk assessment along MOA steps—identify key biochemical measures 

(~5−10) common across toxic endpoints and identify the degree of meaningful change in 

effect or effect variance. Make a table with all options for data set, model, etc.; make 

best estimates/choices and determine which of these choices matter the most to the 

answer. 

• Use expert panels—expert judgment can be collected scientifically (procedures are 

published). But there are known biases; central tendency estimates work much better 

than extremes. 

• Use supporting studies to fill in critical data gaps—Info filling methods do exist (e.g., PK 

modeling). Put short-term studies into the “supporting info” category (unless, of course, 

the risk assessment is for acute exposures, such as chemical spills). 

• Be creative in the analysis of uncertainty. Intermediate steps between AhR binding and 

the end processes can be hypothesized based on data, experiences, and analogies related 

to other chemicals. 

• The 2003 Reassessment presented potency estimates on wide variety of 

endpoints/models; needed to be more transparent in that discussion. Statistical graphics 

can be used to convey uncertainties. 

Reference 

U.S. Nuclear Regulatory Commission. 1975. Reactor Safety Study: An Assessment of Accident 

Risks in U.S. Commercial Nuclear Power Plants. WASH-1400 (NUREG-75-014). Washington, 

DC. 
This document is a draft for review purposes only and does not constitute Agency policy. 

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APPENDIX A: 2009 U.S. EPA DIOXIN WORKSHOP AGENDA 

SCIENTIFIC WORKSHOP 

TO INFORM THE TECHNICAL WORK PLAN FOR U.S. EPA’S RESPONSE TO 

NAS COMMENTS ON THE HEALTH EFFECTS OF DIOXIN 

PRESENTED IN U.S. EPA’S DIOXIN REASSESSMENT 

Cincinnati, OH 

Date: February 18−20, 2009 

BACKGROUND/WORKSHOP OBJECTIVE 

At the request of the U.S. Environmental Protection Agency (U.S. EPA), the National 

Academy of Sciences (NAS) prepared a report, Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment (NAS, 2006), that made a number of 

recommendations to improve the U.S. EPA’s risk assessment for 2,3,7,8-tetrachlorodibenzop-dioxin (TCDD). In response, the U.S. EPA will prepare a technical report that addresses key 

comments on the dose-response assessment for TCDD. The U.S. EPA intends to develop its 

response through a transparent process that provides multiple opportunities for input. 

To assist in this effort, a Workshop will be held to inform the U.S. EPA’s evaluation of 

the NAS recommendations. The Workshop will be open to the public. At the Workshop, the 

U.S. EPA will solicit input from expert scientists and the public. 

The goal of the Workshop is to ensure that the U.S. EPA’s response to the NAS 

comments focuses on the key issues and reflects the most meaningful science. The three main 

objectives of the Workshop are to (1) identify and discuss the technical challenges involved in 

addressing the NAS key comments on the TCDD dose-response assessment in the U.S. EPA 

Reassessment (U.S. EPA, 2003), (2) discuss approaches for addressing these comments, and 

(3) identify key published, independently peer-reviewed literature, particularly studies describing 

epidemiologic and in vivo mammalian bioassays, which are expected to be most useful for 

informing the U.S. EPA response. 

Workshop participants will be encouraged to think broadly about the body of scientific 

information that can be used to inform the U.S. EPA’s response and to participate in open 

dialogue regarding ways in which the science can best be used to address the key dose-response 

issues. This Workshop is similar to scientific workshops being conducted under the new review 

process for the National Ambient Air Quality Standards (NAAQS)1

 that assess health-related 

information for criteria pollutants. 

 

1

 Please see http://www.epa.gov/ttn/naaqs/ for more information on the new NAAQS review process. 
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 The Workshop discussions are expected to build upon two prior publications: 

1. Exposure and Human Health Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin 

(TCDD) and Related Compounds (U.S. EPA, 2003). This external review draft 

provides a comprehensive reassessment of dioxin exposure and human health effects. 

This “dioxin reassessment” was submitted in October 2004 to the National Academy 

of Sciences (NAS) for review. 

2. Health Risks from Dioxin and Related Compounds: Evaluation of the EPA 

Reassessment (NAS, 2006). 

 Workshop participants are encouraged to review both of these documents and other 

relevant materials (e.g., the National Toxicology Program report on TCDD [NTP, 2006]) before 

the meeting because they provide important insights into the key questions and challenges. 

There are a number of open comment periods that are intended to facilitate a broad discussion of 

the issues. 

Scientists with significant expertise and experience relevant to the health effects of 

TCDD or dioxin-like compounds and associated topics will be asked to serve on “expert panels” 

for discussions throughout the Workshop. Workshop panelists will include a wide range of 

experts representing many scientific areas needed to assess TCDD dose-response (e.g., 

epidemiology, human and animal toxicology, nuclear receptor biology, dose-response modeling, 

risk assessment, and uncertainty analysis). The Workshop panelists will be asked to highlight 

significant and emerging research and to make recommendations to the U.S. EPA regarding the 

design and scope of the technical response to NAS comments on the dose-response analysis for 

TCDD—including, but not limited to, recommendations for evaluating associated uncertainty. 

Open comment periods will follow each panel discussion session. Public participation will be 

encouraged by way of these designated open comment periods and, also, by participation in the 

scientific poster session planned for the second evening (February 19). 

U.S. EPA will use the input received during this Workshop as the foundation for its 

development of a technical work plan for responding to the NAS comments on the TCDD doseresponse analysis. The work plan will outline the schedule, process, and approaches for 

evaluating the relevant scientific information and addressing the key issues. The work plan also 

will identify the key literature to be utilized in U.S. EPA’s response. 

As a follow-on activity to this Workshop, a panel is being established under the Federal 

Advisory Committee Act (FACA) to guide and review the U.S. EPA’s response to NAS 

comments. The FACA panel will be asked to conduct a consultation with the Agency on the 

draft technical work plan. At the same time, the public will also have the opportunity to provide 

comments to the FACA panel on the work plan. The final technical work plan will guide the 

development of the technical report that will constitute the U.S. EPA’s response to NAS 

comments. During the development of this response, the U.S. EPA will seek advice from the 

FACA panel and the public several times. Finally, the FACA panel will be asked to review the 

technical report in a public forum. 

The preliminary Agenda presented on the following pages may be revised prior to the 

Workshop following review by the session Co-Chairs; the dates and general timing of the 
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1/15/10 A-26 DRAFT—DO NOT CITE OR QUOTE 

sessions, however, will not change. A final Agenda and a set of charge questions, intended to 

provide general direction for the Workshop discussions, will be posted on the Workshop Internet 

site (http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=199923) prior to the meeting. 

A poster session will be held on the evening of the second day (February 19). The 

purpose of this poster session is to provide a forum for scientists to present recent studies 

relevant to TCDD dose-response assessment and to encourage open discussion about these 

presentations. 

REFERENCES 

NAS (National Academy of Sciences). 2006. Health Risks from Dioxin and Related 

Compounds: Evaluation of the EPA Reassessment. National Academies Press, Washington, DC 

(July). Available at http://www.nap.edu/catalog.php?record_id=11688. 

NTP (National Toxicology Program). 2006. Toxicology and Carcinogenesis Studies of 

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) (CAS No. 1746-01-6) in Female Harlan SpragueDawley Rats (Gavage Studies). U.S. Department of Health and Human Services. NTP TR 521. 

Research Triangle Park, NC (April). 

U.S. EPA (U.S. Environmental Protection Agency). 2003. Exposure and Human Health 

Reassessment of 2,3,7,8-Tetrachlorodibenzo-p-Dioxin (TCDD) and Related Compounds, NAS 

review draft, Volumes 1-3 (EPA/600/P-00/001Cb, Volume 1). U.S. Environmental Protection 

Agency, National Center for Environmental Assessment, Washington, DC (December). 

Available at http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-27 DRAFT—DO NOT CITE OR QUOTE 

WORKSHOP AGENDA 

Day 1

8:00–9:00 Registration 

9:00–9:30 Welcome/Purpose of Meeting/Document Development Process 

9:30–9:45 Panel Comments/Questions on Charge

9:45–2:45 Session 1: Quantitative Dose-Response Modeling Issues 

(Hall of Mirrors)

 9:45–10:10 Background/Introductory Remarks 

 10:10–10:35 TCDD Kinetics: Converting Administered Doses in Animals to 

Human Body Burdens 

 Presenter: Michael Devito 

 10:35–11:30 Panel Discussion

 11:30–1:00 Lunch

 1:00–2:00 Panel Discussion cont.

 2:00–2:45 Open Comment Period 

2:45–3:05 Break 

3:05–5:15 Session 2: Immunotoxicity (Hall of Mirrors)

 3:05–3:15 Background/Introductory Remarks 

 

 3:15–4:45 Panel Discussion

 4:45–5:15 Open Comment Period 
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Day 2

8:00–8:30 Report-Outs for Sessions 1 and 2 (Hall of Mirrors)

 8:00–8:15 Report-Out for 1: Quantitative Dose-Response Modeling Issues 

 8:15–8:30 Report-Out for 2: Immunotoxicity 

8:30–11:30 Sessions 3A and 3B (concurrent sessions)

8:30–11:30 Session 3A: Dose-Response for Neurotoxicity and 

Nonreproductive Endocrine Effects (Hall of Mirrors)

 

 8:30–8:45 Background/Introductory Remarks 

 

 8:45–11:00 Panel Discussion

 11:00–11:30 Open Comment Period

8:30–11:30 Session 3B: Dose-Response for Cardiovascular Toxicity and 

Hepatotoxicity (Rookwood Room)

 8:30–8:45 Background/Introductory Remarks 

 

 8:45–11:00 Panel Discussion 

 11:00–11:30 Open Comment Period

11:30–1:00 Lunch 

1:00–2:00 Report-Outs for Sessions 3A and 3B (Hall of Mirrors)

The structure of the session report-outs will include the following: 

 Summary of session presentation including minority opinion 

 Public comments 

 Discussion 

 1:00–1:15 Report-Out for 3A: Dose-Response for Neurotoxicity and 

Nonreproductive Endocrine Effects 

 1:15–1:30 Open Comment Period 
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 1:30–1:45 Report-Out for 3B: Dose-Response for Cardiovascular Toxicity and 

Hepatotoxicity 

 1:45–2:00 Open Comment Period 

2:00–5:15 Sessions 4A and 4B (concurrent sessions)

2:00–5:15 Session 4A: Dose-Response for Cancer (Hall of Mirrors)

 2:00–2:15 Background/Introductory Remarks 

 

 2:15–4:45 Panel Discussion

 4:45–5:15 Open Comment Period 

2:00–5:15 Session 4B: Dose-Response for 

Reproductive/Developmental Toxicity (Rookwood Room)

 2:00–2:15 Background/Introductory Remarks 

 

 2:15–4:45 Panel Discussion

 4:45–5:15 Open Comment Period 

6:45–8:15 Poster Session (Rosewood Room)

Day 3

8:30–9:30 Report-Outs for Sessions 4A and 4B (Hall of Mirrors)

 8:30–8:45 Report-Out for 4A: Dose-Response for Cancer 

 8:45–9:00 Open Comment Period 

 9:00–9:15 Report-Out for 4B: Dose-Response for Reproductive/Developmental 

Toxicity 

 9:15–9:30 Open Comment Period
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9:30–3:30 Session 5: Quantitative Uncertainty Analysis of DoseResponse (Hall of Mirrors)

 9:30–9:40 Background/Introductory Remarks

 9:40–10:10 Evidence of a Decline in Background Dioxin Exposures in Americans 

Between the 1990s and 2000s

 Presenter: Matt Lorber 

10:10–10:30 Break 

 10:30–11:30 Panel Discussion 

 11:30–1:00 Lunch 

 1:00–2:15 Panel Discussion cont.

 2:15−2:30 Break 

 2:30–3:00 Open Comment Period 

 3:00–3:15 Report-Out for 5: Quantitative Uncertainty Analysis of DoseResponse 

 3:15–3:30 Closing Remarks 

3:30 Adjourn 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-31 DRAFT—DO NOT CITE OR QUOTE 

APPENDIX B: 2009 U.S. EPA DIOXIN WORKSHOP 

QUESTIONS TO GUIDE PANEL DISCUSSIONS 

SESSION 1 

Dose Metric 

Considering all of the endpoints or target tissues, and species that U.S. Environmental Protection 

Agency (U.S. EPA)’s dose-response modeling might evaluate, what are the best measures of 

dose (e.g., ingested, tissue concentrations, body burden, receptor occupancy, other surrogate) and 

why? 

Developing Dose-Response Models from Mammalian Bioassays 

How best can the point of departure (POD) be determined when the response range is 

incompletely characterized (i.e., high response at the lowest dose or low response at the highest 

dose; observed in several key 2,3,7,8-Tetrachlorodibenzo-p-Dioxin [TCDD] studies)? 

If considered to be biologically plausible, how can a threshold be incorporated into a doseresponse function (e.g., for TCDD cancer data)? 

How can nonmonotonic responses be incorporated into the dose-response function? 

Developing Dose-Response Models from Epidemiological Studies 

How can the epidemiological data be utilized best to inform the TCDD exposure-response 

modeling? Which epidemiological studies are most relevant? 

Supporting Information 

For those toxicological endpoints that are Ah receptor-mediated, how would the receptor kinetics 

influence the shape of the dose-response curve? How would downstream cellular events affect 

the shape of the dose-response curve? How can this cascade of cellular events be incorporated 

into a quantitative model of dose-response? 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-32 DRAFT—DO NOT CITE OR QUOTE 

SESSIONS 2, 3A, 3B, 4A, AND 4B 

Key Study Selection 

For this endpoint, what refinements should be made to the draft criteria for selection of key 

studies? 

What are the specific effects of concern for human health for this endpoint? 

Based on the draft criteria for the selection of key studies, what are the key studies informing the 

shape of the dose-response curve above the POD and the choice of the POD for this endpoint? 

Epidemiological Study Utility 

How and to what extent do the epidemiological data inform the choice of critical effect? 

How can the epidemiological data inform the quantitative dose-response modeling? 

Animal Model Utility 

Are there types of effects observed in animal models that are more relevant to humans than 

others? To what extent does information on mode of action (MOA) influence the choice of 

animal model (species, strain, sex)? 

Supporting Information 

Are there studies that establish a sufficient justification for departure from the default procedures 

that address the shape of the dose-response curve below the POD under the cancer guidelines? 

Are there studies that establish a sufficient justification for departing from U.S. EPA’s default 

approaches for noncancer endpoints? 

To what extent can MOA information clarify the identification of endpoints of concern and doseresponse metric for this endpoint? How can the cascade of cellular events for this endpoint be 

incorporated into a quantitative model of dose response? 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 A-33 DRAFT—DO NOT CITE OR QUOTE 

SESSION 5 

For cancer and noncancer TCDD dose-response assessments, U.S. EPA is interested in 

developing a quantitative uncertainty analysis addressing both parameter and model uncertainty, 

if feasible. Uncertainties will include, among others, choice of endpoint; underlying study 

uncertainties; choice of dose metric; interspecies extrapolations such as kinetic uncertainties; and 

choice of dose-response model, including threshold models. The U.S. EPA is currently 

examining techniques and tools for uncertainty analysis—including Bayesian and frequentist 

approaches. 

Identification of Important Uncertainties 

What are the major uncertainties pertaining to modeling the animal data? 

Consider the dose metric (species or tissue specificity), vehicle of administration, 

exposure frequency, exposure duration, and POD determination (e.g., benchmark 

response selection or no-observed-adverse-effect level/lowest-observed-adverse-effect 

level identification). 

What are the major uncertainties pertaining to dose-response modeling below the POD? 

Consider how receptor kinetics and downstream cellular event information might be used 

to bound the uncertainties associated with dose-response modeling below the POD. 

What are the major uncertainties in cross-species extrapolation (e.g., half-lives, tissue 

distribution, and toxicodynamics)? 

Consider the primary species dosed with TCDD: mice, hamsters, rats, guinea pigs, and 

monkeys. 

What are the major uncertainties pertaining to intrahuman variability? 

Consider what data sets would be useful to represent sensitive subpopulations. 

What are other significant sources of uncertainty for the cancer and noncancer assessments? 

Considerations for Conducting Uncertainty Analysis 

What data sets could be used to quantify uncertainties in cancer and noncancer TCDD doseresponse assessments? 

 Consider dioxin-like compound dose-response data. 

 Consider MOA information. 

What are the appropriate techniques for the TCDD dose-response uncertainty analysis, and what 

are their respective strengths and weaknesses of these approaches as applied to TCDD? 
This document is a draft for review purposes only and does not constitute Agency policy

1/15/10 A-34 DRAFT: DO NOT CITE OR QUOTE APPENDIX C: 2009 U.S. EPA DIOXIN WORKSHOP DRAFT SELECTION CRITERIA TO IDE

VIVO MAMMALIAN STUDIES THAT INFORM DOSE-RESPONSE MODELING F

2,3,7,8-TETRACHLORODIBENZO-p-DIOXIN (TCDD)a Study Feature Selection Rationale Primaryb Secondaryc Cur

Chemical, purity, matrix/medium TCDD-only doses included, purity specified, matrix in which TCDD is administered is identified TCDD purity or matrix not clearly identified Studies of dio

(DLCs) or m

Peer review Independently peer-reviewed, publicly available Supplementary materials accompanying peer-reviewed publication Not formally 

not publicly a

Study design, execution, and reporting Clearly documented and consistent with standard toxicological principles, testing protocols, and practice (i.e., endpoint-appropriate, particularly for negative findings) Testing protocol provides incomplete coverage of relevant endpoint-specific measures, particularly for negative findings Studies not m

principles an

Study subject: species, strain, and sensitivity for given endpoint; litter; life stage; gender Mammalian species Strain and gender identified Animal age at beginning of treatment identified Litter confounders (within/between) accounted for Mammalian species, in vivo, but only studying an artificially sensitive subject (e.g., knockout mouse) Non-mamma

Exposure route Oral Parenteral (e.g., intravenous, intramuscular, intraperitoneal, subcutaneous) Inhalation, dDose level Lowest dose ≤200 ng/kg-d for noncancer endpoints and ≤1 μg/kg-d for cancer Lowest dose >200 ng/kg-d for noncancer endpoints, or >1.0 μg/kg-d for cancer Exposure frequency, duration, and timing Dosing regimen characterized and explained Characteriza

missing or ca

Controls Appropriate and well characterized Effect reported, but with no negative control Response Effect relevant to human health Magnitude outside range of normal variability Precursor effects, or adaptive responses potentially relevant to human health Lethality Statistical evaluation Clearly described and appropriate to the endpoint and study design (e.g., per error variance, magnitude of effect) Limited statistical context 

a NAS (2006) commented that the selection of data sets for quantitative dose-response modeling needed to be more transparent. Thes

offered for consideration at the kickoff workshop. These criteria would be used to identify candidate studies of non-human mammal

define the point-of-departure (POD). These criteria are not designed for hazard identification or weight-of-evidence determinations. 

other than direct TCDD dose-response in mammals (including toxicokinetic data on absorption, distribution, metabolism, or eliminatphysiologically-based pharmacokinetic [PBPK] modeling, and mode of action data) will be evaluated separately. b Presents preliminary draft criteria for evaluating a study being considered for estimating a POD in a TCDD dose-response model. c Presents preliminary draft criteria that could qualify a study as primary with support from other lines of evidence (e.g., PBPK modeling

endpoint meets the “primary” criteria. 

DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX B 

Evaluation of Cancer and Noncancer 

Epidemiological Studies for Inclusion in 

TCDD Dose-Response Assessment 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-ii —DO NOT CITE OR QUOTE 

CONTENTS—Appendix B: Evaluation of Cancer and Noncancer Epidemiological Studies 

for Inclusion in TCDD Dose-Response Assessment 

LIST OF TABLES.....................................................................................................................B-iii

APPENDIX B. EVALUATION OF CANCER AND NONCANCER 

EPIDEMIOLOGICAL STUDIES FOR INCLUSION IN 

TCDD DOSE-RESPONSE ASSESSMENT ...................................................................B-1 

B.1. EVALUATION OF CANCER STUDIES..............................................................B-1 

B.1.1. NIOSH Cohort Studies ...............................................................................B-1 

B.1.2. BASF Cohort Studies..................................................................................B-8 

B.1.3. The Hamburg Cohort ................................................................................B-11 

B.1.4. The Seveso Cohort Studies .......................................................................B-16 

B.1.5. The Chapaevsk Study ...............................................................................B-22 

B.1.6. The Air Force Health (“Ranch Hands”) Study .........................................B-23 

B.1.7. Other Studies of Potential Relevance to Dose-Response Modeling.........B-26 

B.2. EVALUATION OF NONCANCER STUDIES ...................................................B-31 

B.2.1. NIOSH Cohort ..........................................................................................B-31 

B.2.2. BASF Cohort ............................................................................................B-33 

B.2.3. Hamburg Cohort .......................................................................................B-35 

B.2.4. The Seveso Women’s Health Study .........................................................B-36 

B.2.5. Other Seveso Noncancer Studies..............................................................B-45 

B.2.6. Chapaevsk Study.......................................................................................B-54 

B.2.7. Air Force Health (“Ranch Hands”) Study ................................................B-55 

B.2.8. Other Noncancer Studies of Dioxin..........................................................B-56 

B.3. REFERENCES .....................................................................................................B-60 
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LIST OF TABLES 

B-1. Fingerhut et al., 1991—All cancer sites, site-specific analysis ................................... B-1 

B-2. Steenland et al., 1999—All cancer sites combined, site-specific analysis .................. B-2 

B-3. Steenland et al., 2001—All cancer sites combined...................................................... B-4 

B-4. Cheng et al., 2006—All cancer sites combined........................................................... B-5 

B-5. Collins et al., 2009—All cancer sites combined, site-specific analysis....................... B-6 

B-6. Zober et al., 1990—All cancer sites combined, site-specific analysis......................... B-8 

B-7. Ott and Zober, 1996—All cancer sites combined........................................................ B-9 

B-8. Manz et al., 1991—All cancer sites combined, site-specific analyses ...................... B-11 

B-9. Flesch-Janys et al., 1995; Flesch-Janys et al., 1996 erratum—All cancer sites 

combined.................................................................................................................... B-12 

B-10. Flesch-Janys et al., 1998—All cancer sites combined, site-specific analysis ........... B-13 

B-11. Becher et al., 1998—All cancer sites combined........................................................ B-14 

B-12. Bertazzi et al., 2001—All cancer sites combined, site-specific analyses .................. B-16 

B-13. Pesatori et al., 2003—All cancer sites combined, site-specific analyses................... B-17 

B-14. Consonni et al., 2008—All cancer sites combined, site-specific analyses ................ B-18 

B-15. Baccarelli et al., 2006—Site-specific analysis........................................................... B-19 

B-16. Warner et al., 2002—Breast cancer incidence........................................................... B-21 

B-17. Revich et al., 2001—All cancer sites combined, and site-specific analyses ............. B-22 

B-18. Akhtar et al., 2004—All cancer sites combined and site-specific analyses............... B-23 

B-19. Michalek and Pavuk, 2008—All cancer sites combined ........................................... B-24 

B-20. ‘t Mannetje et al., 2005—All cancer sites combined, site specific analyses ............. B-26 

B-21. McBride et al., 2009b—All cancer sites combined, site-specific analysis................ B-27 

B-22. McBride et al., 2009a—All cancer sites combined, site-specific analysis ................ B-28 

B-23. Hooiveld et al., 1998—All cancer sites combined, site-specific analysis ................. B-29 

B-24. Steenland et al., 1999—Mortality (noncancer).......................................................... B-31 

B-25. Collins et al., 2009—Mortality (noncancer).............................................................. B-32
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LIST OF TABLES (continued) 

B-26. Ott and Zober, 1996—Mortality (noncancer)............................................................ B-33 

B-27. Flesch-Janys et al., 1995; Flesch-Janys et al., 1996 erratum—Mortality 

(noncancer) ................................................................................................................ B-35 

B-28. Eskenazi et al., 2002a—Menstrual cycle characteristics........................................... B-36 

B-29. Eskenazi et al., 2002b—Endometriosis ..................................................................... B-37 

B-30. Eskenazi et al., 2003—Birth outcomes...................................................................... B-39 

B-31. Warner et al., 2004—Age at menarche...................................................................... B-40 

B-32. Eskenazi et al., 2005—Age at menopause................................................................. B-41 

B-33. Warner et al., 2007—Ovarian function...................................................................... B-42 

B-34. Eskenazi et al., 2007—Uterine leiomyoma ............................................................... B-43 

B-35. Mocarelli et al., 2008—Semen quality ...................................................................... B-45 

B-36. Mocarelli et al., 2000—Sex ratio............................................................................... B-46 

B-37. Baccarelli et al., 2008—Neonatal thyroid function ................................................... B-47 

B-38. Alaluusua et al., 2004—Oral hygiene........................................................................ B-48 

B-39. Bertazzi et al., 2001—Mortality (Noncancer) ........................................................... B-50 

B-40. Consonni et al., 2008—Mortality (Noncancer) ......................................................... B-51 

B-41. Baccarelli et al., 2005—Chloracne ............................................................................ B-52 

B-42. Baccarelli et al, 2002 and 2004—Immunological effects.......................................... B-53 

B-43. Revich et al., 2001—Mortality (noncancer) and reproductive health ....................... B-54 

B-44. Michalek and Pavuk, 2008—Diabetes....................................................................... B-55 

B-45. McBride et al., 2009a—Mortality (Noncancer)......................................................... B-56 

B-46. McBride et al., 2009b—Mortality (noncancer) ......................................................... B-58 

B-47. Ryan et al., 2002—Sex ratio...................................................................................... B-59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-1 —DO NOT CITE OR QUOTE 

1 APPENDIX B. EVALUATION OF CANCER AND NONCANCER 

2 EPIDEMIOLOGICAL STUDIES FOR INCLUSION IN TCDD 

3 DOSE-RESPONSE ASSESSMENT 

4 

5 

6 B.1. EVALUATION OF CANCER STUDIES 

7 B.1.1. NIOSH Cohort Studies 

8 

9 Table B-1. Fingerhut et al., 1991—All cancer sites, site-specific analysis 

10 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The data sources to ascertain vital status and cause of death 

information were the Social Security death files, the National Death Index, and the Internal 

Revenue Service. Vital status could be determined for 98% of the cohort. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. While the authors provide compelling arguments that suggest 

risks are not unduly biased by lack of cigarette smoking data, they acknowledge potential 

biases that could exist for other occupational exposure (e.g., asbestos) for which data were 

lacking. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. There was not a statistically significant linear trend of increasing 

mortality with increased duration of exposure. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. This study used duration of exposure, at an individual level, as a 

surrogate measure of TCDD. Duration of exposure determined by number of years workers 

were involved in processes involving TCDD contamination. Exposure was determined by 

reviewing, at each plant, operating conditions, job duties, records of TCDD levels in industrial 

hygiene samples, intermediate reactants, products, and wastes. Exposure assessment was 

limited and the uncertainty related to exposure measures not fully addressed. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. This is the largest of the occupational cohorts that has been exposed 

to TCDD. The cohort consisted of 5,172 workers and a total of 265 cancer deaths. Sitespecific mortality analyses, including soft tissue sarcoma (n = 4), was limited by small 

numbers. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-2 —DO NOT CITE OR QUOTE 

Response Criteria satisfied. New England Journal of Medicine, 1991; 324:212–218. Authors address 

the possibility of bias from lack of control for potential confounders such as smoking and other 

occupational exposures. They address limitations of using death certificates for identifying 

certain causes of deaths, and limitations of using duration of employment as an exposure 

metric. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Since this study used duration of exposure as the exposure metric, doseresponse relationships cannot be quantified. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Models incorporated period of latency, and a surrogate measure of 

cumulative TCDD exposure was modeled. The follow-up interval was sufficiently long 

(1942–1987). 

Conclusion Overall, quantitative exposure data are lacking on an individual-level basis. Further doseresponse analysis should consider updated data for this cohort that includes serum-based 

measures of TCDD, in addition to an extension of the follow-up period. Given these 

limitations, this study is not further evaluated for TCDD dose-response assessment. 

 1 

 2 

3 Table B-2. Steenland et al., 1999—All cancer sites combined, site-specific 

4 analysis 

 5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The study evaluated mortality from all cancer sites (combined). As 

described in the paper, the sources of vital status and cause of death information were received 

from the Social Security death files, the National Death Index, and the Internal Revenue 

Service. Vital status was known for 99.4% of the cohort members, cause of death information 

is available for 98% of the decedents. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Occupational exposure to asbestos and 4-aminobiphenyl contributed 

to some excess cancer, but no evidence of confounding for the relationship between TCDD 

and all cancer mortality was detected following removal of workers who died of bladder 

cancer. No information is available for cigarette smoking, although dose-response patterns 

were stronger for nonsmoking related cancers. This finding suggests that smoking is not 

responsible for excess cancer risk that was observed in the cohort. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. When a 15-year lag interval was incorporated into the exposure 

metric a statistically significant dose-response pattern was observed for all cancer sites 

combined with both a continuous measure of TCDD (p = 0.05) as well as one that was logtransformed (p < 0.001). 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-3 —DO NOT CITE OR QUOTE 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The study conducted detailed sensitivity analyses and evaluated 

different assumptions regarding latency, log-transformed TCDD exposures, and half-life 

values for TCDD. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. This is the largest of the occupational cohorts with exposures to 

TCDD. The cohort consisted of 5,132 male workers and a total of 377 cancer deaths. This 

permits characterization of risk for all cancer sites (combined). 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Journal of the National Cancer Institute, 1999; 91(9):779–786. The authors 

discussed the potential for bias from smoking, and other occupational exposures for which 

data for both were lacking at an individual basis. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Exposure scores assigned on an individual level using a job-exposure 

matrix. The job-exposure matrix was based on estimated factor of contact with TCDD in 

each job, level of TCCD contamination of materials at each plant over time, and proportion of 

day worker could be in contact with materials. These factors were multiplied together to 

derive a daily exposure score, which was accumulated over the working history of each 

worker to obtain a cumulative measure of TCDD. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. The follow-up of the cohort extended from 1942 until the end of 1993. 

Greater than 25 years of follow-up have accrued in cohort allowing for latency to be 

examined. Different assumptions on the half-life of TCDD were evaluated and produced 

similar results. Latency intervals were incorporated, with strongest associations noted with an 

interval of 15 years. 

Conclusion This study meets the criteria and considerations noted above but has been superseded and 

updated by Steenland et al. (2001). Therefore, this study was considered for further doseresponse analyses. 

 1 

 2 

 3 

 4 

 5 

 6 

 7 

 8 

 9 

 10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-4 —DO NOT CITE OR QUOTE 

1 Table B-3. Steenland et al., 2001—All cancer sites combined 

2 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The study evaluated mortality from all cancer sites (combined). As 

described by Steenland et al., (1999) the sources of vital status and cause of death information 

were received from the Social Security death files, the National Death Index, and the Internal 

Revenue Service. Vital status was known for 99.4% of the cohort members, cause of death 

information is available for 98% of the decedents. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Occupational exposure to asbestos and 4-aminobiphenyl contributed 

to some excess cancer, but no evidence of confounding for the relationship between TCDD 

and all cancer mortality was detected following removal of workers who died of bladder 

cancer. No information is available for cigarette smoking, although dose-response patterns 

were similar between smoking and nonsmoking related cancers. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Increased risk estimates were observed in the higher cumulative 

exposure categories. The dose-response curve was not linear at higher doses. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. 

Exposure metrics considered included cumulative TCDD, log10TCDD, average exposure, and 

a cubic spline model was also evaluated. Exposure response relationships were also evaluated 

using TEQs. Exposure scores were assigned on an individual level using a job-exposure 

matrix. The job-exposure matrix was based on estimated factor of contact with TCDD in each 

job, level of TCCD contamination of materials at each plant over time, and proportion of day 

worker could be in contact with materials. Serum levels were measured in 199 workers at one 

of 8 plants in 1998. Different estimate of the half-life of TCDD were used, and similar results 

were produced. The paper presented a range in risk estimates thereby conveying the range of 

uncertainties in risk estimates derived using different measures of exposure. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. This is the largest of the occupational cohorts with exposures to 

TCDD. The cohort consisted of 3,538 male workers and a total of 256 cancer deaths. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied Am J Epidem, 2001, 154(5):451–458. However, additional details to assess 

uncertainties associated with characterizing serum data in a subset of workers to remainder of 

cohort are lacking. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-5 —DO NOT CITE OR QUOTE 

Response Criteria satisfied. The metrics considered included cumulative TCDD, log10TCDD, average 

exposure, and a cubic spline model was also evaluated. Exposure response relationships were 

also evaluated using TEQs. Serum lipid TCDD measurements from 170 workers whose 

TCDD levels were greater than 10 ppt (the upper ranges of a background level) were used 

along with JEM information, work histories, and a pharmacokinetic elimination model to 

estimate dose rates per unit exposure score. In this regression model, the estimated TCDD 

level at the time of last exposure was modeled as a function of exposure scores. The 

coefficient relating serum levels and exposure scores was then used to estimate serum TCDD 

levels over time from occupational exposure (minus the background level) for all 3,538 

workers. Time-specific serum levels were then integrated over time to derive a cumulative 

serum lipid concentration due to occupational exposure for each worker. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Greater than 25 years of follow-up have accrued in cohort allowing for 

latency to be examined. Different assumptions on the half-life of TCDD were evaluated 

producing similar results. 

Conclusion Overall, criterion has been satisfied and it is recommended that this study be considered for 

dose-response analysis. 

1 

2 

3 Table B-4. Cheng et al., 2006—All cancer sites combined 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The study evaluated cancer mortality. The vital status and the 

information regarding the cause of death were extracted from the Social Security death files, 

the National Death Index, and the Internal Revenue Service (Steenland et al., 1999). Vital 

status was known for 99.4% of the cohort members, while cause of death information is 

available for 98% of the decedents. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. This is the same data set used in the Steenland et al., (2001) paper. 

Occupational exposure to asbestos and 4-aminobiphenyl contributed to some excess cancer, 

but no evidence of confounding for the relationship between TCDD and all cancer mortality 

was detected following removal of workers who died of bladder cancer. No information is 

available for cigarette smoking, although dose-response patterns were similar between 

smoking and nonsmoking related cancers. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Slope coefficients are available for all cancers combined under a 

varying set of assumptions. Little evidence of an association was found when lag interval was 

not taken into account. Associations strengthened with incorporation of a 10 to 15 year lag 

interval. Dose-response was nonlinear at higher exposures, suggesting a nonlinear 

relationship or increased exposure misclassification at higher levels. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-6 —DO NOT CITE OR QUOTE 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Compared to the 1st order models, the concentration, and age 

dependent model (CADM) provided a better fit for the serum sampling data. CADM model 

exposure estimates are higher than those based on an age only, constant 8.7-year half-life 

model. As discussed by Aylward et al. (2005b), model exposure estimates are influenced not 

only by choice of elimination model, but also by choices in regression procedure (e.g., log 

transformation, use of intercept, and incorporation of background dose term). Other 

limitations or uncertainties in exposure assessment include the following 

• Job-exposure matrix based on limited sampling data, and subjective judgment on contact 

times and factors 

• Inability to take into account inter-individual variability in TCDD elimination kinetics 

• Dose-rate regressions are based on a small sample of the cohort with serum measures; 

therefore, regression results may not be representative of remainder of the cohort. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Largest cohort of TCDD exposed workers. The risk estimates are 

based on a total of 256 cancer deaths. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Risk Analysis, 2006; 4:1059–1071. Additional details to assess 

uncertainties associated with characterizing serum data can be found in Aylward et al. 

(2005b); Risk Anal. 25(4):945–956. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Cumulative serum lipid concentrations were estimated for each worker. No 

other dioxin-like compounds were assessed in this analysis. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Concentration and age-dependence of TCDD elimination and two 

compartments (hepatic and adipose tissue) were taken into account when estimating TCDD 

exposures. Nearly 50 years of follow-up were available permitting an evaluation of latency. 

Conclusion This study met the main criteria and considerations. These data were considered for further 

dose-response analyses. 

 1 

 2 

3 Table B-5. Collins et al., 2009—All cancer sites combined, site-specific 

4 analysis 

 5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Vital status complete for all but two workers. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-7 —DO NOT CITE OR QUOTE 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. No information collected on smoking status, but no excess in lung 

cancer or nonmalignant respiratory diseases noted. Analyses took into account potential for 

exposure to pentachlorophenol. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. No dose-response pattern was observed with all cancer sites 

combined, however, a dose-response pattern was observed with soft tissue sarcoma. The study 

found no association between TCDD and death from most types of cancer. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The authors used these serum from 280 former TCP workers to 

estimate historical exposure levels of TCDD, furans, and polychlorinated biphenyls for all 

1,615 workers. Exposure assessment included detailed work history, industrial hygiene 

monitoring, and the presence of chloracne cases among groups of workers. This data was 

integrated into a 1-compartment, first-order pharmacokinetic to determine the average TCDD 

dose associated with jobs in each group, after accounting for the presence of background 

exposures estimated from the residual serum TCDD concentration in the sampled individuals. 

The authors did not evaluate departures from linearity, or examine skewness at higher 

exposures. Exposure levels were not provided. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Largest study of workers employed in one center, and a total of 177 

deaths from cancer were observed. Limited precision for soft tissue sarcomas for which a 

positive association has been demonstrated. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in Am J Epidemiol, 2009, 170(4):501–506. The authors discuss 

limitations of using death certificates for identifying deaths from soft tissue sarcoma for which 

a positive association was noted, assumptions in exposure characterization, and effects of 

cigarette smoking. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. This study has the largest number of serum samples obtained from a specific 

plant. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. While the cohort did have sufficient follow-up, no evaluation of possible 

latent effects was presented. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-8 —DO NOT CITE OR QUOTE 

Conclusion Study is not suitable for further evaluation or dose-response modeling since an exposureresponse relationship was not demonstrated. The evaluation of exposure metrics and latency 

considerations should be expanded beyond that presented in the paper. Previous analyses of 

these same workers found positive associations between cancer mortality and TCDD 

(Steenland et al., 2001). The reasons for the discrepancy in the findings from the two papers 

may be due to Steenland et al.’s use of nonlinear exposure metrics, incorporation of a 15-year 

lag interval, or differences in the TCDD exposure estimates themselves. 

1 

2 B.1.2. BASF Cohort Studies 

 3 

4 Table B-6. Zober et al., 1990—All cancer sites combined, site-specific 

5 analysis 

6 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. A large component of the cohort (94 out of 247 workers) was 

assembled by actively seeking out workers who were alive in 1986 through the “Dioxin 

Investigation Programme.” As a result, it is likely a number of deaths were missed due to the 

recruitment of survivors. This underascertainment is supported by much lower all cancer 

SMR one component of the cohort (SMR = 0.48, 95% CI: 0.13–1.23) relative to the general 

population. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. See above discussion of underascertainment in mortality for some of 

the cohort members. Although it is likely that other co-exposures occurred (e.g., among 

firefighters), confounding could only occur if these co-exposures were associated with both 

the endpoint and exposure (TCDD) being considered. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. Workers were not categorized on the basis of their exposure, but 

rather their mortality experience compared to control cohort and the general population. The 

design of the study does not allow for dose-response to be examined. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. Although years since first exposure was examined, exposure 

assessment was based on working in various occupational cohorts. Since there was no 

quantitative assignment of TCDD exposures, the associated uncertainties could not be 

evaluated. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration not satisfied. There were only 23 cancer deaths in the entire cohort. As such, 

this study lacked adequate statistical power to detect cancer mortality differences that were 

moderate in magnitude. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-9 —DO NOT CITE OR QUOTE 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Int Arch Occup Envir Health, 1990, 62:139–157. The authors address 

issues related to the healthy worker effect, multiple comparisons, smoking, and small size of 

the cohort. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Risks were derived by comparing mortality rates of the three cohort 

subsets relative to a control cohort and the general population by time since first exposure 

categories. Workers were not assigned exposures. There were no quantitative estimates of 

TCDD exposure. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. While the study was able to indirectly look at variations in risk estimates 

related to latency by using time since exposure, there were no quantitative estimates of TCDD 

exposure. 

Conclusion This study is not suitable for dose-response analysis, as it failed the inclusion criteria. Most 

notably, the lack of exposure data does not permit the use of these data for a dose-response 

analysis. 

1 

2 

3 Table B-7. Ott and Zober, 1996—All cancer sites combined 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Mortality ascertainment appeared to be fairly complete. The 

ascertainment of cancer incidence is more difficult to judge as geographical area not covered 

by a cancer registry. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Information was collected on smoking status, body mass index, and 

other occupational exposures, however a large portion of the cohort was firefighters who may 

have been exposed to other occupational carcinogens. However, the recruitment of survivors 

may results in under-ascertainment of mortality. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Increased cancer incidence was observed in the highest TCDD 

cumulative exposure category. Risks were most pronounced when a period of 20 years since 

first exposure was incorporated into the model. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-10 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. Cumulative measure of TCDD expressed was derived from serum 

measures. Exposure was also estimated by chloracne status of the cohort members. The 

authors have not addressed the potential implication of deriving TCDD exposure estimates for 

the whole cohort using sera data that were available for only about half of the cohort. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all cancer sites combined, there were 31 deaths. It is the smallest 

of the occupational cohorts, but the deaths can be grouped into quartiles to allow for 

evaluation of dose-response relationships. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Occupational and Environmental Medicine, 1996, 53:606–612. A large 

component of the cohort (94 out of 247 workers) was assembled by actively seeking out 

workers who were alive in 1986 through the “Dioxin Investigation Programme.” As a result, 

it is likely a number of deaths were missed due to the recruitment of survivors. This 

underascertainment is supported by much lower all cancer SMR one component of the cohort 

(SMR = 0.48, 95% CI: 0.13–1.23) relative to the general population (Zober et al., 1990). 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum samples, taken in 1989, were available for 138 surviving workers out 

of 254 and allowed for cumulative TCDD levels to be estimated using regression techniques in 

the remainder of the cohort. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Exposure assignment took into the affect that body mass index had on 

TCDD half-lives. TCDD levels estimates through back-extrapolation of serum levels based on 

half-life estimates obtained from previous studies. Latency was considered with stronger 

association observed in external comparisons incorporating a latency of 20 years. The followup of the cohort was lengthy (>50 years). 

Conclusion Given a part of the cohort was based solely on survivors in the in the mid-1980s, the SMR 

statistic derived from this study underestimates excess mortality relative to the general 

population. The cohort also includes a fair number of firefighters who are recognized to be 

exposed to other carcinogenic agents—these exposures may be confounding the associations 

that were reported. However, exposure to TCDD was quantified and the effective dose and 

oral exposure estimable. Therefore, quantitative dose-response analyses were considered for 

these data. 

1 

2 

3 

4 

5 

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-11 —DO NOT CITE OR QUOTE 

1 B.1.3. The Hamburg Cohort 

2 

3 Table B-8. Manz et al., 1991—All cancer sites combined, site-specific 

4 analyses 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Deaths were identified through medical records of the cohort 

members. A review of death certificates of the identified cancer deaths found a high degree of 

concordance (51/54). One of the 136 noncancer death certificates examined indicated an 

“occult” neoplasm. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Smoking data were similar between exposed and nonexposed cohort 

based on independent samples. Occupational exposure for which individual data are lacking 

unlikely to explain dose-response with TCDD. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Dose-response patterns across three levels of exposure observed 

among those who started work before 1954, and among those who worked for 20 years or 

longer. Dose-response patterns not evident across whole cohort, among those with less than 

20 years of employment, or among those who started after 1954. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Categorical exposures were based on TCDD concentrations in 

precursor materials, products, waste, and soil from the plant grounds, measured after the plant 

closed in 1984. Exposure uncertainty examined using a separate group of 48 workers who 

provided adipose tissue samples. Other surrogate measures of exposure were considered in 

this study, including duration of exposure and year of first employment. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all cancer sites combined, there were 65 cancer deaths for the 

comparison to the comparison cohort of gas workers. The study is underpowered to look at 

site-specific cancers. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Lance,t 1991, 338:959–964. The authors discussed potential for 

misclassification using death certificates, healthy worker effect and their related use of a 

comparison cohort of gas supply workers, other occupational exposures present at the plant, 

potential impact and the lack of smoking data. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Exposure consisted of a large DLC component that was not quantified. 

Given crude TCDD exposure categorization data, no quantitative exposure metric was derived.
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-12 —DO NOT CITE OR QUOTE 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Exposure metrics were constructed that took into account duration of 

exposure, and periods when exposure was highest. However, exposure estimates did not 

consider lagged exposure. 

Conclusion This study is not amenable to further TCDD dose-response analysis because it consisted of a 

large DLC component that was quantified and no quantitative exposure metric was derived. 

The dose-response patterns of risks observed across the three exposure groups provide 

compelling support for an association between TCDD and cancer mortality, particularly, given 

the associations observed when analyses restricted to those who were hired when TCDD 

exposures were known to be much higher, and among those who worked for at least 20 years. 

Subsequent studies improved the exposure assessment through the use of serum measures. 

 1 

 2 

3 Table B-9. Flesch-Janys et al., 1995; Flesch-Janys et al., 1996 erratum—All 

4 cancer sites combined 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Medical records used to identify deaths over the period 1952–1992. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Similarity in smoking rates between control cohort and the exposed 

workers was similar based on independent surveys. Occupational exposures to benzene, and 

dimethyl sulfate were unlikely to bias dose-response pattern observed as these exposures 

occurred in production departments with low-medium levels of exposure. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Dose-response relationship observed across 6 exposure categories, 

with the cohort of gas supply workers used as the referent. 

4. Consideration Consideration satisfied. Exposure assessment methodology is clear and adequately 

characterizes individual-level exposures. The limitations and uncertainties in the exposure 

assessment are considered. 

Response The exposure measure was an integrated TCDD concentration over time estimate that backcalculated TCDD exposures to the end of the employment. Categorical and continuous TCDD 

exposures were examined in relation to the health outcome. These efforts improve the 

exposure assessment of earlier studies. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all cancer sites combined, there were 124 deaths in the exposed 

cohort, and 283 in the cohort of gas supply workers. No site-specific cancers were examined 

in this paper. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-13 —DO NOT CITE OR QUOTE 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 1995, 1442:1165–1175. The authors discuss the potential 

role of other occupational exposures (i.e., dimethyl sulfate, solvents, and benzene), smoking, 

and suitability of the comparison cohort of gas supply workers. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum and adipose tissues were used to estimate TCDD exposure in 190 

workers. A one-compartment first-order kinetic model was used to estimate exposure at end 

of exposure for these workers. Regression methods were then used to estimates TCDD 

exposures for all workers. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. Exposure was based on half-life estimates from individuals with 

repeated serum measures. Other dioxin-like compounds were considered with the TOTTEQ 

exposure metric. No consideration, however, was given to latency or lagged exposures. 

Conclusion The exposure data used within this study are well-suited to a dose-response analysis given the 

associations observed, the characterization of exposure using serum, and quality of 

ascertainment of cancer outcomes. However, subsequent methods have been applied to the 

cohort to derive different exposures to TCDD using area under the curve approaches, which 

updates the analysis herein. Therefore, subsequent studies (i.e., Becher et al., 1998) will 

supersede this evaluation. 

1 

2 

3 Table B-10. Flesch-Janys et al., 1998—All cancer sites combined, site4 specific analysis 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Mortality follow-up was extended until the end of 1992, an increase 

in 3 years from previous analyses of the cohort. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Exposure was well characterized using sera data. While serum 

samples provided only from a subsample of surviving workers, these levels were consistent 

with expected levels in different production departments. The authors examined other 

potential occupational co-exposures (e.g., β-hexachlorocyclohexane) and indirectly examined 

the potential effect of smoking on the associations that were detected. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. A dose-response relationship across quartiles of TCDD was observed 

with cancer mortality based on the SMR statistic (SMRs = 1.24, 1.34, 1.34, 1.73), and a linear 

test for trend was statistically significant (p = 0.01). 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-14 —DO NOT CITE OR QUOTE 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The exposure measure was an integrated TCDD concentration over 

time estimate that back-calculated TCDD exposures to the end of the employment. 

Categorical and continuous TCDD exposures were examined in relation to the health outcome. 

These efforts improve the exposure assessment of earlier studies. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all cancer sites combined, there were 124 cancer deaths. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect, 1998, 106(2):655–662. The authors address 

uncertainties in the estimation of exposure, describe the potential for confounding from β2,4,5-T, hexachlorocyclohexane, and cigarette smoking. In fact, they showed that blood levels 

of TCDD were not associated with smoking in a sub-sample suggesting little bias from lack of 

smoking data. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum samples, taken from 190 workers were used to derive TCDD levels 

for the entire cohort. Methods used to estimate exposure took into account elimination of 

TCDD during employment periods when exposure took place, and the methods of the area 

under the curve was used as it takes into account variations in concentration over time, and 

reflects cumulative exposure. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Exposure estimated based on half-lives observed in individuals with 

repeated samples. Area under the curve approach was used which is an improvement from 

past characterizations of exposure in this cohort. 

Conclusion The study provides data suitable for dose-response modeling. Derivation of exposure was 

done using current understanding of elimination of TCDD. Estimates of risks were derived 

from external comparisons to the general population that are unlikely to be biased by healthy 

worker effect, but risks generated using internal cohort comparisons would be preferable. 

Becher et al,. (1998) assessed this same data taking cancer latency into account, therefore 

Flesch-Janys et al., (1998) will not be further considered for dose-response modeling. 

1 

2 

3 Table B-11. Becher et al., 1998—All cancer sites combined 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Medical records used to identify deaths over the period 1952–1992. 

The follow-up interval was lengthy. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-15 —DO NOT CITE OR QUOTE 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Risks adjusted for exposures to TEQ, β-hexachlorbenzene, and 

employment characteristics. Smoking was shown to be similar to the comparison cohort of 

gas workers. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. A variety of exposure measures for both TCDD and TEQs found 

positive associations with cancer mortality. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The exposure measure was an integrated TCDD concentration over 

time estimate that back-calculated TCDD exposures to the end of the employment. 

Categorical and continuous TCDD exposures were examined in relation to the health outcome. 

Different models explored the shape of the dose-response curve. These efforts improve the 

exposure assessment of earlier studies. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all cancer sites combined, there were 124 cancer deaths. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect, 1998, 106(2):663–670. The authors discuss 

uncertainties associated with their use of exposure metrics, inability to evaluate effects for 

PCDD/Fs other than dioxin due to high correlations with β-HCH, and inability to characterize 

risks associated with exposures in children. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. The authors derived a measure of cumulative dose as a time-dependent 

variable (“area under curve”) using serum measures available in a sample of 275 workers. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. TCDD levels estimates through back-extrapolation of serum levels based on 

half-life estimates obtained from previous studies. Latency was considered, and a variety of 

exposure metrics including nonlinear relationships were evaluated. 

Conclusion In this paper, a variety of exposure metrics were found to be positively associated with cancer 

mortality. The additional lifetime risk of cancer corresponded to a daily intake of 1pg ranged 

between .01 and 0.001. This study was modeled in the 2003 Reassessment and is considered 

for further dose-response evaluations herein. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-16 —DO NOT CITE OR QUOTE 

1 B.1.4. The Seveso Cohort Studies 

2 

3 Table B-12. Bertazzi et al., 2001—All cancer sites combined, site-specific 

4 analyses 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Mortality appears to be well captured from the vital statistics 

registries in the region (99% complete). Vital status was ascertained using similar methods for 

both the exposed and reference populations. Both cancer and noncancer mortality outcomes 

were evaluated. Ideally, would have evaluated incident rather than decedent outcomes for 

cancer. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Individual-level data on potential confounders (i.e., age, calendar 

period, and gender) were adjusted for. Information from other independent surveys suggests 

similarity between smoking behaviors across the regions. Comparison of cancer mortality 

rates before the time of the accident between the regions also revealed no differences. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied (for all cancers combined). No statistically significant excesses noted 

in Zone A, or Zone B relative to reference area. Evidence of an exposure-response 

relationship was detected for lymphatic and hematopoietic tissues by number of years since 

first exposure. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. Subjects were assigned to one of the zones (A, B, R, or 

reference) based on official residence on the day of the accident or at entry into the area. 

Exposure misclassification is likely and lack of individual-level data precludes an examination 

of this source of error.

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. In total, 27, and 222, cancer deaths were found among residents of 

Zones A, and B, respectively. This allowed examined of gender-specific effects. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 2001 Jun 1; 153(11):1031–1044. Authors discuss 

completeness of mortality ascertainment, diagnostic accuracy of death certificates particularly 

with respect to diabetes, limited available of blood dioxin measures that did not permit 

estimation of TCDD dose on an individual-level basis. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-17 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. Individual-level exposure data are unavailable. Exposure based on place 

of residence at time of the explosion. Soil sampling performed indicated considerable 

variability in TCDD levels within each region. In addition, place of residency at time of 

explosion does not ensure individuals were at their home around the time of the accident. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. An ecological measure of exposure (region of residency at time of 

accident) was used to categorize individuals according to their possible exposure. Latencies 

were considered. While such an approach has value for identifying wherever excesses 

occurred among highly exposed populations, it is not precise enough to conduct a quantitative 

dose-response analysis. 

Conclusion The lack of individual-level exposure data precludes quantitative dose-response modeling 

using these data. 

 1 

 2 

3 Table B-13. Pesatori et al., 2003—All cancer sites combined, site-specific 

4 analyses 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Mortality appears to be well captured from the vital statistics 

registries in the region (99% complete). 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Individual-level data on potential confounders (i.e., age, calendar 

period, and gender) were adjusted for. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. While excesses of mortality were observed for several health 

conditions in Zone A, a dose-response pattern was not observed across Zones A, B and R. 

Among men, excess mortality observed in zone A included chronic ischemic disease, and 

chronic obstructive pulmonary diseases. Among females, an excess in Zone A was observed 

with hypertension. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. Subjects were assigned to one of the zones (A, B, R, or 

reference) based on official residence on the day of the accident or at entry into the area. 

Exposure misclassification is likely and lack of individual-level data precludes an examination 

of this source of error. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-18 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. Only 39 deaths observed among men in Zone A; 39 deaths observed 

among their female counterparts. Among females, only 3 deaths from hypertension observed 

in Zone A, and only 4 deaths observed among males for chronic obstructive pulmonary 

disease. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Occup Env Med, 1998; 55:126–131. Authors discuss limitations such as 

residency-based exposure assignment, absence of smoking, differential and death certification 

in exposed versus nonexposed areas. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Individual-level exposure data are unavailable. Exposure based on place 

of residence at time of the explosion. Soil sampling performed indicated considerable 

variability in TCDD levels within each region. In addition, place of residency at time of 

explosion does not ensure individuals were at their home around the time of the accident. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. An ecological measure of exposure (region of residency at time of 

accident) was used to categorize individuals according to their possible exposure. Latencies 

were considered. While such an approach has value for identifying wherever excesses 

occurred among highly exposed populations, it is not precise enough to conduct a quantitative 

dose-response analysis. 

Conclusion No dose-response patterns evident in the study, and the study lacked quantifiable measures of 

TCDD at an individual-level basis. The data are not well suited for dose-response analysis. 

1 

2 

3 Table B-14. Consonni et al., 2008—All cancer sites combined, site-specific 

4 analyses 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Mortality appears to be well captured from the vital statistics 

registries in the region (99% complete. Both cancer and noncancer mortality evaluated), 

although diagnostic accuracy of death certificates is likely low. Ideally, would have evaluated 

incident rather than decedent outcomes for cancer. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Individual-level data on potential confounders (i.e., age, calendar 

period, and gender) were adjusted for. Comparison of cancer mortality rates before the time of 

the accident between the regions also revealed no differences. Information from other 

independent surveys suggests similarity between smoking behaviors across the regions. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-19 —DO NOT CITE OR QUOTE 

Response Consideration satisfied for some outcomes. For all cancer sites combined, no evidence of 

dose-response was observed relative to general population across Zones A, B and R. Only 

statistically significant excess found in Zone A was for chronic rheumatic disease but based on 

only three deaths. Higher cancer excesses were found in Zone A after a latency period was 

incorporated; however, no dose-response relationship observed with this latency period. 

Evidence of an exposure-response relationship was detected for lymphatic and hematopoietic 

tissues by zone of residence. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. Subjects were assigned to one of the zones (A, B, R, or 

reference) based on official residence on the day of the accident or at entry into the area. 

Exposure misclassification is likely and lack of individual-level data precludes an examination 

of this source of error. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. In total, 42, 244, and 1,848 cancer deaths were found among residents 

of Zones A, B, and R respectively. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 2008, 167:847–858. Authors discuss potential for 

selection bias, limitation of residential based measure of exposure, similarities of mortality 

ascertainment in exposed and referent populations, and multiple testing. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Individual-level exposure data are unavailable. Exposure based on place 

of residence at time of the explosion. Soil sampling performed indicated considerable 

variability in TCDD levels within each region. In addition, place of residency at time of 

explosion does not ensure individuals were at their home around the time of the accident. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. An ecological measure of exposure (region of residency at time of 

accident) was used to categorize individuals according to their possible exposure. Latencies 

were considered. While such an approach has value for identifying wherever excesses 

occurred among highly exposed populations, it is not precise enough to conduct a quantitative 

dose-response analysis. 

Conclusion The lack of individual-level exposure data precludes quantitative dose-response modeling 

using these data. 

1 

2 

3 Table B-15. Baccarelli et al., 2006—Site-specific analysis 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-20 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. Polymerase chain reaction (PCR) methods were used to describe 

outcome measures. The prevalence of t(14; 18) was estimated as those individuals having a 

t(14; 18) positive blood sample divided by the t(14; 18) frequency (number of copies per 

million lymphocytes). 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Questionnaire data were used to collect information on cigarette 

smoking. Other potential confounders (age, smoking status, and duration of smoking). In 

addition, both exposure and outcome were objectively and accurately measured. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration was not satisfied. Associations were detected between the frequency of t(14; 

18) and plasma TCDD levels as well as zone of residence at the time of the explosion. No 

association was detected for these exposure measures and prevalence of t(14; 18). A doseresponse trend was detected for TCDD and the mean number of t(14;18) translocations/106

lymphocytes, however the relevance of t(14; 18) in lymphocytes to Non-Hodgin’s lymphoma 

is uncertain. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The authors highlight that exposure metrics represent both past and 

current body burdens. They employ several different exposure metrics of TCDD: place of 

residence (Zone A, B, R or reference), categorical serum measures, a linear term, log (base 10) 

transformed TCDD, and individuals with chloracne diagnosed after the accident. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Analyses are made using 72 highly exposed, and 72 low exposed 

individuals. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Carcinogenesis, 2006, 27(10):2001–2007. The authors discuss the 

limitation of using t(14; 18) translocations as an outcome measure, and the uncertain role it 

plays in the development of non-Hodgkin’s lymphoma. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. A total of 144 subjects were included in the study. This included 72 

subjects who had low exposures, and 72 who had high exposures based on serum 

concentrations. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. A variety of measures were employed including current TCDD levels, as 

well as surrogates of exposure at the time of the accident. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-21 —DO NOT CITE OR QUOTE 

Conclusion While an association was observed with the frequency of t(14; 18) translocation, it is uncertain 

whether this translates into an increased risk of non-Hodgkin’s lymphoma. Given the 

speculative nature of this endpoint and lack of demonstrated adverse effect, dose-response 

analyses for this outcome were not conducted. 

1 

2 

3 Table B-16. Warner et al., 2002—Breast cancer incidence 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Diagnoses of incident breast cancer were based on interview and 

information from medical records appears thorough. Of the 15 cases of breast cancer, 13 were 

confirmed by pathology and the remaining 2 by surgery report only. Three cases of breast 

cancer were excluded which represents a large proportion of the total cases identified. This 

would reduce sample size and could result in bias if the exclusion was association with TCDD 

exposure. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Information was collected on an extensive series of risk factors by 

using an interviewer administered questionnaire. Participation rates for the survey were fairly 

good (80%). 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Limited evidence (not statistically significant) of a dose-response 

when TCDD was analyzed as a categorical variable; only one breast cancer case was in the 

referent exposure category. In the analysis of TCDD as a continuous measure (log10TCDD), 

the hazard ratio associated with a 10-fold increase in TCDD serum levels was 2.1 (95% CI: 

1.0–4.6). 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Different exposure metrics were considered in these analyses 

(categorical, continuous, measures on a log-scale). Exposure data are of high quality as they 

are based on serum samples taken among women near the time of the accident. As such, 

exposure assignment is not dependent on as many assumption as used in occupational cohorts 

were back-extrapolation for many years had to be performed. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration somewhat satisfied. Inadequate follow-up for cancer limited the number of 

cases available. Sample size also limited the conclusions draw from the categorical analysis 

based on very few cases for some exposure categories. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Paper published in Environ Health Perspect, 2002 Jul, 110(7):625–628. . 

A major limitation of the study is the small number of incident cases of breast cancer (n = 15), 

discussed important strengths of the study including characterization of TCDD using serum 

collected near the time of the accident. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-22 —DO NOT CITE OR QUOTE 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum was used to estimate TCDD levels in 981 of 1271 eligible women 

who had lived in either of the two contaminated sites in 1976. Data represent an objective 

measure of TCDD near the time of the exposure. Data obtained near the time of exposure 

which minimized the potential for exposure misclassification. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Exposure characterized using serum measures obtained close to the time of 

the accident. 

Conclusion While characterization of exposure and availability of other risk factor data at an individuallevel basis are important strengths of this study, small sample size (n = 15 cases) based on 

inadequate follow-up is a key limitation. Quantitative dose-response analyses were conducted 

using this study, but continued follow-up of the study population or consideration of all cancer 

outcomes would be valuable. 

1 

2 

3 B.1.5. The Chapaevsk Study 

4 

5 Table B-17. Revich et al., 2001—All cancer sites combined, and site-specific 

6 analyses 

7 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration cannot be evaluated. Insufficient details are provided in the paper to gauge the 

completeness and coverage of the cancer registry and mortality data. Health outcomes were 

studied on the basis of information in the official medical statistics. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Given that this is an ecological study, bias may be present. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration cannot be evaluated. Dose-response was not evaluated as exposure was based on 

residency in the region vs. no residency. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. No individual-level exposure estimates were used. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. A total of 476 cancer deaths were observed among males, and 376 

cancer deaths observed among females. The precision of the SMRs is demonstrated with fairly 

narrow confidence intervals for many causes of death. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-23 —DO NOT CITE OR QUOTE 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria not satisfied. Published in Chemosphere, 2001, 43(4–7):951–966. Authors do not 

address the completeness of the mortality follow-up, and whether there are differences in death 

registrations between regions. The authors do acknowledge, however, that new investigations 

being undertaken would characterize exposure using serum-based measures. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. It is a cross-sectional study that compares mortality rates between 

regions. No individual-level exposure data available. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is 

consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. No individual-level exposure estimates were used in the study. 

Conclusion These cancer data are cross-sectional in nature and not appropriate for a dose-response analysis.

1 

2 

3 B.1.6. The Air Force Health (“Ranch Hands”) Study 

4 

5 Table B-18. Akhtar et al., 2004—All cancer sites combined and site-specific 

6 analyses 

7 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Cancer incidence and mortality based on information from repeated 

medical examinations, medical records and death certificate. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. The risk estimates were adjusted for a number of factors 

measured on an individual level including smoking. However, analyses are unable to 

distinguish between exposure to TCDD and 2,4-D as both were used in equal parts in the 

formulation of Agent Orange. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. There is evidence of a dose-response for all cancers and for some 

site-specific cancers (i.e., malignant melanoma, and prostate cancer). 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. High quality exposure data for most veterans was collected, so 

extrapolation to other members of the cohort was not required. The serum dioxin 

measurements also correlated well with reported skin exposure to herbicide in Vietnam, but 

collection of the samples 25 years later required back-extrapolation. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-24 —DO NOT CITE OR QUOTE 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. In total, 117 incidence cancers identified in the Ranch Hands cohort. 

For those sites with a dose-response association, malignant melanoma and prostate cancer, 

there were 16 and 34 incident cases, respectively. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in J Occup Environ Med, 2004, 46(2):123–136. Authors 

highlight that this is only cancer incidence study in US veterans, and the lengthy interval of 

follow-up (35–40 years)–both important strengths of the study. They addressed potential bias 

from healthy-worker effect, and uncertainties surrounding the estimation of TCDD exposure 

(extrapolation 30 years after exposure), as well as exposure to other chemical exposures. 

Study uses incident outcomes for cancer. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Individual exposure estimates are based on measurements of dioxin serum 

lipid concentrations. They were available for 1,009 Ranch Hands and 1,429 in the 

comparison cohort. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. TCDD exposures at the end of duty were estimated by back-extrapolating 

1987 serum values. 

Conclusion The major limitation of the study is the inability to isolate effects of TCDD from other 

chemicals used in the formulation of the herbicides. This limitation precludes dose-response 

modeling of the TCDD and cancer outcomes data. 

 1 

 2 

3 Table B-19. Michalek and Pavuk, 2008—All cancer sites combined 

 4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Cancer incidence was ascertained through the use of medical records. 

Death certificate were used to identify some malignancies. Little data is provided on the 

number of individuals lost to follow-up, however the same mechanisms of case ascertainment 

were applied to both the comparison and Ranch Hand cohorts. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Information collected from repeated physical examinations 

allowed for the adjustment of risk factors such as smoking. Agent Orange was a 50% mixture 

of 2,4-D and TCDD; therefore, potential for confounding by other coexposures is likely. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-25 —DO NOT CITE OR QUOTE 

Response Consideration satisfied for some comparisons. Statistically significant associations were 

noted with cancer incidence and TCDD when analyses were restricted to workers who served 

at most two years in Southeast Asia and those who sprayed more than 30 days before 1967. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Initial TCDD dose were estimated at the end of the tour of duty for 

the Ranch Hands. Individual-level serum dioxin measurements correlated well with 

correlated with days of spraying and calendar period of service, but collection of the samples 

roughly 20 years later required back-extrapolation. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. A total of 347 incident cases of cancer were used in the analyses. 

For stratified analyses, statistical power is more limited. For example, only 67 incident 

cancer in the subset of workers who spent less than 2 years in Southeast Asia, and sprayed for 

at least 30 days before 1967. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied J Occup Environ Med 2008; 50:330–340. The authors discuss issues related 

to exposure misclassification error, and suggest approaches for improving characterization of 

days of spraying. Congener specific data were unavailable, thereby not allowing for congener 

specific risks or adjustments to be made. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. TCDD data was available for 986 veterans in the Ranch Hand cohort, and 

1,597 members of the comparison cohort. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. TCDD exposures at the end of duty were estimated by back-extrapolating 

1987 serum values. 

Conclusion Ranch Hand veterans were exposed to other contaminants in the herbicides that were mixed, 

thereby making it difficult to determine independent effects of TCDD on cancer. In 

particular, 2,4-D has been shown to be associated with some cancers, notable cancer of the 

prostate. In our view, this limitation precludes dose-response modeling of TCDD and cancer 

using data from this cohort. 

1 

2 

3 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-26 —DO NOT CITE OR QUOTE 

1 B.1.7. Other Studies of Potential Relevance to Dose-Response Modeling 

2 

3 Table B-20. ‘t Mannetje et al., 2005—All cancer sites combined, site specific 

4 analyses 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. National records for death registrations through the New 

Zealand Health Information Service (NZHIS). Subjects not registered as having died during 

the study period were confirmed to be actually alive and resident in New Zealand using the 

New Zealand Electoral Roll, drivers’ license, and social security records. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Seventeen percent of workers were lost to follow up but it is 

unclear if bias resulted. The dichotomous exposure measure was based on exposure to 

TCDD, chlorinated dioxins and phenoxy herbicides, so confounding is a possibility by these 

coexposures. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Dose-response evidence for duration of employment and elevated 

mortality noted only in synthesis workers. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Exposure measures were limited to duration of employment and exposed/unexposed. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all cancer sites combined, there were 43 cancer deaths among the 

production workers, and 35 such deaths among the sprayers. Site-specific cancer analyses are 

limited by small sample sizes. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria not satisfied Occup Env Med, 2005; 62:34–40. A high percentage of the cohort was 

lost to follow-up (17%). The authors fail to mention this important limitation in this paper. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. This study used duration of exposure, at an individual level, as a 

surrogate measure of TCDD. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. Exposure was defined according to duration, and not concentrations of 

TCDD. Latency intervals were not evaluated. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-27 —DO NOT CITE OR QUOTE 

Conclusion Overall, quantitative exposure data are lacking for TCDD and limited dose-response 

relationships were observed across duration of exposure categories. Furthermore confounding 

by coexposures is a possibility. Taken together, these data are not suitable for inclusion in a 

dose-response analysis 

1 

2 

3 Table B-21. McBride et al., 2009b—All cancer sites combined, site-specific 

4 analysis 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The New Zealand Health Information Service Mortality Collection 

and the Registrar-General’s Index to Deaths. Additional searches were based on the last 

known address from the work record; the electoral roll and the habitation index; the telephone 

book; the internet; and Terranet property information database. An additional search was 

carried out through the Births, Deaths, and Marriages office of the New Zealand Department 

of Internal Affairs. Lastly, automated personnel and pension records were also used to locate 

past New Plymouth workers and identify some deaths. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Considerable amount of workers were lost to follow up (22%), but 

it is unclear if bias resulted. The dichotomous exposure measure was based on exposure to 

TCDD, chlorinated dioxins and phenoxy herbicides, so confounding is a possibility by these 

coexposures. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. There was no examination of dose-response effects. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Dichotomous exposure (exposed/unexposed) and duration of 

employment were examined from job exposure classification assessed via occupational history 

records industrial hygienists/factory personnel knowledge and questionnaires. Authors discuss 

limitations in the assignment of exposure among cohort members. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration not satisfied. A low number of deaths (n = 76) may have limited ability to 

detect effects small in magnitude and exposure-response relationships. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in Occup Medicine, 2009; 59(4):255–263. The authors highlight 

cohort lost to follow-up, the limited size of the cohort, differences in cohort definitions 

between sprayers and producers, and the potential for other exposures during employment at 

the plant. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-28 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. TCDD exposures were not quantified. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. Effective dose could not be estimated given the lack of individual-level 

exposure data. 

Conclusion The study lacks the quantification of exposures at an individual level precluded dose-response 

analysis. 

1 

2 

3 Table B-22. McBride et al., 2009a—All cancer sites combined, site-specific 

4 analysis 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The New Zealand Health Information Service Mortality Collection 

and the Registrar-General’s Index to Deaths were used to identify deaths. Additional searches 

were based on the last known address from the work record; the electoral roll and the 

habitation index; the telephone book; the internet; and several other public databases in New 

Zealand. An additional search was carried out through the Births, Deaths, and Marriages 

office of the New Zealand Department of Internal Affairs. Lastly, automated personnel and 

pension records were also used to locate past New Plymouth workers and identify some 

deaths. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Workers lost to follow-up were an unlikely source of bias especially 

for internal analyses. Confounding by other coexposures (e.g., 2,4,6-TCP) unlikely to have 

resulted in bias, due to presumed poor correlation with TCDD. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. The linear test for trend for TCDD exposure was not statistically 

significant for all cancer sites (combined), as well as lung cancer mortality. Dose-response 

relationships were not apparent across quartiles of TCDD exposure for all cancer sites 

combined, digestive cancers, lung cancer, soft tissue sarcomas or Non-Hodgkin’s Lymphoma. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Cumulative exposure to TCDD as a time-dependent metric was 

estimated for each worker from serum samples, but the authors did not examine a continuous 

measure of TCDD exposure (lagged or unlagged). 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-29 —DO NOT CITE OR QUOTE 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in J Occup Environ Med 51:1049-1056. This paper discussed the 

22% of the cohort lost to follow-up, differences in cohort definitions between sprayers and 

producers, and the potential for other exposures during employment at the plant. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum measures available for 346 workers were used to derive TCDD 

exposures for the entire cohort using the area under the curve approach. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria satisfied. Effective dose could be estimated from serum-derived cumulative exposure 

estimates. 

Conclusion Given that no dose-response associations were found, the data are not suited to dose-response 

analysis. 

1 

2 

3 Table B-23. Hooiveld et al., 1998—All cancer sites combined, site-specific 

4 analysis 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Outcomes were mortality. Few deaths expected to be missed since 

only 5% of the cohort was lost to follow-up or had emigrated. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Although dioxin-like compounds (PCDDs, PCDFs, and PCBs) 

were measured in the serum samples, these were not incorporated into the analysis. Therefore, 

confounding cannot be ruled out as an explanation of the reported association. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. A dose-response pattern was observed for internal cohort comparison 

for all cancer mortality, with RRs of 5.0 and 5.6 for the medium and high exposure, 

respectively. Dose-response patterns evident fort lung cancer as well. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Detailed occupational histories to assign dichotomous exposures 

(exposed/unexposed) based on maximum exposure levels. Although serum data also collected 

for TCDD and other coexposures (PCDDs, PCDFs, and PCBs), study only presents data for 

TCDD exposure. TCDD exposures at time of maximum exposure were extrapolated from 

measured serum. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-30 —DO NOT CITE OR QUOTE 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration not satisfied for internal cohort comparisons in either men or women. Among 

men, only 7 cancer deaths were observed among those in the unexposed part of the cohort, and 

51 among exposed workers. For external cohort comparisons, a total of 20 deaths were 

observed. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 1998, 147:891–901. The authors address potential 

limitations of estimating TCDD exposure from a sub-sample of surviving workers, lack of 

smoking data, the healthy worker effect, and relevance of other occupational exposures. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum samples were obtained from 94 of 144 subjects who were asked to 

participate in serum measurement study. Of these, a further 44 excluded due to absence due to 

holiday or work (n = 22), and nonexposed workers excluded because matching exposed 

worker not participating (n = 20). TCDD levels were extrapolated to the time of maximum 

exposure. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. 

Response Criteria not satisfied. Exposures assigned based on levels at maximum exposure. Assignment 

of exposure based on nonrepresentative sample of 50 survivors among the occupational cohort.

Conclusion The small number of identified cancer deaths, limitations in terms of the exposure assignment 

(based on nonrepresentative sample, and maximum exposure level) and concern over potential 

confounding by coexposures preclude using these data for a dose-response analysis. 

1 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-31 —DO NOT CITE OR QUOTE 

1 B.2. EVALUATION OF NONCANCER STUDIES 

2 B.2.1. NIOSH Cohort 

3 

4 Table B-24. Steenland et al., 1999—Mortality (noncancer) 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The study evaluated mortality from all cancer sites (combined). As 

described in the paper, the sources of vital status and cause of death information were received 

from the Social Security death files, the National Death Index, and the Internal Revenue 

Service. Vital status was known for 99.4% of the cohort members, cause of death information 

is available for 98% of the decedents. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. External comparisons for all-cause and cardiovascular mortality 

do not appear to be affected by the “healthy worker effect” as similar patterns were observed 

with internal cohort comparisons. Nonetheless, internal cohort comparisons are unable to 

adjust for many of the individual-level risk factors for cardiovascular disease. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. A dose-response relationship was observed with ischemic heart 

disease (linear test for trend p = 0.05), and with TCDD on a log-transformed scale the p-value 

was <0.001. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The study conducted detailed sensitivity analyses and evaluated 

different assumptions regarding latency, log-transformed TCDD exposures, and half-life 

values for TCDD. Associations were stronger for log-transformed values, and latency 

intervals of 15 years. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. This is the largest of the occupational cohorts with exposures to 

TCDD. The cohort consisted of 5,132 male workers and a total of 456 deaths from ischemic 

heart disease. This permits characterization of risk for all cancer sites (combined) 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied Journal of the National Cancer Institute, 1999, 91(9):779–786. The authors 

discussed the potential for bias from smoking, and other occupational exposures for which 

data for both were lacking at an individual basis. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-32 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. Exposure scores assigned at an individual level based on job-exposure 

matrix (JEM). The JEM was based on estimated factor of contact with TCDD in each job, 

level of TCCD contamination of materials at each plant over time, and proportion of day 

worker could be in contact with materials. These factors were multiplied together to derive a 

daily exposure score, which was accumulated over the working history of each worker to 

obtain a cumulative measure of TCDD. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. The follow-up of the cohort extended from 1942 until the end of 1993. 

Greater than 25 years of follow-up have accrued in cohort allowing for latency to be 

examined. Different assumptions on the half-life of TCDD were evaluated and produced 

similar results. Latency intervals were incorporated, with strongest associations noted no lag. 

Suggests mechanisms occur at the same time as exposure. However, noncancer mortality is 

not a viable endpoint to consider for further dose-response analysis. 

Conclusion TCDD exposures were quantified in this study, and a dose-response relationship was observed 

with ischemic heart disease mortality. The sample size was sufficient, and the follow-up 

interval was lengthy. However, no individual-level data were available for cardiovascular 

conditions, and the inability to adjust for these exposures introduces considerable uncertainty 

into the risk estimates. Furthermore, noncancer mortality is not considered a viable endpoint 

for dose-response analysis. 

1 

2 

3 Table B-25. Collins et al., 2009—Mortality (noncancer) 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Vital status complete for all but two workers. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. No information collected on smoking status, but no excess in lung 

cancer or nonmalignant respiratory diseases noted. Analyses took into account potential for 

exposure to pentachlorophenol. External cohort comparisons should be interpreted cautiously 

due to healthy worker effect, but internal cohort comparisons should not be influence by this 

bias. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. No statistically significant mortality excess for any noncancer 

mortality outcome evaluated. This included ischemic heart disease, stroke, nonmalignant 

respiratory disease, ulcers, cirrhosis, and external causes of death (accidents). Modeling of 

continuous measure of TCDD was not related to diabetes, ischemic heart disease, or 

nonmalignant respiratory mortality. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-33 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. The authors used these serum from 280 former TCP workers to 

estimate historical exposure levels of TCDD, furans, and polychlorinated biphenyls for all 

1,615 workers. Exposure assessment included detailed work history, industrial hygiene 

monitoring, and the presence of chloracne cases among groups of workers. This data was 

integrated into a 1-compartment, first-order pharmacokinetic to determine the average TCDD 

dose associated with jobs in each group, after accounting for the presence of background 

exposures estimated from the residual serum TCDD concentration in the sampled individuals. 

The authors did not evaluate departures from linearity, or examine skewness at higher 

exposures. No presentation of exposure levels was provided. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. A total of 662 deaths were observed. Of these, 218 were from 

ischemic heart disease, and 16 from diabetes (two outcomes for which associations have been 

noted elsewhere). 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in Am J Epidemiol, 2009, 170(4):501–506. The authors discuss 

potential for exposure misclassification, large size of the cohort, lengthy follow-up interval, 

and large number of workers who provided serum from which TCDD exposures were 

estimated. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. This study has the greatest number of serum samples obtained from a 

specific plant. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. Noncancer mortality is not a viable endpoint to consider for further 

dose-response analysis. 

Conclusions No dose-response associations were noted for noncancer mortality outcomes. The data are, 

therefore, not suited for dose-response modeling. 

1 

2 

3 B.2.2. BASF Cohort 

4 

5 Table B-26. Ott and Zober, 1996—Mortality (noncancer) 

6 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Mortality ascertainment appeared to be fairly complete. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-34 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. Information was collected on smoking status, body mass index, and 

other occupational exposures, however a large portion of the cohort was firefighters who may 

have been exposed to other occupational carcinogens. However, the recruitment of survivors 

may results in under-ascertainment of mortality. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. For external cohort comparisons across the three TCDD exposure 

categories, there was no dose-response pattern observed for any of the noncancer causes of 

death. Cox regression risk estimates for all cause or circulatory disease mortality when TCDD 

was modeled as a continuous variable were not statistically significant. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Cumulative measure of TCDD expressed was derived from serum 

measures. Exposure was also estimated by chloracne status of the cohort members. The 

authors have not addressed the potential implication of deriving TCDD exposure estimates for 

the whole cohort using sera data that were available for only about half of the cohort. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all causes of death, there were 92 deaths, while 37 circulatory 

deaths. Many of the cause-specific death had less than 5 deaths in the upper exposure 

category. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Occup Environ Med, 1996, 53:606–612. A large component of the cohort 

was assembled by actively seeking out workers who were alive in the mid 1980s. As a result, 

it is likely a number of deaths were missed. This is supported by much lower SMRs in this 

component of the cohort published in earlier studies of the cohort. This underascertainment of 

mortality results in biased SMR statistics (underestimated). The authors do highlight the value 

of the serum based measures to estimate TCDD exposure 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum samples, taken in 1989, were available for 138 surviving workers out 

of 254 and allowed for cumulative TCDD levels to be estimated using regression techniques in 

the remainder of the cohort. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. Exposure assignment took into the affect that body mass index had on 

TCDD half-lives. TCDD levels estimates through back-extrapolation of serum levels based on 

half-life estimates obtained from previous studies. Latency was considered with stronger 

association observed in external comparisons incorporating a latency of 20 years. The followup of the cohort was lengthy (>50 years). However, noncancer mortality is not a viable 

endpoint to consider for further dose-response analysis. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-35 —DO NOT CITE OR QUOTE 

Conclusion No associations noted with any noncancer deaths. External comparisons should be treated 

cautiously especially for cardiovascular mortality which is recognized to often be biased by 

the healthy-worker effect. In the absence of any outcome with an association with TCDD 

exposure, no dose-response analyses of these data are recommended. 

1 B.2.3. Hamburg Cohort 

2 

3 Table B-27. Flesch-Janys et al., 1995; Flesch-Janys et al., 1996 erratum—

4 Mortality (noncancer) 

5 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Medical records used to identify deaths over the period 1952–1992. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Similarity in smoking rates between control cohort and the exposed 

workers was similar based on independent surveys. Occupational exposures to benzene, and 

dimethyl sulfate were unlikely to bias dose-response pattern observed as these exposures 

occurred in production departments with low to medium levels of TCDD exposure. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Dose-response relationship observed for all-cause mortality, 

cardiovascular mortality, and ischemic heart disease mortality across 6 exposure categories, 

with the cohort of gas supply workers used as the referent. The linear tests for trend for these 

three outcomes were all statistically significant (p < 0.05). 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. The exposure measures was an integrated TCDD concentration over 

time estimate that back-calculated TCDD exposures to the end of the employment. 

Categorical and continuous TCDD exposures were examined in relation to the health outcome. 

These efforts improve the exposure assessment of earlier studies. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For all causes of death combined, there were 414 deaths in the 

exposed cohort, and 943 in the cohort of gas supply workers. A total of 157 and 76 deaths 

from cardiovascular disease, and ischemic heart disease were noted. The corresponding 

number in the cohort of gas supply workers was 459, and 205, respectively. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 1995, 1442:1165–1175. The authors discuss the potential 

role of other occupational exposures (i.e., dimethyl sulfate, solvents, benzene), smoking, and 

suitability of the comparison cohort of gas supply workers. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-36 —DO NOT CITE OR QUOTE 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum and adipose tissues were used to estimate TCDD exposure in 190 

workers. A one-compartment first-order kinetic model was used to estimate exposure at end 

of exposure for these workers. Regression methods were then used to estimates TCDD 

exposures for all workers. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. Exposure based on half-life estimates from individuals with repeated 

serum measures. Other dioxin-like compounds were considered with the TOTTEQ exposure 

metric. Noncancer mortality, however, is not a viable endpoint to consider for further doseresponse analysis. 

Conclusion Although, the exposure data used within this study are well-suited to a dose-response analysis 

for all-cause and cardiovascular mortality given the associations observed, use of noncancer 

mortality endpoint is not amenable for further dose-response analysis. 

1 B.2.4. The Seveso Women’s Health Study 

2 

3 Table B-28. Eskenazi et al., 2002a—Menstrual cycle characteristics 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Information was also obtained from medical records for all obstetric 

and gynecologic conditions. Information on menstrual cycles was obtained from 

questionnaires. Women were asked about length of cycles, regularity, how many days flow 

lasted, and heaviness of menstrual flow (scanty, moderate, or heavy). Measurement error is 

likely for the subjective nature of self-reported menstrual parameters but specificity and 

sensitivity is difficult to ascertain due to lack of validation data for these measures. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Detailed risk factor information was collected from questionnaire, 

allowing for the potential confounding influence of many risk factors to be controlled for. The 

length of cycle study findings may have been affected by the presence of a few outliers. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. A positive dose-response relationship was found with TCDD among 

women who were premenarcheal at time of the explosion and longer menstrual cycle. Increased 

TCDD resulted in a reduced odds of scanty menstrual flow. No association was noted with 

these two outcomes among postmenarcheal women. A decreased risk of irregular cycles was 

observed with higher TCDD levels. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-37 —DO NOT CITE OR QUOTE 

Response Criteria satisfied. Serum concentrations of TCDD offer improved exposure assessment, 

although delineating the critical exposure window is challenging given the nature of the very 

high initial exposure. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure adequate 

statistical power. 

Response Consideration satisfied. Cohort was large enough as analyses were conducted on 301 women. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion of 

the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 2002; 156(4) 383–392. Limitations included an inability to 

assess affects on menstrual cycle at time body burdens were the highest (at time of the 

accident). Also, TCDD was estimated for 1976, not concurrent with their cycles in the previous 

year, and a large number of women were excluded due to intrauterine device or oral 

contraceptive use. Strengths included population-based nature of study, with characterization 

of exposure using serum, and levels of other polychlorinated dibenzo-p-dioxins and 

dibenzofurans were at background levels. Findings for length of menstrual cycle may be 

unduly influenced by the presence of some outliers. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. The study population was based on 301 women as those who were over the 

age of 44 were excluded, as well as women with surgical of natural menopause, women with 

Turner’s syndrome, those who had been pregnant or breastfed in the past year, and those who 

had used an intrauterine device or oral contraceptives. For 272 women, TCDD levels were 

based on serum data provided in 1976; TCDD levels were back-extrapolated to 1976 levels for 

the other 29 women. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is consistent 

with a toxicologically relevant dose. Latency and appropriate window(s) of exposure 

examined. Response had to be a nonfatal endpoint. 

Response Criteria satisfied. Ideally, TCDD exposures would be concurrent with reporting of cycle 

characteristics. Herein, TCDD exposures were based on levels in 1976; however, given the 

long half-life of TCDD and the same follow-up interval for all women, TCDD exposures in 

1976 should correlate well with levels near the time of interview. Further, the critical window 

of exposure can be estimated for the women that were premenarcheal at the time of the accident 

(13 years). 

 

Conclusion This study meets all of the criteria and considerations for further dose-response analysis. The 

determination of the relevant time interval over which TCDD dose should be considered is 

uncertain . 

1 

2 

3 Table B-29. Eskenazi et al., 2002b—Endometriosis 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration not satisfied. Results of a pilot study showed that ultrasounds had excellent 

specificity and sensitivity for ovarian endometriosis. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-38 —DO NOT CITE OR QUOTE 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design or 

statistical analysis. 

Response Consideration not satisfied. More than half of the women were classified as ‘uncertain’ with 

respect to endometriosis disease status. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of an 

exposure-response relationship. 

Response Consideration not satisfied. While an increased risk of endometriosis was observed across the 3 

TCDD categories, these risks were not statistically significant relative to the lowest exposure 

category. The test for trend based on a continuous measure (log10TCDD) was also not statistically 

significant. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Criteria satisfied. Serum concentrations of TCDD offer improved exposure assessment, although 

delineating the critical exposure window is challenging given the nature of the very high initial 

exposure. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure adequate 

statistical power. 

Response Consideration not satisfied. Only a total of 19 cases of endometriosis were identified. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion of 

the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect 2002; 110(7) 629–634. Author’s highlight that this is 

the first study to examine the relationship between TCDD and endometriosis, and the availability 

of sera data to estimate TCDD levels. Limitations included the small number of women with 

endometriosis, and inability to confirm disease status using laparoscopy. Finally, young women 

may have been underrepresented due to cultural difficulties in examining women who had never 

been sexually active. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response relationships 

can be assessed. 

Response Criteria satisfied. Eligible study subjects were women between 1 month and 40 years of age at 

time of accident. These analyses excluded virgins, those with Turner’s syndrome, and women 

who refused the examination of ultrasound. Serum data were available for the 601 participants on 

which the analyses are based. Of these, 559 had serum measures taken in 1976/77, 25 between 

1978 and 1981, and 17 women in 1996. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is consistent 

with a toxicologically relevant dose. Latency and appropriate window(s) of exposure examined. 

Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. TCDD exposure was estimated at the time of “conception attempt” using 

serum measures, with extrapolation from 1976 levels using half-life assumptions. It is difficult to 

identify the relevant time interval over which TCDD dose should be considered for dose-response 

analysis. The critical window of exposure is unknown. 

 

Conclusion The lack of a statistically significant association coupled with a large number of women for which 

endometriosis disease status was “uncertain”, precludes the use of these data to conduct doseresponse analysis. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-39 —DO NOT CITE OR QUOTE 

1 Table B-30. Eskenazi et al., 2003—Birth outcomes 

2 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration not satisfied. Outcomes were identified through self-reported questionnaires. 

Women were found to over-report birth weight, and have a tendency to underreport birth 

defects in children. As a large number of women in Seveso underwent voluntary abortion in 

the first year after the explosion, an awareness bias may have contributed to differential 

reporting of pregnancy histories. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. See above. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. There was no association between spontaneous abortions and 

log10TCDD, or with births small for gestational age. An inverse association with birth weight 

was noted in first eight years following the accident as were the number of births small for 

gestational age; however, none achieved statistical significance at p < 0.05. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Criteria satisfied. Serum concentrations of TCDD offer improved exposure assessment, 

although delineating the critical exposure window is challenging given the nature of the very 

high initial exposure. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For spontaneous abortions there were 769 pregnancies. Fetal growth 

and gestational age analysis was carried out on 608 singleton births that occurred postexplosion. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect, 2003, 111(7):947–953. The authors highlight 

potential limitation of reliance on self-reported data to ascertain pregnancy outcomes. They 

also address the relevance of paternal exposures to TCDD on the developing fetus—such 

exposure data were not considered in this study. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. A total of 745 women in the SWHS had reported getting pregnant, of these 

510 women were pregnant after the explosion (888 pregnancies). Analyses of spontaneous 

abortions based on 476 women (excludes those with voluntary abortion, ectopic pregnancy, or 

molar pregnancy. TCDD measured for 413 women in 1976/77, 12 women between 1978 and 

1981, and 1996 for 19 women. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-40 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. TCDD exposures were extrapolated to 1976 values. However, it is 

difficult to identify the relevant time interval over which TCDD dose should be considered for 

dose-response analysis. 

Conclusion The findings of the study are somewhat limited due to the reliance on self-reported information 

for pregnancy outcomes, and lack of paternal exposures. The findings were not statistically 

significant. Taken together, quantitative dose-response analyses for this study population is 

not recommended. 

1 

2 

3 Table B-31. Warner et al., 2004—Age at menarche 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. In this study age at menarche was based on retrospective recall 5 to 

19 years before the interview. Previous work suggests moderate to high correlations between 

actual and recalled menarche, misclassification of outcome would bias risk estimates towards 

the null (assuming nondifferential misclassification.) 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Data collected from self-reported questionnaires allow for the 

potential confounding influence of many risk factors to be taken into account. Some 

misclassification of outcome may bias risk estimates towards the null. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. There was no association between TCDD levels and the age at 

menarche with either the continuous or categorical measures of TCDD. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Criteria satisfied. Serum concentrations of TCDD offer improved exposure assessment, 

although delineating the critical exposure window is challenging given the nature of the very 

high initial exposure. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Cohort was large enough as analyses were performed using 282 

women who were premenarcheal at the time of the explosion. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect, 2004, 112:1289–1292. Authors discuss use of 

pooled serum from residents of the unexposed zone, and that those in lowest exposure group 

had high exposures relative with contemporary levels for the area. Strengths of study include 

use of serum to estimate TCDD exposure. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-41 —DO NOT CITE OR QUOTE 

Response Criteria satisfied. The SWHS included women between 1 month and 40 years of age at time of 

accident who attempted to get pregnant after the explosion (n = 463). This study is restricted 

to those who were premenarcheal at the time of the explosion (n = 282). Serum was collected 

for these women, primarily in 1976–1977 (n = 257), between 1978 and 1981 for 23, and in 

1996–1997 for the 2 remaining women. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. TCDD exposures in 1976 were estimated by extrapolation serum levels 

obtained after this date using the Filser model. Both categorical and continuous measures of 

exposure were modeled. In utero measures of exposure are likely most relevant exposure 

based on findings from animal studies. 

Conclusion No association between TCDD levels and age at menarche was found. There may be some 

misclassification of age at menarche based on self-report, and biologically, the most relevant 

dose as suggested by animal studies occurs in utero. Additionally, it is difficult to identify the 

relevant time interval over which TCDD dose should be considered for dose-response analysis. 

For these reasons, these data are not suited to a dose-response analysis. 

1 

2 

3 Table B-32. Eskenazi et al., 2005—Age at menopause 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Outcome measures were obtained based on self-reported data 

collected from questionnaires. Studies have shown that self-reports of age at menopause are 

reported with accuracy and reliability, and among women with surgical menopause, the selfreported age correlated well with that on the medical records. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Data obtained from the questionnaire allow for the potential 

confounding influence of several potential confounders to be controlled for. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. Although risks of earlier menopause increased in the first four 

quintiles, with a statistically significant trend, no increased risk was noted in the highest 

exposure category (hazard ratio = 1.0 relative to lowest exposure group). Study authors 

suggest this is due to the “inverted U” dose response often seen with hormonally active 

compounds. Additionally, no statistically significant association was noted with log10TCDD 

for the individual quintiles. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Criteria satisfied. Serum concentrations of TCDD offer improved exposure assessment, 

although delineating the critical exposure window is challenging given the nature of the very 

high initial exposure. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-42 —DO NOT CITE OR QUOTE 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. The study included 616 women. Of these, 260 were premenopausal, 

169 classified as natural menopause, 83 as surgical menopause, 24 as impending menopause, 

33 as premenopausal, and 58 in an “other” category. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect, 113:858–862 (2005). Authors highlight this is 

first study to look at relationship between dioxin and age at menopause. Other limitations of 

the study include lowest exposure group (≤ 20.4 ppt) includes exposures level that are far 

higher than background, and age at menopause was based on retrospective recall. Strength of 

study is ability to characterize TCDD using serum measures. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. The Seveso Women’s Health Study collected serum sample which allowed 

TCDD exposures to be characterized. Those women (n = 616) who had not reached natural 

menopause at the time of the accident were included in the study. Serum measures collected 

in 1976/77 were available for 564 women, for 28 women, sera was collected between 1978 

and 1981, while for 24 women, sera was collected in 1996/97. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. TCDD levels were estimated at the time of the explosion using available 

information on TCDD half-life. However, it is difficult to identify the relevant time interval 

over which TCDD dose should be considered for dose-response analysis. The critical window 

of exposure can be estimated but is large and highly uncertain. 

Conclusion The findings do not provide strong support for a dose-response relationship. As such, they are 

not well suited to a quantitative dose-response analysis. 

1 

2 

3 Table B-33. Warner et al., 2007—Ovarian function 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Ovarian cyst analysis based on women who underwent ultrasound 

(n = 310). Ovarian follicle analysis based on self-report on menstrual cycle and done in 

women in pre-ovulatory cycle (n = 96) at time of ultrasound. Hormonal analysis based on 

women in last 14 days of cycle (n = 129). 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Data collected from self-reported questionnaires allow for the 

potential confounding influence of many risk factors to be taken into account. Some 

misclassification of outcome based on self-reports of menstrual cycle may bias risk estimates 

towards the null. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-43 —DO NOT CITE OR QUOTE 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. There was no association between serum TCDD levels and the 

number or size of ovarian follicles. TCDD was also not associated wit the odds of ovulation. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Criteria satisfied. Serum concentrations of TCDD offer improved exposure assessment, 

although delineating the critical exposure window is challenging given the nature of the very 

high initial exposure. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Cohort was large enough as analyses were performed using 129 

women for ovulation outcome, and hormone analyses based on 87 women in luteal, and 55 in 

midluteal phases. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environ Health Perspect, 2007,115:336–340. An important limitation cited 

by the authors was that women may not have been exposed at critical period (prenatally). 

Phases of the cycle may also have been misclassified as this was based on self-reported data. 

Strength, first study to have examined ovarian function and TCDD exposures. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. The SWHS included women between 1 month and 40 years of age at time of 

accident who were between 20–40 years of age and not using oral contraceptives at follow-up 

(n = 363).Of these, serum was collected for 330 women between 1976 and 1977, between 

1978 and 1982 for 25 women, and between 1996 and 1997 for 8 women. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. The women may not have been exposed at critical period (prenatally). 

Conclusion No association between TCDD levels and ovarian function was found. There may be some 

misclassification of period of the cycle based on self-report, and biologically, the most relevant 

dose as suggested by animal studies occurs in utero. For these reasons, these data are not 

suited to a dose-response analysis. 

1 

2 

3 Table B-34. Eskenazi et al., 2007—Uterine leiomyoma 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-44 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. Outcomes were determined using two definitions: current fibroids, or 

past diagnosis of fibroids. For past diagnosis of fibroids, self-reported data and medical 

records were used to determine whether women were previously diagnosed with fibroids, these 

were confirmed with medical records. A total of 25 women indicated they had never been 

diagnosed with fibroids. Medical records indicate a past diagnosis for these women, and they 

were classified as such. For current fibroids, this was determined at the time of the interview 

for 634 women using transvaginal ultrasound examinations. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. In the SWHS questionnaires were administered to the participants and 

detailed data for reproductive characteristics, smoking, body mass index, and alcohol use were 

collected so risks could readily be adjusted for these covariates. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied, but inversely. An inverse dose-response pattern with the percentage of 

women diagnosed (current & past history–combined) with fibroids across 3 categories of 

exposure. Namely, the percentages of women with fibroids in the ≤20, 20.1–75.0, and >75.0 

ppt categories were 41.1%, 26.8%, and 20.0%, respectively. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. A variety of different exposure metrics were considered including 

linear, categorical, splines, and log10TCDD. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. A total of 251 women were found to have fibroids, and there were 62, 

110, and 79 women with fibroids diagnosed in the 3 TCDD exposure categories. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 2007, 166:79–87. In this study, the authors found an 

inverse association between TCDD and uterine leiomyoma risk. The authors highlighted 

strengths of the study that included the longitudinal design, serum measures taken at an 

individual-level basis and most taken within 2 years of the accident, ability to include 

outcomes among those who did not take an ultrasound by using an adapted statistical 

approach. An important limitation that was the differences in risk by the stage of development 

could not be assessed as all women were exposed postnatally, and only 4 cases were observed 

among those who were premenarcheal at the time of exposure. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Final sample consisted of 956 women in the Seveso Women’s Health Study 

without a history of fibroids. For 872 of these women, serum was collected in 1976 and 1977. 

For 56 women, TCDD was measured in women between 1978 and 1981, and for 28 women 

the serum was collected in 1996. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-45 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. TCDD exposures were back extrapolated to expected levels in 1976 (at 

the time of the accident). However, it is difficult to identify the relevant time interval over 

which TCDD dose should be considered for dose-response analysis. The critical window of 

exposure is unknown. 

Conclusion The data suggest an inverse (protective) effect between fibroids and exposure to TCDD. As 

such, these data are not suited to further dose-response analyses. 

1 

2 

3 B.2.5. Other Seveso Noncancer Studies 

4 

5 Table B-35. Mocarelli et al., 2008—Semen quality 

6 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Serum levels of TCDD were measured on an individual basis for men 

in exposed areas; pooled samples from men in uncontaminated areas were measured to assess 

background TCDD exposure levels. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. While compliance rates may have introduced some possible bias, this 

does not seem likely as different effects noted between the 22–31 and 32–39 year old age 

groups. Information collected for other risks factors, which have been used as adjustment 

factors in the models. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Figure 3 suggests dose-response relationship among those aged 1–9 at 

the time of the accident for sperm concentration and motility. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Serum concentrations of TCDD offer improved exposure assessment, 

although delineating the critical exposure window is challenging. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Analyses are based on 135 males exposed to TCDD. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environmental Health Perspective s, 2008, 116(1):70–77. The authors 

describe strengths associated with characterization of exposure (using serum samples), and 

representativeness of study population. Limitation of study includes low compliance (but high 

for semen sample studies), namely, 60% among a group of healthy men. The compliance rate 

was higher among exposed group (69%). 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-46 —DO NOT CITE OR QUOTE 

Response Criteria satisfied. Involved males, < 16 years old at time of accident. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria satisfied. TCDD exposures were based on serum samples. Serum samples were 

drawn (in 1997/1998) from participants whose 1976 samples were above 15 ppt. Pooled 

samples obtained in 1997/98 were used to describe background TCDD levels in 

uncontaminated areas. The associated between TCDD exposure and semen quality was found 

statistically significant for the boys with 1 and 9 years of age at the time of the accident. This 

provides a critical window of exposure to estimate TCDD concentration. 

Conclusion Health outcomes are exposures are well characterized using serum data. However, the men 

exposed between the ages of 1 and 9 to elevated TCDD levels had reduced semen quality 22 

years later. It is difficult to discern whether this effect is a consequence of the initial high 

exposure between 1 and 9 years of age or a function of the cumulative exposure for this entire 

exposure window beginning at the early age. Nonetheless, quantitative dose-response analyses 

for this outcome were conducted. 

1 

2 

3 Table B-36. Mocarelli et al., 2000—Sex ratio 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Birth records examined for those who lived in parents who lived in 

the area and who provided serum samples. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Paternal TCDD exposures were associated with an increased 

probability of female births (p = 0.008). 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Serum samples were used to estimate maternal and paternal TCDD 

levels. No discussion of exposure levels in reference population. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Statistically significant findings achieved. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria not satisfied. The Lancet, 2000, 355:1858–1863. There is no discussion on the 

strengths and limitations of this study. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-47 —DO NOT CITE OR QUOTE 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum levels of TCDD were obtained from parents using samples provided 

in 1976/77. Serum measures available for 296 mothers and 239 fathers. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. Serum based measures of TCDD were obtained shortly after the 

accident. TCDD levels were also extrapolated to the time of conception. However, it is 

difficult to identify the relevant time interval over which TCDD dose should be considered for 

dose-response analysis. The critical window of exposure is unknown. 

Conclusion The data from this study demonstrate a positive dose-response relationship with paternal 

TCDD levels at the time of the accident and increased likelihood for female births. However, 

It is difficult to identify the relevant time interval over which TCDD dose should be 

considered; specifically, it is difficult to discern whether this effect is a consequence of the 

initial high exposure during childhood or a function of the cumulative exposure for this entire 

exposure window beginning at the early age. Using the initial exposures in a dose-response 

model would yield LOAELs that are too high to be relevant to factor into the RfD calculation. 

Dose-response analysis for this outcome is, therefore, was not conducted. 

1 

2 

3 Table B-37. Baccarelli et al., 2008—Neonatal thyroid function 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Measures of b-TSH are taken using a standardized protocol 72 hours 

after birth. These b-TSH measures are taken on all newborns born in the region of Lombardy of 

which Seveso if a part of. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design or 

statistical analysis. 

Response Consideration satisfied for component of the study based on plasma dioxin measures. For the 

comparisons involving place of residence at the time of the accident, exposure misclassification is 

likely given variability in soil TCDD exposure levels within these areas. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of an 

exposure-response relationship. 

Response Consideration satisfied. Mean neonatal b-TSH was 0.98μU/ml [0.90–1.08] in the reference area, 

1.35μU/ml [1.22–1.49] in zone B, and 1.66μU/ml [1.19–2.31] in zone A (p < 0.001). The plotted 

frequency distributions have similar shapes, but have shifted to the right for areas of higher 

exposures. Neonatal b-TSH was correlated with current maternal plasma TCDD (β-0.47, p < 

0.001) in the 51 newborns for which individual maternal serum TCDD values were available. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-48 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. TEQs were measured among the 38 women for which serum samples 

were available and were defined for a mixture of dioxin-like compounds. Maternal mean total 

TEQs (PCDDs, PCDFs, coplanar PCBs, and noncoplanar PCBs) was 41.8 ppt. Two measures of 

exposure included place of residence at time of accident and plasma samples obtained from 

mothers at the time of delivery. Similarities in positive dose-response relationships give stronger 

weight to the findings. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure adequate 

statistical power. 

Response Consideration satisfied for exposure metric that was based on ‘place of residence’. For plasma 

based estimate of maternal TCDD there were only 51 mother-child pairs. Only seven children in 

total were found to have b-TSH levels in excess of 5 uU/ml; this implies limited statistical power 

involving this health outcome. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion of 

the strengths and limitations. 

Response Criteria satisfied. PLOS Medicine 2008; 5(7)1133–1142. The authors discuss the strength of the 

study related to characterization of exposure using serum sampling, and ability to adjust for 

factors related to b-TSH or TCDD levels (gender, birth weight, birth order, maternal age, hospital 

and type of delivery. They also highlight that a limitation of study was that the influence of 

mother-child dioxin transfer through colostrum could not be assessed because no information on 

breastfeeding before b-TSH measurement was available. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response relationships 

can be assessed. 

Response Criteria satisfied. In the population-based study, eligible women who resided in zones A and B at 

the time of the accident (n = 1,772) were matched to nonexposed women. In the study based on 

plasma dioxin measurements, participants were the 51 children born to 38 women from zones A, 

B, R, or a reference zone for which plasma dioxin measurements were available. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is consistent 

with a toxicologically relevant dose. Latency and appropriate window(s) of exposure examined. 

Response has to be a nonfatal endpoint. 

Response Criteria satisfied. Maternal TCDD levels were estimated at the time of delivery based on plasma 

samples, and the critical window of exposure can be defined as the 9 month gestation period. 

Conclusion The data provide an opportunity for quantitative dose-response analyses. 

 1 

 2 

3 Table B-38. Alaluusua et al., 2004—Oral hygiene 

 4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Ascertainment of dental health was done blind to place of residence, 

used standard protocol for caries developed by the WHO, and the clinical examination 

supplemented by radiographic examination. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-49 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. Additional risk factor information was collected on questionnaires. 

These factors were considered as adjustment factors. Findings potentially susceptible to 

participation biases. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Increased prevalence of developmental enamel effects found with 

increased TCDD serum measures. Namely, prevalence in unexposed region was 26%, 

whereas in the low, middle, and high TCCD groups the prevalence was 10, 40, and 60%, 

respectively. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. TCDD exposure level based on serum lipids. No discussion of 

exposure levels in reference population. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Criteria satisfied. Despite small numbers, statistically significant findings were achieved. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Environmental Health Perspectives, 2004, 112(13)1313–1318. Authors 

mention two important strength of the study: characterization of TCDD exposure using serum 

collected shortly after the time of the accident, and the fact that developmental defects are 

permanent in nature. Therefore, they represent a health outcome can evaluated years later. 

Little discussion was made of the impact of differential compliance rates between the exposed 

(74%) and nonexposed (58%) groups. Authors mention two important strength of the study: 

characterization of TCDD exposure using serum collected shortly after the time of the 

accident, and the fact that developmental defects are permanent in nature. Therefore, they 

represent a health outcome can evaluated years later. Little discussion was made of the impact 

of differential compliance rates between the exposed (74%) and nonexposed (58%) groups. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum levels of TCDD could be estimated for children in exposed areas. 

No serum levels were available for reference group of children, and assumption of zero 

exposure was made. This seems reasonable. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria satisfied. It is difficult to discern whether this effect is a consequence of the initial 

high exposure during childhood or a function of the cumulative exposure of the entire 

exposure window beginning at early age. However, assumptions can be made regarding the 

critical window of exposure and the relevant dose can be calculated. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-50 —DO NOT CITE OR QUOTE 

Conclusion The considerations for conducting a dose-response analysis have been satisfied with the study 

population of only those subjects who lived in the ABR zone at the time of the accident; 

exposure data are unavailable for those in the referent area. While is difficult to identify the 

relevant time interval over which TCDD dose should be considered, quantitative doseresponse analysis for this outcome was conducted. 

 1 

 2 

3 Table B-39. Bertazzi et al., 2001—Mortality (Noncancer) 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied for some causes of death, but not others. Mortality appears to be well 

captured from the vital statistics registries in the region (99% complete). Some health 

outcomes (e.g., diabetes) are subject to misclassification using death certificate data. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Although individual-level data for individual risk factors are not 

available, the potential for confounding is likely minimal. For e.g., independent surveys 

suggests similarity between smoking behaviors across the regions. Exposure misclassification 

based on place of residency likely to bias risk estimates towards the null. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied for most causes of death. An exception was the dose-response 

relationship was observed for chronic obstructive pulmonary disease across Zones A, and B. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. Exposure classification was based on the address of the 

residence on the date of the accident or when the person first entered the area. Although 

TCDD blood levels were also measured, these were not examined with respect to health 

outcomes. The lack of individual-level data also precluded an examination of these 

uncertainties. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. A total of 494 non-cancer deaths were found among residents of 

Zones A, and B, respectively. This allowed examined of gender-specific effects. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 2001, 153:1031–1044. Authors discuss lack of individuallevel exposure data and other risk factors (e.g., smoking), difficulties in extrapolating to 

background levels, diagnostic accuracy of using death certificates. Strengths included 

similarities between exposed and comparison population for several risk factors, completeness 

of follow-up, and consistent methods to identify mortality outcomes in the exposed and 

comparison populations. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-51 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. Individual-level exposure data are unavailable. Exposure based on place 

of residence at time of the explosion. Soil sampling performed indicated considerable 

variability in TCDD levels within each region. In addition, place of residency at time of 

explosion does not ensure individuals were at their home around the time of the accident. 

3. Critieria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. An ecological measure of exposure (region of residency at time of 

accident) was used to categorize individuals according to their possible exposure. Latencies 

were considered. While such an approach has value for identifying whether excesses occurred 

among highly exposed populations, it is not precise enough to conduct a quantitative doseresponse analysis. Furthermore, noncancer mortality is not a viable endpoint to consider for 

further dose-response analysis. 

Conclusion Study is not suitable for dose-response analysis due to mortality as endpoint and lack of 

individual-level exposure data. 

1 

2 

3 Table B-40. Consonni et al., 2008—Mortality (Noncancer) 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied for some causes of death, but not others. Mortality appears to be well 

captured from the vital statistics registries in the region (99% complete). Some health 

outcomes (e.g., diabetes) are subject to misclassification using death certificate data. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Although individual-level data for individual risk factors are not 

available, the potential for confounding is likely minimal. For e.g., information from other 

independent surveys suggests similarity between smoking behaviors across the regions. 

Exposure misclassification based on place of residency is likely to bias risk estimates towards 

the null. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. Statistically significant association noted in most highly exposed 

area for chronic rheumatic disease and chronic obstructive pulmonary disease. Dose-response 

pattern noted across Zones A, B and R for circulatory disease mortality 5–9 years after the 

accident. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. Lack of individual-level data precludes an examination of these 

uncertainties. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-52 —DO NOT CITE OR QUOTE 

Response Consideration satisfied for some causes of death but not others. For example, only three 

deaths from diabetes occurred among residents of Zone A. The limitation related to statistical 

power is exacerbated for stratified analyses carried out by number of years since the accident. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Am J Epidemiol, 2008, 167:847–858. Authors discuss potential for selection 

bias, limitation of residential based measure of exposure, similarities of mortality 

ascertainment in exposed and referent populations, and multiple testing. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Individual-level exposure data are unavailable. Exposure based on place 

of residence at time of the explosion. Soil sampling performed indicated considerable 

variability in TCDD levels within each region. In addition, place of residency at time of 

explosion does not ensure individuals were at their home around the time of the accident. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. An ecological measure of exposure (region of residency at time of 

accident) was used to categorize individuals according to their possible exposure. Latencies 

were considered. While such an approach has value for identifying whether excesses occurred 

among highly exposed populations, it is not precise enough to conduct a quantitative doseresponse analysis. Furthermore, noncancer mortality is not a viable endpoint to consider for 

further dose-response analysis. 

Conclusion Study is not suitable further dose-response evaluation due to noncancer morality endpoint. 

1 

2 

3 Table B-41. Baccarelli et al., 2005—Chloracne 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Chloracne cases identified using standardized criteria. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Plasma TCDD was associated with an increased risk of chloracne. 

The odds ratios increased in a dose-response pattern across zone of residence. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Authors discussed implications of differential elimination rates by age 

and body growth. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-53 —DO NOT CITE OR QUOTE 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. A total of 101 chloracne cases were identified, and 211 controls were 

selected. Statistically significant findings were observed in several comparisons. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. British Journal of Dermatology, 2005, 152, 459–465. The authors detail the 

limited statistical power they had available in the study. They also highlight a strength of the 

study that included uniqueness of age and sex distribution of chloracne cases, characterization 

of TCDD that could be done using sera samples, and availability of both clinical and 

epidemiological data. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. TCDD was estimated in both chloracne cases and control using serum 

measures. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria satisfied. Serum based measures of TCDD were obtained shortly after the accident. 

Chloracne is thought to be caused by the initial high exposure. 

Conclusion Exposure to TCDD at sufficiently high levels is recognized to cause chloracne. This study 

provides limited relevance to dose-response modeling of TCDD as exposure levels typically 

observed in the general population are much lower. 

1 

2 

3 Table B-42. Baccarelli et al, 2002 and 2004—Immunological effects 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Common methods were used to describe blood levels of plasma 

immunoglobulins (IgA, IgG, and IgM) and complement components (C3 and C4). 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Both exposure and outcome were objectively and accurately measured.

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration satisfied. Plasma IgG levels were inversely related with TCDD. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Both categorical (quintiles) and continuous measures of TCDD were 

examined in the dose-response analysis. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-54 —DO NOT CITE OR QUOTE 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Analyses are made using 72 highly exposed, and 72 low exposed 

individuals. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Toxicology letters, 2004, 149:287–293 and Environ Health Perspect, 2002, 

110(12):1169–1173. The authors highlight that few studies have looked at immunological 

effects of TCDD in humans, that the current study was able to exclude those with concurrent 

medical conditions, and the ability to characterize exposure using serum measures. Limitations 

addressed were the uncertainty about the clinical relevance of the dose-response pattern found, 

and the relatively small size of the study population. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. A total of 120 subjects were included in the study. This included 62 

randomly selected from the high exposed zone, and 58 selected from the reference area. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is 

consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. Dose-response relationships were examined using current TCDD levels. 

However, it is difficult to identify the relevant time interval over which TCDD dose should be 

considered for dose-response analysis. 

Conclusion An inverse dose-response association between IgG and TCDD was observed, however, because 

the relationship can not be described in terms of clinical relevance with respect to a specific 

health outcome, it is our view that these data are not suited to dose-response modeling. 

 1 

 2 

3 B.2.6. Chapaevsk Study 

4 

5 Table B-43. Revich et al., 2001—Mortality (noncancer) and reproductive 

6 health 

7 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration cannot be evaluated. Insufficient details are provided in the paper to gauge the 

completeness and coverage of the cancer registry and mortality data. Health outcomes were 

studied on the basis of information in the official medical statistics 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. It is an ecological study. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-55 —DO NOT CITE OR QUOTE 

Response Consideration cannot be evaluated. Dose-response was not evaluated as exposure was based on 

residency in the region vs. no residency. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. No individual-level exposure estimates were used. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. Population-based data over several years were used to make ecological 

comparisons. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in Chemosphere, 2001, 43(4–7):951–966. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. It is a cross-sectional study that compares mortality rates between 

regions. No individual-level exposure data available. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is 

consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. No exposure estimates were used in the study. 

Conclusion These cancer data are cross-sectional in nature and not appropriate for a dose-response analysis.

1 B.2.7. Air Force Health (“Ranch Hands”) Study 

2 

3 Table B-44. Michalek and Pavuk, 2008—Diabetes 

4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. Prevalent diabetes identified from medical records from repeated 

medical check-ups. Preferred method of ascertaining outcome relative to use of death 

certificates. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Adjustment was made for a number of risk factors related to 

diabetes (e.g., BMI, family history, smoking). However, Agent Orange was a 50% mixture of 

2,4-D and TCDD; therefore, potential for confounding by other coexposures is likely. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-56 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. The RR for an increase in 10 units was 1.29 (p < 0.001), and the risks 

across the background, low and high exposure categories, relative to the unexposed were 0.86, 

1.45, and 1.68. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Initial TCDD dose were estimated at the end of the tour of duty for 

the Ranch Hands. Individual-level serum dioxin measurements correlated well with correlated 

with days of spraying and calendar period of service, but collection of the samples roughly 20 

years later required back-extrapolation. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. There were a total of 439 cases of diabetes identified. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. J Occup Environ Medicine, 2008, 50:330–340. The authors address 

strengths and limitations related to the accuracy of the one-compartment pharmacokinetic 

model, impact of the covariate time spent in Southeast Asia, and potential exposure 

misclassification on days sprayed. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. TCDD estimates were derived using serum samples. However, Ranch 

Hand veterans were exposed to other compounds in the herbicides, such as 2,4-D. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria satisfied. TCDD levels at the end of service were estimated. Extrapolation was done 

using a half-life of 7.6 years. Exposures were grouped into comparison, background, low and 

high. This allows for a shape of the dose-response curve to be evaluated. A continuous 

measure of TCDD was also examined (log10TCDD). 

Conclusion Ranch Hand veterans were exposed to other contaminants in the herbicides that were mixed, 

thereby making it difficult to determine independent effects of TCDD on diabetes. In our 

view, this limitation precludes dose-response modeling of TCDD and diabetes using data from 

this cohort. 

1 

2 

3 B.2.8. Other Noncancer Studies of Dioxin 

 4 

5 Table B-45. McBride et al., 2009a—Mortality (Noncancer) 

 6 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-57 —DO NOT CITE OR QUOTE 

Response Consideration satisfied. The New Zealand Health Information Service Mortality Collection 

and the Registrar-General’s Index to Deaths were used to identify deaths. Additional searches 

were based on the last known address from the work record; the electoral roll and the 

habitation index; the telephone book; the internet; and Terranet property information database. 

An additional search was carried out through the Births, Deaths, and Marriages office of the 

New Zealand Department of Internal Affairs. Lastly, automated personnel and pension 

records were also used to locate past New Plymouth workers and identify some deaths. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration satisfied. Workers lost to follow-up were an unlikely source of bias especially 

for internal analyses. Confounding by other coexposures (e.g., 2,4,6-TCP) unlikely to have 

resulted in bias, due to presumed poor correlation with TCDD. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. There was no cause of death among those considered for which a 

dose-response trend was observed across four exposure categories of TCDD. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Dichotomous exposure (exposed/unexposed) and duration of 

employment were examined from job exposure classification assessed via occupational history 

records industrial hygienists/factory personnel knowledge and questionnaires. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration not satisfied. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in J Occup Environ Med, 2009, 51:1049–1056. The other studies 

in the cohort highlight the 22% of the cohort lost to follow-up, the limited size of the cohort 

tissue sarcomas, differences in cohort definitions between sprayers and producers, and the 

potential for other exposures during employment at the plant. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria satisfied. Serum measures available for 346 workers were used to derive TCDD 

exposures for the entire cohort using the area under the curve approach. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. Dichotomous exposure assessment did not allow individual estimates of 

dose to be developed. However, noncancer mortality is not a viable endpoint to consider for 

further dose-response analysis. 

Conclusion A considerable portion of the cohort was lost to follow-up, and no dose-response associations 

noted. As a result, the data are not suited to dose-response analysis. 

1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-58 —DO NOT CITE OR QUOTE 

1 Table B-46. McBride et al., 2009b—Mortality (noncancer) 

2 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration satisfied. The New Zealand Health Information Service Mortality Collection 

and the Registrar-General’s Index to Deaths were used to identify deaths. Additional searches 

were based on the last known address from the work record; the electoral roll and the 

habitation index; the telephone book; the internet; and Terranet property information database. 

An additional search was carried out through the Births, Deaths, and Marriages office of the 

New Zealand Department of Internal Affairs. Lastly, automated personnel and pension 

records were also used to locate past New Plymouth workers and identify some deaths. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. Considerable amount of workers were lost to follow up (22%), 

but it is unclear if bias resulted. The dichotomous exposure measure was based on exposure 

to TCDD, chlorinated dioxins and phenoxy herbicides, so confounding is a possibility by 

these coexposures. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. Because no individual exposure estimates were available for 

these analyses, dose-response could not be evaluated. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration satisfied. Consideration satisfied. Dichotomous exposure 

(exposed/unexposed) and duration of employment were examined from job exposure 

classification assessed via occupational history records industrial hygienists/factory personnel 

knowledge and questionnaires. Authors discuss limitations in the assignment of exposure 

among cohort members. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria satisfied. Published in Occup Medicine, 2009, 59(4):255–263. The authors highlight 

cohort lost to follow-up, the limited size of the cohort, differences in cohort definitions 

between sprayers and producers, and the potential for other exposures during employment at 

the plant. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 

Response Criteria not satisfied. Exposures were not quantified. The dichotomous exposure measure 

was based on exposure to TCDD, chlorinated dioxins and phenoxy herbicides. 

3. Critiera The effective dose and oral exposure can be reasonably estimated and the measures of 

exposure are consistent with the current biological understanding of dose. The reported dose 

is consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-59 —DO NOT CITE OR QUOTE 

Response Effective dose could not be estimated given the lack of individual-level exposure data. 

Noncancer mortality is not a viable endpoint to consider for further dose-response analysis. 

Conclusion The study lacks the quantification of exposures at an individual level, and a considerable 

portion of the cohort was lost to follow-up. As a result, the data are not suited to doseresponse analysis. 

1 

2 

3 Table B-47. Ryan et al., 2002—Sex ratio 

 4 

1. Consideration Methods used to ascertain health outcomes identified were unbiased, highly sensitive, and 

specific. 

Response Consideration not satisfied. Company records were used to identify births, the date of birth, 

and the sex of the child. No information was provided on the expected completeness of 

identifying births in this manner. Moreover, the study was expanded to include workers who 

heard about the study in a public forum. Therefore, the study could be influenced by 

participation bias. 

2. Consideration Risk estimates are not susceptible to biases from confounding exposures or from study design 

or statistical analysis. 

Response Consideration not satisfied. See above. 

3. Consideration Study demonstrates an association between TCDD and adverse health effect with evidence of 

an exposure-response relationship. 

Response Consideration not satisfied. The study compared birth ratios among men and women employed 

at the plant to the general population. No categories of exposure were examined. 

4. Consideration Exposure assessment methodology is clear and adequately characterizes individual-level 

exposures. The limitations and uncertainties in the exposure assessment are considered. 

Response Consideration not satisfied. This is not relevant as no analyses were done in relation to 

exposure levels. 

5. Consideration Study size and follow-up are large enough to yield precise estimates of risk and ensure 

adequate statistical power. 

Response Consideration satisfied. For the categories of exposure used (yes/no), and the stratified 

analyses by sex and subcohort, the study allows for the birth ratios to be estimated with 

sufficient precision. 

1. Criteria Study is published in the peer-reviewed scientific literature and has an appropriate discussion 

of the strengths and limitations. 

Response Criteria not satisfied. Published in Environ Health Perspect, 2002, 110(11):A699–A701. The 

authors discussed the limitations of using serum collected many years after they stopped 

working to estimate TCDD exposures when the preferred metric would be TCDD levels at the 

time of conception. They did not address issues about the representativeness of the study 

participants to the entire cohort of workers, nor did they address the limitation of not being able 

to conduct dose-response analyses using individual-level TCDD data. 

2. Criteria Exposure must be primarily TCDD and is properly quantified so that dose-response 

relationships can be assessed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-60 —DO NOT CITE OR QUOTE 

Response Criteria not satisfied. While serum measures were available for 84 of the 198 participants of 

the study, birth ratios were compared between the cohort of 2,4,5-T and 2,4,5-trichlorphgenol 

workers relative to the city of Ufa. There was no attempt to derive birth ratios in relation to 

exposure levels. The serum data were only used to demonstrate that these workers, on average, 

had TCDD levels 30 times higher than Ufa residents. 

3. Criteria The effective dose and oral exposure can be reasonably estimated and the measures of exposure 

are consistent with the current biological understanding of dose. The reported dose is 

consistent with a toxicologically relevant dose. Latency and appropriate window(s) of 

exposure examined. Response has to be a nonfatal endpoint. 

Response Criteria not satisfied. TCDD exposures were based on serum measures taken in some cases 

many years after children were born; no attempt was made to back-extrapolate to the time of 

conception. 

Conclusion The data are not suitable for dose-response modeling. Risk estimates have not been derived in 

relation to TCDD exposure levels. There exist uncertainties about the representativeness of the 

participants in relation to the cohort as a whole, and insufficient details are provided to evaluate 

the extent in which all births were identified. While these data should not be used for 

quantitative dose-response modeling, the much lower M/F birth ratio among exposed fathers is 

consistent with the finding by Mocarelli et al, and lends support to those findings. 

 1 

 2 

3 B.3. REFERENCES 

4 Akhtar, FZ; Garabrant, DH; Ketchum, NS; et al. (2004) Cancer in US Air Force veterans of the Vietnam War. J 

5 Occup Environ Med 46(2):123−136. 

6 Alaluusua, S; Calderara, P; Gerthoux, PM; et al. (2004) Developmental dental aberrations after the dioxin accident 

7 in Seveso. Environ Health Perspect 112(13):1313−1318. 

Aylward, LL; Brunet, RC; Starr, TB; et al. (2005a) Exposure reconstruction for the TCDD-exposed NIOSH cohort 

using a concentration- and age-dependent model of elimination. Risk Anal 25(4):945−956. 

Aylward, LL; Brunet, RC; Carrier, G; et al. (2005b) Concentration-dependent TCDD elimination kinetics in 

humans: toxicokinetic modeling for moderately to highly exposed adults from Seveso, Italy, and Vienna, Austria, 

and impact on dose estimates for the NIOSH cohort. J Expo Anal Environ Epidemiol 15(1):51−65. 

8 Baccarelli, A; Mocarelli, P; Patterson, DG, Jr.; et al. (2002) Immunologic effects of dioxin: new results from Seveso 

9 and comparison with other studies. Environ Health Perspect 110(12):1169−1173. 

10 Baccarelli, A; Pesatori, AC; Masten, SA; et al. (2004) Aryl-hydrocarbon receptor-dependent pathway and toxic 

11 effects of TCDD in humans: a population-based study in Seveso, Italy. Toxicol Lett 149(1−3):287−293. 

12 Baccarelli, A; Pesatori, AC; Consonni, D; et al. (2005) Health status and plasma dioxin levels in chloracne cases 20 

13 years after the Seveso, Italy accident. Br J Dermatol 152(3):459−465. 

14 Baccarelli, A; Hirt, C; Pesatori, AC; et al. (2006) t(14;18) translocations in lymphocytes of healthy dioxin-exposed 

15 individuals from Seveso, Italy. Carcinogenesis 27(10):2001−2007. 

16 Baccarelli, A; Giacomini, SM; Corbetta, C; et al. (2008) Neonatal thyroid function in Seveso 25 years after maternal 

17 exposure to dioxin. PLoS Med 5(7):1133-1142. 

18 Becher, H; Steindorf, K; Flesch-Janys, D. (1998) Quantitative cancer risk assessment for dioxins using an 

19 occupational cohort. Environ Health Perspect 106(Suppl 2):663−670. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-61 —DO NOT CITE OR QUOTE 

1 Bertazzi, PA; Consonni, D; Bachetti, S; et al. (2001) Health effects of dioxin exposure: a 20-year mortality study. 

2 Am J Epidemiol 153(11):1031−1044. 

3 Cheng, H; Aylward, L; Beall, C; et al. (2006) TCDD exposure-response analysis and risk assessment. Risk Anal 

4 26:1059−1071. 

5 Collins, JJ; Bodner, K; Aylward, LL; et al. (2009) Mortality rates among trichlorophenol workers with exposure to 

6 2,3,7,8-tetrachlorodibenzo-p-dioxin. Am J Epidemiol 170(4):501−506. 

7 Consonni, D; Pesatori, AC; Zocchetti, C; et al. (2008) Mortality in a population exposed to dioxin after the Seveso, 

8 Italy, accident in 1976: 25 years of follow-up. Am J Epidemiol 167(7):847−858. 

9 Eskenazi, B; Warner, M; Mocarelli, P; et al. (2002a) Serum dioxin concentrations and menstrual cycle 

10 characteristics. Am J Epidemiol 156(4):383−392. 

11 Eskenazi, B; Mocarelli, P; Warner, M; et al. (2002b) Serum dioxin concentrations and endometriosis: a cohort study 

12 in Seveso, Italy. Environ Health Perspect 110(7):629−634. 

13 Eskenazi, B; Mocarelli, P; Warner, M; et al. (2003) Maternal serum dioxin levels and birth outcomes in women of 

14 Seveso, Italy. Environ Health Perspect, 111(7), 947-953. 

15 Eskenazi, B; Warner, M; Marks, AR; et al. (2005) Serum dioxin concentrations and age at menopause. Environ 

16 Health Perspect 113(7):858−862. 

17 Eskenazi, B; Warner, M; Samuels, S; et al. (2007) Serum dioxin concentrations and risk of uterine leiomyoma in the 

18 Seveso Women's Health Study. Am J Epidemiol 166(1):79−87. 

19 Fingerhut, MA; Halperin, WE; Marlow, DA; et al. (1991) Cancer mortality in workers exposed to 

20 2,3,7,8-tetrachlorodibenzo-p-dioxin. N Engl J Med 324(4):212−218. 

21 Flesch-Janys, D; Berger, J; Gurn, P; et al. (1995) Exposure to polychlorinated dioxins and furans (PCDD/F) and 

22 mortality in a cohort of workers from a herbicide-producing plant in Hamburg, Federal Republic of Germany. Am J 

23 Epidemiol 142(11):1165−1175. 

24 Flesch-Janys, D; Becher, H; Gurn, P; et al. (1996) Elimination of polychlorinated dibenzo-p-dioxins and 

25 dibenzofurans in occupationally exposed persons. J Tox Environ Health 47(4):363−378. 

26 Flesch-Janys, D; Steindorf, K; Gurn, P; et al. (1998) Estimation of the cumulated exposure to polychlorinated 

27 dibenzo-p-dioxins/furans and standardized mortality ratio analysis of cancer mortality by dose in an occupationally 

28 exposed cohort. Environ Health Perspect 106(Suppl 2):655−662. 

29 Hooiveld, M; Heederik, DJ; Kogevinas, M; et al. (1998) Second follow-up of a Dutch cohort occupationally 

30 exposed to phenoxy herbicides, chlorophenols, and contaminants. Am J Epidemiol 147(9):891−901. 

31 Manz, A; Berger, J; Dwyer, JH; et al. (1991) Cancer mortality among workers in chemical plant contaminated with 

32 dioxin. Lancet 338(8773):959−964. 

33 McBride, DI; Collins, JJ; Humphry, NF; et al. (2009a) Mortality in workers exposed to 2,3,7,8-tetrachlorodibenzo34 p-dioxin at a trichlorophenol plant in New Zealand. J Occup Environ Med 51(9):1049-1056. 

35 McBride, DI; Burns, CJ; Herbison, GP; et al. (2009b) Mortality in employees at a New Zealand agrochemical 

36 manufacturing site. Occup Med (Oxford, England) 59(4):255−263. 

37 Michalek, JE; Pavuk, M. (2008) Diabetes and cancer in veterans of Operation Ranch Hand after adjustment for 

38 calendar period, days of spraying, and time spent in Southeast Asia. J Occup Environ Med 50(3):330−340. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT B-62 —DO NOT CITE OR QUOTE 

1 Mocarelli, P; Gerthoux, PM; Ferrari, E; et al. (2000) Paternal concentrations of dioxin and sex ratio of offspring. 

2 Lancet 355(9218):1858−1863. 

3 Mocarelli, P; Gerthoux, PM; Patterson, DG, Jr.; et al. (2008) Dioxin exposure, from infancy through puberty, 

4 produces endocrine disruption and affects human semen quality. Environ Health Perspect 116(1):70−77. 

5 Ott, MG; Zober, A. (1996) Cause specific mortality and cancer incidence among employees exposed to 

6 2,3,7,8-TCDD after a 1953 reactor accident. Occup Environ Med 53(9):606−612. 

7 Pesatori, AC; Consonni, D; Bachetti, S; et al. (2003) Short- and long-term morbidity and mortality in the population 

8 exposed to dioxin after the “Seveso accident”. Ind Health 41(3):127−138. 

9 Revich, B; Aksel, E; Ushakova, T; et al. (2001) Dioxin exposure and public health in Chapaevsk, Russia. 

10 Chemosphere 43(4−7):951−966. 

11 Ryan, JJ; Amirova, Z; Carrier, G. (2002) Sex ratios of children of Russian pesticide producers exposed to dioxin.

12 Environ Health Perspect, 110(11):A699-701. 

13 Steenland, K; Piacitelli, L; Deddens, J; et al. (1999) Cancer, heart disease, and diabetes in workers exposed to 

14 2,3,7,8-tetrachlorodibenzo-p-dioxin. J Natl Cancer I 91(9):779−786. 

15 Steenland, K; Deddens, J; Piacitelli, L. (2001) Risk assessment for 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) 

16 based on an epidemiologic study. Am J Epidemiol 154(5):451-458. 

17 ’t Mannetje, A; McLean, D; Cheng, S; et al. (2005) Mortality in New Zealand workers exposed to phenoxy 

18 herbicides and dioxins. Occup Environ Med 62(1):34−40. 

19 Warner, M; Eskenazi, B; Mocarelli, P; et al. (2002) Serum dioxin concentrations and breast cancer risk in the 

20 Seveso Women’s Health Study. Environ Health Perspect 110(7):625−628. 

21 Warner, M; Samuels, S; Mocarelli, P; et al. (2004) Serum dioxin concentrations and age at menarche. Environ 

22 Health Perspect 112(13):1289−1292. 

23 Warner, M; Eskenazi, B; Olive, DL; et al. (2007) Serum dioxin concentrations and quality of ovarian function in 

24 women of Seveso. Environ Health Perspect 115(3):336−340. 

25 Zober, A; Messerer, P; Huber, P. (1990) Thirty-four-year mortality follow-up of BASF employees exposed to 

26 2,3,7,8-TCDD after the 1953 accident. Int Arch Occup Environ Health 62(2):139−157.
DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX C 

Kinetic Modeling 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-ii DRAFT—DO NOT CITE OR QUOTE 

CONTENTS—APPENDIX C: Kinetic Modeling 

1 APPENDIX C. KINETIC MODELING...................................................................................C-1 

2 C.1. LITERATURE SEARCH STRATEGY AND RESULTS—IDENTIFYING 

3 RECENT PUBLICATIONS FOR UPDATING TCDD TOXICOKINETIC 

4 MODEL INPUT PARAMETERS...............................................................................C-1 

5 C.1.1. Data Bases Searched .......................................................................................C-1 

6 C.1.2. Literature Search Strategy and Approach .......................................................C-2 

C.1.2.1. Chemical Search Terms—DIALOG Search...................................C-2 

C.1.2.2. Primary Search Terms (Species)—DIALOG Search .....................C-2 

C.1.2.3. Secondary Search Terms (Toxicology)—DIALOG Search ...........C-3 

7 C.1.3. Citation Screening Procedures and Results.....................................................C-3 

8 C.1.4. References Selected for More Detailed Review for Updating the PBPK 

9 Models.............................................................................................................C-6 

10 C.1.5. Brief Descriptions of DIALOG Bibliographic Data Bases Searched .............C-8 

11 C.2. TOXICOKINETIC MODELING CODE (EMOND ET AL., 2005)........................C-10 

12 C.2.1. Human Standard Model.................................................................................C-10 

C.2.1.1. Model Code...................................................................................C-10 

C.2.1.2. Input File.......................................................................................C-20 

13 C.2.2. Human Gestational Model.............................................................................C-21 

C.2.2.1. Model Code...................................................................................C-21 

C.2.2.2. Input File.......................................................................................C-35 

14 C.2.3. Rat Standard Model.......................................................................................C-36 

C.2.3.1. Model Code...................................................................................C-36 

C.2.3.2. Input Files .....................................................................................C-46 

15 C.2.3.2.1. Cantoni et al. (1981). ..................................................C-46 

16 C.2.3.2.2. Chu et al. (2007). ........................................................C-46 

17 C.2.3.2.3. Crofton et al. (2005)....................................................C-47 

18 C.2.3.2.4. Fattore et al. (2000).....................................................C-48 

19 C.2.3.2.5. Hassoun et al. (2000). .................................................C-48 

20 C.2.3.2.6. Kitchin and Woods (1979)..........................................C-49 

21 C.2.3.2.7. Kociba et al. (1976) (13 weeks)..................................C-50 

22 C.2.3.2.8. Kociba et al. (1978) (female) (104 weeks). ................C-51 

23 C.2.3.2.9. Kociba et al. (1978) (male) (104 weeks). ...................C-51 

24 C.2.3.2.10. Latchoumycandane and Mathur. (2002).....................C-52 

25 C.2.3.2.11. Li et al. (1997).............................................................C-53 

26 C.2.3.2.12. Murray et al. (1979). ...................................................C-53 

27 C.2.3.2.13. NTP (1982) (female) (chronic). ..................................C-54 

28 C.2.3.2.14. NTP (1982) (male) (chronic). .....................................C-55 

29 C.2.3.2.15. NTP (2006) 31 weeks. ................................................C-55 

30 C.2.3.2.16. NTP (2006) 53 weeks. ................................................C-56 

31 C.2.3.2.17. NTP (2006) 2 year. .....................................................C-57 

32 C.2.3.2.18. Sewall et al. (1995). ....................................................C-58 

33 C.2.3.2.19. Shi et al. (2007), adult portion. ...................................C-58 

34 C.2.3.2.20. Van Birgelen et al. (1995)...........................................C-59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-iii DRAFT—DO NOT CITE OR QUOTE 

1 CONTENTS (continued) 

 2 

 3 

4 C.2.3.2.21. Vanden Heuvel et al. (1994). ......................................C-60 

5 C.2.4. Rat Gestational Model...................................................................................C-60 

C.2.4.1. Model Code...................................................................................C-60 

C.2.4.2. Input Files .....................................................................................C-74 

6 C.2.4.2.1. Bell et al. (2007). ........................................................C-74 

7 C.2.4.2.2. Hojo et al. (2002). .......................................................C-75 

8 C.2.4.2.3. Ikeda et al. (2005). ......................................................C-76 

9 C.2.4.2.4. Kattainen et al. (2001).................................................C-77 

10 C.2.4.2.5. Markowski et al. (2001)..............................................C-78 

11 C.2.4.2.6. Miettinen et al. (2006).................................................C-78 

12 C.2.4.2.7. Murray et al. (1979). ...................................................C-79 

13 C.2.4.2.8. Nohara et al. (2000). ...................................................C-80 

14 C.2.4.2.9. Ohsako et al. (2001)....................................................C-81 

15 C.2.4.2.10. Schantz et al. (1996) and Amin et al. (2000). .............C-82 

16 C.2.4.2.11. Seo et al. (1995). .........................................................C-82 

17 C.2.4.2.12. Shi et al. (2007)...........................................................C-83 

18 C.2.5. Mouse Standard Model .................................................................................C-84 

C.2.5.1. Model Code...................................................................................C-84 

C.2.5.2. Input Files .....................................................................................C-94 

19 C.2.5.2.1. Hassoun et al. (1998) (13 weeks)................................C-94 

20 C.2.5.2.2. NTP (1982) (male) (chronic). .....................................C-96 

21 C.2.5.2.3. Smialowicz et al. (2008). ............................................C-96 

22 C.2.5.2.4. Toth et al. (1979) (1 year)...........................................C-97 

23 C.2.5.2.5. Toth et al. (1979) (2 year)...........................................C-98 

24 C.2.5.2.6. White et al. (1986). .....................................................C-99 

25 C.2.6. Mouse Gestational Model ...........................................................................C-100 

C.2.6.1. Model Code.................................................................................C-100 

C.2.6.2. Input Files ...................................................................................C-113 

26 C.2.6.2.1. Keller et al. (2007). ...................................................C-113 

27 C.2.6.2.2. Li et al. (2005)...........................................................C-114 

28 C.3. TOXICOKINETIC MODELING RESULTS FOR KEY ANIMAL 

29 BIOASSAY STUDIES............................................................................................C-115 

30 C.3.1. Nongestational Studies ................................................................................C-115 

C.3.1.1. Cantoni et al. (1981) ...................................................................C-115 

C.3.1.2. Chu et al. (2007) .........................................................................C-117 

C.3.1.3. Crofton et al. (2005)....................................................................C-119 

C.3.1.4. Fattore et al. (2000).....................................................................C-122 

C.3.1.5. Hassoun et al. (1998) ..................................................................C-124 

C.3.1.6. Hassoun et al. (2000) ..................................................................C-126 

C.3.1.7. Kitchin and Woods (1979)..........................................................C-129 

C.3.1.8. Kociba et al. (1976).....................................................................C-132 

C.3.1.9. Kociba et al. (1978) Female........................................................C-134 

 31 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-iv DRAFT—DO NOT CITE OR QUOTE 

1 CONTENTS (continued) 

 2 

 3 

C.3.1.10. Kociba et al. (1978) Male ...........................................................C-136 

C.3.1.11. Latchoumycandane and Mathur (2002)......................................C-138 

C.3.1.12. Li et al. (1997).............................................................................C-139 

C.3.1.13. NTP (1982)—Female Rats, Chronic...........................................C-143 

C.3.1.14. NTP (1982)—Male Rats, Chronic ..............................................C-144 

C.3.1.15. NTP (1982)—Female Mice, Chronic .........................................C-146 

C.3.1.16. NTP (1982)—Male Mice, Chronic.............................................C-148 

C.3.1.17. NTP (2006) 31 Weeks ................................................................C-150 

C.3.1.18. NTP (2006) 53 Weeks ................................................................C-152 

C.3.1.19. NTP (2006) 2 Years....................................................................C-154 

C.3.1.20. Sewall et al. (1995) .....................................................................C-156 

C.3.1.21. Smialowicz et al. (2008) .............................................................C-158 

C.3.1.22. Toth et al., 1 Year (1979)............................................................C-160 

C.3.1.23. Van Birgelen (1995) ...................................................................C-162 

C.3.1.24. Vanden Heuvel et al. (1994) .......................................................C-164 

C.3.1.25. White et al. (1986) ......................................................................C-167 

4 C.3.2. Gestational Studies......................................................................................C-170 

C.3.2.1. Bell et al. (2007) .........................................................................C-170 

C.3.2.2. Hojo et al. (2002) ........................................................................C-171 

C.3.2.3. Ikeda et al. (2005) .......................................................................C-173 

C.3.2.4. Kattainen et al. (2001).................................................................C-174 

C.3.2.5. Keller et al. (2007) ......................................................................C-175 

C.3.2.6. Li et al. (2006) 3-Day..................................................................C-177 

C.3.2.7. Markowski et al. (2001)..............................................................C-178 

C.3.2.8. Mietinnen et al. (2006)................................................................C-180 

C.3.2.9. Murray et al. (1979) Gestational Portion ....................................C-181 

C.3.2.10. Murray et al. (1979) Adult Portion .............................................C-183 

C.3.2.11. Nohara et al. (2000) ....................................................................C-185 

C.3.2.12. Ohsako et al. (2001)....................................................................C-186 

C.3.2.13. Schantz et al. (1995) and Amin et al. (2000) ..............................C-188 

C.3.2.14. Seo et al. (1995) ..........................................................................C-189 

C.3.2.15. Shi et al. (2007) Gestational Portion...........................................C-191 

C.3.2.16. Shi et al. (2007) Adult Portion....................................................C-192 

5 C.4. REFERENCES........................................................................................................C-196 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-1 DRAFT—DO NOT CITE OR QUOTE 

1 APPENDIX C. KINETIC MODELING 

2 

3 

4 C.1. LITERATURE SEARCH STRATEGY AND RESULTS—IDENTIFYING RECENT 

5 PUBLICATIONS FOR UPDATING TCDD TOXICOKINETIC MODEL INPUT 

6 PARAMETERS 

7 The purpose of this literature search was to identify recent publications that address the 

8 input parameters for the physiologically based pharmacokinetic (PBPK) models Aylward and 

9 colleagues described in 2004–2005 and Emond and colleagues described in 2004–2006. This 

10 literature search was part of the U.S. Environmental Protection Agency (EPA)’s preparation of a 

11 response to the National Academy of Sciences’ review (Health Risks from Dioxin and Related 

12 Compounds: Evaluation of the EPA Reassessment, NAS, 2006]) of EPA Reassessment of Health 

13 Risks From Dioxin and Related Compounds (2003 Reassessment, U.S. EPA, 2003). English14 only references from 2003 to May 2009 were searched using bibliographic data bases relevant to 

15 health effects and toxicology of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). The search 

16 focused on toxicokinetic data that could be used to update the dynamic disposition of 

17 2,3,7,8-TCDD in mice, rats, guinea pigs, monkeys, and humans. 

18 In the primary search, EPA identified 775 distinct citations based on the literature search 

19 criteria described below. EPA also performed an independent supplemental search to avoid 

20 missing key studies. EPA identified 28 papers for further analysis that appeared on first review 

21 to report data to update the input parameters of the Aylward and Emond PBPK models; 

22 considerations for selection are described in Section C.1.3. 

23 

24 C.1.1. Data Bases Searched 

25 EPA used the following DIALOG bibliographic data bases in the primary search. Brief 

26 descriptions of the DIALOG data bases searched are provided in Section C.1.5. 

27 

28 1. File 6: NTIS 

29 2. File 41: Pollution Abstracts 

30 3. File 55: Biosis 

31 4. File 153: IPA Toxicology 

32 5. File 155: MedLine 

33 6. File 156: ToxFile 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-2 DRAFT—DO NOT CITE OR QUOTE 

1 7. File 157: Biosis Toxicology 

2 8. File 159: CancerLit 

3 9. File 336: RTECS 

 4 

5 The PUBMED data base was used for the supplemental search. 

 6 

7 C.1.2. Literature Search Strategy and Approach 

8 The primary search used a tiered key-word approach, as documented below. The 

9 principal search term was the Chemical Abstract Service Registry Number (CASRN) or specific 

10 chemical name, 2,3,7,8-tetrachlorodibenzo-p-dioxin or 2,3,7,8-TCDD. The next tier of search 

11 terms was species, and finally toxicokinetic keywords, as listed below. The period of the search 

12 was 2003 through May 2009, and articles were limited to English language. 

13 The supplemental PUBMED search was limited to the most recent five years (2004 to 

14 present) and used four combinations of key words: 

15 

16 • TCDD + pharmacokinetic + humans, 

17 • TCDD + toxicokinetic + humans, 

18 • TCDD + pharmacokinetic + animals, and 

19 • TCDD + toxicokinetic + animals. 

20 

21 C.1.2.1. Chemical Search Terms—DIALOG Search

22 • CASRN: 1746-01-6 

23 • 2,3,7,8-tetrachlorodibenzo-p-dioxin 

24 • 2,3,7,8-TCDD 

25 

26 C.1.2.2. Primary Search Terms (Species)—DIALOG Search

27 • Guinea pig(s) 

28 • Human(s) 

29 • Monkey(s) 

30 • Mouse 

31 • Mice 
This document is a draft for review purposes only and does not constitute Agency policy. 

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1 • Rodent(s) 

2 • Rat(s) 

3 

4 C.1.2.3. Secondary Search Terms (Toxicology)—DIALOG Search 

 5 

1. Absor* 

2. ADME 

3. Aryl hydrocarbon 

receptor 

4. AhR 

5. Bioavail* 

6. Biliar* 

7. Biotransform* 

8. Cytochrome 

9. CYP* 

10. CYP1A1 

11. CYP1A2 

12. Diet, dietary, diets 

13. Disposit* 

14. Distrib* 

15. Drink* 

16. Elimin* 

17. Excret* 

18. Epidemiolog* 

19. Feces 

20. Feed* 

21. First order kinetics 

22. Food* 

23. Gastro* 

24. Gavage* 

25. Half-life 

26. Induct* 

27. Ingest* 

28. In silico 

29. Kinetic* 

30. Liver 

31. Lymph* 

32. Mechanism (1w) 

action 

33. Metabo* 

34. Oral* 

35. P450 

36. Partition coefficient 

37. PBPK 

38. Pharmacodynamic* 

39. Pharmacokinetic* 

40. Physiologically 

based 

41. pharmacokinetic 

42. Protein bind* 

43. Toxicokinetic* 

44. Urin*

1 

2 ADME = absorption, distribution, metabolism, elimination; AhR = aryl hydrocarbon receptor; CYP = 

3 cytochrome P450; * = truncated; 1w = terms are within 1 word of each other and in the order 

4 specified (see search term 32

 5 

 6 

7 C.1.3. Citation Screening Procedures and Results

8 Initial DIALOG searches resulted in a very large number of citation hits. Therefore, 

9 some title and key word restrictions were applied iteratively to screen out less relevant citations 

10 (e.g., requiring some search terms in title, requiring 2,3,7,8-TCDD rather than just TCDD). 

11 Then, using reference management software, pooled information obtained from the various 

12 DIALOG data bases was screened to remove duplicates. Citations then were numbered 

13 sequentially (as a unique identifier). Information retrieved included the following (when 

14 available): author(s), publication year, title, source document name, volume, and page numbers. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-4 DRAFT—DO NOT CITE OR QUOTE 

1 The DIALOG search and duplicate removal procedure produced 775 unique citations. In 

2 the next step, all 775 citations were screened for potential applicability to updating parameters in 

3 the Aylward and Emond PBPK models. Of these 775 citations, 26 were selected for more 

4 detailed review to determine their potential applicability, and full publications were retrieved. 

5 Two citations were added from the supplemental search, giving a total of 28 articles identified 

6 for further review. 

7 Bibliographic information for the 28 articles selected for full review is provided in the 

8 reference list at the end of this section. Table C-1 summarizes the model input parameters 

9 potentially addressed by the selected articles. 

10 During 2003 to May 2009, the authors of the two kinetic models under consideration 

11 published several articles. For the Emond model, which was first published in 2004 (Emond et 

12 al., 2004), two subsequent papers have been published (Emond et al., 2005, 2006). The Aylward 

13 model, which originated from the 1995 papers by Carrier et al. (1995a, b), was later updated by 

14 the same group (Aylward et al., 2004, 2005). The major change implemented in the last two 

15 papers was the description of a desorption process in the digestive tract. The transfer rate 

16 described is slow, but for a low body burden of TCDD, this process remains significant. This 

17 concept was reported in 2002 by Moser and McLachlan (2002). The major modifications 

18 expected to update the Emond model are (1) consideration of the desorption process in the 

19 gastrointestinal tract and (2) rearrangement of the elimination constant, which will have a 

20 negligible impact on the simulation. These changes are motivated by plausible observations 

21 reported in the literature. 

22 Because of the body burden found in humans and the importance of selecting an 

23 appropriate dose metric in human risk assessment, the physiological model is an important tool 

24 for assessing the kinetics following exposure to TCDD (Kim et al., 2003). Based on the 

25 literature identified in this search, the major contributions that should be reviewed with respect to 

26 the Aylward and Emond kinetic models are not modes of action or pharmacokinetic mechanisms, 

27 but rather information for verifying or improving the accuracy of some model parameters. 

28 Pharmacokinetics typically refers to four distinct steps including absorption, distribution, 

29 metabolism, and excretion. Physiologically-based models consider each step. In the model each 

30 step is parameterized to reflect better predictions of the real observations. Occasionally, 

31 reviewing these models is essential to determine if any key processes or parameters might be 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-5 DRAFT—DO NOT CITE OR QUOTE 

1 described with better accuracy. This perspective underlies the review of the literature described 

2 here. The review indicates TCDD disposition has become recognized as relatively significant 

3 since the publication of the Emond and Aylward models. The literature that provides 

4 information related to improving these models, however, is limited. For the benefit of this 

5 exercise, EPA selected the literature that would likely contribute significantly to model response, 

6 or to clarify or confirm different key issues driving the model results. Regarding the two TCDD 

7 models, the two major issues that should be evaluated with respect to the recent literature 

8 identified are the elimination profile and the induction of CYP1A2. 

9 Reviewing the elimination variation in different species and testing variable elimination 

10 with a data set appears to be appropriate. The literature reports that various factors might 

11 influence elimination rate. Recent publications report the influence of diverse predictors such 

12 age, body fat, or smoking habit on the elimination half-life (Milbrath et al., 2009; Kerger et al., 

13 2006, 2007). Determining whether using the Milbrath et al. information would help account for 

14 intraspecies variability in elimination rate in the Emond and Aylward kinetic models would be 

15 useful. In 2006, Emond et al. reviewed the influence of body fat mass and CYP1A2 induction on 

16 the pharmacokinetics of TCDD. These two factors appear to contribute significantly to 

17 elimination and their influences seem to be driven by TCDD body burden. Mullerova and 

18 Kopecky (2007) discussed the influence of adipose tissue and the “yo-yo” effects on various 

19 diseases that might be influenced by persistent organic pollutant distribution. One group 

20 explored the importance of variable elimination and compared these predictions to first-order 

21 elimination using the Aylward and Emond models and supported these approaches for risk 

22 assessment (Heinzl et al., 2007). Two groups of authors considered a one-compartment model to 

23 derive the elimination half-life (Aylward et al., 2009; Nadal et al., 2008). Comparing the 

24 half-life they obtained using this approach for a range of body burden to the variable elimination 

25 half-life would be interesting. 

26 The second important mechanism driving the distribution and elimination of TCDD is the 

27 induction of CYP1A2, identified as the major ligand protein in liver (Diliberto et al., 1997). For 

28 that process, authors suggested different aspects that should be investigated, including the 

29 importance of the dose metrics in the target tissue and the inducible level of CYP1A2 (Wilkes 

30 et al., 2008; Staskal et al., 2005). Other papers address the intraspecies variability of lethal 

31 potency in mature species versus the developing fetus (Kransler et al., 2007; Korkalainen et al., 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-6 DRAFT—DO NOT CITE OR QUOTE 

1 2004). Still others point out pronounced differences among species (namely, guinea pigs, 

2 hamsters, mice, and rats) (Bohonowych and Denison, 2007), as observed in studies of long-term 

3 effects of low TCDD dose in liver and in studies comparing hepatic accumulation and clearance 

4 of TCDD (Korenaga et al., 2007; Boverhof et al., 2005). The interspecies variation of the 

5 binding affinity constant of AhR also has been reported (Connor and Aylward, 2006; Nohara 

6 et al., 2006). 

7 The articles identified in this literature review should be adequate to update the Aylward 

8 and Emond models, which need to be evaluated according to the same structure of compartments 

9 described in the literature by the two model authors. 

10 

11 C.1.4. References Selected for More Detailed Review for Updating the PBPK Models 

Aylward, LL; Brunet, RC; Carrier, G; et al. (2004) Concentration-dependent TCDD elimination kinetics in humans: 

toxicokinetic modeling for moderately to highly exposed adults from Seveso, Italy, and Vienna, Austria, and impact 

on dose estimates for the NIOSH cohort. J Expo Anal Environ Epidemiol 15(1):51−65. 

Aylward, LL; Brunet, RC; Starr, TB; et al. (2005) Exposure reconstruction for the TCDD-exposed NIOSH cohort 

using a concentration- and age-dependent model of elimination. Risk Anal 25(4):945−956. 

Aylward, LL; Bodner, KM; Collins, JJ; et al. (2009) TCDD exposure estimation for workers at a New Zealand 

2,4,5-T manufacturing facility based on serum sampling data. J Expo Sci Environ Epidemiol. doi: 

10.1038/jes.2009.31. 

Bohonowych, JE; Denison, MS. (2007) Persistent binding of ligands to the aryl hydrocarbon receptor. Toxicol Sci 

98(1):99–109. 

Boverhof, DR; Burgoon, LD; Tashiro, C; et al. (2005) Temporal and dose-dependent hepatic gene expression 

patterns in mice provide new insights into TCDD-mediated hepatotoxicity. Toxicol Sci 85(2):1048−1063. 

Connor, KT; Aylward, LL. (2006) Human response to dioxin: aryl hydrocarbon receptor (AhR) molecular structure, 

function, and dose-response data for enzyme induction indicate an impaired human AhR. J Toxicol Environ Health 

B 9(2):147−171. 

Heinzl, H; Mittlback, M; Edler, L. (2007) On the translation of uncertainty from toxicokinetic to toxicodynamic 

models - the TCDD example. Chemosphere 67(9):S365−S374. 

Irigaray, P; Mejean, L; Laurent, F. (2005) Behaviour of dioxin in pig adipocytes. Food Chem Toxicol 

43(3):457−460. 

Kerger, BD; Leung, HW; Scott, P; et al. (2006) Age- and concentration-dependent elimination half-life of 2,3,7,8-

tetrachlorodibenzo-p-dioxin in Seveso children. Environ Health Perspect 114(10):1596−1602. 

Kerger, BD; Leung, HW; Scott, PK; et al. (2007) Refinements on the age-dependent half-life model for estimating 

child body burdens of polychlorodibenzodioxins and dibenzofurans. Chemosphere 67(9):S272−S278. 

Kim, AH; Kohn, MC; Nyska, A; et al. (2003) Area under the curve as a dose metric for promotional responses 

following 2,3,7,8-tetrachlorodibenzo-p-dioxin exposure. Toxicol Appl Pharmacol 191(1):12−21. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-7 DRAFT—DO NOT CITE OR QUOTE 

Korenaga, T; Fukusato, T; Ohta, M; et al. (2007) Long-term effects of subcutaneously injected 2,3,7,8-

tetrachlorodibenzo-p-dioxin on the liver of rhesus monkeys. Chemosphere 67(9):S399−S404. 

Korkalainen, M; Tuomisto, J; Pohjanvirta, R. (2004) Primary structure and inducibility by 2,3,7,8-

tetrachlorodibenzo-p-dioxin (TCDD) of aryl hydrocarbon receptor repressor in a TCDD-sensitive and a TCDDresistant rat strain. Biochem Biophys Res Communications 315(1):123−131. 

Kransler, KM; McGarrigle, BP; Olson, JR. (2007) Comparative developmental toxicity of 2,3,7,8-

tetrachlorodibenzo-p-dioxin in the hamster, rat and guinea pig. Toxicology 229(3):214−225. 

Maruyama, W; Yoshida, K; Tanaka, T; et al. (2002) Determination of tissue-blood partition coefficients for a 

physiological model for humans, and estimation of dioxin concentration in tissues. Chemosphere 46(7):975−985. 

Maruyama, W; Yoshida, K; Tanaka, T; et al. (2003) Simulation of dioxin accumulation in human tissues and 

analysis of reproductive risk. Chemosphere 53(4):301-313. 

Maruyama, W; Aoki, Y. (2006) Estimated cancer risk of dioxins to humans using a bioassay and physiologically 

based pharmacokinetic model. Toxicol Appl Pharmacol 214(2):188−198. 

Milbrath, MO; Wenger, Y; Chang, C-W; et al. (2009) Apparent Half-Lives of Dioxins, Furans, and Polychlorinated 

Biphenyls as a Function of Age, Body Fat, Smoking Status, and Breast-Feeding. Environ Health Perspect 

117(3):417−425. 

Moser, GA; McLachlan, MS. (2002) Modeling digestive tract absorption and desorption of lipophilic organic 

contaminants in humans. Environ Sci Technol 36(15):3318−25. 

Mullerova, D; Kopecky, J. (2007) White adipose tissue: storage and effector site for environmental pollutants. 

Physiol Res 56(4):375−381. 

Nadal, M; Perello, G; Schuhmacher, M; et al. (2008) Concentrations of PCDD/PCDFs in plasma of subjects living 

in the vicinity of a hazardous waste incinerator: Follow-up and modeling validation. Chemosphere 73(6):901−906. 

Nohara, K; Ao, K; Miyamoto, Y; et al. (2006) Comparison of the 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD)-

induced CYP1A1 gene expression profile in lymphocytes from mice, rats, and humans: Most potent induction in 

humans. Toxicology 225(2-3):204−213. 

Olsman, H; Engwall, M; Kammann, U; et al. (2007) Relative differences in aryl hydrocarbon receptor-mediated 

response for 18 polybrominated and mixed halogenated dibenzo-p-dioxins and -furans in cell lines from four 

different species. Environ Toxicol Chem 26(11):2448−2454. 

Saghir, SA; Lebofsky, M; Pinson, DM; et al. (2005) Validation of Haber's Rule (doseX time=constant) in rats and 

mice for monochloroacetic acid and 2,3,7,8-tetrachlorodibenzo-p-dioxin under conditions of kinetic steady state. 

Toxicology 215(1−2):48−56. 

Schecter, A; Pavuk, M; Popke, O; et al. (2003) Dioxin, dibenzofuran, and coplanar PCB Levels in Laotian blood and 

milk from Agent Orange-sprayed and nonsprayed areas, 2001. J Toxicol Environ Health A 66(21):2067−2075. 

Staskal, DF; Diliberto, JJ; Devito, MJ; et al. (2005) Inhibition of human and rat CYP1A2 by TCDD and dioxin-like 

chemicals. Toxicol Sci 84(2):225−231. 

Toyoshiba, H; Walker, NJ; Bailer, AJ; et al. (2004) Evaluation of toxic equivalency factors for induction of 

cytochromes P450 CYP1A1 and CYP1A2 enzyme activity by dioxin-like compounds. Toxicol Appl Pharmacol 

194(2):156−168. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-8 DRAFT—DO NOT CITE OR QUOTE 

Wilkes, JG; Hass, BS; Buzatu, DA; et al. (2008) Modeling and assaying dioxin-like biological effects for both 

dioxin-like and certain non-dioxin-like compounds. Toxicol Sci 102(1):187−195. 

1 C.1.5. Brief Descriptions of DIALOG Bibliographic Data Bases Searched 

2 The National Technical Information Service (NTIS) database comprises summaries of 

3 U.S. government-sponsored research, development, and engineering, plus analyses prepared by 

4 federal agencies, their contractors, or grantees. It is the means through which unclassified, 

5 publicly available, unlimited distribution reports are made available for sale from 240 agencies. 

6 Additionally, some state and local government agencies contribute summaries of their reports to 

7 the database. NTIS also provides access to the results of government-sponsored research and 

8 development from countries outside the United States. Organizations that currently contribute to 

9 the NTIS database include but are not limited to the following: the Japan Ministry of 

10 International Trade and Industry (MITI); laboratories administered by the United Kingdom 

11 Department of Industry; the German Federal Ministry of Research and Technology (BMFT); and 

12 the French National Center for Scientific Research (CNRS). 

13 Pollution Abstracts provides access to environmental information that combines 

14 information on scientific research and government policies in a single resource. Topics of 

15 growing concern are extensively covered from the standpoints of atmosphere, emissions, 

16 mathematical models, effects on people and animals, and environmental action in response to 

17 global pollution issues. This database also contains material from conference proceedings and 

18 hard-to-find summarized documents along with information from primary journals in the field of 

19 pollution. 

20 BIOSIS Previews® contains citations from Biological Abstracts® (BA) and Biological 

21 Abstracts/Reports, Reviews, and Meetings® (BA/RRM) (formerly BioResearch Index®), the 

22 major publications of BIOSIS®. These publications constitute the major English-language 

23 service providing comprehensive worldwide coverage of research in the biological and 

24 biomedical sciences. Biological Abstracts includes approximately 350,000 accounts of original 

25 research yearly from nearly 5,000 primary journal and monograph titles. BA/RRM includes an 

26 additional 200,000+ citations a year from meeting abstracts, reviews, books, book chapters, 

27 notes, letters, and selected reports. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-9 DRAFT—DO NOT CITE OR QUOTE 

1 IPA Toxicology provides focused toxicology information on all phases of the 

2 development and use of drugs and on professional pharmaceutical practice. The scope of the 

3 database ranges from the clinical and practical to the theoretical aspects of toxicology literature. 

4 A unique feature of abstracts reporting clinical studies is the inclusion of the study design, 

5 number of patients, dosage, dosage forms, and dosage schedule. 

6 Medical Literature, Analysis, and Retrieval System Online (MEDLINE®), produced by 

7 the U.S. National Library of Medicine (NLM), is NLM’s premier bibliographic database. It 

8 contains more than 15 million references to journal articles in life sciences with a concentration 

9 on biomedicine. The broad coverage of the database includes basic biomedical research and the 

10 clinical sciences since 1950, including nursing, dentistry, veterinary medicine, pharmacy, allied 

11 health, and pre-clinical sciences. MEDLINE® also covers life sciences that are vital to 

12 biomedical practitioners, researchers, and educators, including some aspects of biology, 

13 environmental science, marine biology, and plant and animal science, as well as biophysics and 

14 chemistry. MEDLINE® is indexed using NLM's controlled vocabulary, Medical Subject 

15 Headings (MeSH®). Approximately 400,000 records are added per year, of which more than 76 

16 percent are in English. MEDLINE® contains AIDSLINE, HealthSTAR, Toxline, In Process 

17 (formerly known as Pre-MEDLINE®), In Data Review, and POPLINE. 

18 ToxFile covers the toxicological, pharmacological, biochemical, and physiological 

19 effects of drugs and other chemicals. Adverse drug reactions, chemically induced diseases, 

20 carcinogenesis, mutagenesis, teratogenesis, environmental pollution, waste disposal, radiation, 

21 and food contamination are typical areas of coverage. The databases Environmental Mutagen 

22 Information Center (EMIC), Developmental and Reproductive Toxicology (DART), and Toxic 

23 Substances Control Act Test Submissions (TSCATS) are included in ToxFile. It is not clearly 

24 stated whether the Chemical Carcinogenesis Research Information System (CCRIS), Hazardous 

25 Substances Data Bank (HSDB), or Genetic Toxicology Data Bank (GENE-TOX) are included in 

26 ToxFile. Consequently, a separate, on-line search was conducted to ensure that these databases 

27 were searched. 

28 BIOSIS® Toxicology contains citations from BA and BA/RRM (formerly BioResearch 

29 Index®), the major publications of BIOSIS®, that focus on toxicology and related topics. 

30 Records are drawn from journal articles, conference papers, monographs and book chapters, 

31 notes, letters, and reports, as well as original research. U.S. patent records are also included. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-10 DRAFT—DO NOT CITE OR QUOTE 

1 CANCERLIT® is produced by the International Cancer Research DataBank Branch 

2 (ICRDB) of the U.S. National Cancer Institute. The database consists of bibliographic records 

3 referencing cancer research publications dating from 1963 to 2002. Most records contain 

4 abstracts, and all records contain citation information and additional descriptive fields such as 

5 document type and language. Beginning with the June 1983 CANCERLIT update, records from 

6 the MEDLINE® database dealing with cancer topics have been added to CANCERLIT. 

7 The Registry of Toxic Effects of Chemical Substances (RTECS®) is a comprehensive 

8 database of basic toxicity information for over 150,000 chemical substances including 

9 prescription and non-prescription drugs, food additives, pesticides, fungicides, herbicides, 

10 solvents, diluents, chemical wastes, reaction products of chemical waste, and substances used in 

11 both industrial and household situations. Reports of the toxic effects of each compound are 

12 cited. In addition to toxic effects and general toxicology reviews, data on skin and/or eye 

13 irritation, mutation, reproductive consequences and tumorigenicity are provided. Federal 

14 standards and regulations, National Institute for Occupational Safety and Health (NIOSH) 

15 recommended exposure limits and information on the activities of EPA, NIOSH, National 

16 Toxicology Program (NTP), and Occupational Safety and Health Administration (OSHA) 

17 regarding the substance are also included. The toxic effects are linked to literature citations from 

18 both published and unpublished governmental reports, and published articles from the scientific 

19 literature. The database corresponds to the print version of the RTECS®, formerly known as the 

20 Toxic Substances List, which was started in 1971. Originally prepared by the NIOSH, the 

21 RTECS® database is now produced and distributed by Symyx Technologies, Inc. 

 22 

23 C.2. TOXICOKINETIC MODELING CODE (Emond et al., 2005) 

24 C.2.1. Human Standard Model 

25 C.2.1.1. Model Code 

26 PROGRAM: 'Three Compartment PBPK Model for TCDD in Human: Standard Model 

27 (Non-Gestation)' 

28 

29 !HUM_NON_GEST_ICF_F083109.csl 

30 !***************************************************** 

 31 

32 INITIAL !INITIALIZATION OF PARAMETERS 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-11 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !SIMULATION PARAMETERS ==== 

3 CONSTANT EXP_TIME_ON = 0. ! TIME AT WHICH EXPOSURE BEGINS 

4 (HOUR) 

5 CONSTANT EXP_TIME_OFF = 6.132e5 ! TIME AT WHICH EXPOSURE ENDS 

6 (HOUR) 

7 CONSTANT DAY_CYCLE = 24.0 ! NUMBER OF HOURS BETWEEN DOSES 

8 (HOUR) 

9 CONSTANT BCK_TIME_ON = 6.132e5 ! TIME AT WHICH BACKGROUND 

10 EXPOSURE BEGINS (HOUR) 

11 CONSTANT BCK_TIME_OFF = 6.132e5 ! TIME AT WHICH BACKGROUND 

12 EXPOSURE ENDS (HOUR) 

 13 

14 !EXPOSURE DOSES 

15 CONSTANT MSTOTBCKGR = 0.0 ! ORAL BACKGROUND EXPOSURE DOSE 

16 (NG/KG) 

17 CONSTANT MSTOT = 1.0E-7 ! ORAL EXPOSURE DOSE (NG/KG) 

18 CONSTANT DOSEIV = 0.0 ! INJECTED DOSE (NG/KG) 

19 CONSTANT MW = 322.0 ! MOLECULAR WEIGHT (G/MOL) 

20 MSTOT_NM = MSTOT/MW ! CONVERTS THE DOSE TO NMOL/KG 

21 MSTOT_NMBCKGR = MSTOTBCKGR/MW !CONVERTS THE BACKGROUND DOSE 

22 TO NMOL/KG 

23 DOSEIV_NM = DOSEIV/MW ! CONVERTS THE INJECTED DOSE TO 

24 NMOL/KG 

 25 

26 !INITIAL GUESS OF THE FREE CONCENTRATION IN THE LIGAND 

27 (COMPARTMENT INDICATED BELOW) ==== 

28 CONSTANT CFLLI0 = 0.0 ! LIVER (NMOL/L) 

 29 

30 !BINDING CAPACITY (AhR) FOR NON LINEAR BINDING (COMPARTMENT 

31 INDICATED BELOW) === 

32 CONSTANT LIBMAX = 0.35 ! LIVER (NMOL/L) 

 33 

34 ! PROTEIN AFFINITY CONSTANTS (1A2 OR AhR, COMPARTMENT INDICATED 

35 BELOW) === 

36 CONSTANT KDLI = 0.1 ! LIVER (AhR) (NMOL/L) WANG ET AL.. 1997 

37 CONSTANT KDLI2 = 40.0 ! LIVER (1A2) (NMOL/L) EMOND ET AL. 2004 

 38 

39 !EXCRETION AND ABSORPTION CONSTANTS 

40 CONSTANT KST = 0.01 ! GASTRIC RATE CONSTANT (HR-1), EMOND 

41 ET AL., 2005 

42 CONSTANT KABS = 0.06 ! INTESTINAL ABSORPTION CONSTANT (HR-1), 

43 EMOND ET AL. 2005 

 44 

45 !ELIMINATION CONSTANTS 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-12 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT CLURI = 4.17D-8 ! URINARY CLEARANCE (L/HR), EMOND ET 

2 AL., 2005 

3 CONSTANT KELV = 1.1e-3 ! INTERSPECIES VARIABLE ELIMINATION 

4 CONSTANT (1/HOUR) 

 5 

6 !CONSTANT TO DIVIDE THE ABSORPTION INTO LYMPHATIC AND PORTAL 

7 FRACTIONS 

8 CONSTANT A = 0.7 ! LYMPHATIC FRACTION, WANG ET AL. 

9 (1997) 

 10 

11 !PARTITION COEFFICIENTS 

12 CONSTANT PF = 1.0e2 ! ADIPOSE TISSUE/BLOOD, WANG ET AL. 

1997 13 

14 CONSTANT PRE = 1.5 ! REST OF THE BODY/BLOOD, WANG ET AL. 

1997 15 

16 CONSTANT PLI = 6.0 ! LIVER/BLOOD, WANG ET AL. 1997 

 17 

18 !PARAMETERS FOR INDUCTION OF CYP1A2 

19 CONSTANT PAS_INDUC = 1.0 ! INCLUDE INDUCTION? (1 = YES, 0 = NO) 

20 CONSTANT CYP1A2_1OUTZ = 1.6e3 ! DEGRADATION CONCENTRATION 

21 CONSTANT OF 1A2 (NMOL/L) 

22 CONSTANT CYP1A2_1A1 = 1.6e3 ! BASAL CONCENTRATION OF 1A1 

23 (NMOL/L) 

24 CONSTANT CYP1A2_1EC50 = 1.3e2 ! DISSOCIATION CONSTANT TCDD-CYP1A2 

25 (NMOL/L) 

26 CONSTANT CYP1A2_1A2 = 1.6e3 ! BASAL CONCENTRATION OF 1A2 

27 (NMOL/L) 

28 CONSTANT CYP1A2_1KOUT = 0.1 ! FIRST ORDER RATE OF DEGRADATION 

29 (H-1) 

30 CONSTANT CYP1A2_1TAU = 0.25 ! HOLDING TIME (H) 

31 CONSTANT CYP1A2_1EMAX = 9.3e3 ! MAXIMUM INDUCTION OVER BASAL 

32 EFFECT (UNITLESS) 

33 CONSTANT HILL = 0.6 !HILL CONSTANT; COOPERATIVELY LIGAND 

34 BINDING EFFECT CONSTANT (UNITLESS) 

35 ! DIFFUSIONAL PERMEABILITY FRACTION 

36 CONSTANT PAFF = 0.12 ! ADIPOSE (UNITLESS) 

37 CONSTANT PAREF = 0.03 ! REST OF BODY (UNITLESS) 

38 CONSTANT PALIF = 0.35 ! LIVER (UNITLESS) 

 39 

40 !TISSUE BLOOD FLOW EXPRESSED AS A FRACTION OF CARDIAC OUTPUT 

41 ========= 

42 CONSTANT QFF = 0.05 ! ADIPOSE TISSUE BLOOD FLOW FRACTION 

43 (UNITLESS), KRISHNAN 2008 

44 CONSTANT QLIF = 0.26 ! LIVER (UNITLESS), KRISHNAN 2008 

 45 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-13 DRAFT—DO NOT CITE OR QUOTE 

1 !COMPARTMENT TISSUE BLOOD EXPRESSED AS A FRACTION OF THE TOTAL 

2 COMPARTMENT VOLUME ========= 

3 CONSTANT WFB0 = 0.050 ! ADIPOSE TISSUE, WANG ET AL. 1997 

4 CONSTANT WREB0 = 0.030 ! REST OF THE BODY, WANG ET AL. 1997 

5 CONSTANT WLIB0 = 0.266 ! LIVER, WANG ET AL. 1997 

 6 

7 !EXPOSURE SCENARIO FOR UNIQUE OR REPETITIVE WEEKLY OR MONTHLY 

8 EXPOSURE 

9 !NUMBER OF EXPOSURES PER WEEK 

10 CONSTANT WEEK_LACK = 0.0 ! DELAY BEFORE EXPOSURE ENDS 

11 (WEEK) 

12 CONSTANT WEEK_PERIOD = 168.0 ! NUMBER OF HOURS IN THE WEEK 

13 (HOURS) 

14 CONSTANT WEEK_FINISH = 168.0 ! TIME EXPOSURE ENDS (HOURS) 

15 !NUMBER OF EXPOSURES PER MONTH 

16 CONSTANT MONTH_LACK = 0.0 ! DELAY BEFORE EXPOSURE BEGINS 

17 (MONTH) 

 18 

19 !SET FOR BACKGROUND EXPOSURE=========== 

20 !TIME CONSTANT FOR BACKGROUND EXPOSURE=========== 

21 CONSTANT Day_LACK_BG = 0.0 ! DELAY BEFORE EXPOSURE BEGINS 

22 (HOUR) 

23 CONSTANT Day_PERIOD_BG = 24.0 ! LENGTH OF EXPOSURE (HOUR) 

 24 

25 !TIME CONSTANT FOR WEEKLY EXPOSURE 

26 CONSTANT WEEK_LACK_BG = 0.0 ! DELAY BEFORE BACKGROUND 

27 EXPOSURE BEGINS (WEEK) 

28 CONSTANT WEEK_PERIOD_BG = 168.0 ! NUMBER OF HOURS IN THE WEEK 

29 (HOURS) 

30 CONSTANT WEEK_FINISH_BG = 168.0 ! TIME EXPOSURE ENDS (HOURS) 

 31 

32 ! CONSTANT USED IN CARDIAC OUTPUT EQUATION 

33 CONSTANT QCC = 15.36 ! (L/KG-H), EMOND ET AL. 2004 

 34 

35 ! COMPARTMENT LIPID EXPRESSED AS THE FRACTION OF TOTAL LIPID 

36 !Data from Emonds Thesis 2001 

37 CONSTANT F_TOTLIP = 0.8000 ! ADIPOSE TISSUE (UNITLESS) 

38 CONSTANT B_TOTLIP = 0.0057 ! BLOOD (UNITLESS) 

39 CONSTANT RE_TOTLIP = 0.0190 ! REST OF THE BODY (UNITLESS) 

40 CONSTANT LI_TOTLIP = 0.0670 ! LIVER (UNITLESS)

41 CONSTANT MEANLIPID = 974.0 

 42 

43 END ! END OF THE INITIAL SECTION 

 44 

 45 

46 DYNAMIC ! DYNAMIC SIMULATION SECTION 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-14 DRAFT—DO NOT CITE OR QUOTE 

1 ! 

2 ALGORITHM IALG = 2 ! GEAR METHOD 

3 CINTERVAL CINT = 10.0 ! COMMUNICATION INTERVAL 

4 MAXTERVAL MAXT = 1.0e+10 !MAXIMUM INTERVAL CALCULATION 

5 MINTERVAL MINT = 1.0E-10 !MINIMUM INTERVAL CALCULATION 

6 VARIABLE T = 0.0 

7 CONSTANT TIMELIMIT = 1.752e5 !SIMULATION LIMIT TIME (HOUR) 

8 CONSTANT Y0 = 0.0 ! AGE (YEARS) AT BEGINNING OF SIMULATION 

9 CONSTANT GROWON = 1.0 ! INCLUDE BODY WEIGHT AND HEIGHT 

10 GROWTH? (1 = YES, 0 = NO) 

11 CINTXY = CINT 

12 PFUNC = CINT 

 13 

14 DAY=T/24.0 ! TIME IN DAYS 

15 WEEK =T/168.0 ! TIME IN WEEKS 

16 MONTH =T/730.0 ! TIME IN MONTHS 

17 YEAR=Y0+T/8760.0 ! TIME IN YEARS 

18 GYR =Y0 + growon*T/8760.0 ! TIME FOR USE IN GROWTH EQUATION (YEARS) 

 19 

20 DERIVATIVE ! PORTION OF CODE THAT SOLVES DIFFERENTIAL EQUATIONS 

 21 

22 ! CHRONIC OR SUBCHRONIC EXPOSURE SCENARIO ======= 

23 ! NUMBER OF EXPOSURES PER DAY 

24 DAY_LACK = EXP_TIME_ON ! DELAY BEFORE EXPOSURE BEGINS (HOURS) 

25 DAY_PERIOD = DAY_CYCLE ! EXPOSURE PERIOD (HOURS) 

26 DAY_FINISH = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

27 MONTH_PERIOD = TIMELIMIT ! EXPOSURE PERIOD (MONTHS) 

28 MONTH_FINISH = EXP_TIME_OFF ! LENGTH OF EXPOSURE (MONTHS) 

 29 

 30 

31 ! NUMBER OF EXPOSURES PER DAY AND MONTH 

32 DAY_FINISH_BG = CINTXY 

33 MONTH_LACK_BG = BCK_TIME_ON !DELAY BEFORE BACKGROUD EXPOSURE 

34 BEGINS (MONTHS) 

35 MONTH_PERIOD_BG = TIMELIMIT ! BACKGROUND EXPOSURE PERIOD 

36 (MONTHS) 

37 MONTH_FINISH_BG = BCK_TIME_OFF ! LENGTH OF BACKGROUND EXPOSURE 

38 (MONTHS) 

 39 

40 B = 1.0-A ! FRACTION OF DIOXIN ABSORBED IN THE PORTAL FRACTION OF THE 

41 LIVER 

 42 

43 !HUMAN BODY WEIGHT GROWTH EQUATION======== 

44 ! POLYNOMIAL REGRESSION EXPRESSION WRITTEN 

45 !APRIL 10 2008, OPTIMIZED WITH DATA OF PELEKIS ET AL. 2001 

46 ! POLYNOMIAL REGRESSION EXPRESSION WRITTEN WITH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-15 DRAFT—DO NOT CITE OR QUOTE 

1 !HUH AND BOLCH 2003 FOR BMI CALCULATION 

 2 

3 ! BODY WEIGHT CALCULATION 

4 WT0 = (0.0006*GYR**3 - 0.0912*GYR**2 + 4.32*GYR + 3.652) 

 5 

6 ! BODY MASS INDEX CALCULATION 

7 BH = -2D-5*GYR**4+4.2D-3*GYR**3.0-0.315*GYR**2.0+9.7465*GYR+72.098 

8 !HEIGHT EQUATION FORMULATED FOR USE FROM 0 TO 70 YEARS 

9 BHM= (BH/100.0) !HUMAN HEIGHT IN METERS (BHM) 

10 HBMI= WT0/(BHM**2.0) ! HUMAN BODY MASS INDEX (BMI) 

 11 

12 ! ADIPOSE TISSUE FRACTION 

13 WT0GR= WT0*1.0e3 ! BODY WEIGHT IN GRAMS 

14 WF0= -6.36D-20*WT0GR**4.0 +1.12D-14*WT0GR**3.0 -5.8D-10*WT0GR**2.0 +1.2D15 5*WT0GR+5.91D-2 

 16 

17 ! LIVER,VOLUME, 

18 ! APPROACH BASED ON LUECKE (2007) 

19 WLI0= (3.59D-2 -(4.76D-7*WT0GR)+(8.50D-12*WT0GR**2.0)-(5.45D-17*WT0GR**3.0)) 

 20 

21 WRE0 = (0.91 -(WLIB0*WLI0+WFB0*WF0+WLI0+WF0))/(1.0+WREB0) 

22 !REST OF THE BODY FRACTION; UPDATED FOR EPA 

23 ASSESSMENT 

24 QREF = 1.0-(QFF+QLIF) !REST OF BODY BLOOD FLOW 

25 QTTQF = QFF+QREF+QLIF ! SUM MUST EQUAL 1 

 26 

27 !COMPARTMENT VOLUME (L OR KG) ========= 

28 WF = WF0 * WT0 ! ADIPOSE 

29 WRE = WRE0 * WT0 ! REST OF THE BODY 

30 WLI = WLI0 * WT0 ! LIVER 

31 WB=0.075*WT0 ! BLOOD 

 32 

33 !COMPARTMENT TISSUE BLOOD (L OR KG) ========= 

34 WFB = WFB0 * WF ! ADIPOSE 

35 WREB = WREB0 * WRE ! REST OF THE BODY 

36 WLIB = WLIB0 * WLI ! LIVER 

37 !CARDIAC OUTPUT FOR THE GIVEN BODY WEIGHT 

38 QC= QCC*(WT0**0.75) ! [L BLOOD/HOUR] 

 39 

40 QF = QFF*QC ! ADIPOSE TISSUE BLOOD FLOW RATE [L/HR] 

41 QLI = QLIF*QC ! LIVER TISSUE BLOOD FLOW RATE [L/HR] 

42 QRE = QREF*QC !REST OF THE BODY BLOOD FLOW RATE [L/HR] 

 43 

44 QTTQ = QF+QRE+QLI ! TOTAL FLOW RATE [L/HR] 

 45 

46 !PERMEABILITY ORGAN FLOW [L/HR]======= 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-16 DRAFT—DO NOT CITE OR QUOTE 

1 PAF = PAFF*QF ! ADIPOSE 

2 PARE = PAREF*QRE ! REST OF THE BODY 

3 PALI = PALIF*QLI ! LIVER TISSUE 

 4 

5 ! ABSORPTION SECTION 

6 ! INTRAVENOUS 

7 IV = DOSEIV_NM * WT0 !AMOUNT IN NMOL 

8 MSTTBCKGR = MSTOT_NMBCKGR *WT0 !AMOUNT IN (NMOL) 

9 MSTT = MSTOT_NM * WT0 !AMOUNT IN NMOL 

 10 

11 !REPETITIVE ORAL BACKGROUND EXPOSURE SCENARIOS 

12 DAY_EXPOSURE_BG = PULSE(DAY_LACK_BG,DAY_PERIOD_BG,DAY_FINISH_BG) 

13 WEEK_EXPOSURE_BG = 

14 PULSE(WEEK_LACK_BG,WEEK_PERIOD_BG,WEEK_FINISH_BG) 

15 MONTH_EXPOSURE_BG = 

16 PULSE(MONTH_LACK_BG,MONTH_PERIOD_BG,MONTH_FINISH_BG) 

 17 

18 MSTTCH_BG = 

19 (DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG)*MSTTBCK

20 GR 

21 MSTTFR_BG = MSTTBCKGR/CINT 

 22 

23 CYCLE_BG =DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG 

 24 

 25 

26 ! CONDITIONAL ORAL EXPOSURE (BACKGROUND EXPOSURE) 

27 IF (MSTTCH_BG.EQ.MSTTBCKGR) THEN 

28 ABSMSTT_GB= MSTTFR_BG 

29 ELSE 

30 ABSMSTT_GB = 0.0 

31 END IF 

 32 

 33 

34 !REPETITIVE ORAL MAIN EXPOSURE SCENARIO 

35 DAY_EXPOSURE = PULSE(DAY_LACK,DAY_PERIOD,DAY_FINISH) 

36 WEEK_EXPOSURE = PULSE(WEEK_LACK,WEEK_PERIOD,WEEK_FINISH) 

37 MONTH_EXPOSURE = PULSE(MONTH_LACK,MONTH_PERIOD,MONTH_FINISH) 

 38 

39 MSTTCH = (DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE)*MSTT 

40 CYCLE = DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE 

41 MSTTFR=MSTT/CINT 

 42 

43 !CONDITIONAL ORAL EXPOSURE 

44 IF (MSTTCH.EQ.MSTT) THEN 

45 ABSMSTT= MSTTFR 

46 ELSE 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-17 DRAFT—DO NOT CITE OR QUOTE 

1 ABSMSTT = 0. 

2 END IF 

 3 

4 CYCLETOT=INTEG(CYCLE,0.0) 

 5 

6 ! MASS Balance CHANGE IN THE LUMEN 

7 RMSTT= -(KST+KABS)*MST+ABSMSTT +ABSMSTT_GB ! RATE OF CHANGE 

8 (NMOL/H) 

9 MST = INTEG(RMSTT,0.) !AMOUNT REMAINING IN GI TRACT (NMOL) 

 10 

11 ! ABSORPTION IN LYMPH CIRCULATION 

12 LYRMLUM = KABS*MST*A 

13 LYMLUM = INTEG(LYRMLUM,0.0) 

 14 

15 ! ABSORPTION IN PORTAL CIRCULATION 

16 LIRMLUM = KABS*MST*B 

17 LIMLUM = INTEG(LIRMLUM,0.0) 

 18 

19 ! PERCENT OF DOSE REMAINING IN THE GI TRACT 

20 PRCT_remain_GIT = 100.0*MST/(MSTT+1E-30) 

 21 

22 !IV ABSORTPION SCENARIO --------- 

23 IVR= IV/PFUNC ! RATE FOR IV INFUSION IN BLOOD 

24 EXPIV= IVR * (1.0-STEP(PFUNC)) 

25 IVDOSE = integ(EXPIV,0.0) 

 26 

27 !SYSTEMIC BLOOD COMPARTMENT 

28 ! MODIFICATION OCT 8 2009 

29 CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM)/(QC+CLURI) ! 

30 CA = CB !CONCENTRATION (NMOL/L) 

 31 

32 !CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM-RAURI)/QC ! 

33 ! CA = CB ! CONCENTRATION (NMOL/L) 

 34 

35 !URINARY EXCRETION BY KIDNEY 

36 ! MODIFICATION OCT 8 2009 

37 RAURI = CLURI *CB 

38 AURI = INTEG(RAURI,0.0) 

 39 

 40 

41 !CONCENTRATION UNIT 

42 PRCT_B = 100.0*CB/(MSTT+1E-30) ! PERCENT OF DOSE 

43 CBSNGKGLIADJ = CB*MW/(0.55*B_TOTLIP) !serum concentration in lipid adjust (PG/G 

44 LIPID=PPT) 

45 CBPPT = CBSNGKGLIADJ 

46 CBNGKG = CB*MW 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-18 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 CBpptRH = CB*MW*10000/(0.55*MEANLIPID) !SERUM CONCENTRATION IN LIPID 

3 ADJUST (PG/G LIPID=PPT) 

 4 

5 AUC_CBSNGKGLIADJ=INTEG(CBSNGKGLIADJ,0.0) 

 6 

7 !ADIPOSE TISSUE COMPARTMENT 

8 RAFB= QF*(CA-CFB)-PAF*(CFB-CF/PF) !(NMOL/HR) 

9 AFB = INTEG(RAFB,0.0) !(NMOL) 

10 CFB = AFB/WFB !(NMOL/KG) 

11 !TISSUE SUBCOMPARTMENT 

12 RAF = PAF*(CFB-CF/PF) !(NMOL/HR) 

13 AF = INTEG(RAF,0.0) !(NMOL) 

14 CF = AF/WF !(NMOL/KG) 

 15 

16 !POST SIMULATION UNIT CONVERSION 

17 CFTOTAL = (AF + AFB)/(WF + WFB) ! TOTAL CONCENTRATION NMOL/ML 

18 PRCT_F = 100.0*CFTOTAL/(MSTT+1E-30) 

19 CFNGKG =CFTOTAL*MW 

 20 

21 !REST OF THE BODY COMPARTMENT======== 

22 RAREB= QRE*(CA-CREB)-PARE*(CREB-CRE/PRE) !(NMOL/HR) 

23 AREB = INTEG(RAREB,0.0) !(NMOL) 

24 CREB = AREB/WREB !(NMOL/KG) 

25 !TISSUE SUBCOMPARTMENT 

26 RARE = PARE*(CREB-CRE/PRE) !(NMOL/HR) 

27 ARE = INTEG(RARE,0.0) !(NMOL) 

28 CRE = ARE/WRE !(NMOL/KG) 

 29 

30 !POST SIMULATION UNIT CONVERSION 

31 CRETOTAL = (ARE + AREB)/(WRE + WREB) ! TOTAL CONCENTRATION IN NMOL/ML 

32 PRCT_RE = 100.0*CRETOTAL/(MSTT+1E-30) ! PERCENT OF DOSE 

 33 

34 !LIVER COMPARTMENT 

35 !TISSUE BLOOD SUBCOMPARTMENT 

36 RALIB = QLI*(CA-CLIB)-PALI*(CLIB-CFLLIR)+LIRMLUM !(NMOL/HR) 

37 ALIB = INTEG(RALIB,0.0) !(NMOL) 

38 CLIB = ALIB/WLIB 

39 !TISSUE SUBCOMPARTMENT 

40 RALI = PALI*(CLIB-CFLLIR)-REXCLI !(NMOL/HR) 

41 ALI = INTEG(RALI,0.0) !(NMOL) 

42 CLI = ALI/WLI !(NMOL/KG) 

 43 

 44 

45 !FREE TCDD IN LIVER 

46 ! MODIFICATION OCTOBER 8 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-19 DRAFT—DO NOT CITE OR QUOTE 

1 CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR)) & 

2 +((CYP1A2_1O3*CFLLIR/(KDLI2+CFLLIR)*PAS_INDUC)))-CFLLI,CFLLI0) ! 

3 CONCENTRATION OF FREE TCDD IN LIVER 

4 CFLLIR=DIM(CFLLI,0.0) 

 5 

6 !MODIFIED FROM: 

7 !PARAMETER (LIVER_1RMN = 1.0E-30) 

8 ! CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR & ! 

9 +LIVER_1RMN))+((CYP1A2_1O3*CFLLIR/(KDLI2+CFLLIR & 

10 ! +LIVER_1RMN)*PAS_INDUC)))-CFLLI,CFLLI0) 

11 ! CFLLIR=DIM(CFLLI,0.0) 

 12 

 13 

14 CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR) !CONC OF TCDD BOUDN TO AhR 

 15 

16 !CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR+LIVER_1RMN) !CONC BIND 

 17 

18 !POST SIMULATION UNIT CONVERSION 

19 CLITOTAL = (ALI + ALIB)/(WLI + WLIB) ! TOTAL CONCENTRATION IN NMOL/ML 

20 PRCT_LI = 100.0*CLITOTAL/(MSTT+1.0E-30) 

21 rec_occ_AHR= 100.0*CFLLIR/(KDLI+CFLLIR+1.0) ! PERCENT BOUND TO AhR 

22 OCCUPANCY 

23 PROT_occ_1A2= 100.0*CFLLIR/(KDLI2+CFLLIR) ! PERCENT BOUND TO 1A2 

24 OCCUPANCY 

25 CLINGKG= CLITOTAL*MW ![NG TCDD/KG] 

26 CBNDLINGKG = CBNDLI*MW 

 27 

28 !FRACTION INCREASE OF INDUCTION OF CYP1A2 

29 fold_ind=CYP1A2_1OUT/CYP1A2_1A2 

30 VARIATIONOFAC =(CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2 

 31 

32 !VARIABLE ELIMINATION BASED ON THE CYP1A2 

33 KBILE_LI_T = Kelv*VARIATIONOFAC! 

 34 

35 REXCLI = KBILE_LI_T*CFLLIR*WLI ! DOSE-DEPENDENT RATE OF BILLIARY 

36 EXCRETION OF DIOXIN 

37 EXCLI = INTEG(REXCLI,0.0) !TOTAL AMOUNT OF DIOXIN EXCRETED 

 38 

39 !CHEMICAL IN CYP450 (1A2) COMPARTMENT 

40 !PARAMETER FOR INDUCTION OF CYP1A2 

 41 

42 CYP1A2_1KINP = CYP1A2_1KOUT*CYP1A2_1OUTZ ! BASAL RATE OF CYP1A2 

43 PRODUCTION SET EQUAL TO BASAL RATE OF DEGRDATION AT STEADY STATE 

 44 

45 ! MODIFICATION OCTOBER 8 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-20 DRAFT—DO NOT CITE OR QUOTE 

1 CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1.0 + CYP1A2_1EMAX *(CBNDLI+1.0e2 30)**HILL & 

3 /(CYP1A2_1EC50**HILL + (CBNDLI+1.0e-30)**HILL)) & 

4 - CYP1A2_1KOUT*CYP1A2_1OUT, CYP1A2_1OUTZ) ! LEVELS OF CYP1A2 

5 ! MODEIFIED FROM: 

6 !PARAMETER (CYP1A2_1RMN = 1e-30) 

7 !CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1 + CYP1A2_1EMAX *(CBNDLI & 

8 ! +CYP1A2_1RMN)**HILL/(CYP1A2_1EC50 + (CBNDLI + CYP1A2_1RMN)**HILL) & 

9 ! +CYP1A2_1RMN) - CYP1A2_1KOUT*CYP1A2_1& 

10 ! OUT, CYP1A2_1OUTZ) 

 11 

12 ! EQUATIONS INCORPORATING DELAY OF CYP1A2 PRODUCTION (NOT USED IN 

13 SIMULATIONS) 

14 CYP1A2_1RO2 = (CYP1A2_1OUT - CYP1A2_1O2)/ CYP1A2_1TAU 

15 CYP1A2_1O2 =INTEG(CYP1A2_1RO2, CYP1A2_1A1) 

16 CYP1A2_1RO3 = (CYP1A2_1O2 - CYP1A2_1O3)/ CYP1A2_1TAU 

17 CYP1A2_1O3 =INTEG(CYP1A2_1RO3, CYP1A2_1A2) 

 18 

19 !CHECK MASS BALANCE 

20 BDOSE= LYMLUM+LIMLUM+IVDOSE 

21 BMASSE = EXCLI+AURI+AFB+AF+AREB+ARE+ALIB+ALI 

22 BDIFF = BDOSE-BMASSE 

23 ! BODY BURDEN IN TERMS OF CONCENTRATION (NG/KG) 

24 BBNGKG = (AFB+AF+AREB+ARE+ALIB+ALI)*MW/WT0 ! 

 25 

26 !COMMAND END OF THE SIMULATION 

27 TERMT (T.GE. TIMELIMIT, 'Time limit has been reached.') 

 28 

29 END ! END OF THE DERIVATIVE SECTION 

30 END ! END OF THE DYTNAMIC SECTION 

31 END ! END OF THE PROGRAM 

 32 

33 C.2.1.2. Input File 

34 % base file name = "TESTJULY2009.m" 

35 %clear @variable 

36 output @clear 

37 prepare @clear year T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

38 CBNGKG 

39 %output @all 

40 % PARAMETERS FOR SIMULATION 

41 CINT = 1 %0.5 

42 EXP_TIME_ON = 0. % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

43 EXP_TIME_OFF = 613200 %324120 % HOUR/YEAR !TIME AT WHICH EXPOSURE 

44 ENDS (HOUR) 

45 DAY_CYCLE = 24 % NUMBER OF HOURS BETWEEN DOSES (HOUR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-21 DRAFT—DO NOT CITE OR QUOTE 

1 BCK_TIME_ON = 613200 %324120 % TIME AT WHICH BACKGROUND 

2 EXPOSURE BEGINS (HOUR) 

3 BCK_TIME_OFF = 613200 %324120 % TIME AT WHICH BACKGROUND 

4 EXPOSURE ENDS (HOUR) 

5 TIMELIMIT = 613200 %324120 %324120 % SIMULATION TIME LIMIT (HOUR) 

6 MSTOTBCKGR = 0. % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 7 

8 % oral dose oral dose oral dose 

9 MSTOT = 9.97339283634997E-07 % ORAL DAILY EXPOSURE DOSE (NG/KG) 

10 DOSEIV = 0 %NG/KG 

11 % oral dose oral dose oral dose 

 12 

13 MEANLIPID = 730 % 

14 PAS_INDUC= 1 % INDUCTION INCLUDED? (1=YES, 0=NO) 

15 

16 C.2.2. Human Gestational Model 

17 C.2.2.1. Model Code 

18 PROGRAM: 'Three Compartment PBPK Model for TCDD in Human (Gestation)' 

19 ! Parameters were change may 16, 2002 

20 ! Come from {8MAI_CHR_PRE-EXP_GD} 

21 ! Come from {12_Mouse_GD}file 

22 !******************************************** 

23 !{{IMPORTANT-IMPORTANT-IMPORTANT-IMPORTANT}} 

24 ! REDUCTION OF MOTHER AND FETUS COMPARTMENT 

25 ! 2M_R_TCDD_JULY2002 ////(JULY 18,2002)//// 

26 !TCDD_RED_4Species_2003_4 ////(APR 8 ,2003)//// 

27 !TCDD_RED_4Species_2003_9 ////(APR 17 ,2003)//// 

28 !TCDD_RED_4Species_2003_12 ////(APR 17 ,2003)//// 

29 !***************************************************** 

30 !APRIL 18 2003 

31 !TCDD_4C_4SP_2003 ////(APR 18 ,2003)//// 

32 ! was ''Gest 4 species 1.csl'' but update July 2009 

 33 

34 !GEST_HUM_0_45Y_4_ICF_afterKKfix_v3_humangestational.csl 

35 !HUM_GESTATIONAL_ICF_F083109.csl 

36 !HUM_GESTATIONAL_ICF_F100709.csl 

37 !***************************************************** 

 38 

39 !Legend/Legend/Legend/Legend/Legend/Legend/Legend/Legend/ 

40 !Legend for this PBPK model 

41 !Mating: control the tenure of exchange between fetus and 

42 !Mother and also control imitated tissue growth 

43 !Control: WTFE, WPLA0, QPLAF 

44 !(for rat, mouse, human, and monkey) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-22 DRAFT—DO NOT CITE OR QUOTE 

1 !Control transfer from mother to fetus and fetus to mother by TRANSTIME_ON 

2 !SWITCH_trans = 0 NO TRANSFER 

3 !SWITCH_trans = 1 TRANSFER OCCURS 

4 ! These switches are also controlled by mating parameters 

 5 

6 INITIAL ! 

 7 

8 !SIMULATION PARAMETERS 

9 CONSTANT PARA_ZERO = 1e-30 

10 CONSTANT EXP_TIME_ON = 0.0 !TIME AT WHICH EXPOSURE BEGINS 

11 (HOURS) 

12 CONSTANT EXP_TIME_OFF = 530.0 !TIME AT WHICH EXPOSURE ENDS (HOURS) 

13 CONSTANT DAY_CYCLE = 24.0 !NUMBER OF HOURS BETWEEN DOSES 

14 (HOURS) 

15 CONSTANT BCK_TIME_ON = 0.0 !TIME AT WHICH BACKGROUND EXPOSURE 

16 BEGINS (HOURS) 

17 CONSTANT BCK_TIME_OFF = 0.0 !TIME AT WHICH BACKGROUND EXPOSURE 

18 ENDS (HOURS) 

19 CONSTANT TRANSTIME_ON = 0.0 !CONTROL TRANSFER FROM MOTHER TO 

20 FETUS AT 9 WEEKS OR 1512 HOURS OF GESTATION 

 21 

22 ! INTRAVENOUS SEQUENCY 

23 CONSTANT IV_LACK = 0.0 

24 CONSTANT IV_PERIOD = 0.0 

 25 

26 !PREGNANCY PARAMETER 

27 CONSTANT MATTING = 0.0 !BEGINNING OF MATING (HOUR) 

28 CONSTANT PFETUS = 4.0 !PARTITION COEFFICIENT 

29 CONSTANT CLPLA_FET = 1.0e-3 !CLEARANCE TRANSFER FOR MOTHER TO 

30 FETUS (L/HR) 

 31 

32 !CONSTANT EXPOSURE CONTROL 

33 !ACUTE, SUBCHRONIC, CHRONIC EXPOSURE ===== 

34 !OR BACKGROUND EXPOSURE (IN THIS CASE 3 TIMES A DAY)=== 

35 CONSTANT MSTOTBCKGR = 0.0 ! ORAL BACKGROUND EXPOSURE DOSE 

36 (NG/KG) 

37 CONSTANT MSTOT = 0.0 ! ORAL EXPOSURE DOSE (NG/KG) 

 38 

39 !ORAL ABSORPTION 

40 ! MSTT= MSTOT/1000 *WT0 *1/322*1000 !AMOUNT IN NMOL 

41 MSTOT_NM = MSTOT/MW !CONVERTS THE DOSE TO NMOL/KG 

 42 

43 !INTRAVENOUS ABSORPTION 

44 CONSTANT DOSEIV = 0.0 ! INJECTED DOSE (NG/KG) 

45 DOSEIV_NM = DOSEIV/MW ! CONVERTS THE INJECTED DOSE TO NMOL/KG 

46 CONSTANT DOSEIVLATE = 0.0 !INJECTED DOSE LATE (UG/KG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-23 DRAFT—DO NOT CITE OR QUOTE 

1 DOSEIVNMlate = DOSEIVLATE/MW !AMOUNT IN NMOL/G 

 2 

3 !INITIAL GUESS OF THE FREE CONCENTRATION IN THE LIGAND 

4 (COMPARTMENT INDICATED BELOW)==== 

5 CONSTANT CFLLI0 = 0.0 !LIVER (NMOL/L) 

6 CONSTANT CFLPLA0 = 0.0 !PLACENTA (NMOL/L) 

 7 

8 !BINDING CAPACITY (AhR) FOR NON LINEAR BINDING (COMPARTMENT 

9 INDICATED BELOW) (NMOL/L) === 

10 CONSTANT LIBMAX = 0.35 ! LIVER (NMOL/L) 

11 CONSTANT PLABMAX = 0.2 !TEMPORARY PARAMETER 

 12 

13 !PROTEIN AFFINITY CONSTANTS (1A2 OR AhR, COMPARTMENT INDICATED 

14 BELOW) (NMOL/ML)=== 

15 CONSTANT KDLI = 0.1 !LIVER (AhR) (NMOL/L), WANG ET AL. 1997 

16 CONSTANT KDLI2 = 40.0 !LIVER (1A2) (NMOL/L), EMOND ET AL. 2004 

17 CONSTANT KDPLA = 0.1 !ASSUME IDENTICAL TO KDLI (AhR) 

 18 

19 !EXCRETION AND ABSORPTION CONSTANT 

20 CONSTANT KST = 0.01 ! GASTRIC RATE CONSTANT (HR-1), EMOND ET AL. 

2005 21 

22 CONSTANT KABS = 0.06 ! INTESTINAL ABSORPTION CONSTANT (HR-1), 

23 EMOND ET AL. (2005) 

 24 

25 !INTERSPECIES ELIMINATION CONSTANT 

26 !TEST ELIMINATION VARIABLE, EMOND ET AL. 2005 

27 CONSTANT KELV = 1.1e-3 !4.0D-3 ! INTERSPECIES VARIABLE 

28 ELIMINATION CONSTANT (1/HOUR) 

 29 

30 ! ELIMINATION CONSTANTS 

31 CONSTANT CLURI = 4.17e-8 ! URINARY CLEARANCE (L/HR), EMOND ET AL. 

2005 32 

 33 

34 ! CONSTANT TO DIVIDE THE ABSORPTION INTO LYMPHATIC AND PORTAL 

35 FRACTIONS 

36 CONSTANT A = 0.7 ! LYMPHATIC FRACTION, WANG ET AL. 1997 

 37 

38 !PARTITION COEFFICIENTS 

39 CONSTANT PF = 1.0e2 ! ADIPOSE TISSUE/BLOOD, WANG ET AL. 1997 

40 CONSTANT PRE = 1.5 ! REST OF THE BODY/BLOOD, WANG ET AL. 1997 

41 CONSTANT PLI = 6.0 ! LIVER/BLOOD, WANG ET AL. 1997 

42 CONSTANT PPLA = 1.5 ! TEMPORARY PARAMETER NOT CONFIGURED, 

43 WANG ET AL. 1997 

 44 

45 !PARAMETER FOR INDUCTION OF CYP 1A2, WANG ET AL. 1997 

46 CONSTANT PAS_INDUC = 1.0 ! INCLUDE INDUCTION? (1 = YES, 0 = NO) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-24 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT CYP1A2_1OUTZ = 1.6e3 ! DEGRADATION CONCENTRATION 

2 CONSTANT OF 1A2 (NMOL/L) 

3 CONSTANT CYP1A2_1A1 = 1.6e3 ! BASAL CONCENTRATION OF 1A1 (NMOL/L) 

4 CONSTANT CYP1A2_1EC50 = 1.3e2 ! DISSOCIATION CONSTANT TCDD-CYP1A2 

5 (NMOL/L) 

6 CONSTANT CYP1A2_1A2 = 1.6e3 !BASAL CONCENTRATION OF 1A2 (NMOL/ML) 

7 CONSTANT CYP1A2_1KOUT = 0.1 ! FIRST ORDER RATE OF DEGRADATION (H-1) 

8 CONSTANT CYP1A2_1TAU = 0.25 !HOLDING TIME (H) 

9 CONSTANT CYP1A2_1EMAX = 9.3e3 ! MAXIMUM INDUCTION OVER BASAL 

10 EFFECT (UNITLESS) 

11 CONSTANT HILL = 0.6 !HILL CONSTANT; COOPERATIVELY LIGAND 

12 BINDING EFFECT CONSTANT (UNITLESS) 

 13 

14 !DIFFUSIONAL PERMEABILITY FRACTION, WANG ET AL (1997) 

15 CONSTANT PAFF = 0.12 ! ADIPOSE (UNITLESS) 

16 CONSTANT PAREF = 0.03 ! REST OF THE BODY (UNITLESS) 

17 CONSTANT PALIF = 0.35 ! LIVER (UNITLESS) 

18 CONSTANT PAPLAF = 0.3 ! OPTIMIZED PARAMETER 

 19 

20 !TISSUE BLOOD FLOW EXPRESSED AS A FRACTION OF CARDIAC OUTPUT, 

21 KRISHNAN 2007 

22 CONSTANT QFF = 0.05 ! ADIPOSE TISSUE BLOOD FLOW FRACTION 

23 (UNITLESS), KRISHNAN 2008 

24 CONSTANT QLIF = 0.26 ! LIVER (UNITLESS), KRISHNAN 2008 

 25 

26 !===FRACTION OF TISSUE BLOOD WEIGHT Wang et al . (1997) 

27 CONSTANT WFB0 = 0.050 !ADIPOSE TISSUE, WANG ET AL. 1997 

28 CONSTANT WREB0 = 0.030 !REST OF THE BODY, WANG ET AL. 1997 

29 CONSTANT WLIB0 = 0.266 !LIVER, WANG ET AL. 1997 

30 CONSTANT WPLAB0 = 0.500 !ASSUME HIGHLY VASCULARIZED 

 31 

32 ! EXPOSURE SCENARIO FOR UNIQUE OR REPETITIVE WEEKLY OR MONTHLY 

33 EXPOSURE 

34 ! NUMBER OF EXPOSURES PER WEEK 

35 CONSTANT WEEK_LACK = 0.0 !DELAY BEFORE EXPOSURE ENDS (WEEK) 

36 CONSTANT WEEK_PERIOD = 168.0 ! NUMBER OF HOURS IN THE WEEK 

37 (HOURS) 

38 CONSTANT WEEK_FINISH = 168.0 ! TIME EXPOSURE ENDS (HOURS) 

 39 

40 ! NUMBER OF EXPOSURES PER MONTH 

41 CONSTANT MONTH_LACK = 0.0 !DELAY BEFORE EXPOSURE BEGINS 

42 (MONTHS) 

 43 

44 !======= CONSTANT FOR BACKGROUND EXPOSURE=========== 

45 CONSTANT Day_LACK_BG = 0.0 ! DELAY BEFORE EXPOSURE BEGINS 

46 (HOURS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-25 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT Day_PERIOD_BG = 24.0 !LENGTH OF EXPOSURE (HOURS) 

 2 

3 ! NUMBER OF EXPOSURES PER WEEK 

4 CONSTANT WEEK_LACK_BG = 0.0 !DELAY BEFORE BACKGROUD EXPOSURE 

5 BEGINS (WEEK) 

6 CONSTANT WEEK_PERIOD_BG = 168.0 ! NUMBER OF HOURS IN THE WEEK 

7 (HOURS) 

8 CONSTANT WEEK_FINISH_BG = 168.0 !TIME EXPOSURE ENDS (HOURS) 

 9 

 10 

11 ! CONSTANT USED IN CARDIAC OUTPUT EQUATION 

12 CONSTANT QCC = 15.36 ![L/KG-H], EMOND ET AL. 2004 

 13 

14 ! COMPARTMENT LIPID EXPRESSED AS THE FRACTION OF TOTAL LIPID 

15 !Data from Emonds Thesis 2001 

16 CONSTANT F_TOTLIP = 0.8000 ! ADIPOSE TISSUE (UNITLESS) 

17 CONSTANT B_TOTLIP = 0.0057 ! BLOOD (UNITLESS) 

18 CONSTANT RE_TOTLIP = 0.0190 ! REST OF THE BODY (UNITLESS) 

19 CONSTANT LI_TOTLIP = 0.0670 ! LIVER (UNITLESS) 

20 CONSTANT PLA_TOTLIP = 0.019 ! PLACENTA (UNITLESS) 

21 CONSTANT FETUS_TOTLIP = 0.019 ! FETUS (UNITLESS) 

 22 

23 CONSTANT MEANLIPID = 974 

 24 

25 END ! END OF THE INITIAL SECTION 

 26 

27 DYNAMIC ! DYNAMIC SIMULATION SECTION 

 28 

29 ALGORITHM IALG = 2 ! GEAR METHOD 

30 CINTERVAL CINT = 0.1 ! COMMUNICATION INTERVAL 

31 MAXTERVAL MAXT = 1.0e+10 ! MAXIMUM CALCULATION INTERVAL 

32 MINTERVAL MINT = 1.0E-10 ! MINIMUM CALCULATION INTERVAL 

33 VARIABLE T = 0.0 

34 CONSTANT TIMELIMIT = 100 !SIMULATION LIMIT TIME (HOUR) 

35 CONSTANT Y0 = 0.0 ! AGE (YEARS) AT BEGINNING OF 

36 SIMULATION 

37 CONSTANT GROWON = 1.0 ! INCLUDE BODY WEIGHT AND HEIGHT 

38 GROWTH? (1=YES, 0=NO) 

 39 

40 CINTXY = CINT 

41 PFUNC = CINT 

 42 

43 !TIME TRANSFORMATION 

44 DAY= T/24.0 

45 WEEK =T/168.0 

46 YEAR=Y0+T/8760.0 ! TIME IN YEARS 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-26 DRAFT—DO NOT CITE OR QUOTE 

1 GYR =Y0 + growon*T/8760.0 ! TIME FOR USE IN GROWTH EQUATION 

 2 

3 DERIVATIVE ! PORTION OF CODE THAT SOLVES DIFFERENTIAL EQUATIONS 

 4 

5 !====== CHRONIC OR SUBCHRONIC EXPOSURE SCENARIO ======= 

6 ! NUMBER OF EXPOSURES PER DAY 

 7 

8 DAY_LACK = EXP_TIME_ON ! DELAY BEFORE EXPOSURE BEGINS (HOURS) 

9 DAY_PERIOD = DAY_CYCLE ! EXPOSURE PERIOD (HOURS) 

10 DAY_FINISH = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

11 MONTH_PERIOD = TIMELIMIT ! EXPOSURE PERIOD (MONTHS) 

12 MONTH_FINISH = EXP_TIME_OFF ! LENGTH OF EXPOSURE (MONTHS) 

 13 

 14 

15 ! NUMBER OF EXPOSURES PER DAY AND MONTH 

16 DAY_FINISH_BG = CINTXY 

17 MONTH_LACK_BG = BCK_TIME_ON !DELAY BEFORE BACKGROUND 

18 EXPOSURE BEGINS (MONTHS) 

19 MONTH_PERIOD_BG = TIMELIMIT !BACKGROUND EXPOSURE PERIOD 

20 (MONTHS) 

21 MONTH_FINISH_BG = BCK_TIME_OFF !LENGTH OF BACKGROUND EXPOSURE 

22 (MONTHS) 

 23 

24 ! INTRAVENOUS LATE 

25 IV_FINISH = CINTXY 

26 B = 1-A ! FRACTION OF DIOXIN ABSORBED IN THE PORTAL FRACTION OF THE 

27 LIVER 

 28 

29 ! MOTHER BODY WEIGHT GROWTH EQUATION 

30 ! MODIFICATION TO ADAPT THIS MODEL AT HUMAN MODEL 

31 ! BECAUSE LINEAR DESCRIPTION IS NOT GOOD ENOUGH FOR MOTHER GROWTH 

32 ! MOTHER BODY WEIGHT GROWTH 

33 ! HUMAN BODY WEIGHT (0 TO 45 YEARS) 

34 ! POLYNOMIAL REGRESSION EXPRESSION WRITTEN 

35 !APRIL 10 2008, OPTIMIZED WITH DATA OF PELEKIS ET AL. 2001 

36 ! POLYNOMIAL REGRESSION EXPRESSION WRITTEN WITH 

37 !HUH AND BOLCH 2003 FOR BMI CALCULATION 

 38 

39 ! BODY WEIGHT CALCULATION. UNIT IN KG FOR GESTATIONAL PORTION 

 40 

41 WT0 = (0.0006*GYR**3 - 0.0912*GYR**2 + 4.32*GYR + 3.652) 

 42 

43 !BODY MASS INDEX CALCULATION 

 44 

45 BH = -2D-5*GYR**4+4.2D-3*GYR**3.0-0.315*GYR**2.0+9.7465*GYR+72.098 

46 !HEIGHT EQUATION FORMULATED FOR USE FROM 0 TO 70 YEARS 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-27 DRAFT—DO NOT CITE OR QUOTE 

1 BHM= (BH/100.0)!HUMAN HEIGHT IN METER (BHM) 

2 HBMI= WT0/(BHM**2.0) ! HUMAN BODY MASS INDEX (BMI) 

 3 

 4 

5 !MODIFICATION IN KG 

6 RTESTGEST= T-MATTING ! STARTING TIME FOR FETAL GROWTH 

7 TESTGEST=DIM(RTESTGEST,0.0) 

8 ! GROWTH OF FETAL TISSUE 

9 GESTATTION_FE=((4d-15*TESTGEST**4 -3d-11*TESTGEST**3 +1d-7*TESTGEST**2 -

10 8d-5*TESTGEST +0.0608)) 

11 WTFER= DIM(GESTATTION_FE,0.0) ! FETAL COMPARTMENT WEIGHT 

12 WTFE= WTFER 

 13 

14 !/////////////////////////////////////////////////////////////////////// 

15 ! FAT GROWTH EXPRESSION LINEAR DURING PREGNANCY 

16 ! FROM O'FLAHERTY_1992 

17 !/////////////////////////////////////////////////////////////////////// 

 18 

19 WT0GR= WT0*1.0e3 ! MOTHER BODY WEIGHT IN G 

 20 

21 WF0 =(-6.36D-20*WT0GR**4.0 +1.12D-14*WT0GR**3.0 & 

22 -5.8D-10*WT0GR**2.0+1.2D-5*WT0GR+5.91D-2) ! MOTHER FAT 

23 COMPARTMENT GROWTH 

 24 

25 !/////////////////////////////////////////////////////////////////////// 

26 ! WPLA PLACENTA GROWTH EXPRESSION, SINGLE EXPONENTIAL WITH OFFSET 

27 ! FROM O'FLAHERTY_1992 ! FOR EACH PUP 

28 !/////////////////////////////////////////////////////////////////////// 

29 !SAME EQUATION THEN THE FORST MODEL. BODY WEIGHT KEPT IN G 

30 !A CORRECTION FOR THE BODY WEIGHT (WTO(KG)*1000 = WTOGR) 

 31 

32 WPLA0N_HUMAN= (850*exp(-9.434*(exp(-5.23d-4*(TESTGEST))))) 

33 WPLA0R = WPLA0N_HUMAN/WT0GR 

34 WPLA0W = DIM(WPLA0R,0.0) ! PLACENTA WEIGHT 

35 WPLA0=WPLA0W 

 36 

37 !/////////////////////////////////////////////////////////////////////// 

38 ! QPLA PLACENTA GROWTH EXPRESSION, DOUBLE EXPONENTIAL WITH OFFSET 

39 ! FROM O'FLAHERTY_1992 

40 !/////////////////////////////////////////////////////////////////////// 

 41 

42 QPLAF_HUMAN= SWITCH_trans*((1d-10*TESTGEST**3.0 -5D-7*TESTGEST**2.0 

43 +0.0017*TESTGEST+1.1937)/QC) 

44 GEST_QPLAF=DIM(QPLAF_HUMAN,0.0) ! PLACENTA BLOOD FLOW RATE 

45 QPLAF =GEST_QPLAF 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-28 DRAFT—DO NOT CITE OR QUOTE 

1 ! LIVER,VOLUME (HUMAN 0 TO 70 YEARS) 

2 ! APPROACH BASED ON LUECKE (2007) 

3 WLI0= (3.59D-2 -(4.76D-7*WT0GR)+(8.50D-12*WT0GR**2.0)-(5.45D-17*WT0GR**3.0)) ! 

4 LIVER VOLUME IN GROWING HUMAN 

 5 

6 ! VARIABILITY OF REST OF THE BODY DEPENDS ON OTHER ORGAN 

7 WRE0 = (0.91-(WLIB0*WLI0+WFB0*WF0+ WPLAB0*WPLA0 + WLI0 + WF0 + 

8 WPLA0))/(1+WREB0) 

9 QREF = 1-(QFF+QLIF+QPLAF) !REST BODY BLOOD FLOW (ML/HR) 

10 QTTQF = QFF+QREF+QLIF+QPLAF ! SUM MUST EQUAL 1 

 11 

12 ! COMPARTMENT TISSUE BLOOD VOLUME (L) ========= 

13 WF = WF0 * WT0 ! ADIPOSE TISSUE 

14 WRE = WRE0 * WT0 ! REST OF THE BODY 

15 WLI = WLI0 * WT0 ! LIVER 

16 WPLA= WPLA0* WT0 ! PLACENTA 

 17 

18 ! COMPARTMENT TISSUE VOLUME (L) ========= 

19 WFB = WFB0 * WF ! ADIPOSE TISSUE 

20 WREB = WREB0 * WRE ! REST OF THE BODY 

21 WLIB = WLIB0 * WLI ! LIVER 

22 WPLAB = WPLAB0* WPLA ! PLACANTA 

 23 

24 ! TOTAL VOLUME OF COMPARTMENT (L)====== 

25 WFT = WF ! TOTAL ADIPOSE TISSUE 

26 WRET = WRE ! TOTAL REST OF THE BODY 

27 WLIT = WLI ! TOTAL LIVER TISSUE 

28 WPLAT= WPLAB ! TOTAL PLACENTA TISSUE 

 29 

30 ! CONSTANT USED IN CARDIAC OUTPUT EQUATION 

 31 

32 ! UNIT CHANGED ON JULY 14 2009 (L/HR) 

33 QC= QCC*(WT0)**0.75 

 34 

35 QF = QFF*QC ! ADIPOSE TISSUE BLOOD FLOW RATE (L/HR) 

36 QLI = QLIF*QC ! LIVER TISSUE BLOOD FLOW RATE (L/HR) 

37 QRE = QREF*QC !REST OF THE BODY BLOOD FLOW RATE (L/HR) 

38 QPLA = QPLAF*QC !PLACENTA TISSUE BLOOD FLOW RATE (L/HR) 

39 QTTQ = QF+QRE+QLI+QPLA !TOTAL FLOW RATE (L/HR) 

 40 

41 ! ========= DIFFUSIONAL PERMEABILITY FACTORS FRACTION ORGAN FLOW 

42 ========= 

43 PAF = PAFF*QF ! ADIPOSE TISSUE BLOOD FLOW RATE (L/HR) 

44 PARE = PAREF*QRE ! REST OF THE BODY BLOOD FLOW RATE (L/HR) 

45 PALI = PALIF*QLI ! LIVER TISSUE BLOOD FLOW RATE (L/HR) 

46 PAPLA = PAPLAF*QPLA ! PLACENTA TISSUE BLOOD FLOW RATE (L/HR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-29 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !************************************** 

3 ! ABSORPTION SECTION 

4 ! ORAL 

5 ! INTRAPERITONEAL 

6 ! SUBCUTANEOUS 

7 ! INTRAVENOUS 

8 !************************************** 

 9 

10 !BACKGROUND EXPOSURE 

11 !EXPOSURE FOR STEADY STATE CONSIDERATION 

12 !REPETITIVE EXPOSURE SCENARIO 

 13 

14 MSTOT_NMBCKGR = MSTOTBCKGR/322 !AMOUNT IN NMOL/G 

15 MSTTBCKGR =MSTOT_NMBCKGR *WT0 

 16 

17 DAY_EXPOSURE_BG = PULSE(DAY_LACK_BG,DAY_PERIOD_BG,DAY_FINISH_BG) 

18 WEEK_EXPOSURE_BG = 

19 PULSE(WEEK_LACK_BG,WEEK_PERIOD_BG,WEEK_FINISH_BG) 

20 MONTH_EXPOSURE_BG = 

21 PULSE(MONTH_LACK_BG,MONTH_PERIOD_BG,MONTH_FINISH_BG) 

 22 

23 MSTTCH_BG = 

24 (DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG)*MSTTBCK

25 GR 

26 MSTTFR_BG = MSTTBCKGR/CINT 

 27 

28 CYCLE_BG =DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG 

 29 

30 ! CONDITIONAL ORAL EXPOSURE (BACKGROUND EXPOSURE) 

 31 

32 IF (MSTTCH_BG.EQ.MSTTBCKGR) THEN 

33 ABSMSTT_GB= MSTTFR_BG 

34 ELSE 

35 ABSMSTT_GB = 0.0 

36 END IF 

 37 

38 CYCLETOTBG=INTEG(CYCLE_BG,0.0) 

 39 

40 !************************************** 

41 !MULTIROUTE EXPOSURE 

42 !REPETITIVE EXPOSURE SCENARIO 

43 !************************************** 

44 MSTT= MSTOT_NM * WT0 !AMOUNT IN NMOL 

45 DAY_EXPOSURE = PULSE(DAY_LACK,DAY_PERIOD,DAY_FINISH) 

46 WEEK_EXPOSURE = PULSE(WEEK_LACK,WEEK_PERIOD,WEEK_FINISH) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-30 DRAFT—DO NOT CITE OR QUOTE 

1 MONTH_EXPOSURE = PULSE(MONTH_LACK,MONTH_PERIOD,MONTH_FINISH) 

 2 

3 MSTTCH = (DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE)*MSTT 

 4 

5 MSTTFR = MSTT/CINT 

 6 

7 CYCLE = DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE 

 8 

9 SUMEXPEVENT= INTEG (CYCLE,0.0) !NUMBER OF CYCLES GENERATED DURING 

10 SIMULATION 

 11 

12 ! CONDITIONAL ORAL EXPOSURE 

13 IF (MSTTCH.EQ.MSTT) THEN 

14 ABSMSTT= MSTTFR 

15 ELSE 

16 ABSMSTT = 0.0 

17 END IF 

 18 

 19 

20 CYCLETOT=INTEG(CYCLE,0.0) 

 21 

22 ! MASS CHANGE IN THE LUMEN 

23 RMSTT= -(KST+KABS)*MST +ABSMSTT +ABSMSTT_GB ! RATE OF CHANGE 

24 (NMOL/H) 

25 MST = INTEG(RMSTT,0.0) !AMOUNT REMAINING IN DUODENUM 

26 (NMOL) 

 27 

28 ! ABSORPTION IN LYMPH CIRCULATION 

29 LYRMLUM = KABS*MST*A 

30 LYMLUM = INTEG(LYRMLUM,0.0) 

 31 

32 ! ABSORPTION IN PORTAL CIRCULATION 

33 LIRMLUM = KABS*MST*B 

34 LIMLUM = INTEG(LIRMLUM,0.0) 

 35 

 36 

37 !IV ABSORPTION SCENARIO--------- 

38 IV= DOSEIV_NM * WT0 !AMOUNT IN NMOL 

39 IVR= IV/PFUNC ! RATE FOR IV INFUSION IN BLOOD 

40 EXPIV= IVR * (1-STEP(PFUNC)) 

41 IVDOSE = integ(EXPIV,0.0) 

 42 

43 !IV LATE IN THE CYCLE 

44 !MODIFICATION JANUARY 13 2004 

45 IV_RlateR = DOSEIVNMlate*WT0 

46 IV_EXPOSURE=PULSE(IV_LACK,IV_PERIOD,IV_FINISH) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-31 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 IV_lateT = IV_EXPOSURE *IV_RlateR 

3 IV_late = IV_lateT/CINT 

 4 

5 SUMEXPEVENTIV= integ(IV_EXPOSURE,0.0) !NUMBER OF CYCLE GENERATE 

6 DURING SIMULATION 

 7 

8 !SYSTEMIC BLOOD COMPARTMENT 

9 ! MODIFICATION OCT 8 2009 

10 CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM+QPLA*CPLAB+IV_late)/(QC

11 +CLURI) ! 

12 CA = CB ! CONCENTRATION (NMOL/L) 

 13 

14 !CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM+QPLA*CPLAB+IV_late15 RAURI)/QC !(NMOL/L) 

 16 

17 !URINARY EXCRETION BY KIDNEY 

18 ! MODIFICATION OCT 8 2009 

19 RAURI = CLURI *CB 

20 AURI = INTEG(RAURI,0.0) 

 21 

22 !RAURI = CLURI * CRE 

23 !AURI = INTEG(RAURI,0.0) 

 24 

25 !UNIT CONVERSION POST SIMULATION 

26 CONSTANT MW=322 !MOLECULAR WEIGHT (NG/NMOL) 

27 CONSTANT SERBLO = 0.55 

28 CONSTANT UNITCORR = 1.0e3 

 29 

30 CBSNGKGLIADJ = CB*MW/(0.55*B_TOTLIP) !NG SERUM LIPID ADJUSTED/KG 

31 AUCBS_NGKGLIADJ=integ(CBSNGKGLIADJ,0.) 

32 CBNGKG= CB*MW !NG/KG 

33 PRCT_B = 100.0*CB/(MSTT+1E-30) !PERCENT OF ORAL DOSE IN BLOOD 

34 PRCT_BIV = 100.0*CB/(IV_RlateR+1E-30) ! PERCENT OF IV DOSE IN BLOOD 

 35 

36 !ADIPOSE COMPARMTENT 

37 !TISSUE BLOOD SUBCOMPARTMENT 

38 RAFB= QF*(CA-CFB)-PAF*(CFB-CF/PF) !(NMOL/H) 

39 AFB = INTEG(RAFB,0.0) !(NMOL) 

40 CFB = AFB/WFB !(NMOL/L) 

41 !TISSUE SUBCOMPARTMENT 

42 RAF = PAF*(CFB-CF/PF) !(NMOL/H) 

43 AF = INTEG(RAF,0.0) !(NMOL) 

44 CF = AF/WF !(NMOL/L) 

 45 

46 !UNIT CONVERSION POST SIMULATION 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-32 DRAFT—DO NOT CITE OR QUOTE 

1 CFTOTAL= (AF + AFB)/(WF + WFB) ! TOTAL CONCENTRATION IN NMOL/ML 

2 PRCT_F = 100.0*CFTOTAL/(MSTT+1E-30) !PERCENT OF ORAL DOSE IN FAT 

3 PRCT_FIV = 100.0*CFTOTAL/(IV_RlateR+1E-30) !PERCENT OF IV DOSE IN FAT 

4 CFNGKG=CFTOTAL*MW ! FAT CONCENTRATION IN NG/KG 

5 AUCF_NGKGH=integ(CFNGKG,0.) 

 6 

 7 

8 !REST OF THE BODY COMPARTMENT 

9 !TISSUE BLOOD SUBCOMPARTMENT 

10 RAREB= QRE *(CA-CREB)-PARE*(CREB-CRE/PRE) !(NMOL/H) 

11 AREB = INTEG(RAREB,0.0) !(NMOL) 

12 CREB = AREB/WREB !(NMOL/L) 

13 !TISSUE SUBCOMPARTMENT 

14 RARE = PARE*(CREB - CRE/PRE) !(NMOL/H) 

15 ARE = INTEG(RARE,0.0) !(NMOL) 

16 CRE = ARE/WRE !(NMOL/L) 

17 ARETOT = ARE +AREB 

 18 

19 !POST SIMULATION UNIT CONVERSION 

20 CRETOTAL= (ARE + AREB)/(WRE + WREB) ! TOTAL CONCENTRATION 

21 (NMOL/L) 

22 PRCT_RE = 100.0*CRETOTAL/(MSTT+1E-30) ! PERCENT OF ORAL DOSE IN REST OF 

23 BODY 

24 PRCT_REIV = 100.0*CRETOTAL/(IV_RlateR+1E-30) ![ PERCENT OF IV DOSE IN REST 

25 OF BODY 

26 CRENGKG=CRETOTAL*MW ! REST OF THE BODY CONCENTRATION 

27 (NG/KG) 

 28 

 29 

30 !LIVER COMPARTMENT 

31 !TISSUE BLOOD SUBCOMPARTMENT 

32 RALIB = QLI*(CA-CLIB)-PALI*(CLIB-CFLLIR)+LIRMLUM ! (NMOL/HR) 

33 ALIB = INTEG(RALIB,0.0) !(NMOL) 

34 CLIB = ALIB/WLIB !(NMOL/L) 

35 !TISSUE SUBCOMPARMTENT 

36 RALI = PALI*(CLIB - CFLLIR)-REXCLI ! (NMOL/HR) 

37 ALI = INTEG(RALI,0.0) !(NMOL) 

38 CLI = ALI/WLI !(NMOL/L) 

 39 

40 !FREE TCDD CONCENTRATION IN LIVER 

41 ! MODIFICATION OCTOBER 8 2009 

42 CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR)) & 

43 +((CYP1A2_1O3*CFLLIR/(KDLI2+CFLLIR)*PAS_INDUC)))-CFLLI,CFLLI0) 

44 CFLLIR=DIM(CFLLI,0.0) ! FREE TCDD CONCENTRATION IN LIVER 

45 !MODIFIED FROM: 

46 !PARAMETER (LIVER_1RMN = 1.0E-30) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-33 DRAFT—DO NOT CITE OR QUOTE 

1 ! CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR & 

2 !+LIVER_1RMN))+((CYP1A2_1O3*CFLLIR/(KDLI2 + CFLLIR & 

3 !+LIVER_1RMN)*PAS_INDUC)))-CFLLI,CFLLI0) 

4 !CFLLIR=DIM(CFLLI,0.0) 

 5 

6 ! MODIFICATION OCTOBER 8 2009 

7 CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR) !BOUND CONCENTRATION (NMOL/L) 

 8 

9 !POST SIMULATION UNIT CONVERSION 

10 CLITOTAL= (ALI + ALIB)/(WLI + WLIB) ! TOTAL CONCENTRATION (NMOL/L) 

11 PRCT_LI = 100.0*CLITOTAL/(MSTT+1E-30) ! PERCENT OF ORAL DOSE IN LIVER 

12 PRCT_LIIV = 100.0*CLITOTAL/(IV_RlateR+1E-30) ! PERCENT OF IV DOSE IN LIVER 

13 Rec_occ= CFLLIR/(KDLI+CFLLIR) 

14 CLINGKG=CLITOTAL*MW ! LIVER CONCENTRATION IN NG/KG 

15 AUCLI_NGKGH=integ(CLINGKG,0.0) 

16 CBNDLINGKG = CBNDLI*MW ! BOUND CONCENTRATION IN NG/KG 

17 AUCBNDLI_NGKGH =INTEG(CBNDLINGKG,0.0) 

 18 

19 !FRACTION INCREASE OF INDUCTION OF CYP1A2 

20 fold_ind=CYP1A2_1OUT/CYP1A2_1A2 

21 VARIATIONOFAC =(CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2 

 22 

23 !VARIABLE ELIMINATION BASED ON THE CYP1A2 

24 ! MODIFICATION OCTOBER 8 2009 

25 KBILE_LI_T = Kelv*VARIATIONOFAC! ! DOSE-DEPENDENT EXCRETION RATE 

26 CONSTANT 

 27 

28 REXCLI = KBILE_LI_T*CFLLIR*WLI ! DOSE-DEPENDENT BILLIARY EXCRETION 

29 RATE 

30 EXCLI = INTEG(REXCLI,0.0) 

 31 

32 !KBILE_LI_T =((CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2)*Kelv ! 

 33 

 34 

35 !CHEMICAL IN CYP450 (1A2) COMPARTMENT 

 36 

37 CYP1A2_1KINP = CYP1A2_1KOUT* CYP1A2_1OUTZ ! BASAL PRODCUTION RATE OF 

38 CYP1A2 SET EQUAL TO BASAL DEGREDATION RATE 

 39 

40 ! MODIFICATION OCTOBER 8 2009 

41 CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1.0 + CYP1A2_1EMAX *(CBNDLI+1.0e42 30)**HILL & 

43 /(CYP1A2_1EC50**HILL + (CBNDLI+1.0e-30)**HILL)) & 

44 - CYP1A2_1KOUT*CYP1A2_1OUT, CYP1A2_1OUTZ) 

45 !MODIFIED FROM: 

46 !PARAMETER (CYP1A2_1RMN = 1E-30) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-34 DRAFT—DO NOT CITE OR QUOTE 

1 !CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1 + CYP1A2_1EMAX *(CBND& 

2 !LI +CYP1A2_1RMN)**HILL/(CYP1A2_1EC50 + (CBNDLI + CYP1A2_1& 

3 !RMN)**HILL) +CYP1A2_1RMN) - CYP1A2_1KOUT*CYP1A2_1& 

4 !OUT, CYP1A2_1OUTZ) 

 5 

6 ! EQUATIONS INCORPORATING DELAY OF CYP1A2 PRODUCTION (NOT USED IN 

7 SIMULATIONS) 

8 CYP1A2_1RO2 = (CYP1A2_1OUT - CYP1A2_1O2)/ CYP1A2_1TAU 

9 CYP1A2_1O2 =INTEG(CYP1A2_1RO2, CYP1A2_1A1) 

 10 

11 CYP1A2_1RO3 = (CYP1A2_1O2 - CYP1A2_1O3)/ CYP1A2_1TAU 

12 CYP1A2_1O3 =INTEG(CYP1A2_1RO3, CYP1A2_1A2) 

 13 

14 !PLACENTA COMPARTMENT 

15 !TISSUE BLOOD SUBCOMPARTMENT 

16 RAPLAB= QPLA*(CA - CPLAB)-PAPLA*(CPLAB -CFLPLAR) ! NMOL/HR) 

17 APLAB = INTEG(RAPLAB,0.0) ! (NMOL) 

18 CPLAB = APLAB/(WPLAB+1E-30) ! (NMOL/ML) 

19 !TISSUE SUBCOMPARTMENT 

20 RAPLA = PAPLA*(CPLAB-CFLPLAR)-RAMPF + RAFPM ! (NMOL/HR) 

21 APLA = INTEG(RAPLA,0.0) ! (NMOL) 

22 CPLA = APLA/(WPLA+1e-30) ! (NMOL/ML) 

 23 

24 ! NEW EQUATION AUGUST 28 2009 

25 PARAMETER (PARA_ZERO = 1.0E-30) 

26 CFLPLA= IMPLC(CPLA-(CFLPLAR*PPLA +(PLABMAX*CFLPLAR/(KDPLA& 

27 +CFLPLAR+PARA_ZERO)))-CFLPLA,CFLPLA0) 

28 CFLPLAR=DIM(CFLPLA,0.0) 

 29 

30 !POST SIMULATION UNIT CONVERSION 

31 CPLATOTAL = ((APLAB+APLA)/(WPLAB+WPLA)) 

32 PRCT_PLA = (CPLATOTAL/(MSTT+1E-30))*100 

33 PRCT_PLAIV = (CPLATOTAL/(IV_RlateR+1E-30))*100 

 34 

35 !FETUS COMPARTMENT 

36 RAFETUS= RAMPF-RAFPM 

37 AFETUS=INTEG(RAFETUS,0.0) 

38 CFETUS=AFETUS/(WTFE+1.0e-30) 

39 CFETOTAL= CFETUS 

40 CFETUS_v = CFETUS/PFETUS 

 41 

42 !POST SIMULATION UNIT CONVERSION 

43 CFETUSNGKG = CFETUS*MW !(NG/KG) 

44 PRCT_FE = 100.0*CFETOTAL/(MSTT+1E-30) 

45 PRCT_FEIV = 100.0*CFETOTAL/(IV_RlateR+1E-30) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-35 DRAFT—DO NOT CITE OR QUOTE 

1 !TRANSFER OF DIOXIN FROM PLACENTA TO FETUS 

2 !FETAL EXPOSURE ONLY DURING EXPOSURE 

 3 

4 IF (T.LT.TRANSTIME_ON) THEN 

5 SWITCH_trans = 0.0 

6 ELSE 

7 SWITCH_trans = 1 

8 END IF 

 9 

10 !TRANSFER OF DIOXIN FROM PLACENTA TO FETUS 

11 ! MODIFICATION 26 SEPTEMBER 2003 

 12 

13 RAMPF = (CLPLA_FET*CPLA)*SWITCH_trans 

14 AMPF=INTEG(RAMPF,0.0) 

 15 

16 !TRANSFER OF DIOXIN FROM FETUS TO PLACENTA 

17 RAFPM = (CLPLA_FET*CFETUS_v)*SWITCH_trans! 

18 AFPM = INTEG(RAFPM,0.0) 

 19 

20 !CHECK MASS BALANCE ---------- 

21 BDOSE= IVDOSE +LYMLUM+LIMLUM 

22 BMASSE = EXCLI+AURI+AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB+AFETUS ! 

23 BDIFF = BDOSE-BMASSE 

 24 

25 !BODY BURDEN (NMOL) 

26 BODY_BURDEN = AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB 

 27 

28 !BODY BURDEN CONCENTRATION (NG/KG) 

29 BBNGKG =(AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB)*MW/WT0 

 30 

31 ! END SIMULATION COMMAND 

 32 

33 TERMT (T.GE. TimeLimit, 'Time limit has been reached.') 

 34 

35 END ! END OF THE DERIVATIVE SECTION 

36 END ! END OF THE DYNAMIC SECTION 

37 END ! END OF THE PROGRAM 

 38 

39 C.2.2.2. Input File 

40 output @clear 

41 prepare @clear T year CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

42 CBNGKG 

 43 

44 CINT = 1 %168 %100 %INTEGRATION TIME 

45 %EXPOSURE SCENARIO 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-36 DRAFT—DO NOT CITE OR QUOTE 

1 EXP_TIME_ON = 0 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

2 EXP_TIME_OFF = 401190 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

3 DAY_CYCLE = 24 %NUMBER OF HOURS BETWEEN DOSES (HOUR) 

4 BCK_TIME_ON = 401190 %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

5 (HOUR) 

6 BCK_TIME_OFF = 401190 %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

7 (HOUR) 

8 IV_LACK = 401190 

9 IV_PERIOD = 401190 

10 %GESTATION CONTROL 

11 MATTING = 393120 % BEGINNING OF MATING (HOUR) AT 45 YEARS OLD 

12 TIMELIMIT = 399840 %SIMULATION TIME LIMIT (HOUR) 

13 TRANSTIME_ON = 394632 % TRANSFER FROM MOTHER TO FETUS AT 1512 

14 HOURS GESTATION 

15 %EXPOSURE DOSE 

16 MSTOT = 9.97339283634997E-07 % NG OF TCDD PER KG OF BW 

17 MSTOTBCKGR = 0. %0.1 % ORAL BACKGROUND EXPOSURE DOSE (NG/KG) 

18 DOSEIV = 0. %10 

19 DOSEIVLATE = 0. %10 

 20 

21 % TRANFER MOTHER TO FETUS CLEARANCE 

22 CLPLA_FET = 0.001 % MOTHER TO FETUS TRANFER CLEARANCE (L/HR) 

23 

24 C.2.3. Rat Standard Model 

25 C.2.3.1. Model Code 

26 PROGRAM: 'Three Compartment PBPK Model in Rat: Standard Model (Non27 Gestation)' 

 28 

29 !Rat_Dioxin_3C June09_2clean_icf_afterKKfix_v3_ratnongest.csl 

30 !RAT_NON_GEST_ICF_F083109.CSL 

31 !RAT_NON_GEST_ICF_F100609.CSL 

32 !***************************************************** 

 33 

34 INITIAL ! INITIALIZATION OF PARAMETERS 

 35 

36 !SIMULATION PARAMETERS 

37 CONSTANT PARA_ZERO = 1d-30 

38 CONSTANT EXP_TIME_ON = 0.0 ! TIME AT WHICH EXPOSURE BEGINS 

39 (HOURS) 

40 CONSTANT EXP_TIME_OFF = 900.0 ! TIME AT WHICH EXPOSURE ENDS 

41 (HOURS) 

42 CONSTANT DAY_CYCLE = 900.0 ! NUMBER OF HOURS BETWEEN DOSES 

43 (HOURS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-37 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT BCK_TIME_ON = 0.0 ! TIME AT WHICH BACKGROUND 

2 EXPOSURE BEGINS (HOURS) 

3 CONSTANT BCK_TIME_OFF = 0.0 ! TIME AT WHICH BACKGROUND 

4 EXPOSURE ENDS (HOURS) 

 5 

6 CONSTANT MW=322 !MOLECULAR WEIGHT (NG/NMOL) 

7 CONSTANT SERBLO = 0.55 

8 CONSTANT UNITCORR = 1000 

 9 

 10 

11 !EXPOSURE DOSES 

12 CONSTANT MSTOTBCKGR = 0.0 !ORAL BACKGROUND EXPOSURE DOSE 

13 (UG/KG) 

14 CONSTANT MSTOT = 10 !ORAL EXPOSURE DOSE (UG/KG) 

15 CONSTANT MSTOTsc = 0.0 !SUBCUTANEOUS EXPOSURE DOSE (UG/KG) 

16 CONSTANT DOSEIV = 0.0 ! INJECTED DOSE (UG/KG) 

 17 

18 !ORAL DOSE 

19 MSTOT_NM = MSTOT/MW !AMOUNT IN NMOL/G 

20 MSTOT_NMBCKGR = MSTOTBCKGR/MW !AMOUNT IN NMOL/G 

 21 

22 !INTRAVENOUS DOSE 

23 DOSEIV_NM = DOSEIV/MW !AMOUNT IN NMOL/G 

 24 

25 !INITIAL GUESS OF THE FREE CONCENTRATION IN THE LIGAND 

26 (COMPARTMENT INDICATED BELOW)==== 

27 CONSTANT CFLLI0 = 0.0 !LIVER (NMOL/ML) 

 28 

29 !BINDING CAPACITY (AhR) FOR NON LINEAR BINDING (COMPARTMENT 

30 INDICATED BELOW) (NMOL/ML) === 

31 CONSTANT LIBMAX = 3.5e-4 ! LIVER (NMOL/ML), WANG ET AL. 1997 

 32 

33 ! PROTEIN AFFINITY CONSTANTS (1A2 OR AhR, COMPARTMENT INDICATED 

34 BELOW) (NMOL/ML)=== 

35 CONSTANT KDLI = 1.0e-4 ! LIVER (AhR) (NMOL/ML), WANG ET AL. 1997 

36 CONSTANT KDLI2 = 4.0e-2 !LIVER (1A2) (NMOL/ML), EMOND ET AL. 

2004 37 

 38 

39 !EXCRETION AND ABSORPTION CONSTANT [RAT] 

40 CONSTANT KST = 0.36 ! GASTRIC RATE CONSTANT (HR-1), WANG ET 

41 AL. (1997) 

42 CONSTANT KABS = 0.48 !INTESTINAL ABSORPTION CONSTANT (HR43 1), WANG ET AL. 1997 

 44 

45 !URINARY ELIMINATION CLEARANCE (ML/HR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-38 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT CLURI = 0.01 !URINARY CLEARANCE (ML/HR), EMOND ET 

2 AL. 2004 

 3 

4 !INTERSPECIES VARIABLE ELIMINATION 

5 CONSTANT KELV = 0.15 ! INTERSPECIES VARIABLE ELIMINATION 

6 CONSTANT (1/HOUR) (OPTIMIZED), EMOND ET AL. 2004 

 7 

8 ! CONSTANT TO DIVIDE THE ABSORPTION INTO LYMPHATIC AND PORTAL 

9 FRACTIONS 

10 CONSTANT A = 0.7 ! LYMPHATIC FRACTION, WANG ET AL. 1997 

 11 

12 !PARTITION COEFFICIENTS 

13 CONSTANT PF = 100 ! ADIPOSE TISSUE/BLOOD, WANG ET AL. 1997 

14 CONSTANT PRE = 1.5 ! REST OF THE BODY/BLOOD, WANG ET AL. 

1997 15 

16 CONSTANT PLI = 6.0 ! LIVER/BLOOD, WANG ET AL. 1997 

 17 

18 !PARAMETER FOR INDUCTION OF CYP 1A2 [MOUSE] === 

19 CONSTANT PAS_INDUC = 1.0 ! INCLUDE INDUCTION? (1 = YES, 0 = NO) 

20 CONSTANT CYP1A2_1OUTZ = 1.6 ! DEGRADATION CONCENTRATION 

21 CONSTANT OF 1A2 (NMOL/ML), WANG ET AL. 1997 

22 CONSTANT CYP1A2_1A1 = 1.6 ! BASAL CONCENTRATION OF 1A1 

23 (NMOL/ML), WANG ET AL. 1997 

24 CONSTANT CYP1A2_1EC50 = 0.13 ! DISSOCIATION CONSTANT TCDD25 CYP1A2 (NMOL/ML) , WANG ET AL. 1997 

26 CONSTANT CYP1A2_1A2 = 1.6 ! BASAL CONCENTRATION OF 1A2 

27 (NMOL/ML) Wang et al (1997) 

28 CONSTANT CYP1A2_1KOUT = 0.1 ! FIRST ORDER RATE OF DEGRADATION 

29 (H-1), WANG ET AL. 1997 

30 CONSTANT CYP1A2_1TAU = 0.25 ! HOLDING TIME (H), WANG ET AL. 1997 

31 CONSTANT CYP1A2_1EMAX = 600 ! MAXIMUM INDUCTION OVER BASAL 

32 EFFECT (UNITLESS), WANG ET AL. 1997 

33 CONSTANT HILL = 0.6 !HILL CONSTANT; COOPERATIVELY LIGAND 

34 BINDING EFFECT CONSTANT (UNITLESS) 

 35 

36 !TISSUE BLOOD FLOW EXPRESSED AS A FRACTION OF CARDIAC OUTPUT 

37 CONSTANT QFF = 0.069 ! ADIPOSE TISSUE BLOOD FLOW FRACTION 

38 (UNITLESS), WANG ET AL. 1997 

39 CONSTANT QLIF = 0.183 ! LIVER (UNITLESS), WANG ET AL. 1997 

 40 

41 !DIFFUSIONAL PERMEABILITY FRACTION 

42 CONSTANT PAFF = 0.0910 ! ADIPOSE (UNITLESS), WANG ET AL. 1997 

43 CONSTANT PAREF = 0.0298 ! REST OF THE BODY (UNITLESS), WANG ET 

44 AL. 1997 

45 CONSTANT PALIF = 0.35 ! LIVER (UNITLESS), WANG ET AL. 1997 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-39 DRAFT—DO NOT CITE OR QUOTE 

1 !FRACTION OF TISSUE VOLUME (UNITLESS) 

2 CONSTANT WLI0 = 0.0360 ! LIVER, WANG ET AL. 1997 

3 CONSTANT WF0 = 0.069 ! BLOOD, WANG ET AL. 1997 

 4 

5 !COMPARTMENT TISSUE BLOOD EXPRESSED AS A FRACTION OF THE TOTAL 

6 COMPARTMENT VOLUME ========= 

7 CONSTANT WFB0 = 0.050 ! ADIPOSE TISSUE, WANG ET AL. 1997 

8 CONSTANT WREB0 = 0.030 ! REST OF THE BODY, WANG ET AL. 1997 

9 CONSTANT WLIB0 = 0.266 ! LIVER , WANG ET AL. 1997 

 10 

11 !EXPOSURE SCENARIO FOR UNIQUE OR REPETITIVE WEEKLY OR MONTHLY 

12 EXPOSURE 

13 ! NUMBER OF EXPOSURES PER WEEK 

14 CONSTANT WEEK_LACK = 0.0 ! DELAY BEFORE EXPOSURE ENDS 

15 (WEEK) 

16 CONSTANT WEEK_PERIOD = 168.0 ! NUMBER OF HOURS IN THE WEEK 

17 (HOURS) 

18 CONSTANT WEEK_FINISH = 168.0 ! TIME EXPOSURE ENDS (HOURS) 

 19 

20 !NUMBER OF EXPOSURES PER MONTH 

21 CONSTANT MONTH_LACK = 0.0 ! DELAY BEFORE EXPOSURE BEGINS 

22 (MONTH) 

 23 

24 !SET FOR BACKGROUND EXPOSURE=========== 

25 !CONSTANT FOR BACKGROUND EXPOSURE=========== 

26 CONSTANT Day_LACK_BG = 0.0 ! DELAY BEFORE EXPOSURE BEGINS 

27 (HOURS) 

28 CONSTANT Day_PERIOD_BG = 24.0 ! LENGTH OF EXPOSURE (HOURS) 

 29 

30 !NUMBER OF EXPOSURES PER WEEK 

31 CONSTANT WEEK_LACK_BG = 0.0 ! DELAY BEFORE BACKGROUND 

32 EXPOSURE (WEEK) 

33 CONSTANT WEEK_PERIOD_BG = 168.0 !NUMBER OF HOURS IN THE WEEK 

34 (HOURS) 

35 CONSTANT WEEK_FINISH_BG = 168.0 ! TIME EXPOSURE ENDS (HOURS) 

 36 

37 !GROWTH CONSTANT FOR RAT 

38 !CONSTANT FOR MOTHER BODY WEIGHT GROWTH ====== 

39 CONSTANT BW_T0 = 250.0 !CHANGED FOR SIMULATION 

 40 

41 ! CONSTANT USED IN CARDIAC OUTPUT EQUATION 

42 CONSTANT QCCAR =311.4 !CONSTANT (ML/MIN/KG), WANG ET AL. 

 43 

44 ! COMPARTMENT LIPID EXPRESSED AS THE FRACTION OF TOTAL LIPID 

45 CONSTANT F_TOTLIP = 0.855 !ADIPOSE TISSUE (UNITLESS) 

46 CONSTANT B_TOTLIP = 0.0033 !BLOOD (UNITLESS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-40 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT RE_TOTLIP = 0.019 !REST OF THE BODY (UNITLESS) 

2 CONSTANT LI_TOTLIP = 0.06 !LIVER (UNITLESS) 

 3 

4 END !END OF THE INITIAL SECTION 

 5 

6 DYNAMIC !DYNAMIC SIMULATION SECTION 

 7 

8 ALGORITHM IALG = 2 ! GEAR METHOD 

9 CINTERVAL CINT = 0.1 ! COMMUNICATION INTERVAL 

10 MAXTERVAL MAXT = 1.0e+10 ! MAXIMUM CALCULATION INTERVAL 

11 MINTERVAL MINT = 1.0E-10 ! MINIMUM CALCULATION INTERVAL 

12 VARIABLE T = 0.0 

13 CONSTANT TIMELIMIT = 900.0 !SIMULATION TIME LIMIT (HOURS) 

14 CINTXY = CINT 

15 PFUNC = CINT 

 16 

17 !TIME CONVERSION 

18 DAY=T/24.0 ! TIME IN DAYS 

19 WEEK =T/168.0 ! TIME IN WEEKS 

20 MONTH =T/730.0 ! TIME IN MONTHS 

21 YEAR=T/8760.0 ! TIME IN YEARS 

 22 

 23 

24 DERIVATIVE ! PORTION OF CODE THAT SOLVES DIFFERENTIAL EQUATIONS 

 25 

26 !CHRONIC OR SUBCHRONIC EXPOSURE SCENARIO ======= 

27 !NUMBER OF EXPOSURES PER DAY 

28 DAY_LACK = EXP_TIME_ON ! DELAY BEFORE EXPOSURE BEGINS 

29 (HOURS) 

30 DAY_PERIOD = DAY_CYCLE ! EXPOSURE PERIOD (HOURS) 

31 DAY_FINISH = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

32 MONTH_PERIOD = TIMELIMIT ! EXPOSURE PERIOD (MONTHS) 

33 MONTH_FINISH = EXP_TIME_OFF ! LENGTH OF EXPOSURE (MONTHS) 

 34 

35 !NUMBER OF EXPOSURES PER DAY AND MONTH 

36 DAY_FINISH_BG = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

37 MONTH_LACK_BG = BCK_TIME_ON ! DELAY BEFORE BACKGROUND 

38 EXPOSURE BEGINS (MONTHS) 

39 MONTH_PERIOD_BG = TIMELIMIT ! BACKGROUND EXPOSURE PERIOD 

40 (MONTHS) 

41 MONTH_FINISH_BG = BCK_TIME_OFF ! LENGTH OF BACKGROUND 

42 EXPOSURE (MONTHS) 

 43 

 44 

45 B = 1-A ! FRACTION OF DIOXIN ABSORBED IN THE PORTAL 

46 FRACTION OF THE LIVER 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-41 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 ! BODY WEIGHT GROWTH EQUATION======== 

3 PARAMETER (BW_RMN = 1.0E-30) 

4 WT0= (BW_T0 *(1.0+(0.41*T)/(1402.5+T+BW_RMN))) 

 5 

6 !VARIABILITY OF REST OF THE BODY DEPEND OTHERS ORGAN 

7 WRE0 = (0.91 - (WLIB0*WLI0 + WFB0*WF0 + WLI0 + WF0))/(1.0+WREB0) !REST OF 

8 THE BODY FRACTION; UPDATED FOR EPA ASSESSMENT 

9 QREF = 1.0-(QFF+QLIF) !REST OF BODY BLOOD FLOW 

10 QTTQF = QFF+QREF+QLIF ! SUM MUST EQUAL 1 

 11 

12 !COMPARTMENT VOLUME (G) ========= 

13 WF = WF0 * WT0 ! ADIPOSE 

14 WRE = WRE0 * WT0 ! REST OF THE BODY 

15 WLI = WLI0 * WT0 ! LIVER 

 16 

17 !COMPARTMENT TISSUE BLOOD VOLUME (G) ========= 

18 WFB = WFB0 * WF ! ADIPOSE 

19 WREB = WREB0 * WRE ! REST OF THE BODY 

20 WLIB = WLIB0 * WLI ! LIVER 

 21 

22 !CARDIAC OUTPUT FOR THE GIVEN BODY WEIGHT 

23 QC= QCCAR*60.0*(WT0/UNITCORR)**0.75 

 24 

25 ! COMPARTMENT BLOOD FLOW (ML/HR) 

26 QF = QFF*QC ! ADIPOSE TISSUE BLOOD FLOW RATE 

27 QLI = QLIF*QC ! LIVER TISSUE BLOOD FLOW RATE 

28 QRE = QREF*QC ! REST OF THE BODY BLOOD FLOW RATE 

29 QTTQ = QF+QRE+QLI ! TOTAL FLOW RATE 

 30 

31 !PERMEABILITY ORGAN FLOW (ML/HR) 

32 PAF = PAFF*QF ! ADIPOSE 

33 PARE = PAREF*QRE ! REST OF THE BODY 

34 PALI = PALIF*QLI ! LIVER TISSUE 

 35 

36 !CONDITIONAL ORAL EXPOSURE (BACKGROUND EXPOSURE) 

37 !EXPOSURE + !REPETITIVE EXPOSURE SCENARIO 

38 IV= DOSEIV_NM * WT0 !AMOUNT IN NMOL 

39 MSTT= MSTOT_NM * WT0 !AMOUNT IN NMOL 

40 MSTTBCKGR =MSTOT_NMBCKGR *WT0 

 41 

42 !REPETITIVE ORAL BACKGROUND EXPOSURE SCENARIOS 

43 DAY_EXPOSURE_BG = 

44 PULSE(DAY_LACK_BG,DAY_PERIOD_BG,DAY_FINISH_BG) 

45 WEEK_EXPOSURE_BG = 

46 PULSE(WEEK_LACK_BG,WEEK_PERIOD_BG,WEEK_FINISH_BG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-42 DRAFT—DO NOT CITE OR QUOTE 

1 MONTH_EXPOSURE_BG = 

2 PULSE(MONTH_LACK_BG,MONTH_PERIOD_BG,MONTH_FINISH_BG) 

 3 

4 MSTTCH_BG = 

5 (DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG)*MSTTBCK

6 GR 

7 MSTTFR_BG = MSTTBCKGR/CINT 

 8 

9 CYCLE_BG =DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG 

 10 

11 IF (MSTTCH_BG.EQ.MSTTBCKGR) THEN 

12 ABSMSTT_GB= MSTTFR_BG 

13 ELSE 

14 ABSMSTT_GB = 0.0 

15 END IF 

 16 

 17 

18 !REPETITIVE ORAL MAIN EXPOSURE SCENARIO 

19 DAY_EXPOSURE = PULSE(DAY_LACK,DAY_PERIOD,DAY_FINISH) 

20 WEEK_EXPOSURE = PULSE(WEEK_LACK,WEEK_PERIOD,WEEK_FINISH) 

21 MONTH_EXPOSURE = PULSE(MONTH_LACK,MONTH_PERIOD,MONTH_FINISH) 

 22 

23 MSTTCH = (DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE)*MSTT 

24 CYCLE = DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE 

25 MSTTFR = MSTT/CINT 

 26 

27 SUMEXPEVENT= integ (CYCLE,0.0) !NUMBER OF CYCLE GENERATE DURING 

28 SIMULATION 

 29 

 30 

31 !CONDITIONAL ORAL EXPOSURE 

32 IF (MSTTCH.EQ.MSTT) THEN 

33 ABSMSTT= MSTTFR 

34 ELSE 

35 ABSMSTT = 0.0 

36 END IF 

 37 

38 CYCLETOT=INTEG(CYCLE,0.0) 

 39 

40 !MASS CHANGE IN THE LUMEN 

41 RMSTT = -(KST+KABS)*MST+ABSMSTT +ABSMSTT_GB ! RATE OF CHANGE 

42 (NMOL/H) 

43 MST = INTEG(RMSTT,0.0) !AMOUNT OF STAY IN DUODENUM (NMOL) 

 44 

45 !ABSORPTION IN LYMPH CIRCULATION 

46 LYRMLUM = KABS*MST*A 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-43 DRAFT—DO NOT CITE OR QUOTE 

1 LYMLUM = INTEG(LYRMLUM,0.0) 

 2 

3 !ABSORPTION IN PORTAL CIRCULATION 

4 LIRMLUM = KABS*MST*B 

5 LIMLUM = INTEG(LIRMLUM,0.0) 

 6 

7 !PERCENT OF DOSE REMAINING IN THE GI TRACT 

8 PRCT_remain_GIT = (MST/(MSTT+PARA_ZERO))*100.0 

 9 

10 !ABSORPTION of Dioxin by IV route--------- 

11 IVR= IV/PFUNC ! RATE FOR IV INFUSION IN BLOOD 

12 EXPIV= IVR * (1.0-STEP(PFUNC)) 

13 IVDOSE = integ(EXPIV,0.0) 

 14 

15 !SYSTEMIC BLOOD COMPARTMENT 

16 ! MODIFICATION ON OCTOBER 6, 2009 

17 CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM)/(QC+CLURI) ! 

18 CA = CB 

 19 

20 !URINARY EXCRETION BY KIDNEY 

21 ! MODIFICATION ON OCTOBER 6, 2009 

22 RAURI = CLURI *CB 

23 AURI = INTEG(RAURI,0.0) 

 24 

25 !CONVERSION EQUATION POST SIMULATION 

26 PRCT_B = (CB/(MSTT+PARA_ZERO))*100.0 

27 CBNGKG = CB*MW*UNITCORR ![NG/KG] 

 28 

 29 

30 CBSNGKGLIADJ= (CB*MW*UNITCORR*(1.0/B_TOTLIP)*(1.0/SERBLO))![NG of TCDD 

31 Serum/Kg OF LIPIP] 

 32 

33 !ADIPOSE TISSUE COMPARTMENT 

34 !TISSUE BLOOD SUBCOMPARTMENT 

35 RAFB = QF*(CA-CFB)-PAF*(CFB-CF/PF) !(NMOL/HR) 

36 AFB = INTEG(RAFB,0.0) !(NMOL) 

37 CFB = AFB/WFB !(NMOL/ML) 

38 !TISSUE SUBCOMPARTMENT 

39 RAF = PAF*(CFB-CF/PF) !(NMOL/HR) 

40 AF = INTEG(RAF,0.0) !(NMOL) 

41 CF = AF/WF !(NMOL/ML) 

 42 

43 !CONVERSION EQUATION POST SIMULATION 

44 CFTOTAL = (AF + AFB)/(WF + WFB) !TOTAL CONCENTRATION IN NMOL/ML 

45 PRCT_F = (CFTOTAL/(MSTT+PARA_ZERO))*100.0 ! PRCENT OF DOSE IN FAT 

46 CFNGKG = CFTOTAL*MW*UNITCORR ! CONCENTRATION [NG/KG] 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-44 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !REST OF THE BODY COMPARTMENT 

3 ! TISSUE BLOOD SUBCOMPARTMENT 

4 RAREB= QRE*(CA-CREB)-PARE*(CREB-CRE/PRE) !(NMOL/HR) 

5 AREB = INTEG(RAREB,0.0) !(NMOL) 

6 CREB = AREB/WREB !(NMOL/ML) 

7 ! TISSUE COMPARTMENT 

8 RARE = PARE*(CREB - CRE/PRE) !(NMOL/HR) 

9 ARE = INTEG(RARE,0.0) !(NMOL) 

10 CRE = ARE/WRE !(NMOL/ML) 

 11 

12 !CONVERSION EQUATION POST SIMULATION 

13 CRETOTAL= (ARE + AREB)/(WRE + WREB) ! TOTAL CONCENTRATION IN 

14 NMOL/ML 

15 PRCT_RE = (CRETOTAL/(MSTT+PARA_ZERO))*100.0 

16 CTREPGG= CRETOTAL*MW*UNITCORR !(PG/ML) 

17 AUC_REPPG = integ(CTREPGG,0.0) 

 18 

19 !LIVER COMPARTMENT 

20 !TISSUE BLOOD COMPARTMENT 

21 RALIB = QLI*(CA-CLIB)-PALI*(CLIB-CFLLIR)+LIRMLUM !(NMOL/HR) 

22 ALIB = INTeg(RALIB,0.0) !(NMOL) 

23 CLIB = ALIB/WLIB 

24 !TISSUE COMPARTMENT 

25 RALI = PALI*(CLIB-CFLLIR)-REXCLI !(NMOL/HR) 

26 ALI = integ(RALI,0.0) !(NMOL) 

27 CLI = ALI/WLI !(NMOL/ML) 

 28 

 29 

30 PARAMETER (LIVER_1RMN = 1.0E-30) 

31 CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR & 

32 +LIVER_1RMN))+((CYP1A2_1O3*CFLLIR/(KDLI2+CFLLIR & 

33 +LIVER_1RMN)*PAS_INDUC)))-CFLLIR,CFLLI0) ! FREE TCDD CONCENTRATION IN 

34 LIVER 

35 CFLLIR=DIM(CFLLI,0.0) 

 36 

37 CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR+LIVER_1RMN) !BOUND 

38 CONCENTRATION 

 39 

40 !CONVERSION EQUATION POST SIMULATION 

41 CLITOTAL= (ALI + ALIB)/(WLI + WLIB) ! TOTAL CONCENTRATION IN 

42 NMOL/ML 

43 PRCT_LI = (CLITOTAL/(MSTT+PARA_ZERO))*100.0 

44 rec_occ_AHR= (CFLLIR/(KDLI+CFLLIR+1))*100.0 ! PERCENT OF AhR 

45 OCCUPANCY 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-45 DRAFT—DO NOT CITE OR QUOTE 

1 PROT_occ_1A2= (CFLLIR/(KDLI2+CFLLIR))*100.0 ! PERCENT OF 1A2 

2 OCCUPANCY 

3 CLINGKG =(CLITOTAL*MW*UNITCORR) 

4 CBNDLINGKG = CBNDLI*MW*UNITCORR 

5 AUCLI_NGKGH=INTEG(CLINGKG,0.0) 

6 CLINGG=CLITOTAL*MW 

 7 

8 !VARIABLE ELIMINATION HALF-LIFE BASED ON THE CONCENTRATION OF 

9 CYP1A2 

10 KBILE_LI_T =((CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2)*Kelv ! INDUCED 

11 BILIARY EXCRETION RATE CONSTANT 

 12 

13 REXCLI= (KBILE_LI_T*CFLLIR*WLI) ! DOSE-DEPENDENT BILIARY EXCRETION 

14 RATE 

15 EXCLI = INTEG(REXCLI,0.0) 

 16 

17 !CHEMICAL IN CYP450 (1A2) COMPARTMENT 

18 !===PARAMETER FOR INDUCTION OF CYP1A2 

 19 

20 CYP1A2_1KINP = CYP1A2_1KOUT* CYP1A2_1OUTZ ! BASAL RATE OF CYP1A2 

21 PRODUCTION SET EQUAL TO BASAL RATE OF DEGREDATION 

 22 

 23 

24 ! MODIFICATION ON OCTOBER 6, 2009 

25 CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1.0 + CYP1A2_1EMAX *(CBNDLI+1.0e26 30)**HILL & 

27 /(CYP1A2_1EC50**HILL + (CBNDLI+1.0e-30)**HILL)) &- 

28 - CYP1A2_1KOUT*CYP1A2_1OUT, CYP1A2_1OUTZ) 

 29 

30 ! EQUATIONS INCORPORATING DELAY OF CYP1A2 PRODUCTION (NOT USED IN 

31 SIMULATIONS) 

 32 

33 CYP1A2_1RO2 = (CYP1A2_1OUT - CYP1A2_1O2)/ CYP1A2_1TAU 

34 CYP1A2_1O2 =INTEG(CYP1A2_1RO2, CYP1A2_1A1) 

35 CYP1A2_1RO3 = (CYP1A2_1O2 - CYP1A2_1O3)/ CYP1A2_1TAU 

36 CYP1A2_1O3 =INTEG(CYP1A2_1RO3, CYP1A2_1A2) 

 37 

38 ! ------------CHECK MASS BALANCE ---------- 

39 BDOSE= LYMLUM+LIMLUM+IVDOSE 

40 BMASSE = EXCLI+AURI+AFB+AF+AREB+ARE+ALIB+ALI 

41 BDIFF = BDOSE-BMASSE 

 42 

43 !---------------BODY BURDEN------------------------ 

44 BBNGKG =(((AFB+AF+AREB+ARE+ALIB+ALI)*MW)/(WT0/UNITCORR)) ! 

45 ! ------------ END OF THE SIMULATION COMMAND ---------- 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-46 DRAFT—DO NOT CITE OR QUOTE 

1 TERMT (T.GE. TimeLimit, 'Time limit has been reached.') 

 2 

3 END ! END OF THE DERIVATIVE SECTION 

4 END ! END OF THE DYNAMIC SIMULATION SECTION 

5 END ! END OF THE PROGRAM. 

6 

7 C.2.3.2. Input Files 

8 C.2.3.2.1. Cantoni et al. (1981). 

9 output @clear 

10 prepare @clear 

11 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 12 

13 %Cantoni et al. 1981 

14 %protocol: oral exposure 1 dose/week for 45 weeks; female CD-COBS rats 

15 %dose levels: 0.01, 0.1, 1 ug/kg 1 dose/week for 45 weeks 

16 %dose levels: 10, 100, 1000 ng/kg 1 dose/week for 45 weeks 

17 %dose levels equivalent to: 1.43, 14.3 143 ng/kg 7 days/week for 45 weeks 

 18 

19 MAXT = 0.01 

20 CINT = 0.1 

21 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

22 EXP_TIME_OFF = 7560 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

23 DAY_CYCLE = 168 

24 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

25 (HOUR) 

26 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

27 (HOUR) 

28 TIMELIMIT = 7584 %SIMULATION TIME LIMIT (HOUR) 

29 BW_T0 = 125 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

30 (G) 

 31 

32 %EXPOSURE DOSE SCENARIOS (UG/KG) 

33 %MSTOT = 0.01 % EXPOSURE DOSE IN UG/KG 

34 %MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

35 MSTOT = 1 % EXPOSURE DOSE IN UG/KG 

36 

37 C.2.3.2.2. Chu et al. (2007). 

38 output @clear 

39 prepare @clear 

40 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 41 

42 % Chu et al. 2007 

43 %protocol: oral exposure daily for 28 days 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-47 DRAFT—DO NOT CITE OR QUOTE 

1 %dose levels: 0.0025, 0.025, 0.250, 1.0 ug/kg every day for 28 days 

2 % dose levels = 2.5, 25, 250, 1000 ng/kg every day for 28 days 

3 MAXT = 0.01 

4 CINT = 0.1 

5 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 5 weeks after start of 

6 experiment (age = 12 weeks) 

7 EXP_TIME_OFF = 672. %TIME EXPOSURE STOP (HOUR); 30 doses, 1 every two 

8 weeks 

9 DAY_CYCLE = 24. % once every two weeks 

10 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

11 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

12 TIMELIMIT = 672. %SIMULATION LIMIT TIME (HOUR) 

13 BW_T0 = 200. % Body weight at the beginning of the simulation (g); 

14 corresponds to 12 week old female 

 15 

16 %EXPOSURE DOSE SCENARIOS (UG/KG) 

17 %MSTOT = 0.0025 % ORAL EXPOSURE DOSE (UG/KG) 

18 %MSTOT = 0.025 % ORAL EXPOSURE DOSE (UG/KG) 

19 %MSTOT = 0.250 % ORAL EXPOSURE DOSE (UG/KG) 

20 MSTOT = 1.0 % ORAL EXPOSURE DOSE (UG/KG) 

 21 

22 C.2.3.2.3. Crofton et al. (2005). 

23 output @clear 

24 prepare @clear 

25 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 26 

27 % Crofton et al. 2005 

28 %protocol: oral exposure daily for 4 days 

29 %dose levels: 0.0001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, and 10 ug/kg every day for four days 

30 %dose levels: 0.1, 3, 10, 30, 100, 300, 1000, 3000, and 10000 ng/kg every day for four days 

 31 

32 MAXT = 0.01 

33 CINT = 0.1 

34 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 5 weeks after start of 

35 experiment (age = 12 weeks) 

36 EXP_TIME_OFF = 96. %TIME EXPOSURE STOP (HOUR); 30 doses, 1 every two 

37 weeks 

38 DAY_CYCLE = 24. % once every two weeks 

39 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

40 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

41 TIMELIMIT = 96. %SIMULATION LIMIT TIME (HOUR) 

42 BW_T0 = 250 % Body weight at the beginning of the simulation (g); corresponds 

43 to 12 week old female 

 44 

45 %EXPOSURE DOSE SCENARIOS (UG/KG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-48 DRAFT—DO NOT CITE OR QUOTE 

1 MSTOT = 0.0001 % ORAL EXPOSURE DOSE (UG/KG) 

2 %MSTOT = 0.003 % ORAL EXPOSURE DOSE (UG/KG) 

3 %MSTOT = 0.01 % ORAL EXPOSURE DOSE (UG/KG) 

4 %MSTOT = 0.03 % ORAL EXPOSURE DOSE (UG/KG) 

5 %MSTOT = 0.1 % ORAL EXPOSURE DOSE (UG/KG) 

6 %MSTOT = 0.3 % ORAL EXPOSURE DOSE (UG/KG) 

7 %MSTOT = 1. % ORAL EXPOSURE DOSE (UG/KG) 

8 %MSTOT = 3. % ORAL EXPOSURE DOSE (UG/KG) 

9 MSTOT = 10. % ORAL EXPOSURE DOSE (UG/KG) 

10 

11 C.2.3.2.4. Fattore et al. (2000). 

12 output @clear 

13 prepare @clear 

14 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 15 

16 % Fattore et al. 2000 

17 %built and check in August 7 2009 

18 %protocol: oral exposure in diet for 13 weeks; SD rats 

19 %dose levels: 0.02, 0.1, 0.2, 2 ug/kg 7 days/week for 13 weeks 

20 %dose levels equivalent to: 20, 100, 200, 2000 ng/kg 7 days/week for 13 weeks 

 21 

22 MAXT = 0.01 

23 CINT = 0.1 

24 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

25 EXP_TIME_OFF = 2184 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

26 DAY_CYCLE = 24 

27 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

28 (HOUR) 

29 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

30 (HOUR) 

31 TIMELIMIT = 2184 %SIMULATION TIME LIMIT (HOUR) 

32 BW_T0 = 150 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

33 (G) 

 34 

35 %EXPOSURE DOSE SCENARIOS (UG/KG) 

36 %MSTOT = 0.02 % EXPOSURE DOSE IN UG/KG 

37 %MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

38 %MSTOT = 0.2 % EXPOSURE DOSE IN UG/KG 

39 MSTOT = 2 % EXPOSURE DOSE IN UG/KG 

40 

41 C.2.3.2.5. Hassoun et al. (2000). 

42 output @clear 

43 prepare @clear 

44 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-49 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 % Hassoun et al. 2000 

3 %protocol: oral exposure for 13 weeks; SD rats 

4 %dose levels: 0.003, 0.010, 0.022, 0.046 0.1 ug/kg 5 days/weeks for 13 weeks 

5 %dose levels equivalent to: 3, 10, 22, 46 100 ng/kg 5 days/weeks for 13 weeks 

6 %dose levels equivalent to: 2.14, 7.14, 15.7, 32.9, 71.4 ng/kg 7 days/weeks for 13 weeks 

 7 

8 MAXT = 0.01 

9 CINT = 0.1 

10 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

11 EXP_TIME_OFF = 2184. %TIME EXPOSURE STOP (HOUR) 

12 DAY_CYCLE = 24. 

13 WEEK_PERIOD = 168. 

14 WEEK_FINISH = 119. 

15 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

16 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

17 TIMELIMIT = 2184. %SIMULATION LIMIT TIME (HOUR) 

18 BW_T0 = 215. % Body weight at the beginning of the simulation (g) 

 19 

20 %EXPOSURE DOSE SCENARIOS (UG/KG) 

21 %MSTOT = 0.003 % exposure dose ug/kg 

22 %MSTOT = 0.010 % exposure dose ug/kg 

23 %MSTOT = 0.022 % exposure dose ug/kg 

24 %MSTOT = 0.046 % exposure dose ug/kg 

25 MSTOT = 0.1 % exposure dose ug/kg 

 26 

27 C.2.3.2.6. Kitchin and Woods (1979). 

28 output @clear 

29 prepare @clear 

30 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 31 

32 % Kitchin and Woods 1979 

33 %dose levels: 0.0006, 0.002, 0.004, 0.020, 0.060, 0.200, 0.600, 2.000, 5.000, 20.000 ug/kg 

34 single oral gavage 

35 % dose levels = 0.6, 2, 4, 20, 60, 200, 600, 2000, 5000, 20000 ng/kg single oral gavage with 

36 estimated 0.2 ng/kg/day background dose 

37 MAXT = 0.01 

38 CINT = 0.1 

39 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

40 EXP_TIME_OFF = 23. %TIME EXPOSURE STOP (HOUR) 

41 DAY_CYCLE = 24. % once every two weeks 

42 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

43 BCK_TIME_OFF = 72. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

44 TIMELIMIT = 72. %SIMULATION LIMIT TIME (HOUR) 

45 BW_T0 = 225. % Body weight at the beginning of the simulation (g) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-50 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 %EXPOSURE DOSE SCENARIOS (UG/KG) 

3 %MSTOT = 0.0006 % ORAL EXPOSURE DOSE (UG/KG) 

4 %MSTOT = 0.002 % ORAL EXPOSURE DOSE (UG/KG) 

5 %MSTOT = 0.004 % ORAL EXPOSURE DOSE (UG/KG) 

6 %MSTOT = 0.020 % ORAL EXPOSURE DOSE (UG/KG) 

7 %MSTOT = 0.060 % ORAL EXPOSURE DOSE (UG/KG) 

8 %MSTOT = 0.200 % ORAL EXPOSURE DOSE (UG/KG) 

9 %MSTOT = 0.600 % ORAL EXPOSURE DOSE (UG/KG) 

10 %MSTOT = 2.000 % ORAL EXPOSURE DOSE (UG/KG) 

11 %MSTOT = 5.000 % ORAL EXPOSURE DOSE (UG/KG) 

12 MSTOT = 20.000 % ORAL EXPOSURE DOSE (UG/KG) 

 13 

14 C.2.3.2.7. Kociba et al. (1976) (13 weeks). 

15 output @clear 

16 prepare @clear 

17 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 18 

19 % Kociba et al, 1976. 

20 %built and check in August 7 2009 

21 %protocol: 5 days/week exposure for 13 weeks; SD rats 

22 %dose levels: 0.001, 0.01, 0.1, 1 ug/kg 5 days/week for 13 weeks 

23 %dose levels: 1, 10, 100, 1000 ng/kg 5 days/week for 13 weeks 

24 %dose levels equivalent to: 0.714, 7.14, 71.4, 714 ng/kg/d (adj) 7 days/week for 13 weeks 

 25 

 26 

27 MAXT = 0.01 

28 CINT = 0.1 

29 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

30 EXP_TIME_OFF = 2184 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

31 WEEK_PERIOD = 168 

32 WEEK_FINISH = 119 

33 DAY_CYCLE = 24 

34 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

35 (HOUR) 

36 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

37 (HOUR) 

38 TIMELIMIT = 4368 %SIMULATION TIME LIMIT (HOUR) 

39 BW_T0 = 180 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

40 (G) 

 41 

 42 

43 %EXPOSURE DOSE SCENARIOS (UG/KG) 

44 %MSTOT = 0.001 % EXPOSURE DOSE IN UG/KG 

45 %MSTOT = 0.01 % EXPOSURE DOSE IN UG/KG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-51 DRAFT—DO NOT CITE OR QUOTE 

1 %MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

2 MSTOT = 1 % EXPOSURE DOSE IN UG/KG 

3 

4 C.2.3.2.8. Kociba et al. (1978) (female) (104 weeks). 

5 output @clear 

6 prepare @clear 

7 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 8 

9 % Kociba et al, 1978. 

10 %built and check in August 7 2009 

11 %protocol: daily dietary exposure for 104 weeks; SD rats 

12 %dose levels: 0.001, 0.01, 0.1 ug/kg 7 days/week for 104 weeks 

13 %dose levels: 1, 10, 100 ng/kg 7 days/week for 104 weeks 

 14 

15 MAXT = 0.01 

16 CINT = 0.1 

17 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

18 EXP_TIME_OFF = 17472 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

19 DAY_CYCLE = 24 

20 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

21 (HOUR) 

22 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

23 (HOUR) 

24 TIMELIMIT = 17472 %SIMULATION TIME LIMIT (HOUR) 

25 BW_T0 = 180 % BODY WEIGHT AT THE BEGINNING OF THE 

26 SIMULATION (G) 

 27 

28 %EXPOSURE DOSE SCENARIOS (UG/KG) 

29 %MSTOT = 0.001 % EXPOSURE DOSE IN UG/KG 

30 %MSTOT = 0.01 % EXPOSURE DOSE IN UG/KG 

31 MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

 32 

33 C.2.3.2.9. Kociba et al. (1978) (male) (104 weeks). 

34 output @clear 

35 prepare @clear 

36 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 37 

38 % Kociba et al, 1978. 

39 %built and check in August 7 2009 

40 %protocol: daily dietary exposure for 104 weeks; SD rats 

41 %dose levels: 0.001, 0.01, 0.1 ug/kg 7 days/week for 104 weeks 

42 %dose levels: 1, 10, 100 ng/kg 7 days/week for 104 weeks 

 43 

44 MAXT = 0.01 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-52 DRAFT—DO NOT CITE OR QUOTE 

1 CINT = 0.1 

2 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

3 EXP_TIME_OFF = 17472 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

4 DAY_CYCLE = 24 

5 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

6 (HOUR) 

7 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

8 (HOUR) 

9 TIMELIMIT = 17472 %SIMULATION TIME LIMIT (HOUR) 

10 BW_T0 = 250 % BODY WEIGHT AT THE BEGINNING OF THE 

11 SIMULATION (G) 

 12 

13 %EXPOSURE DOSE SCENARIOS (UG/KG) 

14 %MSTOT = 0.001 % EXPOSURE DOSE IN UG/KG 

15 %MSTOT = 0.01 % EXPOSURE DOSE IN UG/KG 

16 MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

17 

18 C.2.3.2.10. Latchoumycandane and Mathur. (2002). 

19 output @clear 

20 prepare @clear 

21 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 22 

23 % Latchoumycandane and Mathur, 2002. 

24 %built and check in August 7 2009 

25 %protocol: 1 time per day for 45 days oral gavage 

26 %dose levels: 0.001, 0.01, 0.1 ug/kg daily for 45 days 

27 %dose levels: 1, 10, 100 ng/kg daily for 45 days 

 28 

29 MAXT = 0.01 

30 CINT = 0.1 

31 EXP_TIME_ON = 0. % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

32 EXP_TIME_OFF = 1080 % TIME AT WHICH EXPOSURE ENDS(HOUR) 

33 DAY_CYCLE = 24 

34 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

35 (HOUR) 

36 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

37 (HOUR) 

38 TIMELIMIT = 1104 % SIMULATION TIME LIMIT (HOUR) 

39 BW_T0 = 200 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

40 (G) 

 41 

42 %EXPOSURE DOSE SCENARIOS (UG/KG) 

43 %MSTOT = 0.001 % EXPOSURE DOSE IN UG/KG 

44 %MSTOT = 0.01 % EXPOSURE DOSE IN UG/KG 

45 MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-53 DRAFT—DO NOT CITE OR QUOTE 

1 C.2.3.2.11. Li et al. (1997). 

2 output @clear 

3 prepare @clear 

4 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 5 

6 % Li et al 1997 

7 % created 1/10/10 

8 % Non-gestational rat model 

9 % dose levels: 3, 10, 30, 100, 300, 1000, 3000, 10000, 30000 nkd one dose via gavage, sacrificed 

10 24 hrs later 

 11 

12 MAXT = 0.1 

13 CINT = 0.1 

14 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

15 EXP_TIME_OFF = 24. %TIME EXPOSURE STOP (HOUR) 

16 DAY_CYCLE = 24. 

17 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

18 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

19 TIMELIMIT = 24. %SIMULATION LIMIT TIME (HOUR) 

20 BW_T0 = 56.5 % Body weight at the beginning of the simulation (g) 

 21 

22 %EXPOSURE DOSE SCENARIOS (UG/KG) 

23 MSTOT = 0.003 % ORAL EXPOSURE DOSE (UG/KG) 

24 %MSTOT = 0.01 % ORAL EXPOSURE DOSE (UG/KG) 

25 %MSTOT = 0.03 % ORAL EXPOSURE DOSE (UG/KG) 

26 %MSTOT = 0.1 % ORAL EXPOSURE DOSE (UG/KG) 

27 %MSTOT = 0.3 % ORAL EXPOSURE DOSE (UG/KG) 

28 %MSTOT = 1. % ORAL EXPOSURE DOSE (UG/KG) 

29 %MSTOT = 3. % ORAL EXPOSURE DOSE (UG/KG) 

30 %MSTOT = 10. % ORAL EXPOSURE DOSE (UG/KG) 

31 %MSTOT = 30. % ORAL EXPOSURE DOSE (UG/KG) 

 32 

33 C.2.3.2.12. Murray et al. (1979). 

34 output @clear 

35 prepare @clear 

36 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 37 

38 % Murray et al 1979 

39 %built and check in August 7 2009 

40 %protocol: dietary exposure for 3 generations (assume 120 day exposure for each) 

41 %dose levels: 0.001 0.01, 0.1 ug/kg/d 

42 %dose levels: 1, 10, 100 ng/kg/d 

 43 

44 MAXT = 0.01 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-54 DRAFT—DO NOT CITE OR QUOTE 

1 CINT = 0.1 

2 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

3 EXP_TIME_OFF = 2880 %TIME AT WHICH EXPOSURE ENDS (HOUR); 

4 CORRESPONDS TO 120 DAYS OF EXPOSURE 

5 DAY_CYCLE = 24. 

6 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

7 (HOUR) 

8 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

9 (HOUR) 

10 TIMELIMIT = 2880 %SIMULATION TIME LIMIT (HOUR) 

11 BW_T0 = 4.5 % BODY WEIGHT AT THE BEGINNING OF THE 

12 SIMULATION (G) 

 13 

14 %EXPOSURE DOSE SCENARIOS (UG/KG) 

15 %MSTOT = 0.001 % ORAL EXPOSURE DOSE IN UG/KG 

16 %MSTOT = 0.01 % ORAL EXPOSURE DOSE IN UG/KG 

17 MSTOT = 0.1 % ORAL EXPOSURE DOSE IN UG/KG 

18 

19 C.2.3.2.13. NTP (1982) (female) (chronic). 

20 output @clear 

21 prepare @clear 

22 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 23 

24 % NTP 1982 

25 %built and check in August 7 2009 

26 %protocol: twice weekly gavage for 104 weeks + 3 week observation period 

27 %dose levels: 0.005, 0.025, 0.25 ug/kg biweekly for 104 weeks + 3 week observation period 

28 %dose levels: 5, 25, 250 ng/kg biweekly for 104 weeks + 3 week observation period 

29 %dose levels equivalent to: 1.43, 7.14, 71.4 ng/kg/d (adj) 

 30 

31 MAXT = 0.01 

32 CINT = 0.1 

33 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

34 EXP_TIME_OFF = 17472 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

35 DAY_CYCLE = 84 

36 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

37 (HOUR) 

38 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

39 (HOUR) 

40 TIMELIMIT = 17976 %SIMULATION TIME LIMIT (HOUR) 

41 BW_T0 = 250 % BODY WEIGHT AT THE BEGINNING OF THE 

42 SIMULATION (G) 

 43 

44 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 45 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-55 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 %MSTOT = 0.005 % EXPOSURE DOSE IN UG/KG 

3 %MSTOT = 0.025 % EXPOSURE DOSE IN UG/KG 

4 MSTOT = 0.25 % EXPOSURE DOSE IN UG/KG 

5 

6 C.2.3.2.14. NTP (1982) (male) (chronic). 

7 output @clear 

8 prepare @clear 

9 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 10 

11 % NTP 1982 

12 %built and check in August 7 2009 

13 %protocol: twice weekly gavage for 104 weeks + 3 week observation period 

14 %dose levels: 0.005, 0.025, 0.25 ug/kg biweekly for 104 weeks + 3 week observation period 

15 %dose levels: 5, 25, 250 ng/kg biweekly for 104 weeks + 3 week observation period 

16 %dose levels equivalent to: 1.43, 7.14, 71.4 ng/kg/d (adj) 

 17 

18 MAXT = 0.01 

19 CINT = 0.1 

20 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

21 EXP_TIME_OFF = 17472 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

22 DAY_CYCLE = 84 

23 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

24 (HOUR) 

25 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

26 (HOUR) 

27 TIMELIMIT = 17976 %SIMULATION TIME LIMIT (HOUR) 

28 BW_T0 = 350 % BODY WEIGHT AT THE BEGINNING OF THE 

29 SIMULATION (G) 

 30 

31 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 32 

 33 

34 %MSTOT = 0.005 % EXPOSURE DOSE IN UG/KG 

35 %MSTOT = 0.025 % EXPOSURE DOSE IN UG/KG 

36 MSTOT = 0.25 % EXPOSURE DOSE IN UG/KG 

37 

38 C.2.3.2.15. NTP (2006) 31 weeks. 

39 output @clear 

40 prepare @clear 

41 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 42 

43 % NTP 2006 

44 %built and check in August 7 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-56 DRAFT—DO NOT CITE OR QUOTE 

1 %protocol: oral exposure for 31 weeks; SD rats 

2 %Rat_Dioxin_3C June09_2clean.csl 

3 %RAT_NON_GEST_ICF_F083109.CSL (now 09-11-09) 

4 %dose levels: 0.003, 0.010, 0.022, 0.046, 0.1 ug/kg 5 days/week for 31 weeks 

5 %dose levels equivalent to: 3, 10, 22, 46, 100 ng/kg 5 days/week for 31 weeks 

6 %dose levels equivalent to: 2.14, 7.14, 15.7, 32.9, 71.4 ng/kg 7 days/week for 31 weeks 

 7 

8 MAXT = 0.01 

9 CINT = 0.1 

10 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

11 EXP_TIME_OFF = 17640 %TIME EXPOSURE STOP (HOUR) 

12 DAY_CYCLE = 24 

13 WEEK_PERIOD = 168 

14 WEEK_FINISH = 119 

15 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

16 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

17 TIMELIMIT = 5208 %SIMULATION LIMIT TIME (HOUR) 

18 BW_T0 = 215 % Body weight at the beginning of the simulation (g) 

 19 

20 %EXPOSURE DOSE SCENARIOS (UG/KG) 

21 %MSTOT = 0.003 % exposure dose ug/kg 

22 %MSTOT = 0.010 % exposure dose ug/kg 

23 %MSTOT = 0.022 % exposure dose ug/kg 

24 %MSTOT = 0.046 % exposure dose ug/kg 

25 MSTOT = 0.1 % exposure dose ug/kg 

 26 

27 C.2.3.2.16. NTP (2006) 53 weeks. 

28 output @clear 

29 prepare @clear 

30 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 31 

32 % NTP 2006 

33 %built and check in August 7 2009 

34 %protocol: oral exposure for 53 weeks; SD rats 

35 %Rat_Dioxin_3C June09_2clean.csl 

36 %RAT_NON_GEST_ICF_F083109.CSL (now 09-11-09) 

37 %dose levels: 0.003, 0.010, 0.022, 0.046, 0.1 ug/kg 5 days/week for 53 weeks 

38 %dose levels equivalent to: 3, 10, 22, 46, 100 ng/kg 5 days/week for 53 weeks 

39 %dose levels equivalent to: 2.14, 7.14, 15.7, 32.9, 71.4 ng/kg 7 days/week for 53 weeks 

 40 

41 MAXT = 0.01 

42 CINT = 0.1 

43 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

44 EXP_TIME_OFF = 17640 %TIME EXPOSURE STOP (HOUR) 

45 DAY_CYCLE = 24 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-57 DRAFT—DO NOT CITE OR QUOTE 

1 WEEK_PERIOD = 168 

2 WEEK_FINISH = 119 

3 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

4 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

5 TIMELIMIT = 8904 %SIMULATION LIMIT TIME (HOUR) 

6 BW_T0 = 215 % Body weight at the beginning of the simulation (g) 

 7 

8 %EXPOSURE DOSE SCENARIOS (UG/KG) 

9 %MSTOT = 0.003 % exposure dose ug/kg 

10 %MSTOT = 0.010 % exposure dose ug/kg 

11 %MSTOT = 0.022 % exposure dose ug/kg 

12 %MSTOT = 0.046 % exposure dose ug/kg 

13 MSTOT = 0.1 % exposure dose ug/kg 

 14 

15 C.2.3.2.17. NTP (2006) 2 year. 

16 output @clear 

17 prepare @clear 

18 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 19 

20 % NTP 2006 

21 %built and check in August 7 2009 

22 %protocol: oral exposure for 105 weeks; SD rats 

23 %dose levels: 0.003, 0.010, 0.022, 0.046, 0.1 ug/kg 5 days/week for 105 weeks 

24 %dose levels equivalent to: 3, 10, 22, 46, 100 ng/kg 5 days/week for 105 weeks 

25 %dose levels equivalent to: 2.14, 7.14, 15.7, 32.9, 71.4 ng/kg 7 days/week for 105 weeks 

 26 

27 MAXT = 0.01 

28 CINT = 0.1 

29 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

30 EXP_TIME_OFF = 17640 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

31 DAY_CYCLE = 24 

32 WEEK_PERIOD = 168 

33 WEEK_FINISH = 119 

34 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

35 (HOUR) 

36 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

37 (HOUR) 

38 TIMELIMIT = 17640 %SIMULATION TIME LIMIT (HOUR) 

39 BW_T0 = 215 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

40 (G) 

 41 

42 %EXPOSURE DOSE SCENARIOS (UG/KG) 

43 %MSTOT = 0.003 % EXPOSURE DOSE IN UG/KG 

44 %MSTOT = 0.010 % EXPOSURE DOSE IN UG/KG 

45 %MSTOT = 0.022 % EXPOSURE DOSE IN UG/KG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-58 DRAFT—DO NOT CITE OR QUOTE 

1 %MSTOT = 0.046 % EXPOSURE DOSE IN UG/KG 

2 MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

3 

4 C.2.3.2.18. Sewall et al. (1995). 

5 output @clear 

6 prepare @clear 

7 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 8 

9 % Sewall et al. 1995 

10 %Rat_Dioxin_3C June09_2clean.csl 

11 %RAT_NON_GEST_ICF_F083109.CSL (now 09-11-09) 

12 %protocol: gavage every 2 weeks for 30 weeks 

13 %dose levels: 0.049, 0.1498, 0.49, and 1.75 ug/kg every two weeks 

14 %dose levels: 3.5, 10.7, 35, and 125 ng/kg/d or 49, 149.8, 490, and 1750 ng/kg every two weeks 

 15 

16 MAXT = 0.01 

17 CINT = 0.1 

18 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 5 weeks after start of 

19 experiment (age = 12 weeks) 

20 EXP_TIME_OFF = 5030 %TIME EXPOSURE STOP (HOUR); 30 doses, 1 every two 

21 weeks 

22 DAY_CYCLE = 336. % once every two weeks 

23 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

24 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

25 TIMELIMIT = 5040 %SIMULATION LIMIT TIME (HOUR) 

26 BW_T0 = 250 % Body weight at the beginning of the simulation (g); corresponds 

27 to 12 week old female 

 28 

29 %EXPOSURE DOSE SCENARIOS (UG/KG) 

30 MSTOT = 0.049 % ORAL EXPOSURE DOSE (UG/KG) 

31 %MSTOT = 0.1498 % ORAL EXPOSURE DOSE (UG/KG) 

32 %MSTOT = 0.49 % ORAL EXPOSURE DOSE (UG/KG) 

33 %MSTOT = 1.75 % ORAL EXPOSURE DOSE (UG/KG) 

34 

35 C.2.3.2.19. Shi et al. (2007), adult portion. 

36 output @clear 

37 prepare @clear 

38 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 39 

40 % Shi et al 2007 

41 %built and check in August 7 2009 

42 %protocol: gavage once per week for 322 days 

43 %dose levels: 0.001, 0.005, 0.05 and 0.2 ug TCDD:kg body weight by gavage once per week 

44 %dose levels: 1, 5, 50 and 200 ng/kg ng TCDD:kg body weight by gavage once per week 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-59 DRAFT—DO NOT CITE OR QUOTE 

1 % dose equivalent adjusted 0.143, 0.714, 7.14 and 28.6 ng/kg/d 

 2 

3 MAXT = 0.0001 

4 CINT = 0.1 

5 EXP_TIME_ON = 504. % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

6 EXP_TIME_OFF = 7728 %TIME AT WHICH EXPOSURE ENDS (HOUR); 

7 CORRESPONDS TO 322 DAYS OF EXPOSURE 

8 DAY_CYCLE = 168. 

9 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE 

10 BEGINS (HOUR) 

11 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

12 (HOUR) 

13 TIMELIMIT = 7728 %SIMULATION TIME LIMIT (HOUR) 

14 BW_T0 = 4.5 % BODY WEIGHT AT THE BEGINNING OF THE 

15 SIMULATION (G) 

 16 

17 %EXPOSURE DOSE SCENARIOS (UG/KG) 

18 %MSTOT = 0.001 % ORAL EXPOSURE DOSE IN UG/KG 

19 %MSTOT = 0.005 % ORAL EXPOSURE DOSE IN UG/KG 

20 %MSTOT = 0.05 % ORAL EXPOSURE DOSE IN UG/KG 

21 MSTOT = 0.2 % ORAL EXPOSURE DOSE IN UG/KG 

22 

23 C.2.3.2.20. Van Birgelen et al. (1995). 

24 output @clear 

25 prepare @clear 

26 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 27 

28 % Van Birgelen et al. (1995) 

29 %protocol: daily dietary exposure for 13 weeks 

30 %dose levels: 0.0135, 0.0264, 0.0469, 0.320, 1.024 ug/kg every day for 13 weeks 

31 % dose levels = 13.5, 26.4, 46.9, 320, 1024 ng/kg every day for 13 weeks 

32 MAXT = 0.01 

33 CINT = 0.1 

34 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

35 EXP_TIME_OFF = 2184. %TIME EXPOSURE STOP (HOUR) 

36 DAY_CYCLE = 24. % once every two weeks 

37 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

38 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

39 TIMELIMIT = 2184. %SIMULATION LIMIT TIME (HOUR) 

40 BW_T0 = 150. % Body weight at the beginning of the simulation (g) 

 41 

42 %EXPOSURE DOSE SCENARIOS (UG/KG) 

43 %MSTOT = 0.0135 % ORAL EXPOSURE DOSE (UG/KG) 

44 %MSTOT = 0.0264 % ORAL EXPOSURE DOSE (UG/KG) 

45 %MSTOT = 0.0469 % ORAL EXPOSURE DOSE (UG/KG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-60 DRAFT—DO NOT CITE OR QUOTE 

1 %MSTOT = 0.320 % ORAL EXPOSURE DOSE (UG/KG) 

2 MSTOT = 1.024 % ORAL EXPOSURE DOSE (UG/KG) 

3 

4 C.2.3.2.21. Vanden Heuvel et al. (1994). 

5 output @clear 

6 prepare @clear 

7 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 8 

9 % Vanden Heuvel et al., 1994. 

10 %built and check in August 7 2009 

11 %protocol: single gavage 

12 %Rat_Dioxin_3C June09_2clean.csl 

13 %RAT_NON_GEST_ICF_F083109.CSL (now 09-11-09) 

14 %dose levels: 0.00005, 0.0001, 0.001, 0.010, 0.1, 1, 10 ug/kg/d + 4 days post treatment 

15 %dose levels equivalent to: 0.05, 0.1, 1, 10, 100, 1000, 10000 ng/kg/d + 4 days post treatment 

 16 

17 MAXT = 0.01 

18 CINT = 0.01 

19 EXP_TIME_ON = 0. %delay before begin exposure (HOUR) 

20 EXP_TIME_OFF = 120 %TIME EXPOSURE STOP (HOUR) 

21 DAY_CYCLE = 120 

22 BCK_TIME_ON = 0. %DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

23 BCK_TIME_OFF = 0. %TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

24 TIMELIMIT = 120 %SIMULATION LIMIT TIME (HOUR) 

25 BW_T0 = 250 % Body weight at the beginning of the simulation (g) 

 26 

27 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 28 

29 %MSTOT = 0.00005 % exposure dose ug/kg 

30 %MSTOT = 0.0001 % exposure dose ug/kg 

31 %MSTOT = 0.001 % exposure dose ug/kg 

32 %MSTOT = 0.01 % exposure dose ug/kg 

33 %MSTOT = 0.1 % exposure dose ug/kg 

34 MSTOT = 1 % exposure dose ug/kg 

35 %MSTOT = 10 % exposure dose ug/kg 

36 

37 C.2.4. Rat Gestational Model 

38 C.2.4.1. Model Code 

39 PROGRAM: 'Three Compartment PBPK Model for TCDD in Rat (Gestation)' 

40 ! Parameters were change May 16, 2002 

41 ! Come from {8MAI_CHR_PRE-EXP_GD} 

42 ! Come from {12_Mouse_GD}file 

43 !******************************************** 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-61 DRAFT—DO NOT CITE OR QUOTE 

1 !{{IMPORTANT-IMPORTANT-IMPORTANT-IMPORTANT}} 

2 ! REDUCTION OF MOTHER AND FETUS COMPARTMENT 

3 ! 2M_R_TCDD_JULY2002 ////(JULY 18,2002)//// 

4 !TCDD_RED_4Species_2003_4 ////(APR 8 ,2003)//// 

5 !TCDD_RED_4Species_2003_9 ////(APR 17 ,2003)//// 

6 !TCDD_RED_4Species_2003_12 ////(APR 17 ,2003)//// 

7 !***************************************************** 

8 !APRIL 18 2003 

9 !TCDD_4C_4SP_2003 ////(APR 18 ,2003)//// 

10 ! was ''Gest 4 species 1.csl'' but update July 2009 

 11 

12 !DevTCDD4Species_ICF_afterKKfix_v3_ratgest.csl 

13 !RAT_GESTATIONAL_ICF_F083109.csl 

14 !RAT_GESTATIONAL_ICF_F100609.csl 

15 !***************************************************** 

 16 

17 !Legend/Legend/Legend/Legend/Legend/Legend/Legend/Legend/ 

18 !Legend for this PBPK model 

19 !Mating: control the tenure of exchange between fetus and 

20 !Mother and also control imitated tissue growth 

21 !Control: WTFE, WFO, WPLA0, QPLAF,WT0 

22 !(for rat, mouse, human, and monkey) 

23 !Control transfer from mother to fetus or fetus to mother by TRANSTIME_ON 

24 !SWITCH_trans = 0 NO TRANSFER 

25 !SWITCH_trans = 1 TRANSFER OCCURS 

26 !Gest_off = 1 

27 !Gest_on= 0.0 

28 ! These switches are also controlled by mating parameters 

 29 

30 INITIAL ! 

 31 

32 !SIMULATION PARAMETERS ==== 

33 CONSTANT PARA_ZERO = 1E-30 

34 CONSTANT EXP_TIME_ON = 0.0 ! TIME AT WHICH EXPOSURE BEGINS 

35 (HOURS) 

36 CONSTANT EXP_TIME_OFF = 530 ! TIME AT WHICH EXPOSURE ENDS (HOURS) 

37 CONSTANT DAY_CYCLE = 24.0 ! NUMBER OF HOURS BETWEEN DOSES 

38 (HOURS) 

39 CONSTANT BCK_TIME_ON = 0.0 ! TIME AT WHICH BACKGROUND EXPOSURE 

40 BEGINS (HOURS) 

41 CONSTANT BCK_TIME_OFF = 0.0 ! TIME AT WHICH BACKGROUND EXPOSURE 

42 ENDS (HOURS) 

43 CONSTANT TRANSTIME_ON = 144.0 !CONTROL TRANSFER FROM MOTHER TO 

44 FETUS AT GESTATIONAL DAY 6 

 45 

46 !UNIT CONVERSION 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-62 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT MW=322 ! MOLECULAR WEIGHT (NG/NMOL) 

2 CONSTANT SERBLO = 0.55 

3 CONSTANT UNITCORR = 1000 

 4 

 5 

6 !INTRAVENOUS SEQUENCE 

7 constant IV_LACK = 0.0 

8 constant IV_PERIOD = 0.0 

 9 

10 !PREGNANCY PARAMETER ==== 

11 CONSTANT MATTING = 0.0 !BEGINNING OF MATING (HOUR) 

12 CONSTANT N_FETUS = 10.0 !NUMBER OF FETUS PRESENT 

 13 

14 !CONSTANT EXPOSURE CONTROL =========== 

15 !ACUTE, SUBCHRONIC, CHRONIC EXPOSURE ===== 

16 !OR BACKGROUND EXPOSURE (IN THIS CASE 3 TIMES A DAY)=== 

17 CONSTANT MSTOTBCKGR = 0.0 ! ORAL BACKGROUND EXPOSURE DOSE 

18 (UG/KG) 

19 CONSTANT MSTOT = 0.0 ! ORAL EXPOSURE DOSE (UG/KG) 

 20 

21 !ORAL ABSORPTION 

22 MSTOT_NM = MSTOT/MW ! CONVERTS THE DOSE TO NMOL/G 

 23 

24 !INTRAVENOUS ABSORPTION 

25 CONSTANT DOSEIV = 0.0 ! INJECTED DOSE (UG/KG) 

26 DOSEIV_NM = DOSEIV/MW ! CONVERTS THE INJECTED DOSE TO NMOL/G 

27 CONSTANT DOSEIVLATE = 0.0 ! INJECTED DOSE LATE (UG/KG) 

28 DOSEIVNMlate = DOSEIVLATE/MW !AMOUNT IN NMOL/G 

 29 

30 !INITIAL GUESS OF THE FREE CONCENTRATION IN THE LIGAND 

31 (COMPARTMENT INDICATED BELOW)==== 

32 CONSTANT CFLLI0 = 0.0 !LIVER (NMOL/ML) 

33 CONSTANT CFLPLA0 = 0.0 !PLACENTA (NMOL/ML) 

 34 

35 !BINDING CAPACITY (AhR) FOR NON LINEAR BINDING (COMPARTMENT 

36 INDICATED BELOW) (NMOL/ML) === 

37 CONSTANT LIBMAX = 3.5E-4 ! LIVER (NMOL/ML), WANG ET AL. 1997 

38 CONSTANT PLABMAX = 2.0E-4 !TEMPORARY PARAMETER 

 39 

40 ! PROTEIN AFFINITY CONSTANTS (1A2 OR AhR, COMPARTMENT INDICATED 

41 BELOW) (NMOL/ML)=== 

42 CONSTANT KDLI = 1.0E-4 !LIVER (AhR) (NMOL/ML), WANG ET AL. 1997 

43 CONSTANT KDLI2 = 4.0E-2 !LIVER (1A2) (NMOL/ML), EMOND ET AL. 2004 

44 CONSTANT KDPLA = 1.0E-4 !TEMPORARY PARAMETER; ASSUME IDENTICAL 

45 TO KDLI (AhR) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-63 DRAFT—DO NOT CITE OR QUOTE 

1 !EXCRETION AND ABSORPTION CONSTANT 

2 CONSTANT KST = 0.36 ! GASTRIC RATE CONSTANT (HR-1), WANG ET AL. 

1997 3 

4 CONSTANT KABS = 0.48 !INTESTINAL ABSORPTION CONSTANT (HR-1) ), 

5 WANG ET AL. 1997 

 6 

7 ! ELIMINATION CONSTANTS 

8 CONSTANT CLURI = 0.01 ! URINARY CLEARANCE (ML/HR), EMOND ET AL. 

2004 9 

 10 

11 !INTERSPECIES ELIMINATION VARIABLE 

12 CONSTANT kelv = 0.15 ! INTERSPECIES VARIABLE ELIMINATION 

13 CONSTANT (1/HOUR) 

 14 

15 ! CONSTANT TO DIVIDE THE ABSORPTION INTO LYMPHATIC AND PORTAL 

16 FRACTIONS 

17 CONSTANT A = 0.7 ! LYMPHATIC FRACTION, WANG ET AL. 1997 

 18 

19 !PARTITION COEFFICIENTS 

20 CONSTANT PF = 100 ! ADIPOSE TISSUE/BLOOD, WANG ET AL. 1997 

21 CONSTANT PRE = 1.5 ! REST OF THE BODY/BLOOD, WANG ET AL. 1997 

22 CONSTANT PLI = 6.0 ! LIVER/BLOOD, WANG ET AL. 1997 

23 CONSTANT PPLA = 1.5 ! TEMPORARY PARAMETER NOT CONFIGURED, 

24 WANG ET AL. 1997 

 25 

26 !PARAMETER FOR INDUCTION OF CYP 1A2, WANG ET AL. 1997 

27 CONSTANT PAS_INDUC = 1.0 ! INCLUDE INDUCTION? (1 = YES, 0 = NO) 

28 CONSTANT CYP1A2_1OUTZ = 1.6 ! DEGRADATION CONCENTRATION 

29 CONSTANT OF 1A2 (NMOL/ML) 

30 CONSTANT CYP1A2_1A1 = 1.6 ! BASAL CONCENTRATION OF 1A1 (NMOL/ML) 

31 CONSTANT CYP1A2_1EC50 = 0.13 ! DISSOCIATION CONSTANT TCDD-CYP1A2 

32 (NMOL/ML) 

33 CONSTANT CYP1A2_1A2 = 1.6 !BASAL CONCENTRATION OF 1A2 (NMOL/ML) 

34 CONSTANT CYP1A2_1KOUT = 0.1 ! FIRST ORDER RATE OF DEGRADATION (H-1) 

35 CONSTANT CYP1A2_1TAU = 0.25 !HOLDING TIME (H) 

36 CONSTANT CYP1A2_1EMAX = 600 ! MAXIMUM INDUCTION OVER BASAL 

37 EFFECT (UNITLESS) 

38 CONSTANT HILL = 0.6 !HILL CONSTANT; COOPERATIVELY LIGAND 

39 BINDING EFFECT CONSTANT (UNITLESS) 

 40 

41 !DIFFUSIONAL PERMEABILITY FRACTION 

42 CONSTANT PAFF = 0.0910 !ADIPOSE (UNITLESS), WANG ET AL. 1997 

43 CONSTANT PAREF = 0.0298 !REST OF THE BODY (UNITLESS), WANG ET AL. 

1997 44 

45 CONSTANT PALIF = 0.3500 !LIVER (UNITLESS), WANG ET AL. 1997 

46 CONSTANT PAPLAF = 0.3 !TEMPORARY PARAMETER NOT CONFIGURED 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-64 DRAFT—DO NOT CITE OR QUOTE 

1 

2 !FRACTION OF TISSUE WEIGHT ========= 

3 CONSTANT WLI0 = 0.0360 !LIVER, WANG ET AL. 1997 

 4 

5 !TISSUE BLOOD FLOW EXPRESSED AS A FRACTION OF CARDIAC OUTPUT 

6 CONSTANT QFF = 0.069 ! ADIPOSE TISSUE BLOOD FLOW FRACTION 

7 (UNITLESS), WANG ET AL. 1997 

8 CONSTANT QLIF = 0.183 !LIVER (UNITLESS), WANG ET AL. 1997 

 9 

10 !COMPARTMENT TISSUE BLOOD EXPRESSED AS A FRACTION OF THE TOTAL 

11 COMPARTMENT VOLUME 

12 CONSTANT WFB0 = 0.050 !ADIPOSE TISSUE, WANG ET AL. 1997 

13 CONSTANT WREB0 = 0.030 !REST OF THE BODY, WANG ET AL. 1997 

14 CONSTANT WLIB0 = 0.266 !LIVER, WANG ET AL. 1997 

15 CONSTANT WPLAB0 = 0.500 !TEMPORARY PARAMETER NOT CONFIGURED 

 16 

17 !EXPOSURE SCENARIO FOR UNIQUE OR REPETITIVE WEEKLY OR MONTHLY 

18 EXPOSURE 

19 !NUMBER OF EXPOSURES PER WEEK 

20 CONSTANT WEEK_LACK = 0.0 !DELAY BEFORE EXPOSURE ENDS (WEEK) 

21 CONSTANT WEEK_PERIOD = 168 ! NUMBER OF HOURS IN THE WEEK (HOURS) 

22 CONSTANT WEEK_FINISH = 168 ! TIME EXPOSURE ENDS (HOURS) 

 23 

24 !NUMBER OF EXPOSURES PER MONTH 

25 CONSTANT MONTH_LACK = 0.0 !DELAY BEFORE EXPOSURE BEGINS 

26 (MONTHS) 

 27 

28 !CONSTANT FOR BACKGROUND EXPOSURE=========== 

29 CONSTANT Day_LACK_BG = 0.0 !DELAY BEFORE EXPOSURE BEGINS (HOURS) 

30 CONSTANT Day_PERIOD_BG = 24 !LENGTH OF EXPOSURE (HOURS) 

 31 

32 !NUMBER OF EXPOSURES PER WEEK 

33 CONSTANT WEEK_LACK_BG = 0.0 !DELAY BEFORE BACKGROUD EXPOSURE 

34 BEGINS (WEEKS) 

35 CONSTANT WEEK_PERIOD_BG = 168 !NUMBER OF HOURS IN THE WEEK 

36 (HOURS) 

37 CONSTANT WEEK_FINISH_BG = 168 !TIME EXPOSURE ENDS (HOURS) 

 38 

39 !INITIAL BODY WEIGHT 

40 CONSTANT BW_T0 = 250 ! WANG ET AL. 1997 

41 CONSTANT RATIO_RATF_MOUSEF = 1.0 !RATIO OF FETUS MOUSE/RAT AT 

42 GESTATIONAL DAY 22 

 43 

44 ! COMPARTMENT LIPID EXPRESSED AS THE FRACTION OF TOTAL LIPID, POULIN 

45 ET AL 2002 

46 CONSTANT F_TOTLIP = 0.855 ! ADIPOSE TISSUE (UNITLESS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-65 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT B_TOTLIP = 0.0023 ! BLOOD (UNITLESS) 

2 CONSTANT RE_TOTLIP = 0.019 ! REST OF THE BODY (UNITLESS) 

3 CONSTANT LI_TOTLIP = 0.060 ! LIVER (UNITLESS) 

4 CONSTANT PLA_TOTLIP = 0.019 

5 CONSTANT FETUS_TOTLIP = 0.019 

 6 

7 END ! END OF THE INITIAL SECTION 

 8 

9 DYNAMIC ! DYNAMIC SIMULATION SECTION 

10 ALGORITHM IALG = 2 ! GEAR METHOD 

11 CINTERVAL CINT = 0.1 ! COMMUNICATION INTERVAL 

12 MAXTERVAL MAXT = 1.0e+10 ! MAXIMUM CALCULATION INTERVAL 

13 MINTERVAL MINT = 1.0E-10 ! MINIMUM CALCULATION INTERVAL 

14 VARIABLE T = 0.0 

15 CONSTANT TIMELIMIT = 100 !SIMULATION LIMIT TIME (HOURS) 

16 CINTXY = CINT 

17 PFUNC = CINT 

 18 

19 !TIME CONVERSION 

20 DAY = T/24 ! TIME IN DAYS 

21 WEEK = T/168 ! TIME IN WEEKS 

22 MONTH = T/730 ! TIME IN MONTHS 

23 YEAR = T/8760 ! TIME IN YEARS 

 24 

25 DERIVATIVE ! PORTION OF CODE THAT SOLVES DIFFERENTIAL EQUATIONS 

 26 

27 !CHRONIC OR SUBCHRONIC EXPOSURE SCENARIO ======= 

28 !NUMBER OF EXPOSURES PER DAY 

29 DAY_LACK = EXP_TIME_ON ! DELAY BEFORE EXPOSURE BEGINS (HOURS) 

30 DAY_PERIOD = DAY_CYCLE ! EXPOSURE PERIOD (HOURS) 

31 DAY_FINISH = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

32 MONTH_PERIOD = TIMELIMIT ! EXPOSURE PERIOD (MONTHS) 

33 MONTH_FINISH = EXP_TIME_OFF ! LENGTH OF EXPOSURE (MONTHS) 

 34 

35 !NUMBER OF EXPOSURES PER DAY AND MONTH 

36 DAY_FINISH_BG = CINTXY 

37 MONTH_LACK_BG = BCK_TIME_ON !DELAY BEFORE BACKGROUD EXPOSURE 

38 BEGINS (MONTHS) 

39 MONTH_PERIOD_BG = TIMELIMIT !BACKGROUND EXPOSURE (MONTHS) 

40 MONTH_FINISH_BG = BCK_TIME_OFF !LENGTH OF BACKGROUND EXPOSURE 

41 (MONTHS) 

 42 

43 !INTRAVENOUS LATE 

44 IV_FINISH = CINTXY 

45 B = 1-A ! FRACTION OF DIOXIN ABSORBED IN THE PORTAL FRACTION OF THE 

46 LIVER 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-66 DRAFT—DO NOT CITE OR QUOTE 

 1 

 2 

3 !FETUS,VOLUME,FETUS,VOLUME,FETUS,VOLUME,FETUS,VOLUME,FETUS,VOLUM

4 E,FETUS,VOLUME 

5 ! FROM OFLAHERTY_1992 

 6 

7 RTESTGEST= T-MATTING 

8 TESTGEST=DIM(RTESTGEST,0.0) 

 9 

10 WTFER_RODENT= (2.3d-3*EXP(1.49d-2*(TESTGEST))+1.3d-2)*Gest_on 

11 WTFER = (WTFER_RODENT*RATIO_RATF_MOUSEF*N_FETUS) 

12 WTFE = DIM(WTFER,0.0) 

 13 

14 ! 

15 FAT,VOLUME,FAT,VOLUME,FAT,VOLUME,FAT,VOLUME,FAT,VOLUME,FAT,VOLU

16 ME,FAT,VOLUME 

17 ! FAT GROWTH EXPRESSION LINEAR DURING PREGNANCY 

18 ! FROM O'FLAHERTY_1992 

 19 

20 WF0= (((9.66d-5*(TESTGEST))*gest_on)+0.069) 

 21 

22 ! PLACENTA,VOLUME, PLACENTA,VOLUME, PLACENTA,VOLUME, 

23 PLACENTA,VOLUME 

24 ! WPLA PLACENTA GROWTH EXPRESSION, SINGLE EXPONENTIAL WITH OFFSET 

25 ! FROM O'FLAHERTY_1992 ! FOR EACH PUP 

 26 

27 WPLA0N_RODENT = (0.6/(1+(5d+3*EXP(-0.0225*(TESTGEST)))))*N_FETUS 

28 WPLA0R = (WPLA0N_RODENT/WT0)*Gest_on 

29 WPLA0 = DIM(WPLA0R,0.0) 

 30 

31 ! PLACENTA,FLOW RATE, PLACENTA,FLOW RATE, PLACENTA,FLOW RATE, 

32 PLACENTA,FLOW RATE 

33 ! QPLA PLACENTA GROWTH EXPRESSION, DOUBLE EXPONENTIAL WITH OFFSET 

34 ! FROM O'FLAHERTY_1992 

 35 

36 QPLARF = (1.67d-7 *exp(9.6d-3*(TESTGEST)) & 

37 +1.6d-3*exp(7.9d-3*(TESTGEST))+0.0)*Gest_on*SWITCH_trans 

38 QPLAF=DIM(QPLARF,0.0) !FRACTION OF FLOW RATE IN PLACENTA 

 39 

40 ! GESTATION CONTROL 

41 IF (T.LT.MATTING) THEN 

42 Gest_off = 1.0 

43 Gest_on= 0.0 

44 ELSE 

45 Gest_off = 0.0 

46 Gest_on = 1.0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-67 DRAFT—DO NOT CITE OR QUOTE 

1 END IF 

 2 

3 ! MOTHER BODY WEIGHT GROWTH EQUATION======== 

4 ! MODIFICATION TO ADAPT THIS MODEL AT HUMAN MODEL 

5 ! BECAUSE LINEAR DESCRIPTION IS NOT GOOD ENOUGH FOR MOTHER GROWTH 

6 ! MOTHER BODY WEIGHT GROWTH 

 7 

8 PARAMETER (BW_RMN = 1.0E-30) 

9 WT0= BW_T0 *(1+(0.41*T)/(1402.5+T+BW_RMN)) 

 10 

11 ! VARIABILITY OF REST OF THE BODY DEPENDS ON OTHER ORGANS 

12 WRE0 = (0.91 - (WLIB0*WLI0 + WFB0*WF0 +WPLAB0*WPLA0 + WLI0 + WF0 + 

13 WPLA0))/(1+WREB0) ! REST OF THE BODY FRACTION; UPDATED FOR EPA 

14 ASSESSMENT 

15 QREF = 1-(QFF+QLIF+QPLAF) !REST OF BODY BLOOD FLOW RATE (ML/HR) 

16 QTTQF = QFF+QREF+QLIF+QPLAF ! SUM MUST EQUAL 1 

 17 

18 ! COMPARTMENT VOLUME (ML OR G) ========= 

19 WF = WF0 * WT0 ! ADIPOSE TISSUE 

20 WRE = WRE0 * WT0 ! REST OF THE BODY 

21 WLI = WLI0 * WT0 ! LIVER 

22 WPLA= WPLA0* WT0 ! PLACENTA 

 23 

24 ! COMPARTMENT TISSUE BLOOD (ML OR G) ========= 

25 WFB = WFB0 * WF ! ADIPOSE TISSUE 

26 WREB = WREB0 * WRE ! REST OF THE BODY 

27 WLIB = WLIB0 * WLI ! LIVER 

28 WPLAB = WPLAB0* WPLA ! PLACANTA 

 29 

30 ! CARDIAC OUTPUT FOR THE GIVEN BODY WEIGHT (ML/H) ========= 

31 !QC= QCCAR*60*(WT0/1000.0)**0.75 

32 CONSTANT QCC=18684.0 ! EQUIVALENT TO 311.4 * 60 

33 QC= QCC*(WT0/UNITCORR)**0.75 

 34 

35 !COMPARTMENT BLOOD FLOW RATE (ML/HR) 

36 QF = QFF*QC !ADIPOSE TISSUE BLOOD FLOW RATE 

37 QLI = QLIF*QC !LIVER TISSUE BLOOD FLOW RATE 

38 QRE = QREF*QC !REST OF THE BODY BLOOD FLOW RATE 

39 QPLA = QPLAF*QC !PLACENTA TISSUE BLOOD FLOW RATE 

40 QTTQ = QF+QRE+QLI+QPLA !TOTAL FLOW RATE 

 41 

42 !PERMEABILITY ORGAN FLOW (ML/HR)========= 

43 PAF = PAFF*QF ! ADIPOSE TISSUE 

44 PARE = PAREF*QRE ! REST OF THE BODY 

45 PALI = PALIF*QLI ! LIVER TISSUE 

46 PAPLA = PAPLAF*QPLA ! PLACENTA 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-68 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !************************************** 

3 ! ABSORPTION SECTION 

4 ! ORAL 

5 ! INTRAPERITONEAL 

6 ! INTRAVENOUS 

7 !************************************** 

 8 

9 !REPETITIVE ORAL BACKGROUND EXPOSURE SCENARIO 

 10 

11 MSTOT_NMBCKGR = MSTOTBCKGR/MW ! CONVERTS THE BACKGROUND DOSE 

12 TO NMOL/G 

13 MSTTBCKGR =MSTOT_NMBCKGR *WT0 

 14 

15 DAY_EXPOSURE_BG = PULSE(DAY_LACK_BG,DAY_PERIOD_BG,DAY_FINISH_BG) 

16 WEEK_EXPOSURE_BG = 

17 PULSE(WEEK_LACK_BG,WEEK_PERIOD_BG,WEEK_FINISH_BG) 

18 MONTH_EXPOSURE_BG = 

19 PULSE(MONTH_LACK_BG,MONTH_PERIOD_BG,MONTH_FINISH_BG) 

 20 

21 MSTTCH_BG = 

22 (DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG)*MSTTBCK

23 GR 

24 MSTTFR_BG = MSTTBCKGR/CINT 

 25 

26 CYCLE_BG =DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG 

 27 

28 ! CONDITIONAL ORAL EXPOSURE (BACKGROUND EXPOSURE) 

 29 

30 IF (MSTTCH_BG.EQ.MSTTBCKGR) THEN 

31 ABSMSTT_GB= MSTTFR_BG 

32 ELSE 

33 ABSMSTT_GB = 0.0 

34 END IF 

 35 

36 CYCLETOTBG=INTEG(CYCLE_BG,0.0) 

 37 

38 !REPETITIVE ORAL EXPOSURE SCENARIO 

 39 

40 MSTT= MSTOT_NM * WT0 !AMOUNT IN NMOL 

 41 

42 DAY_EXPOSURE = PULSE(DAY_LACK,DAY_PERIOD,DAY_FINISH) 

43 WEEK_EXPOSURE = PULSE(WEEK_LACK,WEEK_PERIOD,WEEK_FINISH) 

44 MONTH_EXPOSURE = PULSE(MONTH_LACK,MONTH_PERIOD,MONTH_FINISH) 

 45 

46 MSTTCH = (DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE)*MSTT 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-69 DRAFT—DO NOT CITE OR QUOTE 

1 MSTTFR = MSTT/CINT 

 2 

3 CYCLE = DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE 

4 SUMEXPEVENT= INTEG (CYCLE,0.0) !NUMBER OF CYCLE GENERATE DURING 

5 SIMULATION 

 6 

7 ! CONDITIONAL ORAL EXPOSURE 

8 IF (MSTTCH.EQ.MSTT) THEN 

9 ABSMSTT= MSTTFR 

10 ELSE 

11 ABSMSTT = 0.0 

12 END IF 

 13 

 14 

15 CYCLETOT=INTEG(CYCLE,0.0) 

 16 

17 ! MASS CHANGE IN THE LUMEN 

18 RMSTT= -(KST+KABS)*MST +ABSMSTT +ABSMSTT_GB ! RATE OF CHANGE 

19 (NMOL/H) 

20 MST = INTEG(RMSTT,0.0) !AMOUNT REMAINING IN DUODENUM 

21 (NMOL) 

 22 

23 ! ABSORPTION IN LYMPH CIRCULATION 

24 LYRMLUM = KABS*MST*A 

25 LYMLUM = INTEG(LYRMLUM,0.0) 

 26 

27 ! ABSORPTION IN PORTAL CIRCULATION 

28 LIRMLUM = KABS*MST*B 

29 LIMLUM = INTEG(LIRMLUM,0.0) 

 30 

 31 

32 ! -----IV EXPOSURE --------- 

 33 

34 IV= DOSEIV_NM * WT0 !AMOUNT IN NMOL 

35 IVR= IV/PFUNC ! RATE FOR IV INFUSION IN BLOOD 

36 EXPIV= IVR * (1.0-STEP(PFUNC)) 

37 IVDOSE = integ(EXPIV,0.0) 

 38 

39 !------IV LATE IN THE CYCLE 

40 ! MODIFICATION ON January 13 2004 

41 IV_RlateR = DOSEIVNMlate*WT0 

42 IV_EXPOSURE=PULSE(IV_LACK,IV_PERIOD,IV_FINISH) 

 43 

44 IV_lateT = IV_EXPOSURE *IV_RlateR 

45 IV_late = IV_lateT/CINT 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-70 DRAFT—DO NOT CITE OR QUOTE 

1 SUMEXPEVENTIV= integ (IV_EXPOSURE,0.0) !NUMBER OF CYCLE GENERATE 

2 DURING SIMULATION 

 3 

4 !SYSTEMIC CONCENTRATION OF TCDD 

 5 

6 ! MODIFICATION ON OCTOBER 6, 2009 

7 CB= 

8 (QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM+QPLA*CPLAB+IV_late)/(QC+CL

9 URI) ! 

10 CA = CB ! CONCENTRATION (NMOL/ML) 

 11 

 12 

13 !URINARY EXCRETION BY KIDNEY 

14 ! MODIFICATION ON OCTOBER 6, 2009 

15 RAURI = CLURI *CB 

16 AURI = INTEG(RAURI,0.0) 

 17 

 18 

 19 

20 !UNIT CONVERSION POST SIMULATION 

21 CBSNGKGLIADJ=(CB*MW*UNITCORR*(1.0/B_TOTLIP)*(1.0/SERBLO))![NG of TCDD 

22 Serum/Kg OF LIPIP] 

23 AUCBS_NGKGLIADJ=integ(CBSNGKGLIADJ,0.0) 

 24 

25 PRCT_B = (CB/(MSTT+1E-30))*100.0 !PERCENT OF ORAL DOSE IN BLOOD 

26 PRCT_BIV = (CB/(IV_RlateR+1E-30))*100.0 ! PERCENT OF IV DOSE IN BLOOD 

27 CBNGKG= CB*MW*UNITCORR 

 28 

 29 

30 !ADIPOSE COMPARTMENT 

31 !TISSUE BLOOD COMPARTMENT 

32 RAFB= QF*(CA-CFB)-PAF*(CFB-CF/PF) !(NMOL/H) 

33 AFB = INTEG(RAFB,0.0) !(NMOL) 

34 CFB = AFB/WFB !(NMOL/ML) 

35 !TISSUE COMPARTMENT 

36 RAF = PAF*(CFB-CF/PF) !(NMOL/H) 

37 AF = INTEG(RAF,0.0) !(NMOL) 

38 CF = AF/WF !(NM/ML) 

 39 

40 !UNIT CONVERSION POST SIMULATION 

41 CFTOTAL= (AF + AFB)/(WF + WFB) ! TOTAL CONCENTRATION IN NMOL/ML 

42 CFTFREE = CFB + CF !TOTAL FREE CONCENTRATION IN FAT (NM/ML) 

43 PRCT_F = (CFTOTAL/(MSTT+1E-30))*100.0 ! PERCENT OF ORAL DOSE IN FAT 

44 PRCT_FIV = (CFTOTAL/(IV_RlateR+1E-30))*100.0 ! PERCENT OF IV DOSE IN FAT 

45 CFNGKG=CFTOTAL*MW*UNITCORR ! FAT CONCENTRATION NG/KG 

46 AUCF_NGKGH=integ(CFNGKG,0.0) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-71 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !REST OF THE BODY COMPARTMENT 

3 RAREB= QRE *(CA-CREB)-PARE*(CREB-CRE/PRE) !(NMOL/H) 

4 AREB = INTEG(RAREB,0.0) !(NMOL) 

5 CREB = AREB/WREB !(NMOL/H) 

6 !TISSUE COMPARTMENT 

7 RARE = PARE*(CREB - CRE/PRE) !(NMOL/H) 

8 ARE = INTEG(RARE,0.0) !(NMOL) 

9 CRE = ARE/WRE !(NMOL/ML) 

 10 

11 !UNIT CONVERSION POST SIMULATION 

12 CRETOTAL= (ARE + AREB)/(WRE + WREB) ! TOTAL CONCENTRATION IN 

13 NMOL/ML 

14 PRCT_RE = (CRETOTAL/(MSTT+1E-30))*100.0 ! PERCENT OF ORAL DOSE IN REST 

15 OF THE BODY 

16 PRCT_REIV = (CRETOTAL/(IV_RlateR+1E-30))*100.0 !PERCENT OF IV DOSE IN 

17 REST OF THE BODY 

18 CRENGKG=CRETOTAL*MW*UNITCORR ! REST OF THE BODY CONCENTRATION 

19 IN NG/KG 

 20 

 21 

22 !LIVER COMPARTMENT 

23 !TISSUE BLOOD COMPARTMENT 

24 RALIB = QLI*(CA-CLIB)-PALI*(CLIB-CFLLIR)+LIRMLUM ! 

25 ALIB = INTEG(RALIB,0.0) !(NMOL) 

26 CLIB = ALIB/WLIB !(NMOL/ML) 

27 !TISSUE COMPARTMENT 

28 RALI = PALI*(CLIB - CFLLIR)-REXCLI ! (NMOL/HR) 

29 ALI = INTEG(RALI,0.0) !(NMOL) 

30 CLI = ALI/WLI !(NMOL/ML) 

 31 

32 !FREE TCDD CONCENTRATION IN LIVER COMPARTMENT 

33 PARAMETER (LIVER_1RMN = 1.0E-30) 

34 CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR & 

35 +LIVER_1RMN))+((CYP1A2_1O3*CFLLIR/(KDLI2 + CFLLIR & 

36 +LIVER_1RMN)*PAS_INDUC)))-CFLLI,CFLLI0) 

37 CFLLIR=DIM(CFLLI,0.0) ! FREE CONCENTRATION IN LIVER 

 38 

39 CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR+LIVER_1RMN) !BOUND 

40 CONCENTRATION 

 41 

42 !VARIABLE ELIMINATION BASED ON THE CYP1A2 

43 KBILE_LI_T =((CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2)*Kelv ! INDUCED 

44 BILIARY EXCRETION RATE CONSTANT IN LIVER 

45 REXCLI = KBILE_LI_T*CFLLIR*WLI ! DOSE-DEPENDENT BILIARY EXCRETION 

46 RATE 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-72 DRAFT—DO NOT CITE OR QUOTE 

1 EXCLI = INTEG(REXCLI,0.0) 

 2 

3 !UNIT CONVERSION POST SIMULATION 

4 CLITOTAL= (ALI + ALIB)/(WLI + WLIB) ! TOTAL CONCENTRATION IN NMOL/ML 

5 PRCT_LI = (CLITOTAL/(MSTT+1E-30))*100 

6 PRCT_LIIV = (CLITOTAL/(IV_RlateR+1E-30))*100.0 

7 Rec_occ= CFLLIR/(KDLI+CFLLIR) 

8 CLINGKG=CLITOTAL*MW*UNITCORR ! LIVER CONCENTRATION NG/KG 

9 AUCLI_NGKGH=INTEG(CLINGKG,0.0) 

10 CBNDLINGKG = CBNDLI*MW*UNITCORR 

11 AUCBNDLI_NGKGH =INTEG(CBNDLINGKG,0.0) 

 12 

 13 

14 !CHEMICAL IN CYP450 (1A2) COMPARTMENT 

15 CYP1A2_1KINP = CYP1A2_1KOUT* CYP1A2_1OUTZ 

 16 

 17 

18 ! MODIFICATION ON OCTOBER 6, 2009 

19 CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1.0 + CYP1A2_1EMAX *(CBNDLI+1.0e20 30)**HILL & 

21 /(CYP1A2_1EC50**HILL + (CBNDLI+1.0e-30)**HILL)) & 

22 - CYP1A2_1KOUT*CYP1A2_1OUT, CYP1A2_1OUTZ) 

 23 

24 ! EQUATIONS INCORPORATING DELAY OF CYP1A2 PRODUCTION (NOT USED IN 

25 SIMULATIONS) 

 26 

27 CYP1A2_1RO2 = (CYP1A2_1OUT - CYP1A2_1O2)/ CYP1A2_1TAU 

28 CYP1A2_1O2 =INTEG(CYP1A2_1RO2, CYP1A2_1A1) 

 29 

30 CYP1A2_1RO3 = (CYP1A2_1O2 - CYP1A2_1O3)/ CYP1A2_1TAU 

31 CYP1A2_1O3 =INTEG(CYP1A2_1RO3, CYP1A2_1A2) 

 32 

33 ! TRANSFER OF DIOXIN FROM PLACENTA TO FETUS 

34 ! FETAL EXPOSURE ONLY DURING EXPOSURE 

 35 

36 IF (T.LT.TRANSTIME_ON) THEN 

37 SWITCH_trans = 0.0 

38 ELSE 

39 SWITCH_trans = 1.0 

40 END IF 

 41 

42 !TRANSFER OF DIOXIN FROM PLACENTA TO FETUS 

43 ! MODIFICATION 26 SEPTEMBER 2003 

 44 

45 CONSTANT PFETUS= 4.0 ! 

46 CONSTANT CLPLA_FET = 0.17 ! 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-73 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 RAMPF = (CLPLA_FET*CPLA) *SWITCH_trans 

3 AMPF=INTEG(RAMPF,0.0) 

 4 

5 !TRANSFER OF DIOXIN FROM FETUS TO PLACENTA 

6 RAFPM = (CLPLA_FET*CFETUS_v)*SWITCH_trans ! 

7 AFPM = INTEG(RAFPM,0.0) 

 8 

9 ! TCDD IN PLACENTA (MOTHER) COMPARTMENT 

10 RAPLAB= QPLA*(CA - CPLAB)-PAPLA*(CPLAB -CFLPLAR) ! NMOL/H) 

11 APLAB = INTEG(RAPLAB,0.0) ! (NMOL) 

12 CPLAB = APLAB/(WPLAB+1E-30) ! (NMOL/ML) 

13 RAPLA = PAPLA*(CPLAB-CFLPLAR)-RAMPF + RAFPM ! (NMOL/H) 

14 APLA = INTEG(RAPLA,0.0) ! (NMOL) 

15 CPLA = APLA/(WPLA+1e-30) ! (NMOL/ML) 

 16 

 17 

18 PARAMETER (PARA_ZERO = 1.0E-30) 

19 CFLPLA= IMPLC(CPLA-(CFLPLAR*PPLA +(PLABMAX*CFLPLAR/(KDPLA& 

20 +CFLPLAR+PARA_ZERO)))-CFLPLA,CFLPLA0) 

21 CFLPLAR=DIM(CFLPLA,0.0) 

 22 

23 !UNIT CONVERSION POST SIMULATION 

24 CPLATOTAL= (APLA + APLAB)/((WPLA + WPLAB)+1e-30)! TOTAL 

25 CONCENTRATION IN NMOL/ML 

26 PRCT_PLA = (CPLATOTAL/(MSTT+1E-30))*100 

27 PRCT_PLAIV = (CPLATOTAL/(IV_RlateR+1E-30))*100 

 28 

 29 

30 !FETUS COMPARTMENT 

31 RAFETUS= RAMPF-RAFPM 

32 AFETUS=INTEG(RAFETUS,0.0) 

33 CFETUS=AFETUS/(WTFE+1E-30) 

34 CFETOTAL= CFETUS 

35 CFETUS_v = CFETUS/PFETUS 

 36 

37 ! UNIT CONVERSION POST SIMULATION 

38 CFETUSNGKG = CFETUS*MW*UNITCORR !(NG/KG) 

39 AUC_FENGKGH = INTEG(CFETUSNGKG,0.0) 

40 PRCT_FE = (CFETOTAL/(MSTT+1E-30))*100 

41 PRCT_FEIV = (CFETOTAL/(IV_RlateR+1E-30))*100 

 42 

 43 

44 ! ------------CONTROL MASS BALANCE ---------- 

45 BDOSE= IVDOSE +LYMLUM+LIMLUM 

46 BMASSE = EXCLI+AURI+AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB+AFETUS 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-74 DRAFT—DO NOT CITE OR QUOTE 

1 BDIFF = BDOSE-BMASSE 

 2 

3 !BODY BURDEN (NG) 

4 BODY_BURDEN = AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB ! 

5 BBFETUSNG = AFETUS*MW*UNITCORR ! UNIT (NG) 

6 ! BODY BURDEN IN TERMS OF CONCENTRATION (NG/KG) 

7 BBNGKG 

8 =(((AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB)/WT0)*MW*UNITCORR) ! 

9 AUC_BBNGKGH=INTEG(BBNGKG,0.0) 

 10 

 11 

12 ! ------------COMMAND OF THE END OF SIMULATION ---------- 

13 TERMT (T.GE. TimeLimit, 'Time limit has been reached.') 

14 END ! END OF THE DERIVATIVE SECTION 

15 END ! END OF THE DYNAMIC SECTION 

16 END ! END OF THE PROGRAM 

17 

18 C.2.4.2. Input Files 

19 C.2.4.2.1. Bell et al. (2007). 

20 output @clear 

21 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

22 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

23 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 24 

25 %output @nciout=1 T BBFETUSNG %AJS turned off 9/21/09 

 26 

27 %Bell et al.2007 (rat species) 

28 %protocol: exposure daily dose in diet for 12 weeks followed by a two week mating time and 21 

29 day gestation period 

30 %DevTCDD4Species.csl 

31 %RAT_GESTATIONAL_ICF_F083109.csl (now 09-11-09) 

32 %dose levels: 0.0024, 0.008, 0.046 ug/kg/d with 0.00003 ug/kg/d background 

33 %dose levels: 2.4, 8, 46 ng/kg/d with 0.03 ng/kg/day background 

 34 

35 %EXPOSURES SCENARIOS 

36 MAXT =.1 

37 CINT = 0.1 % 

38 EXP_TIME_ON = 0 % delay before begin exposure (HOUR) 

39 EXP_TIME_OFF = 2856 % TIME EXPOSURE STOP (HOUR) 12 weeks exposure + 2 

40 weeks for mating + 21 days gestation with exposure 

41 DAY_CYCLE = 24 

42 BCK_TIME_ON = 0. % DELAY BEFORE BACKGROUND EXPOSURE (HOUR) 

43 BCK_TIME_OFF = 2856. % TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

44 IV_LACK = 505. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-75 DRAFT—DO NOT CITE OR QUOTE 

1 IV_PERIOD = 505. 

2 TIMELIMIT = 2856 % SIMULATION LIMIT TIME (HOUR) 

3 BW_T0 = 85 

4 MATTING = 2352 % BEGINNING MATTING (HOUR) 

5 TRANSTIME_ON = 2496 % SHOULD BE MATTING TIME + 6 DAYS(144 HOURS) 

6 N_FETUS = 10 

 7 

8 %EXPOSURE DOSE SCENARIOS (UG/KG) 

9 %MSTOT = 0.00243 % ORAL EXPOSURE DOSE (UG/KG) 

10 

11 %MSTOT = 0.008 % ORAL EXPOSURE DOSE (UG/KG) 

 12 

13 MSTOT = 0.0461 % ORAL EXPOSURE DOSE (UG/KG) 

14 

15 C.2.4.2.2. Hojo et al. (2002). 

16 %TO BE USED AFTER THE 

17 %clear variable 

18 output @clear 

19 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

20 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

21 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

22 %Hojo et al. 2002 

23 %protocol: Single oral dose at GD8 

24 %dose levels: 0.02 0.06, and 0.18 ug/kg at GD8 

25 %dose levels: 20, 60, 180 ng/kg at GD8 

26 % author provided the body weight for each group at the beginning of gestation (g) 

27 %20 ng/kg BW = 275g 

28 %60 ng/kg BW = 262g 

29 %180 ng/kg BW = 278g 

 30 

31 %EXPOSURES SCENARIOS 

32 MAXT=0.1 

33 CINT =0.1 % 

34 EXP_TIME_ON = 192 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

35 EXP_TIME_OFF = 505 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

36 DAY_CYCLE = 505 

37 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

38 (HOUR) 

39 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

40 (HOUR) 

41 IV_LACK = 505 

42 IV_PERIOD = 505 

43 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

44 % BW_T0 = 190 

45 MATTING = 0. % BEGINNING OF MATING (HOUR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-76 DRAFT—DO NOT CITE OR QUOTE 

1 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

2 N_FETUS = 10 

 3 

4 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 5 

6 %MSTOT = 0.02 % ORAL EXPOSURE DOSE IN UG/KG 

7 %BW_T0 = 275 % AT 20 NG/KG, BW = 271g 

 8 

9 %MSTOT = 0.06 % ORAL EXPOSURE DOSE IN UG/KG 

10 %BW_T0 = 262 % AT 60 NG/KG, BW = 275g 

 11 

12 MSTOT = 0.18 % ORAL EXPOSURE DOSE IN UG/KG 

13 BW_T0 = 278 % AT 180 NG/KG, BW = 262g 

14 

15 C.2.4.2.3. Ikeda et al. (2005). 

16 %clear variable 

17 output @clear 

18 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

19 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

20 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 21 

22 %Ikeda et al. 2005 (rat species) 

23 %protocol: loading dose of 400 ng/kg followed by weekly maintenance doses of 80 ng/kg for 6 

24 weeks, 

25 %dose levels: 0.4 ug/kg/day followed by weekly 0.08 ug/kg/day 

26 %dose levels: 400 ng/kg/day followed by weekly 80 ng/kg/day 

 27 

28 %EXPOSURES SCENARIOS 

29 MAXT =.1 

30 CINT = 0.1 % 

31 EXP_TIME_ON = 0 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

32 EXP_TIME_OFF = 1008 % TIME AT WHICH EXPOSURE ENDS (HOUR); PRE33 MATING (2 WEEKS) + MATING (1 WEEK) + GESTATION (3 WEEKS) 

34 DAY_CYCLE = 168 % WEEKLY CYCLE 

35 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

36 (HOUR) 

37 BCK_TIME_OFF = 167. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

38 (HOUR) 

39 IV_LACK = 505. 

40 IV_PERIOD = 505. 

41 TIMELIMIT = 1008 % SIMULATION TIME LIMIT (HOUR) 

42 BW_T0 = 250 

43 MATTING = 504 % BEGINNING OF MATING (HOUR) 

44 TRANSTIME_ON = 648 % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

45 N_FETUS = 10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-77 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 %EXPOSURE DOSE SCENARIOS (UG/KG) 

3 MSTOT = 0.08 % ORAL EXPOSURE DOSE IN UG/KG 

4 MSTOTBCKGR = 0.32 % BACKGROUND EXPOSURE IN UG/KG 

5 

6 C.2.4.2.4. Kattainen et al. (2001). 

7 %clear variable 

8 output @clear 

9 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

10 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

11 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 12 

13 %Kattainen et al. 2001 

14 %protocol: Single gavage at GD15 

15 %dose levels: 0.03 0.1, 0.3, 1 ug/kg at GD15 

16 %dose levels: 30, 100 300, 1000 ng/kg at GD15 

 17 

 18 

 19 

20 MAXT=0.1 

21 CINT =0.1 

 22 

23 %EXPOSURES SCENARIOS 

24 EXP_TIME_ON = 336 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

25 EXP_TIME_OFF = 340 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

26 DAY_CYCLE = 505 

27 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE 

28 BEGINS (HOUR) 

29 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

30 (HOUR) 

31 IV_LACK = 505 

32 IV_PERIOD = 505 

33 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

34 BW_T0 = 190 

35 MATTING = 0. % BEGINNING OF MATING (HOUR) 

36 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 

37 HOURS) 

38 N_FETUS = 10 

 39 

40 %EXPOSURE DOSE SCENARIOS (UG/KG) 

41 %MSTOT = 0.03 % ORAL EXPOSURE DOSE IN UG/KG 

42 %MSTOT = 0.1 % ORAL EXPOSURE DOSE IN UG/KG 

43 %MSTOT = 0.3 % ORAL EXPOSURE DOSE IN UG/KG 

44 MSTOT = 1 % ORAL EXPOSURE DOSE IN UG/KG 

45 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-78 DRAFT—DO NOT CITE OR QUOTE 

1 C.2.4.2.5. Markowski et al. (2001). 

2 %clear variable 

3 output @clear 

4 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

5 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

6 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 7 

8 %Markowski et al.2001 

9 %protocol: Single gavage at GD18 

10 %dose levels: 0.02 0.06, 0.18, 1 ug/kg at GD18 

11 %dose levels: 20, 60, 180 ng/kg at GD18 

 12 

 13 

14 %EXPOSURES SCENARIOS 

15 MAXT=0.1 

16 CINT =0.1 % 

17 EXP_TIME_ON = 408 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

18 EXP_TIME_OFF = 415 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

19 DAY_CYCLE = 505 

20 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

21 (HOUR) 

22 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

23 (HOUR) 

24 IV_LACK = 505 

25 IV_PERIOD = 505 

26 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

27 BW_T0 = 190 

28 MATTING = 0. % BEGINNING OF MATING (HOUR) 

29 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

30 N_FETUS = 10 

 31 

32 %EXPOSURE DOSE SCENARIOS (UG/KG) 

33 %MSTOT = 0.02 % ORAL EXPOSURE DOSE IN UG/KG 

34 %MSTOT = 0.06 % ORAL EXPOSURE DOSE IN UG/KG 

35 MSTOT = 0.18 % ORAL EXPOSURE DOSE IN UG/KG 

36 

37 C.2.4.2.6. Miettinen et al. (2006). 

38 %clear variable 

39 output @clear 

40 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

41 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

42 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 43 

44 %Miettinnen et al 2006 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-79 DRAFT—DO NOT CITE OR QUOTE 

1 %protocol: Single oral dose at GD15 

2 %dose levels: 0.03 0.1, 0.3, 1 ug/kg at GD15 

3 %dose levels: 30, 100, 300, 1000 ng/kg at GD15 

 4 

5 MAXT=0.1 

6 CINT =0.1 % 

 7 

8 %EXPOSURES SCENARIOS 

9 EXP_TIME_ON = 336 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

10 EXP_TIME_OFF = 340 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

11 DAY_CYCLE = 505 

12 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

13 (HOUR) 

14 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

15 (HOUR) 

16 IV_LACK = 505 

17 IV_PERIOD = 505 

18 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

19 BW_T0 = 180 

20 MATTING = 0. % BEGINNING OF MATING (HOUR) 

21 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

22 N_FETUS = 10 

 23 

24 %EXPOSURE DOSE SCENARIOS (UG/KG) 

25 %MSTOT = 0.03 % ORAL EXPOSURE DOSE IN UG/KG 

26 %MSTOT = 0.1 % ORAL EXPOSURE DOSE IN UG/KG 

27 %MSTOT = 0.3 % ORAL EXPOSURE DOSE IN UG/KG 

28 MSTOT = 1 % ORAL EXPOSURE DOSE IN UG/KG 

29 

30 C.2.4.2.7. Murray et al. (1979). 

31 %clear variable 

32 output @clear 

33 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

34 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

35 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 36 

37 %output @nciout=1 T BBFETUSNG %AJS turned off 9/21/09 

 38 

39 %Murray et al.1979 (rat species) 

40 %protocol: dietary exposure for 90 days followed by gestation (21 days) 

41 %dose levels: 0.001 0.01, 0.1 ug/kg/d 

42 %dose levels: 1, 10, 100 ng/kg/d 

 43 

44 %EXPOSURES SCENARIOS 

45 MAXT =.1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-80 DRAFT—DO NOT CITE OR QUOTE 

1 CINT = 0.1 % 

2 EXP_TIME_ON = 0 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

3 EXP_TIME_OFF = 2660 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

4 DAY_CYCLE = 24 

5 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

6 (HOUR) 

7 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

8 (HOUR) 

9 IV_LACK = 2664 

10 IV_PERIOD = 2664 

11 TIMELIMIT = 2664 % SIMULATION TIME LIMIT (HOUR) 

12 BW_T0 = 85 

13 MATTING = 2160 % BEGINNING OF MATING (HOUR) 

14 TRANSTIME_ON = 2304 % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

15 N_FETUS = 10 

 16 

17 %EXPOSURE DOSE SCENARIOS (UG/KG) 

18 %MSTOT = 0.001 % ORAL EXPOSURE DOSE IN UG/KG 

19 %MSTOT = 0.01 % ORAL EXPOSURE DOSE N UG/KG 

20 MSTOT = 0.1 % ORAL EXPOSURE DOSE N UG/KG 

21 

22 C.2.4.2.8. Nohara et al. (2000). 

23 %clear variable 

24 output @clear 

25 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

26 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

27 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 28 

29 %Nohara et al 2000 

30 %protocol: exposure daily dose in diet 

31 %dose levels: 0.0125, 0.050, 0.2 or 0.8 ug TCDD:kg body weight by gavage on GD15. 

32 %dose levels: 12.5, 50, 200 or 800 ng TCDD:kg body weight by gavage on GD15. 

 33 

34 MAXT=0.1 

35 CINT =0.1 % 

 36 

37 %EXPOSURES SCENARIOS 

38 EXP_TIME_ON = 336 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

39 EXP_TIME_OFF = 340 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

40 DAY_CYCLE = 505 TIME AT WHICH BACKGROUND EXPOSURE BEGINS (HOUR) 

41 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

42 (HOUR) 

43 IV_LACK = 505 

44 IV_PERIOD = 505 

45 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-81 DRAFT—DO NOT CITE OR QUOTE 

1 BW_T0 = 180 

2 MATTING = 0. % BEGINNING OF MATING (HOUR) 

3 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

4 N_FETUS = 10 

 5 

6 %EXPOSURE DOSE SCENARIOS (UG/KG) 

7 %MSTOT = 0.0125 % ORAL EXPOSURE DOSE IN UG/KG 

8 %MSTOT = 0.050 % ORAL EXPOSURE DOSE IN UG/KG 

9 %MSTOT = 0.2 % ORAL EXPOSURE DOSE IN UG/KG 

10 MSTOT = 0.8 % ORAL EXPOSURE DOSE IN UG/KG 

11 

12 C.2.4.2.9. Ohsako et al. (2001). 

13 %TO BE USED AFTER THE 

14 %clear variable 

15 output @clear 

16 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

17 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

18 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 19 

20 %Ohsako et al. 2001 

21 %protocol: exposure SINGLE DOSE AT GD15 

22 %dose levels: 0.0125, 0.05, and 0.2 and 0.8 ug/kg AT GD15 

23 %dose levels: 12.5, 50, 200 and 800 ng/kg AT GD15 

 24 

25 %EXPOSURES SCENARIOS 

26 MAXT=0.001 

27 CINT =0.1 % 

28 EXP_TIME_ON = 360 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

29 EXP_TIME_OFF = 505 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

30 DAY_CYCLE = 505 

31 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

32 (HOUR) 

33 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

34 (HOUR) 

35 IV_LACK = 505 

36 IV_PERIOD = 505 

37 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

38 BW_T0 = 200 

39 MATTING = 0. % BEGINNING OF MATING (HOUR) 

40 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

41 N_FETUS = 10 

 42 

43 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 44 

45 %MSTOT = 0.0125 % ORAL EXPOSURE DOSE IN UG/KG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-82 DRAFT—DO NOT CITE OR QUOTE 

1 %MSTOT = 0.05 % ORAL EXPOSURE DOSE IN UG/KG 

2 %MSTOT = 0.20 % ORAL EXPOSURE DOSE IN UG/KG 

3 MSTOT = 0.80 % ORAL EXPOSURE DOSE IN UG/KG 

4 

5 C.2.4.2.10. Schantz et al. (1996) and Amin et al. (2000). 

6 output @clear 

7 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

8 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

9 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 10 

11 %Amin et al 2000 (rat species) and Schantz et al 1995 

12 %protocol: Daily doses during gestation day 10 to 16 

13 %DevTCDD4Species.csl 

14 %RAT_GESTATIONAL_ICF_F083109.csl (now 09-11-09) 

15 %dose levels: 25 and 100 ug/kg/day 

16 %dose levels: 0.25 and 0.100 ng/kg/day 

 17 

18 %EXPOSURES SCENARIOS 

19 MAXT =.1 

20 CINT = 0.1 % 

21 EXP_TIME_ON = 240. % delay before begin exposure (HOUR) 

22 EXP_TIME_OFF = 384. % TIME EXPOSURE STOP (HOUR) 12 weeks exposure + 2 

23 weeks for mating + 21 days gestation with exposure 

24 DAY_CYCLE = 24 % weekly cycle 

25 BCK_TIME_ON = 1000. % DELAY BEFORE BACKGROUND EXPOSURE 

26 (HOUR) 

27 BCK_TIME_OFF = 1000. % TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

28 IV_LACK = 505. 

29 IV_PERIOD = 505. 

30 TIMELIMIT = 384. % SIMULATION LIMIT TIME (HOUR) 

31 BW_T0 = 250. 

32 MATTING = 0 % BEGINNING MATTING (HOUR) 

33 TRANSTIME_ON = 144. % SHOULD BE MATTING TIME + 6 DAYS(144 HOURS) 

34 N_FETUS = 10 

 35 

36 %EXPOSURE DOSE SCENARIOS (UG/KG) 

37 %MSTOT = .025 % ORAL EXPOSURE DOSE (UG/KG) 

38 MSTOT = .100 

39 MSTOTBCKGR = 0 % Background Exposure (UG/KG) 

40 

41 C.2.4.2.11. Seo et al. (1995). 

42 %clear variable 

43 output @clear 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-83 DRAFT—DO NOT CITE OR QUOTE 

1 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

2 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

3 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

 4 

5 %Seo et al. 1995 

6 %protocol: exposure GD 10-16 

7 %DevTCDD4Species.csl 

8 %RAT_GESTATIONAL_ICF_F083109.csl (now 09-11-09) 

9 %dose levels: 0.025 and 0.1 ug/kg GD 10-16 

10 %dose levels: 25 and 100 ng/kg GD 10-16 

 11 

12 MAXT=0.1 

13 CINT =0.1 

 14 

15 %EXPOSURES SCENARIOS 

16 EXP_TIME_ON = 240 % delay before begin exposure (HOUR) 

17 EXP_TIME_OFF = 385 % TIME EXPOSURE STOP (HOUR) 

18 DAY_CYCLE = 24 

19 BCK_TIME_ON = 0. % DELAY BEFORE BACKGROUND EXPOSURE 

20 (HOUR) 

21 BCK_TIME_OFF = 0. % TIME OF BACKGROUND EXPOSURE STOP (HOUR) 

22 IV_LACK = 505 

23 IV_PERIOD = 505 

24 TIMELIMIT = 504 % SIMULATION LIMIT TIME (HOUR) 

25 BW_T0 = 190 

26 MATTING = 0. % BEGINNING MATING (HOUR) 

27 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 

28 HOURS) 

29 N_FETUS = 10 

 30 

31 %EXPOSURE DOSE SCENARIOS (UG/KG) 

32 MSTOT = 0.025 % ORAL EXPOSURE DOSE (UG/KG) 

33 %MSTOT = 0.1 % ORAL EXPOSURE DOSE (UG/KG) 

 34 

35 C.2.4.2.12. Shi et al. (2007). 

36 %clear variable 

37 output @clear 

38 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

39 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

40 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

41 %output @nciout=1 T BBFETUSNG %AJS turned off 9/21/09 

 42 

43 %Shi et al 2007 

44 %protocol: exposure at GD14 and GD21 orl exposure 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-84 DRAFT—DO NOT CITE OR QUOTE 

1 %dose levels: 0.001, 0.005, 0.05 and 0.2 ug TCDD:kg body weight by gavage on GD14 and 

2 GD21. 

3 %dose levels: 1, 5, 50 and 200 ng/kg ng TCDD:kg body weight by gavage on GD14 and GD21. 

4 % dose equivalent adjusted 0.143, 0.714, 7.14 and 28.6 ng/kg/d 

 5 

6 MAXT=0.001 

7 CINT =0.1 % 

8 CFLI0 = 0 

9 CFPLA0 = 0 

10 %EXPOSURES SCENARIOS 

11 EXP_TIME_ON = 312 % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

12 EXP_TIME_OFF = 485 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

13 DAY_CYCLE = 168 

14 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

15 (HOUR) 

16 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

17 (HOUR) 

18 IV_LACK = 505 

19 IV_PERIOD = 505 

20 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

21 BW_T0 = 190 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

22 (G) 

23 MATTING = 0. % BEGINNING OF MATING (HOUR) 

24 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

25 N_FETUS = 10 

 26 

27 %EXPOSURE DOSE SCENARIOS (UG/KG) 

28 %MSTOT = 0.001 % ORAL EXPOSURE DOSE IN UG/KG 

29 MSTOT = 0.005 % ORAL EXPOSURE DOSE IN UG/KG 

30 %MSTOT = 0.05 % ORAL EXPOSURE DOSE IN UG/KG 

31 %MSTOT = 0.2 % ORAL EXPOSURE DOSE IN UG/KG 

32 

33 C.2.5. Mouse Standard Model 

34 C.2.5.1. Model Code 

35 PROGRAM: 'Three Compartment PBPK Model for TCDD in Mice: Standard Model 

36 (Non-Gestation)' 

 37 

38 !Mice_Dioxin_3C_June09_1_icf_afterKKfix_v3_mousenongest.csl 

39 !MICE_NON_GESTAT_ICF_F083109.csl 

40 !MICE_NON_GESTAT_ICF_F093009.csl 

41 !MICE_NON_GESTAT_ICF_F100609.csl 

42 !***************************************************** 

 43 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-85 DRAFT—DO NOT CITE OR QUOTE 

1 INITIAL ! INITIALIZATION OF PARAMETERS 

 2 

3 !SIMULATION PARAMETERS ==== 

4 CONSTANT PARA_ZERO = 1D-30 

5 CONSTANT EXP_TIME_ON = 0.0 ! TIME AT WHICH EXPOSURE BEGINS 

6 (HOURS) 

7 CONSTANT EXP_TIME_OFF = 2832 ! TIME AT WHICH EXPOSURE ENDS 

8 (HOURS) 

9 CONSTANT DAY_CYCLE = 24 ! NUMBER OF HOURS BETWEEN DOSES 

10 (HOURS) 

11 CONSTANT BCK_TIME_ON = 0.0 ! TIME AT WHICH BACKGROUND 

12 EXPOSURE BEGINS (HOURS) 

13 CONSTANT BCK_TIME_OFF = 0.0 ! TIME AT WHICH BACKGROUND 

14 EXPOSURE ENDS (HOURS) 

 15 

16 CONSTANT MW=322 ! MOLECULAR WEIGHT (NG/NMOL) 

17 CONSTANT SERBLO = 0.55 

18 CONSTANT UNITCORR = 1000 

 19 

20 !CONSTANT EXPOSURE CONTROL =========== 

21 !ACUTE, SUBCHRONIC, CHRONIC EXPOSURE ===== 

22 !OR BACKGROUND EXPOSURE (IN THIS CASE 3 TIMES A DAY)=== 

23 CONSTANT MSTOTBCKGR = 0.0 !ORAL BACKGROUND EXPOSURE DOSE 

24 (UG/KG) 

25 CONSTANT MSTOT = 0.15 !ORAL EXPOSURE DOSE (UG/KG) 

26 CONSTANT MSTOTsc = 0.0 ! SUBCUTANEOUS EXPOSURE DOSE (UG/KG) 

 27 

28 !ORAL ABSORPTION 

29 MSTOT_NM = MSTOT/MW !AMOUNT IN NMOL/G 

 30 

31 ! INTRAVENOUS ABSORPTION 

32 CONSTANT DOSEIV = 0.0 !INJECTED DOSE (UG/KG) 

33 DOSEIV_NM = DOSEIV/MW ! CONVERTS THE INJECTED DOSE TO NMOL/G 

 34 

35 !INITIAL GUESS OF THE FREE CONCENTRATION IN THE LIGAND (COMPARTMENT 

36 INDICATED BELOW)==== 

37 CONSTANT CFLLI0 = 0.0 !LIVER (NMOL/ML) 

 38 

39 !BINDING CAPACITY (AhR) FOR NON LINEAR BINDING (COMPARTMENT 

40 INDICATED BELOW) (NMOL/ML) 

41 CONSTANT LIBMAX = 3.5e-4 ! LIVER (NMOL/ML), WANG ET AL. 1997 

 42 

43 ! PROTEIN AFFINITY CONSTANTS (1A2 OR AhR, COMPARTMENT INDICATED 

44 BELOW) (NMOL/ML)=== 

45 CONSTANT KDLI = 1.0e-4 !LIVER (AhR)(NMOL/ML), WANG ET AL. 1997 

46 CONSTANT KDLI2 = 2.0e-2 !LIVER (1A2)(NMOL/ML), EMOND ET AL. 2004 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-86 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !===EXCRETION AND ABSORPTION CONSTANT (OPTIMIZED) 

3 CONSTANT KST = 0.3 ! GASTRIC RATE CONSTANT (HR-1), 

4 CONSTANT KABS = 0.48 !INTESTINAL ABSORPTION CONSTANT (HR-1) ), 

5 WANG ET AL. 1997 

 6 

7 ! ELIMINATION CONSTANTS 

8 CONSTANT CLURI = 0.09 ! URINARY CLEARANCE (ML/HR) 

 9 

10 ! ==test elimination variable 

11 constant kelv = 0.4 ! INTERSPECIES VARIABLE ELIMINATION CONSTANT 

12 (1/HOUR) 

 13 

14 ! CONSTANT TO DIVIDE THE ABSORPTION INTO LYMPHATIC AND PORTAL 

15 FRACTIONS 

16 CONSTANT A = 0.7 ! LYMPHATIC FRACTION, WANG ET AL. 1997 

 17 

18 !PARTITION COEFFICIENTS OPTIMIZED 

19 CONSTANT PF = 400 ! ADIPOSE TISSUE/BLOOD 

20 CONSTANT PRE = 3 ! REST OF THE BODY/BLOOD, WANG ET AL. 2000 

21 CONSTANT PLI = 6 ! LIVER/BLOOD, WANG ET AL. 1997 

 22 

23 !===PARAMETER FOR INDUCTION OF CYP 1A2 

24 CONSTANT PAS_INDUC= 1.0 ! INCLUDE INDUCTION? (1 = YES, 0 = NO) 

25 CONSTANT CYP1A2_1OUTZ = 1.6 ! DEGRADATION CONCENTRATION CONSTANT 

26 OF 1A2 (NMOL/ML) 

27 CONSTANT CYP1A2_1A1 = 1.5 ! BASAL CONCENTRATION OF 1A1 (NMOL/ML) 

28 CONSTANT CYP1A2_1EC50 = 0.13 ! DISSOCIATION CONSTANT TCDD-CYP1A2 

29 (NMOL/ML) 

30 CONSTANT CYP1A2_1A2 = 1.5 ! BASAL CONCENTRATION OF 1A2 (NMOL/ML) 

31 CONSTANT CYP1A2_1KOUT = 0.1 ! FIRST ORDER RATE OF DEGRADATION (H-1) 

32 CONSTANT CYP1A2_1TAU = 1.5 ! HOLDING TIME (H) 

33 CONSTANT CYP1A2_1EMAX = 600 ! MAXIMUM INDUCTION OVER BASAL EFFECT 

34 (UNITLESS) 

35 CONSTANT HILL = 0.6 !HILL CONSTANT; COOPERATIVELY LIGAND 

36 BINDING EFFECT CONSTANT (UNITLESS) 

37 !DIFFUSIONAL PERMEABILITY FRACTION 

38 CONSTANT PAFF = 0.12 ! ADIPOSE (UNITLESS), WANG ET AL. 2000 

39 CONSTANT PAREF = 0.03 ! REST OF THE BODY (UNITLESS) 

40 CONSTANT PALIF = 0.35 ! LIVER (UNITLESS) 

 41 

42 !COMPARTMENT TISSUE BLOOD VOLUME ========= 

43 CONSTANT WLI0 = 0.0549 ! LIVER, ILSI 1994 

44 CONSTANT WF0 = 0.069 ! ADIPOSE 

 45 

46 !TISSUE BLOOD FLOW EXPRESSED AS A FRACTION OF CARDIAC OUTPUT 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-87 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT QFF = 0.070 ! ADIPOSE TISSUE BLOOD FLOW FRACTION 

2 (UNITLESS), LEUNG ET AL. 1990 

3 CONSTANT QLIF = 0.161 ! LIVER (UNITLESS) ILSI ET AL. 1994 

 4 

5 !COMPARTMENT TISSUE BLOOD EXPRESSED AS A FRACTION OF THE TOTAL 

6 COMPARTMENT VOLUME 

7 CONSTANT WFB0 = 0.050 ! ADIPOSE TISSUE, WANG ET AL. 1997 

8 CONSTANT WREB0 = 0.030 ! REST OF THE BODY, WANG ET AL. 1997 

9 CONSTANT WLIB0 = 0.266 ! LIVER, WANG ET AL. 1997 

 10 

11 ! EXPOSURE SCENARIO FOR UNIQUE OR REPETITIVE WEEKLY OR MONTHLY 

12 EXPOSURE 

13 ! NUMBER OF EXPOSURES PER WEEK 

14 CONSTANT WEEK_LACK = 0.0 ! DELAY BEFORE EXPOSURE ENDS (WEEK) 

15 CONSTANT WEEK_PERIOD = 168 ! NUMBER OF HOURS IN THE WEEK (HOURS) 

16 CONSTANT WEEK_FINISH = 120 ! TIME EXPOSURE ENDS (HOURS) 

 17 

18 ! NUMBER OF EXPOSURES PER MONTH 

19 CONSTANT MONTH_LACK = 0.0 ! DELAY BEFORE EXPOSURE (MONTH) 

 20 

21 !SET FOR BACKGROUND EXPOSURE=========== 

22 !CONSTANT FOR BACKGROUND EXPOSURE=========== 

23 CONSTANT Day_LACK_BG = 0.0 ! DELAY BEFORE EXPOSURE BEGINS (HOURS) 

24 CONSTANT Day_PERIOD_BG = 24 ! LENGTH OF EXPOSURE (HOURS) 

 25 

26 ! NUMBER OF EXPOSURES PER WEEK 

27 CONSTANT WEEK_LACK_BG = 0.0 ! DELAY BEFORE BACKGROUD EXPOSURE 

28 (WEEK) 

29 CONSTANT WEEK_PERIOD_BG = 168 !NUMBER OF HOURS IN THE WEEK (HOURS) 

30 CONSTANT WEEK_FINISH_BG = 168 ! TIME EXPOSURE ENDS (HOURS) 

 31 

32 !GROWTH CONSTANT FOR RAT AND MOUSE 

33 !CONSTANT FOR MOTHER BODY WEIGHT GROWTH ====== 

34 CONSTANT BW_T0 = 20 !CHANGED FOR SIMULATION 

 35 

36 !CONSTANT USED IN CARDIAC OUTPUT EQUATION, KRISHNAN 2001 

37 CONSTANT QCCAR =275 !CONSTANT (ML/MIN/KG) 

 38 

39 ! COMPARTMENT LIPID EXPRESSED AS THE FRACTION OF TOTAL LIPID 

40 CONSTANT F_TOTLIP = 0.855 !ADIPOSE TISSUE (UNITLESS) 

41 CONSTANT B_TOTLIP = 0.0033 !BLOOD (UNITLESS) 

42 CONSTANT RE_TOTLIP = 0.019 !REST OF THE BODY (UNITLESS) 

43 CONSTANT LI_TOTLIP = 0.06 !LIVER (UNITLESS) 

 44 

45 END ! END OF THE INITIAL SECTION 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-88 DRAFT—DO NOT CITE OR QUOTE 

1 DYNAMIC ! DYNAMIC SIMULATION SECTION 

 2 

3 ALGORITHM IALG = 2 !GEAR METHOD 

4 CINTERVAL CINT = 1.0 !COMMUNICATION INTERVAL 

5 MAXTERVAL MAXT = 1.0e+10 !MAXIMUM CALCULATION INTERVAL 

6 MINTERVAL MINT = 1.0E-10 !MINIMUM CALCULATION INTERVAL 

7 VARIABLE T = 0.0 !HOUR 

8 CONSTANT TIMELIMIT = 2904.0 !SIMULATION TIME LIMIT (HOURS) 

9 CINTXY = CINT 

10 PFUNC = CINT 

 11 

12 !TIME CONVERSION 

13 DAY = T/24.0 ! TIME IN DAYS 

14 WEEK = T/168.0 ! TIME IN WEEKS 

15 MONTH = T/730.0 ! TIME IN MONTHS 

16 YEAR = T/8760.0 ! TIME IN YEARS 

 17 

18 !NMAX =MAX(T,CTFNGKG) 

19 nmax =max(T,CFNGKG) 

 20 

21 DERIVATIVE ! PORTION OF CODE THAT SOLVES DIFFERENTIAL EQUATIONS 

 22 

23 !CHRONIC OR SUBCHRONIC EXPOSURE SCENARIO ======= 

24 !NUMBER OF EXPOSURES PER DAY 

25 DAY_LACK = EXP_TIME_ON ! DELAY BEFORE EXPOSURE BEGINS (HOURS) 

26 DAY_PERIOD = DAY_CYCLE ! EXPOSURE PERIOD (HOURS) 

27 DAY_FINISH = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

28 MONTH_PERIOD = TIMELIMIT ! EXPOSURE PERIOD (MONTHS) 

29 MONTH_FINISH = EXP_TIME_OFF ! LENGTH OF EXPOSURE (MONTHS) 

 30 

31 !NUMBER OF EXPOSURES PER DAY AND MONTH 

32 DAY_FINISH_BG = CINTXY 

33 MONTH_LACK_BG = BCK_TIME_ON ! DELAY BEFORE BACKGROUD EXPOSURE 

34 BEGINS (MONTHS) 

35 MONTH_PERIOD_BG = TIMELIMIT ! BACKGROUND EXPOSURE PERIOD 

36 (MONTHS) 

37 MONTH_FINISH_BG = BCK_TIME_OFF ! LENGTH OF BACKGROUND EXPOSURE 

38 (MONTHS) 

 39 

40 ! FRACTION OF DIOXIN ABSORBED IN THE PORTAL FRACTION OF THE LIVER 

41 B = 1.0-A 

 42 

 43 

44 !GROWTH UP EQUATION (G) 

 45 

46 PARAMETER (BW_RMN = 1.0E-30) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-89 DRAFT—DO NOT CITE OR QUOTE 

1 WT0= (BW_T0 *(1.0+(0.41*T)/(1402.5+T+BW_RMN))) 

 2 

3 ! VARIABILITY OF REST OF THE BODY DEPENDS ON OTHER ORGANS 

4 !REST OF THE BODY FRACTION; UPDATED FOR EPA ASSESSMENT 

5 WRE0 = (0.91 - (WLIB0*WLI0 + WFB0*WF0 + WLI0 + WF0))/(1+WREB0) 

 6 

7 ! REST OF THE BODY BLOOD FLOW FRACTION 

8 QREF = 1.0-(QFF+QLIF) !REST OF BODY BLOOD FLOW (ML/HR) 

9 !SUMMATION OF BLOOD FLOW FRACTION (SHOULD BE EQUAL TO 1) 

10 QTTQF = QFF+QREF+QLIF ! SUM MUST EQUAL 1 

 11 

12 !COMPARTMENT VOLUME (G) 

13 WF = WF0 * WT0 ! ADIPOSE 

14 WRE = WRE0 * WT0 ! REST OF THE BODY 

15 WLI = WLI0 * WT0 ! LIVER 

 16 

17 !COMPARTMENT TISSUE BLOOD (G) 

18 WFB = WFB0 * WF ! ADIPOSE 

19 WREB = WREB0 * WRE ! REST OF THE BODY 

20 WLIB = WLIB0 * WLI ! LIVER 

 21 

22 !CARDIAC OUTPUT FOR THE GIVEN BODY WEIGHT 

23 QC= QCCAR*60*(WT0/1000.0)**0.75 

 24 

25 QF = QFF*QC ! ADIPOSE TISSUE BLOOD FLOW RATE (ML/HR) 

26 QLI = QLIF*QC ! LIVER TISSUE BLOOD FLOW RATE (ML/HR) 

27 QRE = QREF*QC ! REST OF THE BODY BLOOD FLOW RATE (ML/HR) 

 28 

29 QTTQ = QF+QRE+QLI !TOTAL FLOW RATE (ML/HR) 

 30 

31 !PERMEABILITY ORGAN FLOW (ML/HR) ======= 

32 PAF = PAFF*QF ! ADIPOSE TISSUE 

33 PARE = PAREF*QRE ! REST OF THE BODY 

34 PALI = PALIF*QLI ! LIVER TISSUE 

 35 

36 !ABSORPTION SECTION 

37 !ORAL 

38 !BACKGROUND EXPOSURE 

39 !EXPOSURE FOR STEADY STATE CONSIDERATION 

40 !REPETITIVE EXPOSURE SCENARIO 

 41 

42 MSTOT_NMBCKGR = MSTOTBCKGR/322 !AMOUNT IN NMOL/G 

43 MSTTBCKGR =MSTOT_NMBCKGR *WT0 

 44 

45 !REPETITIVE ORAL BACKGROUND EXPOSURE SCENARIOS 

46 DAY_EXPOSURE_BG = PULSE(DAY_LACK_BG,DAY_PERIOD_BG,DAY_FINISH_BG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-90 DRAFT—DO NOT CITE OR QUOTE 

1 WEEK_EXPOSURE_BG = 

2 PULSE(WEEK_LACK_BG,WEEK_PERIOD_BG,WEEK_FINISH_BG) 

3 MONTH_EXPOSURE_BG = 

4 PULSE(MONTH_LACK_BG,MONTH_PERIOD_BG,MONTH_FINISH_BG) 

 5 

6 MSTTCH_BG = 

7 (DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG)*MSTTBCK

8 GR 

9 MSTTFR_BG = MSTTBCKGR/CINT 

 10 

11 totalBG= integ (MSTTCH_BG,0.0) 

12 CYCLE_BG =DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG 

 13 

 14 

15 !CONDITIONAL ORAL EXPOSURE (BACKGROUND EXPOSURE) 

16 IF (MSTTCH_BG.EQ.MSTTBCKGR) THEN 

17 ABSMSTT_GB= MSTTFR_BG 

18 ELSE 

19 ABSMSTT_GB = 0.0 

20 END IF 

 21 

22 !EXPOSURE + !REPETITIVE EXPOSURE SCENARIO 

23 IV= DOSEIV_NM * WT0 !AMOUNT IN NMOL 

24 MSTT= MSTOT_NM * WT0 !AMOUNT IN NMOL 

 25 

26 DAY_EXPOSURE = PULSE(DAY_LACK,DAY_PERIOD,DAY_FINISH) 

27 WEEK_EXPOSURE = PULSE(WEEK_LACK,WEEK_PERIOD,WEEK_FINISH) 

28 MONTH_EXPOSURE = PULSE(MONTH_LACK,MONTH_PERIOD,MONTH_FINISH) 

 29 

30 MSTTCH = (DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE)*MSTT 

31 CYCLE = DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE 

 32 

33 SUMEXPEVENT= integ (CYCLE,0.0)*cint !NUMBER OF CYCLE GENERATE DURING 

34 SIMULATION 

 35 

36 MSTTFR = MSTT/CINT 

 37 

38 ! CONDITIONAL ORAL EXPOSURE 

39 IF (MSTTCH.EQ.MSTT) THEN 

40 ABSMSTT= MSTTFR 

41 ELSE 

42 ABSMSTT = 0.0 

43 END IF 

 44 

45 CYCLETOT=INTEG(CYCLE,0.0) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-91 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 !MASS CHANGE IN THE LUMEN 

3 RMSTT= -(KST+KABS)*MST+ABSMSTT +ABSMSTT_GB ! RATE OF CHANGE 

4 (NMOL/H) 

5 MST = INTEG(RMSTT,0.0) !AMOUNT OF STAY IN DUODENUM (NMOL) 

 6 

7 !ABSORPTION IN LYMPH CIRCULATION 

8 LYRMLUM = KABS*MST*A 

9 LYMLUM = INTEG(LYRMLUM,0.0) 

 10 

11 !ABSORPTION IN PORTAL CIRCULATION 

12 LIRMLUM = KABS*MST*B 

13 LIMLUM = INTEG(LIRMLUM,0.0) 

 14 

15 !PERCENT OF DOSE REMAINING IN THE GI TRACT 

16 PRCT_remain_GIT = (MST/(MSTT+1E-30))*100 

 17 

18 RFECES = KST*MST + REXCLI 

19 FECES = INTEG(RFECES,0.0) 

20 prctFECES = (FECES/(BDOSE_TOTAL+1E-30))*100 

 21 

 22 

23 !ABSORPTION OF DIOXIN BY IV ROUTE--------- 

24 IVR= IV/PFUNC ! RATE FOR IV INFUSION IN BLOOD 

25 EXPIV= IVR * (1.0-STEP(PFUNC)) 

26 IVDOSE = integ(EXPIV,0.0) 

 27 

28 !SYSTEMIC BLOOD CONCENTRATION (NMOL/ML) 

29 ! MODIFICATION ON OCTOBER 6, 2009 

30 CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM)/(QC+CLURI) ! 

31 CA = CB 

 32 

33 !URINARY EXCRETION BY KIDNEY 

34 ! MODIFICATION ON OCTOBER 6, 2009 

35 RAURI = CLURI *CB 

36 AURI = INTEG(RAURI,0.0) 

 37 

38 prctAURI = (AURI/(BDOSE_TOTAL+1E-30))*100 

 39 

 40 

41 !UNIT CONVERSION POST SIMULATION 

42 PRCT_B = (CB/(MSTT+1E-30))*100 ! PERCENT OF DOSE/G TISSUE 

43 CBNGKG=CB*MW*UNITCORR 

44 CBSNGKGLIADJ= (CB*MW*UNITCORR*(1.0/B_TOTLIP)*(1.0/SERBLO))![NG of TCDD 

45 Serum/Kg OF LIPIP] 

46 CBPMOL_KG= CB*UNITCORR*UNITCORR !CONCENTRATION IN PMOL/KG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-92 DRAFT—DO NOT CITE OR QUOTE 

1 CBNGG = CB*MW 

2 !ADIPOSE TISSUE COMPARTMENT 

3 !TISSUE BLOOD SUBCOMPARTMENT 

4 RAFB = QF*(CA-CFB)-PAF*(CFB-CF/PF) !(NMOL/HR) 

5 AFB = INTEG(RAFB,0.0) !(NMOL) 

6 CFB = AFB/WFB !(NMOL/ML) 

7 !TISSUE SUBCOMPARTMENT 

8 RAF = PAF*(CFB-CF/PF) !(NMOL/HR) 

9 AF = INTEG(RAF,0.0) !(NMOL) 

10 CF = AF/WF !(NMOL/ML) 

 11 

12 !POST SIMULATION UNIT CONVERSION 

13 CFTOTAL = (AF + AFB)/(WF + WFB) ! TOTAL CONCENTRATION IN FAT(NM/ML) 

14 PRCT_F = (CFTOTAL/(MSTT+1E-30))*100 ! PERCENT OF DOSE IN FAT 

15 CFNGKG = CFTOTAL*MW*UNITCORR 

16 CFUGG=(CFTOTAL*MW)/UNITCORR 

17 CFPMOL_KG= CFTOTAL*UNITCORR*UNITCORR !CONCENTRATION IN 

18 PMOL/KG 

19 CFNGG = CFTOTAL*MW 

 20 

21 !REST OF THE BODY COMPARTMENT 

22 !TISSUE BLOOD SUBCOMPARTMENT 

23 RAREB= QRE*(CA-CREB)-PARE*(CREB-CRE/PRE) !(NMOL/HR) 

24 AREB = INTEG(RAREB,0.0) !(NMOL) 

25 CREB = AREB/WREB !(NMOL/ML) 

26 !TISSUE SUBCOMPARTMENT 

27 RARE = PARE*(CREB - CRE/PRE) !(NMOL/HR) 

28 ARE = INTEG(RARE,0.0) !(NMOL) 

29 CRE = ARE/WRE !(NMOL/ML) 

 30 

31 !POST SIMULATION UNIT CONVERSION 

32 CRETOTAL= (ARE + AREB)/(WRE + WREB) ! CONCENTRATION AT STEADY 

33 STATE 

34 PRCT_RE = (CRETOTAL/(MSTT+1E-30))*100 

 35 

 36 

37 !LIVER COMPARTMENT 

38 !TISSUE BLOOD SUBCOMPARTMENT 

39 RALIB = QLI*(CA-CLIB)-PALI*(CLIB-CFLLIR)+LIRMLUM !(NMOL/HR) 

40 ALIB = INTeg(RALIB,0.0) !(NMOL) 

41 CLIB = ALIB/WLIB 

42 !TISSUE SUBCOMPARTMENT 

43 RALI = PALI*(CLIB-CFLLIR)-REXCLI !(NMOL/HR) 

44 ALI = integ(RALI,0.0) !(NMOL) 

45 CLI = ALI/WLI !(NMOL/ML) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-93 DRAFT—DO NOT CITE OR QUOTE 

1 !FREE TCCD CONCENTRATION IN LIVER (NMOL/ML) 

2 PARAMETER (LIVER_1RMN = 1.0E-30) 

3 CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLI & 

4 +LIVER_1RMN))+((CYP1A2_1O3*CFLLIR/(KDLI2+CFLLIR & 

5 +LIVER_1RMN)*PAS_INDUC)))-CFLLI,CFLLI0) 

6 CFLLIR=DIM(CFLLI,0.0) ! FREE CONCENTRATION IN LIVER 

 7 

8 CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR+LIVER_1RMN) !BOUND 

9 CONCENTRATION 

 10 

11 !POST SIMULATION UNIT CONVERSION 

12 CLITOTAL= (ALI + ALIB)/(WLI + WLIB)! 

13 PRCT_LI = (CLITOTAL/(MSTT+1E-30))*100 ! PERCENT OF DOSE IN LIVER 

14 rec_occ_AHR= (CFLLIR/(KDLI+CFLLIR+1E-30))*100.0 ! PERCENT OF AhR 

15 OCCUPANCY 

16 PROT_occ_1A2= (CFLLIR/(KDLI2+CFLLIR))*100.0 ! PERCENT OF 1A2 OCCUPANCY 

17 CLINGKG =(CLITOTAL*MW*UNITCORR) 

18 CBNDLINGKG = CBNDLI*MW*UNITCORR 

19 CLIUGG=(CLITOTAL*MW)/UNITCORR 

20 CLIPMOL_KG= CLITOTAL*UNITCORR*UNITCORR !CONCENTRATION IN 

21 PMOL/KG 

22 CLINGG = CLITOTAL*MW 

 23 

24 !Fraction increase of induction of CYP1A2 

25 fold_ind=(CYP1A2_1OUT/CYP1A2_1A2) 

26 VARIATIONOfAC =(CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2 

 27 

28 !VARIABLE ELIMINATION BASED ON THE CYP1A2 

29 KBILE_LI_T =((CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2)*Kelv !INDUCED BILIARY 

30 EXCRETION RATE CONSTANT 

 31 

32 REXCLI= (KBILE_LI_T*CFLLIR*WLI) !DOSE-DEPENDENT EXCRETION RATE 

33 EXCLI = INTEG(REXCLI,0.0) 

 34 

35 !CHEMICAL IN CYP450 (1A2) COMPARTMENT 

36 !EQUATION FOR INDUCTION OF CYP1A2 

 37 

38 CYP1A2_1KINP = CYP1A2_1KOUT* CYP1A2_1OUTZ 

 39 

40 ! MODIFICATION ON OCTOBER 6, 2009 

41 CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1.0 + CYP1A2_1EMAX *(CBNDLI+1.0e42 30)**HILL & 

43 /(CYP1A2_1EC50**HILL + (CBNDLI+1.0e-30)**HILL)) & 

44 - CYP1A2_1KOUT*CYP1A2_1OUT, CYP1A2_1OUTZ) 

45 ! EQUATIONS INCORPORATING DELAY OF CYP1A2 PRODUCTION (NOT USED IN 

46 SIMULATIONS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-94 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 CYP1A2_1RO2 = (CYP1A2_1OUT - CYP1A2_1O2)/ CYP1A2_1TAU 

3 CYP1A2_1O2 =INTEG(CYP1A2_1RO2, CYP1A2_1A1) 

4 CYP1A2_1RO3 = (CYP1A2_1O2 - CYP1A2_1O3)/ CYP1A2_1TAU 

5 CYP1A2_1O3 =INTEG(CYP1A2_1RO3, CYP1A2_1A2) 

 6 

7 ! MASS BALANCE CONTROL 

8 BDOSE= LYMLUM+LIMLUM+IVDOSE 

9 BMASSE = EXCLI+AURI+AFB+AF+AREB+ARE+ALIB+ALI 

10 BDIFF = BDOSE-BMASSE 

11 ! AMOUNT TOTAL PRESENT IN THE GI TRACT 

12 BDOSE_TOTAL =LYMLUM+LIMLUM+FECES 

 13 

14 !BODY BURDEN IN NG 

15 Body_burden =(AFB+AF+AREB+ARE+ALIB+ALI)*MW 

 16 

17 !BODY BURDEN CONCENTRATION (NG/KG) 

18 BBNGKG =(((AFB+AF+AREB+ARE+ALIB+ALI)*MW)/(WT0/UNITCORR)) ! 

 19 

20 !COMMAND FOR END OF SIMULATION 

21 TERMT (T.GE. TimeLimit, 'Time limit has been reached.') 

 22 

23 END ! END OF THE DERIVATIVE SECTION 

24 END ! END OF THE DYNAMIC SECTION 

25 END ! END OF PROGRAM 

26 

27 C.2.5.2. Input Files 

28 C.2.5.2.1. Hassoun et al. (1998) (13 weeks). 

29 output @clear 

30 prepare @clear 

31 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 32 

33 % Hassoun et al 1998 

34 %built and check in August 7 2009 

35 %protocol: oral exposure single dose 

36 %dose levels: 0.00045, 0.0015, 0.015, 0.15 ug/kg single dose + 7 days post exposure 

37 %dose levels: 0.45, 1.5, 15, 150 ng/kg single dose + 7 days post exposure 

38 %dose levels equivalent 0.321, 1.07, 10.7, 107 ng/kg/day 

 39 

40 MAXT = 0.01 

41 CINT = 0.1 

42 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

43 EXP_TIME_OFF = 2184 %2208 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

44 DAY_CYCLE = 24 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-95 DRAFT—DO NOT CITE OR QUOTE 

1 WEEK_PERIOD = 168 

2 WEEK_FINISH = 119 

3 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

4 (HOUR) 

5 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

6 (HOUR) 

7 TIMELIMIT = 2208 %SIMULATION TIME LIMIT (HOUR) 

8 BW_T0 = 23 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION (G) 

 9 

 10 

11 %EXPOSURE DOSE SCENARIOS (UG/KG) 

12 %MSTOT = 0.00045 % EXPOSURE DOSE IN UG/KG 

13 %MSTOT = 0.0015 % EXPOSURE DOSE IN UG/KG 

14 %MSTOT = 0.015 % EXPOSURE DOSE IN UG/KG 

15 MSTOT = 0.150 % EXPOSURE DOSE IN UG/KG 

 16 

17 NTP (1982) (female) (chronic) 

18 %RAT2.m 

19 %clear variable 

20 output @clear 

21 prepare @clear 

22 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

23 %output @nciout=168 T SUMEXPEVENT 

 24 

 25 

26 % NTP subchronic Mice exposure 1982. 

27 %built and check in September 20, 2009 

28 %protocol: repetitive doses 

29 %MICE_NON_GESTAT_ICF_F092009.csl (now 09-20-09) 

30 %dose levels: 0.02, 0.1, 1 ug/kg/biweekly, ug/kg for 104 weeks + 3 weeks post treatment 

31 %dose levels: 20, 100 and 1000 ng/kg/Biweekly,ng/kg for 104 weeks + 3 weeks post treatment 

32 %dose levels equivalent to: 5.71, 28.57, 285.1 ng/kg/d 

 33 

34 MAXT = 0.01 

35 CINT = 0.1 

36 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

37 EXP_TIME_OFF = 17472 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

38 DAY_CYCLE = 84 

39 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

40 (HOUR) 

41 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

42 (HOUR) 

43 TIMELIMIT = 17976 %SIMULATION TIME LIMIT (HOUR) 

44 BW_T0 = 23 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

45 (G) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-96 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 %EXPOSURE DOSE SCENARIOS (UG/KG) 

3 MSTOT = 0.02 % EXPOSURE DOSE IN UG/KG 

4 %MSTOT = 0.1 % EXPOSURE DOSE IN UG/KG 

5 %MSTOT = 1.0 % EXPOSURE DOSE IN UG/KG 

6 

7 C.2.5.2.2. NTP (1982) (male) (chronic). 

8 %RAT2.m

9 %clear variable 

10 output @clear 

11 prepare @clear 

12 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

13 %output @nciout=168 T SUMEXPEVENT 

 14 

15 % NTP subchronic Mice exposure 1982. 

16 %built and check in September 20, 2009 

17 %protocol: repetitive doses 

18 %dose levels: 0.005, 0.025, 0.25 ug/kg/biweekly, ug/kg for 104 weeks + 3 weeks post treatment 

19 %dose levels: 5, 25 and 250 ng/kg/Biweekly,ng/kg for 104 weeks + 3 weeks post treatment 

20 %dose levels equivalent to: 1.4, 7.1, 71 ng/kg/d 

 21 

22 MAXT = 0.01 

23 CINT = 0.1 

24 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

25 EXP_TIME_OFF = 17472 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

26 DAY_CYCLE = 84 

27 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

28 (HOUR) 

29 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

30 (HOUR) 

31 TIMELIMIT = 17976 %SIMULATION TIME LIMIT (HOUR) 

32 BW_T0 = 25 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

33 (G) 

 34 

 35 

36 %EXPOSURE DOSE SCENARIOS (UG/KG) 

37 %MSTOT = 0.005 % EXPOSURE DOSE IN UG/KG 

38 %MSTOT = 0.025 % EXPOSURE DOSE IN UG/KG 

39 MSTOT = 0.25 % EXPOSURE DOSE IN UG/KG 

40 

41 C.2.5.2.3. Smialowicz et al. (2008). 

42 output @clear 

43 prepare @clear 

44 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-97 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 % Smialowicz et al, 2008. 

3 %built and check in August 7 2009 

4 %protocol: oral exposure single dose 

5 %protocol: 5/7 gavage for 13 wk; Female B6C3F1 mice 

6 %dose levels: 0, 0.0015, 0.015, 0.15, 0.45 ug/kg 

7 %dose levels: 0, 1.5, 15, 150, 450 nkd (0, 1.07, 10.7, 107, 321 nkd adj) 

 8 

9 MAXT = 0.01 

10 CINT = 0.1 

11 TIMELIMIT = 2184 %SIMULATION TIME LIMIT (HOUR) 

12 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

13 EXP_TIME_OFF = 2180 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

14 DAY_CYCLE = 24 

15 WEEK_PERIOD = 168 

16 WEEK_FINISH = 119 

17 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

18 (HOUR) 

19 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

20 (HOUR) 

21 BW_T0 = 28 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

22 (G) 

 23 

24 %EXPOSURE DOSE SCENARIOS (UG/KG) 

25 %MSTOT = 0.0015 % EXPOSURE DOSE IN UG/KG 

26 %MSTOT = 0.015 % EXPOSURE DOSE IN UG/KG 

27 %MSTOT = 0.150 % EXPOSURE DOSE IN UG/KG 

28 MSTOT = 0.450 % EXPOSURE DOSE IN UG/KG 

29 

30 C.2.5.2.4. Toth et al. (1979) (1 year). 

31 output @clear 

32 prepare @clear 

33 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 34 

35 % Toth et al 1979 

36 %built and check in August 7 2009 

37 %protocol: oral exposure single dose 

38 %dose levels: 7, 700, 7000 ng/kg 1/week for 52 weeks (1 year) 

39 %dose levels: 0.007, 0.7 and 7 ug/kg 1/week for 52 weeks (1 year) 

40 %dose equivalent: 1, 100, 1000 ng/kg/day 

 41 

42 MAXT = 0.01 

43 CINT = 0.1 

44 TIMELIMIT = 8736 

45 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-98 DRAFT—DO NOT CITE OR QUOTE 

1 EXP_TIME_OFF = 8736 %2208 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

2 DAY_CYCLE = 168 

3 WEEK_PERIOD = 8760 

4 WEEK_FINISH = 8760 

5 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

6 (HOUR) 

7 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

8 (HOUR) 

9 BW_T0 = 27 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

10 (G) 

 11 

 12 

13 %EXPOSURE DOSE SCENARIOS (UG/KG) 

14 %MSTOT = 0.007 % EXPOSURE DOSE IN UG/KG 

15 %MSTOT = 0.7 % EXPOSURE DOSE IN UG/KG 

16 MSTOT = 7 % EXPOSURE DOSE IN UG/KG 

17 

18 C.2.5.2.5. Toth et al. (1979) (2 year). 

19 output @clear 

20 prepare @clear 

21 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 22 

23 % Toth et al 1979 

24 %built and check in August 7 2009 

25 %protocol: oral exposure single dose 

26 %dose levels: 7, 700, 7000 ng/kg 1/week for 52 weeks (1 year) 

27 %dose levels: 0.007, 0.7 and 7 ug/kg 1/week for 52 weeks (1 year) 

28 %dose levels equivalent: 1, 100, 1000 ng/kg/day 

 29 

30 MAXT = 0.01 

31 CINT = 0.1 

32 TIMELIMIT = 15576 %WEEKLY GAVAGE FOR 1 YEAR; LIFETIME FOLLOW-UP 

33 (AVG 424-649 DAYS); USED MAXIMUM OF 649 DAYS 

34 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

35 EXP_TIME_OFF = 8736 %2208 %tIME AT WHICH EXPOSURE ENDS (HOUR) 

36 DAY_CYCLE = 168 

37 WEEK_PERIOD = 8760 

38 WEEK_FINISH = 8760 

39 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

40 (HOUR) 

41 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS 

42 (HOUR) 

43 BW_T0 = 27 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION 

44 (G) 

 45 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-99 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 %EXPOSURE DOSE SCENARIOS (UG/KG) 

3 %MSTOT = 0.007 % EXPOSURE DOSE IN UG/KG 

4 %MSTOT = 0.7 % EXPOSURE DOSE IN UG/KG 

5 MSTOT = 7 % EXPOSURE DOSE IN UG/KG 

6 

7 C.2.5.2.6. White et al. (1986). 

8 output @clear 

9 prepare @clear 

10 prepare T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CBNDLINGKG 

 11 

12 % White et al 1986 

13 %built and check in August 7 2009 

 14 

15 %protocol: oral exposure single dose 

16 %dose levels: 0.714, 3.57, 7.14, 35.71, 71.43, 142.86 ng /kg/d ug/kg 1/day for 14 consecutive 

17 days 

18 %dose have been modified following Jeff email on Friday August 21 2009 

19 %dose levels: 10, 50, 100, 500, 1000, 2000 ng /kg/d ug/kg 1/day for 14 consecutive days 

20 %dose levels: 0.010, 0.050, 0.100, 0.500, 1.0, 2.0 ug /kg/d ug/kg 1/day for 14 consecutive days 

 21 

22 MAXT = 0.01 

23 CINT = 0.1 

24 TIMELIMIT = 336 

25 EXP_TIME_ON = 0. %TIME AT WHICH EXPOSURE BEGINS (HOUR) 

26 EXP_TIME_OFF = 336 %TIME AT WHICH EXPOSURE ENDS (HOUR) 

27 DAY_CYCLE = 24 

28 WEEK_PERIOD = 336 

29 WEEK_FINISH = 336 

30 BCK_TIME_ON = 0. %TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

31 (HOUR) 

32 BCK_TIME_OFF = 0. %TIME AT WHICH BACKGROUND EXPOSURE ENDS (HOUR) 

33 BW_T0 = 23 % BODY WEIGHT AT THE BEGINNING OF THE SIMULATION (G) 

 34 

35 %EXPOSURE DOSE SCENARIOS (UG/KG) 

36 %MSTOT = 0.010 % EXPOSURE DOSE IN UG/KG 

37 %MSTOT = 0.050 % EXPOSURE DOSE IN UG/KG 

38 %MSTOT = 0.100 % EXPOSURE DOSE IN UG/KG 

39 %MSTOT = 0.500 % EXPOSURE DOSE IN UG/KG 

40 %MSTOT = 1 % EXPOSURE DOSE IN UG/KG 

41 MSTOT = 2 % EXPOSURE DOSE IN UG/KG 

42 

43 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-100 DRAFT—DO NOT CITE OR QUOTE 

1 C.2.6. Mouse Gestational Model 

2 C.2.6.1. Model Code 

3 PROGRAM: 'Three Compartment PBPK Model for TCDD in Mice (Gestation)' 

4 ! Parameters were change may 16, 2002 

5 ! Come from {8MAI_CHR_PRE-EXP_GD} 

6 ! Come from {12_Mouse_GD}file 

7 !******************************************** 

8 !{{IMPORTANT-IMPORTANT-IMPORTANT-IMPORTANT}} 

9 ! REDUCTION OF MOTHER AND FETUS COMPARTMENT 

10 ! 2M_R_TCDD_JULY2002 ////(JULY 18,2002)//// 

11 !TCDD_RED_4Species_2003_4 ////(APR 8 ,2003)//// 

12 !TCDD_RED_4Species_2003_9 ////(APR 17 ,2003)//// 

13 !TCDD_RED_4Species_2003_12 ////(APR 17 ,2003)//// 

14 !***************************************************** 

15 !APRIL 18 2003 

16 !TCDD_4C_4SP_2003 ////(APR 18 ,2003)//// 

17 ! was ''Gest 4 species 1.csl'' but update July 2009 

 18 

19 !DevTCDD4Species_ICF_afterKKfix_v3_ratgest.csl 

20 !MICE_GESTATIONAL_ICF_F092309.csl 

21 !MICE_GESTATIONAL_ICF_F100609.csl 

22 !***************************************************** 

 23 

24 !Legend/Legend/Legend/Legend/Legend/Legend/Legend/Legend/ 

25 !Legend for this PBPK model 

26 !Mating: control the tenure of exchange between fetus and 

27 !Mother and also control imitated tissue growth 

28 !Ctrl: WTFE, WFO, WPLA0, QPLAF,WT0 

29 !(for rat, mouse, human, and monkey) 

30 !Control transfer from mother to fetus and fetus to mother by TRANSTIME_ON 

31 !SWITCH_trans = 0 NO TRANSFER 

32 !SWITCH_trans = 1 TRANSFER OCCURS 

33 !Gest_off = 1 

34 !Gest_on= 0. 

35 ! These switches are also controlled by mating parameters 

 36 

37 INITIAL ! 

 38 

39 !SIMULATION PARAMETERS ==== 

40 CONSTANT PARA_ZERO = 1E-30 

41 CONSTANT EXP_TIME_ON = 288. ! TIME AT WHICH EXPOSURE BEGINS 

42 (HOURS) 

43 CONSTANT EXP_TIME_OFF = 504 ! TIME AT WHICH EXPOSURE ENDS (HOURS) 

44 CONSTANT DAY_CYCLE = 504. ! NUMBER OF HOURS BETWEEN DOSES 

45 (HOURS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-101 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT BCK_TIME_ON = 0.0 ! TIME AT WHICH BACKGROUND EXPOSURE 

2 BEGINS (HOURS) 

3 CONSTANT BCK_TIME_OFF = 0.0 ! TIME AT WHICH BACKGROUND EXPOSURE 

4 ENDS (HOURS) 

5 CONSTANT TRANSTIME_ON = 144 !CONTROL TRANSFER FROM MOTHER TO 

6 FETUS AT GESTATIONAL DAY 6 

 7 

8 !UNIT CONVERSION 

9 CONSTANT MW=322 ! MOLECULAR WEIGHT (NG/NMOL) 

10 CONSTANT SERBLO = 0.55 

11 CONSTANT UNITCORR = 1000 

 12 

13 !INTRAVENOUS SEQUENCY 

14 constant IV_LACK = 0.0 

15 constant IV_PERIOD = 0.0 

 16 

17 !PREGNANCY PARAMETER ==== 

18 CONSTANT MATTING = 0.0 !BEGINNING OF MATING (HOUR) 

19 CONSTANT N_FETUS = 10 !NUMBER OF FETUS PRESENT 

 20 

21 !CONSTANT EXPOSURE CONTROL =========== 

22 !ACUTE, SUBCHRONIC, CHRONIC EXPOSURE ===== 

23 !OR BACKGROUND EXPOSURE (IN THIS CASE 3 TIMES A DAY)=== 

24 CONSTANT MSTOTBCKGR = 0.0 ! ORAL BACKGROUND EXPOSURE DOSE 

25 (UG/KG) 

26 CONSTANT MSTOT = 0.0 ! ORAL EXPOSURE DOSE (UG/KG) 

 27 

28 !ORAL ABSORPTION 

29 MSTOT_NM = MSTOT/MW !CONVERTS THE DOSE TO NMOL/G 

 30 

31 ! INTRAVENOUS ABSORPTION 

32 CONSTANT DOSEIV = 0.0 ! INJECTED DOSE (UG/KG) 

33 DOSEIV_NM = DOSEIV/MW ! CONVERTS THE INJECTED DOSE TO NMOL/G 

34 CONSTANT DOSEIVLATE = 0.0 ! INJECTED DOSE LATE (UG/KG) 

35 DOSEIVNMlate = DOSEIVLATE/MW !AMOUNT IN NMOL/G 

 36 

37 !INITIAL GUESS OF THE FREE CONCENTRATION IN THE LIGAND 

38 (COMPARTMENT INDICATED BELOW)==== 

39 CONSTANT CFLLI0 = 0.0 !LIVER (NMOL/ML) 

40 CONSTANT CFLPLA0 = 0.0 !PLACENTA (NMOL/ML) 

 41 

42 !BINDING CAPACITY (AhR) FOR NON LINEAR BINDING (COMPARTMENT 

43 INDICATED BELOW) (NMOL/ML) === 

44 CONSTANT LIBMAX = 3.5E-4 ! LIVER (NMOL/ML), WANG ET AL. 1997 

45 CONSTANT PLABMAX = 2.0E-4 !TEMPORARY PARAMETER 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-102 DRAFT—DO NOT CITE OR QUOTE 

1 ! PROTEIN AFFINITY CONSTANTS (1A2 OR AhR, COMPARTMENT INDICATED 

2 BELOW) (NMOL/ML)=== 

3 CONSTANT KDLI = 1.0E-4 !LIVER (AhR) (NMOL/ML), WANG ET AL. 1997 

4 CONSTANT KDLI2 = 4.0E-2 !LIVER (1A2) (NMOL/ML), EMOND ET AL. 2004 

5 CONSTANT KDPLA = 1.0E-4 !TEMPORARY PARAMETER (AhR) 

 6 

7 !EXCRETION AND ABSORPTION CONSTANT 

8 CONSTANT KST = 0.3 ! GASTRIC RATE CONSTANT (HR-1) 

9 CONSTANT KABS = 0.48 !INTESTINAL ABSORPTION CONSTANT (HR-1) ), 

10 WANG ET AL. 1997 

 11 

12 ! ELIMINATION CONSTANTS 

13 CONSTANT CLURI = 0.09 ! URINARY CLEARANCE (ML/HR) 

 14 

15 !TEST ELIMINATION VARIABLE 

16 constant kelv = 0.4 ! INTERSPECIES VARIABLE ELIMINATION CONSTANT 

17 (1/HOUR) 

 18 

19 ! CONSTANT TO DIVIDE THE ABSORPTION INTO LYMPHATIC AND PORTAL 

20 FRACTIONS 

21 CONSTANT A = 0.7 ! LYMPHATIC FRACTION, WANG ET AL. 1997 

 22 

23 !PARTITION COEFFICIENTS 

24 CONSTANT PF = 400 ! ADIPOSE TISSUE/BLOOD 

25 CONSTANT PRE = 3 ! REST OF THE BODY/BLOOD, WANG ET AL. 2000 

26 CONSTANT PLI = 6 ! LIVER/BLOOD, WANG ET AL. 1997 

27 CONSTANT PPLA = 3 ! TEMPORARY PARAMETER NOT CONFIGURED 

 28 

29 !PARAMETER FOR INDUCTION OF CYP 1A2, WANG ET AL. 1997 OR OPTIMIZED 

30 CONSTANT PAS_INDUC = 1 ! INCLUDE INDUCTION? (1 = YES, 0 = NO) 

31 CONSTANT CYP1A2_1OUTZ = 1.6 ! DEGRADATION CONCENTRATION 

32 CONSTANT OF 1A2 (NMOL/ML) (OPTIMIZED) 

33 CONSTANT CYP1A2_1A1 = 1.5 ! BASAL CONCENTRATION OF 1A1 (NMOL/ML), 

34 WANG ET AL . (2000) 

35 CONSTANT CYP1A2_1EC50 = 0.13 ! DISSOCIATION CONSTANT TCDD-CYP1A2 

36 (NMOL/ML) 

37 CONSTANT CYP1A2_1A2 = 1.5 !BASAL CONCENTRATION OF 1A2 

38 (NMOL/ML),WANG ET AL. (2000) 

39 CONSTANT CYP1A2_1KOUT = 0.1 ! FIRST ORDER RATE OF DEGRADATION (H-1) 

40 CONSTANT CYP1A2_1TAU = 1.5 !HOLDING TIME (H) (OPTIMIZED), WANG ET 

41 AL . (2000) 

42 CONSTANT CYP1A2_1EMAX = 600 ! MAXIMUM INDUCTION OVER BASAL 

43 EFFECT (UNITLESS) 

44 CONSTANT HILL = 0.6 !HILL CONSTANT; COOPERATIVELY LIGAND 

45 BINDING EFFECT CONSTANT (UNITLESS) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-103 DRAFT—DO NOT CITE OR QUOTE 

1 !DIFFUSIONAL PERMEABILITY FRACTION, WANG ET AL. 1997 

2 CONSTANT PAFF = 0.12 !ADIPOSE (UNITLESS) OPTIMIZED, WANG ET AL. 

2000 3 

4 CONSTANT PAREF = 0.03 !REST OF THE BODY (UNITLESS) 

5 CONSTANT PALIF = 0.35 !LIVER (UNITLESS) 

6 CONSTANT PAPLAF = 0.03 !TEMPORARY PARAMETER NOT CONFIGURED 

 7 

8 !FRACTION OF TISSUE WEIGHT ========= 

9 CONSTANT WLI0 = 0.0549 !LIVER ILSI (1994) 

 10 

11 !TISSUE BLOOD FLOW EXPRESSED AS A FRACTION OF CARDIAC OUTPUT 

12 CONSTANT QFF = 0.070 ! ADIPOSE TISSUE BLOOD FLOW FRACTION 

13 (UNITLESS), LEUNG ET AL. 1990 

14 CONSTANT QLIF = 0.161 !LIVER (UNITLESS), ILSI 1994 

 15 

16 !COMPARTMENT TISSUE BLOOD EXPRESSED AS A FRACTION OF THE TOTAL 

17 COMPARTMENT VOLUME 

18 CONSTANT WFB0 = 0.050 !ADIPOSE TISSUE, WANG ET AL. 1997 

19 CONSTANT WREB0 = 0.030 !REST OF THE BODY, WANG ET AL. 1997 

20 CONSTANT WLIB0 = 0.266 !LIVER, WANG ET AL. 1997 

21 CONSTANT WPLAB0 = 0.500 !TEMPORARY PARAMETER NOT CONFIGURED 

 22 

23 !EXPOSURE SCENARIO FOR UNIQUE OR REPETITIVE WEEKLY OR MONTHLY 

24 EXPOSURE 

25 !NUMBER OF EXPOSURES PER WEEK 

26 CONSTANT WEEK_LACK = 0.0 !DELAY BEFORE EXPOSURE ENDS (WEEK) 

27 CONSTANT WEEK_PERIOD = 168 ! NUMBER OF HOURS IN THE WEEK (HOURS) 

28 CONSTANT WEEK_FINISH = 168 ! TIME EXPOSURE ENDS (HOURS) 

 29 

30 !NUMBER OF EXPOSURES PER MONTH 

31 CONSTANT MONTH_LACK = 0.0 !DELAY BEFORE EXPOSURE BEGINS 

32 (MONTH) 

 33 

34 !CONSTANT FOR BACKGROUND EXPOSURE=========== 

35 CONSTANT Day_LACK_BG = 0.0 ! DELAY BEFORE EXPOSURE BEGINS (HOUR) 

36 CONSTANT Day_PERIOD_BG = 24 !LENGTH OF EXPOSURE (HOUR) 

 37 

38 !NUMBER OF EXPOSURES PER WEEK 

39 CONSTANT WEEK_LACK_BG = 0.0 !DELAY BEFORE BACKGROUD EXPOSURE 

40 (WEEK) 

41 CONSTANT WEEK_PERIOD_BG = 168 ! NUMBER OF HOURS IN THE WEEK 

42 (HOURS) 

43 CONSTANT WEEK_FINISH_BG = 168 !TIME EXPOSURE ENDS (HOURS) 

 44 

45 !INITIAL BODY WEIGHT 

46 CONSTANT BW_T0 = 30 ! WANG ET AL. 1997 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-104 DRAFT—DO NOT CITE OR QUOTE 

1 CONSTANT RATIO_RATF_MOUSEF = 0.2 !RATIO OF FETUS MOUSE/RAT AT 

2 GESTATIONAL DAY 22 

3 ! FOR RAT (1) AND FOR MOUSE (0.2) 

 4 

5 !COMPARTMENT LIPID EXPRESSED AS THE FRACTION OF TOTAL LIPID, POULIN 

6 ET AL. 2002 

7 CONSTANT F_TOTLIP = 0.855 ! ADIPOSE TISSUE (UNITLESS) 

8 CONSTANT B_TOTLIP = 0.0033 ! BLOOD (UNITLESS) 

9 CONSTANT RE_TOTLIP = 0.019 ! REST OF THE BODY (UNITLESS) 

10 CONSTANT LI_TOTLIP = 0.060 ! LIVER (UNITLESS) 

11 CONSTANT PLA_TOTLIP = 0.019 ! PLACENTA (UNITLESS) 

12 CONSTANT FETUS_TOTLIP = 0.019 ! FETUS (UNITLESS) 

 13 

14 END ! END OF THE INITIAL SECTION 

 15 

16 DYNAMIC ! DYNAMIC SIMULATION SECTION 

17 ALGORITHM IALG = 2 ! GEAR METHOD 

18 CINTERVAL CINT = 0.1 ! COMMUNICATION INTERVAL 

19 MAXTERVAL MAXT = 1.0e+10 ! MAXIMUM CALCULATION INTERVAL 

20 MINTERVAL MINT = 1.0E-10 ! MINIMUM CALCULATION INTERVAL 

21 VARIABLE T = 0.0 

22 CONSTANT TIMELIMIT = 313 !SIMULATION LIMIT TIME (HOUR) 

23 CINTXY = CINT 

24 PFUNC = CINT 

 25 

26 !TIME CONVERSION 

27 DAY = T/24 ! TIME IN DAYS 

28 WEEK = T/168 ! TIME IN WEEKS 

29 MONTH = T/730 ! TIME IN MONTHS 

30 YEAR = T/8760 ! TIME IN YEARS 

 31 

32 DERIVATIVE ! PORTION OF CODE THAT SOLVES DIFFERENTIAL EQUATIONS 

 33 

34 !CHRONIC OR SUBCHRONIC EXPOSURE SCENARIO ======= 

35 !NUMBER OF EXPOSURES PER DAY 

36 DAY_LACK = EXP_TIME_ON ! DELAY BEFORE EXPOSURE BEGINS (HOURS) 

37 DAY_PERIOD = DAY_CYCLE ! EXPOSURE PERIOD (HOURS) 

38 DAY_FINISH = CINTXY ! LENGTH OF EXPOSURE (HOURS) 

39 MONTH_PERIOD = TIMELIMIT ! EXPOSURE PERIOD (MONTHS) 

40 MONTH_FINISH = EXP_TIME_OFF ! LENGTH OF EXPOSURE (MONTHS) 

 41 

42 !NUMBER OF EXPOSURES PER DAY AND MONTH 

43 DAY_FINISH_BG = CINTXY 

44 MONTH_LACK_BG = BCK_TIME_ON !DELAY BEFORE BACKGROUD EXPOSURE 

45 BEGINS (MONTHS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-105 DRAFT—DO NOT CITE OR QUOTE 

1 MONTH_PERIOD_BG = TIMELIMIT !BACKGROUND EXPOSURE PERIOD 

2 (MONTHS) 

3 MONTH_FINISH_BG = BCK_TIME_OFF !LENGTH OF BACKGROUND EXPOSURE 

4 (MONTHS) 

 5 

6 !INTRAVENOUS LATE 

7 IV_FINISH = CINTXY 

8 B = 1-A ! FRACTION OF DIOXIN ABSORBED IN THE PORTAL FRACTION OF THE 

9 LIVER 

 10 

 11 

12 !FETUS,VOLUME,FETUS,VOLUME,FETUS,VOLUME,FETUS,VOLUME,FETUS,VOLUM

13 E,FETUS,VOLUME 

14 ! FROM OFLAHERTY_1992 

 15 

16 RTESTGEST= T-MATTING 

17 TESTGEST=DIM(RTESTGEST,0.0) 

 18 

19 WTFER_RODENT= (2.3d-3*EXP(1.49d-2*(TESTGEST))+1.3d-2)*Gest_on 

20 WTFER = (WTFER_RODENT*RATIO_RATF_MOUSEF*N_FETUS) 

21 WTFE = DIM(WTFER,0.0) 

 22 

23 ! 

24 FAT,VOLUME,FAT,VOLUME,FAT,VOLUME,FAT,VOLUME,FAT,VOLUME,FAT,VOLU

25 ME,FAT,VOLUME 

26 ! FAT GROWTH EXPRESSION LINEAR DURING PREGNANCY 

27 ! FROM O'FLAHERTY_1992 

 28 

29 WF0= (((9.66d-5*(TESTGEST))*gest_on)+0.069) 

 30 

31 ! PLACENTA,VOLUME, PLACENTA,VOLUME, PLACENTA,VOLUME, 

32 PLACENTA,VOLUME 

33 ! WPLA PLACENTA GROWTH EXPRESSION, SINGLE EXPONENTIAL WITH OFFSET 

34 ! FROM O'FLAHERTY_1992 ! FOR EACH PUP 

 35 

36 WPLA0N_RODENT = (0.6/(1+(5d+3*EXP(-0.0225*(TESTGEST)))))*N_FETUS 

37 WPLA0R = (WPLA0N_RODENT/WT0)*Gest_on 

38 WPLA0 = DIM(WPLA0R,0.0) 

 39 

40 ! PLACENTA,FLOW RATE, PLACENTA,FLOW RATE, PLACENTA,FLOW RATE, 

41 PLACENTA,FLOW RATE 

42 ! QPLA PLACENTA GROWTH EXPRESSION, DOUBLE EXPONENTIAL WITH OFFSET 

43 ! FROM O'FLAHERTY_1992 

 44 

45 QPLARF = (1.67d-7 *exp(9.6d-3*(TESTGEST)) & 

46 +1.6d-3*exp(7.9d-3*(TESTGEST))+0.0)*Gest_on*SWITCH_trans 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-106 DRAFT—DO NOT CITE OR QUOTE 

1 QPLAF=DIM(QPLARF,0.0) !FRACTION OF FLOW RATE IN PLACENTA 

 2 

3 ! GESTATION CONTROL 

4 IF (T.LT.MATTING) THEN 

5 Gest_off = 1 

6 Gest_on= 0.0 

7 ELSE 

8 Gest_off = 0.0 

9 Gest_on = 1 

10 END IF 

 11 

12 ! MOTHER BODY WEIGHT GROWTH EQUATION======== 

13 ! MODIFICATION TO ADAPT THIS MODEL AT HUMAN MODEL 

14 ! BECAUSE LINEAR DESCRIPTION IS NOT GOOD ENOUGH FOR MOTHER GROWTH 

15 ! MOTHER BODY WEIGHT GROWTH 

 16 

17 PARAMETER (BW_RMN = 1.0E-30) 

18 WT0= BW_T0 *(1.0+(0.41*T)/(1402.5+T+BW_RMN)) 

 19 

20 ! VARIABILITY OF REST OF THE BODY DEPENDS ON OTHER ORGANS 

21 WRE0 = (0.91 - (WLIB0*WLI0 + WFB0*WF0 +WPLAB0*WPLA0 + WLI0 + WF0 + 

22 WPLA0))/(1.0+WREB0) ! REST OF THE BODY FRACTION; UPDATED FOR EPA 

23 ASSESSMENT 

24 QREF = 1.0-(QFF+QLIF+QPLAF) !REST OF BODY BLOOD FLOW RATE (ML/HR) 

25 QTTQF = QFF+QREF+QLIF+QPLAF ! SUM MUST EQUAL 1 

 26 

27 ! COMPARTMENT VOLUME (ML OR G) ========= 

28 WF = WF0 * WT0 ! ADIPOSE TISSUE 

29 WRE = WRE0 * WT0 ! REST OF THE BODY 

30 WLI = WLI0 * WT0 ! LIVER 

31 WPLA= WPLA0* WT0 ! PLACENTA 

 32 

33 ! COMPARTMENT TISSUE BLOOD (ML OR G) ========= 

34 WFB = WFB0 * WF ! ADIPOSE TISSUE 

35 WREB = WREB0 * WRE ! REST OF THE BODY 

36 WLIB = WLIB0 * WLI ! LIVER 

37 WPLAB = WPLAB0* WPLA ! PLACANTA 

 38 

39 ! CARDIAC OUTPUT FOR THE GIVEN BODY WEIGHT 

40 !QC= QCCAR*60*(WT0/1000.0)**0.75 

41 CONSTANT QCC=16500 ! EQUIVALENT TO 275 * 60 

42 QC= QCC*(WT0/UNITCORR)**0.75 

 43 

44 !COMPARTMENT BLOOD FLOW RATE (ML/HR) 

45 QF = QFF*QC !ADIPOSE TISSUE BLOOD FLOW RATE 

46 QLI = QLIF*QC !LIVER TISSUE BLOOD FLOW RATE 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-107 DRAFT—DO NOT CITE OR QUOTE 

1 QRE = QREF*QC !REST OF THE BODY BLOOD FLOW RATE 

2 QPLA = QPLAF*QC !PLACENTA TISSUE BLOOD FLOW RATE 

3 QTTQ = QF+QRE+QLI+QPLA !TOTAL FLOW RATE 

 4 

5 !PERMEABILITY ORGAN FLOW (ML/HR)========= 

6 PAF = PAFF*QF ! ADIPOSE TISSUE 

7 PARE = PAREF*QRE ! REST OF THE BODY 

8 PALI = PALIF*QLI ! LIVER TISSUE 

9 PAPLA = PAPLAF*QPLA ! PLACENTA 

 10 

11 !************************************** 

12 ! ABSORPTION SECTION 

13 ! ORAL, 

14 ! INTRAPERITONEAL, 

15 ! INTRAVENOUS 

16 !************************************** 

 17 

18 !REPETITIVE ORAL BACKGROUND EXPOSURE SCENARIO 

 19 

20 MSTOT_NMBCKGR = MSTOTBCKGR/322 !AMOUNT IN NMOL/G 

21 MSTTBCKGR =MSTOT_NMBCKGR *WT0 

 22 

23 DAY_EXPOSURE_BG = PULSE(DAY_LACK_BG,DAY_PERIOD_BG,DAY_FINISH_BG) 

24 WEEK_EXPOSURE_BG = 

25 PULSE(WEEK_LACK_BG,WEEK_PERIOD_BG,WEEK_FINISH_BG) 

26 MONTH_EXPOSURE_BG = 

27 PULSE(MONTH_LACK_BG,MONTH_PERIOD_BG,MONTH_FINISH_BG) 

 28 

29 MSTTCH_BG = 

30 (DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG)*MSTTBCK

31 GR 

32 MSTTFR_BG = MSTTBCKGR/CINT 

 33 

34 CYCLE_BG =DAY_EXPOSURE_BG*WEEK_EXPOSURE_BG*MONTH_EXPOSURE_BG 

 35 

36 ! CONDITIONAL ORAL EXPOSURE (BACKGROUND EXPOSURE) 

 37 

38 IF (MSTTCH_BG.EQ.MSTTBCKGR) THEN 

39 ABSMSTT_GB= MSTTFR_BG 

40 ELSE 

41 ABSMSTT_GB = 0.0 

42 END IF 

 43 

44 CYCLETOTBG=INTEG(CYCLE_BG,0.0) 

 45 

46 !REPETITIVE ORAL EXPOSURE SCENARIO 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-108 DRAFT—DO NOT CITE OR QUOTE 

 1 

2 MSTT= MSTOT_NM * WT0 !AMOUNT IN NMOL 

 3 

4 DAY_EXPOSURE = PULSE(DAY_LACK,DAY_PERIOD,DAY_FINISH) 

5 WEEK_EXPOSURE = PULSE(WEEK_LACK,WEEK_PERIOD,WEEK_FINISH) 

6 MONTH_EXPOSURE = PULSE(MONTH_LACK,MONTH_PERIOD,MONTH_FINISH) 

 7 

8 MSTTCH = (DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE)*MSTT 

9 MSTTFR = MSTT/CINT 

 10 

11 CYCLE = DAY_EXPOSURE*WEEK_EXPOSURE*MONTH_EXPOSURE 

12 SUMEXPEVENT= INTEG (CYCLE,0.0)/cint !NUMBER OF CYCLES GENERATED 

13 DURING SIMULATION 

 14 

15 ! CONDITIONAL ORAL EXPOSURE 

16 IF (MSTTCH.EQ.MSTT) THEN 

17 ABSMSTT= MSTTFR 

18 ELSE 

19 ABSMSTT = 0.0 

20 END IF 

 21 

 22 

23 CYCLETOT=INTEG(CYCLE,0.0) 

 24 

25 ! MASS CHANGE IN THE LUMEN 

26 RMSTT= -(KST+KABS)*MST +ABSMSTT +ABSMSTT_GB ! RATE OF CHANGE 

27 (NMOL/H) 

28 MST = INTEG(RMSTT,0.0) !AMOUNT REMAINING IN DUODENUM 

29 (NMOL) 

 30 

31 ! ABSORPTION IN LYMPH CIRCULATION 

32 LYRMLUM = KABS*MST*A 

33 LYMLUM = INTEG(LYRMLUM,0.0) 

 34 

35 ! ABSORPTION IN PORTAL CIRCULATION 

36 LIRMLUM = KABS*MST*B 

37 LIMLUM = INTEG(LIRMLUM,0.0) 

 38 

 39 

40 ! -----IV EXPOSURE --------- 

 41 

42 IV= DOSEIV_NM * WT0 !AMOUNT IN NMOL 

43 IVR= IV/PFUNC ! RATE FOR IV INFUSION IN BLOOD 

44 EXPIV= IVR * (1.0-STEP(PFUNC)) 

45 IVDOSE = integ(EXPIV,0.0) 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-109 DRAFT—DO NOT CITE OR QUOTE 

1 !------IV late in the cycle 

2 ! MODIFICATION ON January 13 2004 

3 IV_RlateR = DOSEIVNMlate*WT0 

4 IV_EXPOSURE=PULSE(IV_LACK,IV_PERIOD,IV_FINISH) 

 5 

6 IV_lateT = IV_EXPOSURE *IV_RlateR 

7 IV_late = IV_lateT/CINT 

 8 

9 SUMEXPEVENTIV= integ (IV_EXPOSURE,0.0) !NUMBER OF CYCLE GENERATE 

10 DURING SIMULATION 

 11 

12 !SYSTEMIC CONCENTRATION OF TCDD 

13 ! MODIFICATION ON OCTOBER 6, 2009 

 14 

15 CB=(QF*CFB+QRE*CREB+QLI*CLIB+EXPIV+LYRMLUM+QPLA*CPLAB+IV_late)/(QC

16 +CLURI) ! 

17 CA = CB ! CONCENTRATION (NMOL/ML) 

 18 

19 !URINARY EXCRETION BY KIDNEY 

20 !MODIFICATION ON OCTOBER 6, 2009 

21 RAURI = CLURI *CB 

22 AURI = INTEG(RAURI,0.0) 

 23 

24 !UNIT CONVERSION POST SIMULATION 

25 CBSNGKGLIADJ=(CB*MW*UNITCORR*(1/B_TOTLIP)*(1/SERBLO))![NG of TCDD 

26 Serum/Kg OF LIPIP] 

27 AUCBS_NGKGLIADJ=integ(CBSNGKGLIADJ,0.0) 

 28 

29 PRCT_B = (CB/(MSTT+1E-30))*100 ! PERCENT OF ORAL DOSE IN BLOOD 

30 PRCT_BIV = (CB/(IV_RlateR+1E-30))*100 ! PERCENT OF IV DOSE IN BLOOD 

31 CBNGKG= CB*MW*UNITCORR 

32 CBNGG = CB*MW 

 33 

34 !ADIPOSE COMPARTMENT 

35 !TISSUE BLOOD COMPARTMENT 

36 RAFB= QF*(CA-CFB)-PAF*(CFB-CF/PF) !(NMOL/H) 

37 AFB = INTEG(RAFB,0.0) !(NMOL) 

38 CFB = AFB/WFB !(NMOL/ML) 

39 !TISSUE COMPARTMENT 

40 RAF = PAF*(CFB-CF/PF) !(NMOL/H) 

41 AF = INTEG(RAF,0.0) !(NMOL) 

42 CF = AF/WF !(NMOL/ML) 

 43 

44 !UNIT CONVERSION POST SIMULATION 

45 CFTOTAL= (AF + AFB)/(WF + WFB) ! TOTAL CONCENTRATION IN NMOL/ML 

46 CFTFREE = CFB + CF !TOTAL FREE CONCENTRATION IN FAT (NM/ML) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-110 DRAFT—DO NOT CITE OR QUOTE 

1 PRCT_F = (CFTOTAL/(MSTT+1E-30))*100 ! PERCENT OF ORAL DOSE IN FAT 

2 PRCT_FIV = (CFTOTAL/(IV_RlateR+1E-30))*100 ! PERCENT OF IV DOSE IN FAT 

3 CFNGKG=CFTOTAL*MW*UNITCORR ! FAT CONCENTRATION IN NG/KG 

4 AUCF_NGKGH=integ(CFNGKG,0.0) 

5 CFNGG = CFTOTAL*MW 

 6 

7 !REST OF THE BODY COMPARTMENT 

8 RAREB= QRE *(CA-CREB)-PARE*(CREB-CRE/PRE) !(NMOL/H) 

9 AREB = INTEG(RAREB,0.0) !(NMOL) 

10 CREB = AREB/WREB !(NMOL/H) 

11 !TISSUE COMPARTMENT 

12 RARE = PARE*(CREB - CRE/PRE) !(NMOL/H) 

13 ARE = INTEG(RARE,0.0) !(NMOL) 

14 CRE = ARE/WRE !(NMOL/ML) 

 15 

16 !UNIT CONVERSION POST SIMULATION 

17 CRETOTAL= (ARE + AREB)/(WRE + WREB) ! TOTAL CONCENTRATION IN 

18 NMOL/ML 

19 PRCT_RE = (CRETOTAL/(MSTT+1E-30))*100 ! PERCENT OF ORAL DOSE IN REST OF 

20 BODY 

21 PRCT_REIV = (CRETOTAL/(IV_RlateR+1E-30))*100 ![ PERCENT OF IV DOSE IN REST 

22 OF THE BODY ] 

23 CRENGKG=CRETOTAL*MW*UNITCORR ! REST OF THE BODY CONCENTRATION 

24 IN NG/KG 

 25 

 26 

27 !LIVER COMPARTMENT 

28 !TISSUE BLOOD COMPARTMENT 

29 RALIB = QLI*(CA-CLIB)-PALI*(CLIB-CFLLIR)+LIRMLUM ! 

30 ALIB = INTEG(RALIB,0.0) !(NMOL) 

31 CLIB = ALIB/WLIB !(NMOL/ML) 

32 !TISSUE COMPARTMENT 

33 RALI = PALI*(CLIB - CFLLIR)-REXCLI ! (NMOL/HR) 

34 ALI = INTEG(RALI,0.0) !(NMOL) 

35 CLI = ALI/WLI !(NMOL/ML) 

 36 

37 !FREE TCDD IN LIVER COMPARTMENT 

38 PARAMETER (LIVER_1RMN = 1.0E-30) 

39 CFLLI= IMPLC(CLI-(CFLLIR*PLI+(LIBMAX*CFLLIR/(KDLI+CFLLIR & 

40 +LIVER_1RMN))+((CYP1A2_1O3*CFLLIR/(KDLI2 + CFLLIR & 

41 +LIVER_1RMN)*PAS_INDUC)))-CFLLI,CFLLI0) 

42 CFLLIR=DIM(CFLLI,0.0) ! FREE CONCENTRATION IN LIVER 

 43 

44 CBNDLI= LIBMAX*CFLLIR/(KDLI+CFLLIR+LIVER_1RMN) !BOUND 

45 CONCENTRATION 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-111 DRAFT—DO NOT CITE OR QUOTE 

1 !VARIABLE ELIMINATION BASED ON THE CYP1A2 

2 KBILE_LI_T =((CYP1A2_1OUT-CYP1A2_1A2)/CYP1A2_1A2)*Kelv ! INDUCED 

3 BILIARY EXCRETION RATE CONSTANT 

4 REXCLI = KBILE_LI_T*CFLLIR*WLI ! DOSE-DEPENDENT EXCRETION RATE 

5 EXCLI = INTEG(REXCLI,0.0) 

 6 

7 !UNIT CONVERSION POST SIMULATION 

8 CLITOTAL= (ALI + ALIB)/(WLI + WLIB) ! TOTAL CONCENTRATION IN NMOL/ML 

9 PRCT_LI = (CLITOTAL/(MSTT+1E-30))*100 ! PERCENT ORAL DOSE IN LIVER 

10 PRCT_LIIV = (CLITOTAL/(IV_RlateR+1E-30))*100 ! PERCENT IV DOSE IN LIVER 

11 Rec_occ= CFLLIR/(KDLI+CFLLIR) 

12 CLINGKG=CLITOTAL*MW*UNITCORR ! LIVER CONCENTRATION IN NG/KG 

13 AUCLI_NGKGH=INTEG(CLINGKG,0.0) 

14 CBNDLINGKG = CBNDLI*MW*UNITCORR 

15 AUCBNDLI_NGKGH =INTEG(CBNDLINGKG,0.0) 

16 CLINGG = CLITOTAL*MW 

 17 

18 !CHEMICAL IN CYP450 (1A2) COMPARTMENT 

19 CYP1A2_1KINP = CYP1A2_1KOUT* CYP1A2_1OUTZ ! BASAL RATE OF CYP1A2 

20 PRODUCTION SET EQUAL TO BASAL RATE OF DEGREDATION 

 21 

22 ! MODIFICATION ON OCTOBER 6, 2009 

23 CYP1A2_1OUT =INTEG(CYP1A2_1KINP * (1.0 + CYP1A2_1EMAX *(CBNDLI+1.0e24 30)**HILL & 

25 /(CYP1A2_1EC50**HILL + (CBNDLI+1.0e-30)**HILL)) & 

26 - CYP1A2_1KOUT*CYP1A2_1OUT, CYP1A2_1OUTZ) 

 27 

28 ! EQUATIONS INCORPORATING DELAY OF CYP1A2 PRODUCTION (NOT USED IN 

29 SIMULATIONS) 

 30 

31 CYP1A2_1RO2 = (CYP1A2_1OUT - CYP1A2_1O2)/ CYP1A2_1TAU 

32 CYP1A2_1O2 =INTEG(CYP1A2_1RO2, CYP1A2_1A1) 

 33 

34 CYP1A2_1RO3 = (CYP1A2_1O2 - CYP1A2_1O3)/ CYP1A2_1TAU 

35 CYP1A2_1O3 =INTEG(CYP1A2_1RO3, CYP1A2_1A2) 

 36 

37 ! TRANSFER OF DIOXIN FROM PLACENTA TO FETUS 

38 ! FETAL EXPOSURE ONLY DURING EXPOSURE 

 39 

40 IF (T.LT.TRANSTIME_ON) THEN 

41 SWITCH_trans = 0.0 

42 ELSE 

43 SWITCH_trans = 1 

44 END IF 

 45 

46 !TRANSFER OF DIOXIN FROM PLACENTA TO FETUS 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-112 DRAFT—DO NOT CITE OR QUOTE 

1 ! MODIFICATION 26 SEPTEMBER 2003 

 2 

3 CONSTANT PFETUS= 4 ! 

4 CONSTANT CLPLA_FET = 0.17 ! 

 5 

6 RAMPF = (CLPLA_FET*CPLA) *SWITCH_trans 

7 AMPF=INTEG(RAMPF,0.0) 

 8 

9 !TRANSFER OF DIOXIN FROM FETUS TO PLACENTA 

10 RAFPM = (CLPLA_FET*CFETUS_v)*SWITCH_trans ! 

11 AFPM = INTEG(RAFPM,0.0) 

 12 

13 ! TCDD IN PLACENTA MOTHER COMPARTMENT 

14 RAPLAB= QPLA*(CA - CPLAB)-PAPLA*(CPLAB -CFLPLAR) ! NMOL/H) 

15 APLAB = INTEG(RAPLAB,0.0) ! (NMOL) 

16 CPLAB = APLAB/(WPLAB+1E-30) ! (NMOL/ML) 

17 RAPLA = PAPLA*(CPLAB-CFLPLAR)-RAMPF + RAFPM ! (NMOL/H) 

18 APLA = INTEG(RAPLA,0.0) ! (NMOL) 

19 CPLA = APLA/(WPLA+1e-30) ! (NMOL/ML) 

 20 

21 PARAMETER (PARA_ZERO = 1.0E-30) 

22 CFLPLA= IMPLC(CPLA-(CFLPLAR*PPLA +(PLABMAX*CFLPLAR/(KDPLA& 

23 +CFLPLAR+PARA_ZERO)))-CFLPLA,CFLPLA0) 

24 CFLPLAR=DIM(CFLPLA,0.0) 

 25 

26 !UNIT CONVERSION POST SIMULATION 

27 CPLATOTAL= (APLA + APLAB)/((WPLA + WPLAB)+1e-30)! TOTAL 

28 CONCENTRATION IN NMOL/ML 

29 PRCT_PLA = (CPLATOTAL/(MSTT+1E-30))*100 

30 PRCT_PLAIV = (CPLATOTAL/(IV_RlateR+1E-30))*100 

31 CPLANGG = CPLATOTAL*MW 

 32 

33 !FETUS COMPARTMENT 

34 RAFETUS= RAMPF-RAFPM 

35 AFETUS=INTEG(RAFETUS,0.0) 

36 CFETUS=AFETUS/(WTFE+1E-30) 

37 CFETOTAL= CFETUS 

38 CFETUS_v = CFETUS/PFETUS 

 39 

40 ! UNIT CONVERSION POST SIMULATION 

41 CFETUSNGKG = CFETUS*MW*UNITCORR !(NG/KG) 

42 AUC_FENGKGH = INTEG(CFETUSNGKG,0.0) 

43 PRCT_FE = (CFETOTAL/(MSTT+1E-30))*100 

44 PRCT_FEIV = (CFETOTAL/(IV_RlateR+1E-30))*100 

45 CFETUSNGG = CFETOTAL*MW 

 46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-113 DRAFT—DO NOT CITE OR QUOTE 

1 ! ------------CONTROL MASS BALANCE ---------- 

2 BDOSE= IVDOSE +LYMLUM+LIMLUM 

3 BMASSE = EXCLI+AURI+AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB+AFETUS 

4 BDIFF = BDOSE-BMASSE 

 5 

6 !BODY BURDEN (NG) 

7 BODY_BURDEN = AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB ! 

8 BBFETUSNG = AFETUS*MW*UNITCORR ! NG 

9 ! BODY BURDEN IN TERMS OF CONCENTRATION (NG/KG) 

10 BBNGKG 

11 =(((AFB+AF+AREB+ARE+ALIB+ALI+APLA+APLAB)/WT0)*MW*UNITCORR) ! 

12 AUC_BBNGKGH=INTEG(BBNGKG,0.0) 

 13 

 14 

15 ! ------------COMMAND OF THE END OF SIMULATION ---------- 

16 TERMT (T.GE. TimeLimit, 'Time limit has been reached.') 

17 END ! END OF THE DERIVATIVE SECTION 

18 END ! END OF THE DYNAMIC SECTION 

19 END ! END OF THE PROGRAM 

20 

21 C.2.6.2. Input Files 

22 C.2.6.2.1. Keller et al. (2007). 

23 %TO BE USED AFTER THE 

24 %clear variable 

25 output @clear 

26 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

27 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

28 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

29 %output @nciout=10 T SUMEXPEVENT wt0 

30 %kELLER ET AL 2007 

31 %protocol: SINGLE DOSE from GD13 

32 %dose levels: 0.01, 0.100 1 ug/kg at GD13 

33 %dose levels: 10, 100 1000 ng/kg at GD13 

 34 

35 %EXPOSURES SCENARIOS 

36 MAXT=0.01 

37 CINT =0.1 

38 EXP_TIME_ON = 312. % TIME AT WHICH EXPOSURE BEGINS(HOUR) 

39 EXP_TIME_OFF = 330 % TIME AT WHICH EXPOSURE ENDS (HOUR) 

40 DAY_CYCLE = 505 

41 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

42 (HOUR) 

43 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

44 (HOUR) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-114 DRAFT—DO NOT CITE OR QUOTE 

1 IV_LACK = 505 

2 IV_PERIOD = 505 

3 TIMELIMIT = 504 % SIMULATION TIME LIMIT (HOUR) 

4 BW_T0 = 24 

5 MATTING = 0. % BEGINNING OF MATING (HOUR) 

6 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 

7 N_FETUS = 10 

 8 

9 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 10 

11 %MSTOT = 0.01 % ORAL EXPOSURE DOSE IN UG/KG 

12 %MSTOT = 0.1 % ORAL EXPOSURE DOSE IN UG/KG 

13 MSTOT = 1 % ORAL EXPOSURE DOSE IN UG/KG 

14 

15 C.2.6.2.2. Li et al. (2005). 

16 %TO BE USED AFTER THE 

17 %clear variable 

18 output @clear 

19 prepare @clear T CLINGKG CFNGKG CBSNGKGLIADJ BBNGKG CFETUSNGKG 

20 AUCLI_NGKGH AUCF_NGKGH AUCBS_NGKGLIADJ AUC_BBNGKGH 

21 AUC_FENGKGH CBNDLINGKG AUCBNDLI_NGKGH 

22 %output @nciout=10 T SUMEXPEVENT 

23 %LI ET AL 2006 

24 %protocol: exposure repetitive DOSE from GD1 to GD3 

25 %dose levels: 0.002, 0.050 AND 0.10 ug/kg/day at GD1 TO GD8 

26 %dose levels: 2, 50 and 100 ng/kg/day from GD1 to GD8 

 27 

28 %EXPOSURES SCENARIOS 

29 MAXT=0.001 

30 CINT =0.1 

31 EXP_TIME_ON = 0. % TIME AT WHICH EXPOSURE BEGINS (HOUR) 

32 EXP_TIME_OFF = 70 % TIME AT WHICH EXPOSURE ENDS (HOUR); 2 HOURS 

33 LESS THAN GD8; SET EQUAL TO 70 TO BE SURE ONLY 3 DOSES ADMINISTERED 

34 % BECAUSE i STARTED TIME 0 FOR GD1 

35 DAY_CYCLE = 24 

36 BCK_TIME_ON = 0. % TIME AT WHICH BACKGROUND EXPOSURE BEGINS 

37 (HOUR) 

38 BCK_TIME_OFF = 0. % TIME AT WHICH BACKGROUND EXPOSURE ENDS 

39 (HOUR) 

40 IV_LACK = 505 

41 IV_PERIOD = 505 

42 TIMELIMIT = 216 % SIMULATION TIME LIMIT (HOUR) 

43 BW_T0 = 27 

44 MATTING = 0. % BEGINNING OF MATING (HOUR) 

45 TRANSTIME_ON = 144. % SHOULD BE MATING TIME + 6 DAYS (144 HOURS) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-115 DRAFT—DO NOT CITE OR QUOTE 

1 N_FETUS = 10 

 2 

3 %EXPOSURE DOSE SCENARIOS (UG/KG) 

 4 

5 MSTOT = 0.002 % ORAL EXPOSURE DOSE IN UG/KG 

6 %MSTOT = 0.05 % ORAL EXPOSURE DOSE IN UG/KG 

7 %MSTOT = 0.10 % ORAL EXPOSURE DOSE IN UG/KG 

 8 

9 C.3. TOXICOKINETIC MODELING RESULTS FOR KEY ANIMAL BIOASSAY 

10 STUDIES 

11 The simulated TCDD serum-adjusted lipid concentrations reported in this appendix for 

12 the rodent bioassays were converted to TCDD concentrations in rodent whole blood. Initially, 

13 EPA multiplied the serum-adjusted lipid concentrations by 0.0033, the ratio of lipid content to 

14 total serum volume, then by 0.55, the value of the hematocrit. This product yields the TCDD 

15 concentration in whole rodent blood as predicted by the PBPK model. EPA assumed that the 

16 same whole blood TCDD concentration would result in the same effects in humans and rodents. 

17 This conversion accomplishes the following: 

18 

19 1. Allows the human equivalent dose (HED) to be based on equivalent blood concentration 

20 (that represents serum plus erythrocyte TCDD), which is proportional to tissue exposure; 

21 2. Avoids criticism that the total blood concentration is normalized to serum lipid alone in 

22 an unbalanced way (thus EPA does not contradict Centers for Disease Control and 

23 Prevention (CDC) data or methods); 

24 3. Factors out any impact of the lipid content used in the PBPK model; and 

25 4. TCDD concentration in whole blood is encouraged for use in the assessments by the NAS 

26 (NAS, 2006, p. 43); see additional information in Section 3.3. 

 27 

28 C.3.1. Nongestational Studies 

29 C.3.1.1. Cantoni et al. (1981) 

Type: Rat Dose: 10, 100, 1000 ng/kg/week 

Strain: CD-COBS rats Route: Oral gavage 

Body weight: BW set to 125g Regime: 1 dose/week for 45 weeks 

Sex: Female Simulation 

time: 

7,584 hours 

(45 weeks + 24 hours before sacrifice) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-116 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,018 2,040 (@ 7,392 hours) 982 1.43 

CADM - - - 

Emond 4,868 14,649 (@ 7,392 hours) 4,242 14.29 

CADM - - - 

Emond 27,559 125,300 (@ 7,392 hours) 21,996 142.86 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 247 328 (@ 7,398 hours) 235 

1.43 

CADM 374 431 431 

Emond 2,175 2,860 (@ 7,399 hours) 1,837 14.29 

CADM 3,884 4,330 4,330 

Emond 20,488 26,978 (@ 7,399 hours) 16,255 142.86 

CADM 39,067 43,329 43,329 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 175 200 (@ 7,431 hours) 177 

1.43 

CADM 250 280 244 

Emond 837 938 (@ 7,427 hours) 780 

14.29 

CADM 1,209 1,352 1,167 

Emond 4,739 5,374 (@ 7,424 hours) 4,145 142.86 

CADM 10,050 11,224 9,734 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 26.1 31.7 (@ 7,398 hours) 25.6 1.43 

CADM 32.0 35.0 35.0 

Emond 170 210 (@ 7,398 hours) 149 

14.29 

CADM 225 243 243 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-117 DRAFT—DO NOT CITE OR QUOTE 

Emond 1,336 1,695 (@ 7,398 hours) 1,088 142.86 

CADM 2,106 2,266 2,266 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 6.04 7.76 (@ 7,396 hours) 5.88 1.43 

CADM - - - 

Emond 23.7 29.1 (@ 7,396 hours) 21.6 14.29 

CADM - - - 

Emond 66.8 80.0 (@ 1 hours) 62.0 

142.86 

CADM - - - 

1 C.3.1.2. Chu et al. (2007) 

Type: Rat Dose: 2.5, 25, 250, and 1,000 ng/kg-day 

Strain: Sprague-Dawley Route: Oral gavage 

Body weight: 200 g Regime: 1 dose per day for 28 days 

Sex: Female Simulation time: 672 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 696 1,295 (@ 648 hours) 1,036 2.5 

CADM - - - 

Emond 4,222 8,403 (@ 648 hours) 5,727 25 

CADM - - - 

Emond 26,889 62,067 (@ 648 hours) 35,103 250 

CADM - - - 

Emond 93,213 230,320 (@ 648 hours) 122,200 1,000 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-118 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 148 268 (@ 652 hours) 255 

2.5 

CADM - - - 

Emond 1,777 2,953 (@ 653 hours) 2,806 25 

CADM - - - 

Emond 19,232 30,262 (@ 653 hours) 28,668 250 

CADM - - - 

Emond 77,819 120,400 (@ 653 hours) 113,890 1,000 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 108 180 (@ 668 hours) 180 

2.5 

CADM - - - 

Emond 660 1,020 (@ 659 hours) 1,015 25 

CADM - - - 

Emond 4,210 6,433 (@ 655 hours) 6,354 250 

CADM - - - 

Emond 14,576 22,610 (@ 655 hours) 22,280 1,000 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 16.1 27.5 (@ 652 hours) 26.9 

2.5 

CADM - - - 

Emond 138 222 (@ 652 hours) 214 

25 

CADM - - - 

Emond 1,239 1,935 (@ 652 hours) 1,842 250 

CADM - - - 

Emond 4,801 7,444 (@ 652 hours) 7,067 1,000 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-119 DRAFT—DO NOT CITE OR QUOTE 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 4.15 6.51 (@ 652 hours) 6.21 

2.5 

CADM - - - 

Emond 20.5 28.5 (@ 652 hours) 27.4 

25 

CADM - - - 

Emond 63.3 76.0 (@ 652 hours) 74.7 

250 

CADM - - - 

Emond 90.2 99.0 (@ 653 hours) 98.3 

1,000 

CADM - - - 

1 C.3.1.3. Crofton et al. (2005) 

Type: Rats Dose: 0, 0.1, 3, 10, 30, 100, 300, 1000, 3000, 

and 10,000 ng/kg-day 

Strain: Long Evans Route: Oral gavage 

Body weight: 4 weeks old 

BW set to 190 g 

Regime: One dose per day for four days 

Sex: Female Simulation time: 96 hours 

2 a 3 The CADM model was not run because the dosing duration is lower than the resolution of the model (1 week) 

4 

5 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 11.1 22.4 (@ 72 hours) 13.5 

0.1 

CADM - - - 

Emond 269 605 (@ 72 hours) 321 

3 

CADM - - - 

Emond 763 1,873 (@ 72 hours) 892 

10 

CADM - - - 

Emond 1,905 5,202 (@ 72 hours) 2,169 30 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-120 DRAFT—DO NOT CITE OR QUOTE 

Emond 5,104 15,972 (@ 72 hours) 5,605 100 

CADM - - - 

Emond 12,706 44,982 (@ 72 hours) 13,509 300 

CADM - - - 

Emond 36,170 143,340 (@ 72 hours) 37,554 1000 

CADM - - - 

Emond 99,645 420,850 (@ 72 hours) 102,860 3000 

CADM - - - 

Emond 321,480 1,392,100 (@ 72 

hours) 334,220 10,000 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 0.919 1.55 (@ 75 hours) 1.18 

0.1 

CADM - - - 

Emond 37.4 62.6 (@ 76 hours) 53.3 

3 

CADM - - - 

Emond 145 242 (@ 77 hours) 214 

10 

CADM - - - 

Emond 494 818 (@ 78 hours) 742 

30 

CADM - - - 

Emond 1,839 3,025 (@ 78 hours) 2,793 100 

CADM - - - 

Emond 5,925 9,692 (@ 78 hours) 9,028 300 

CADM - - - 

Emond 20,717 33,738 (@ 79 hours) 31,564 1000 

CADM - - - 

Emond 63,511 103,140 (@ 79 hours) 96,545 3000 

CADM - - - 

Emond 212,890 344,910 (@ 79 hours) 321,960 10,000 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-121 DRAFT—DO NOT CITE OR QUOTE 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1.00 1.93 (@ 96 hours) 1.93 

0.1 

CADM - - - 

Emond 24.6 45.9 (@ 96 hours) 45.9 

3 

CADM - - - 

Emond 70.3 129 (@ 96 hours) 129 

10 

CADM - - - 

Emond 177 317 (@ 96 hours) 317 

30 

CADM - - - 

Emond 480 838 (@ 96 hours) 838 

100 

CADM - - - 

Emond 1,206 2,065 (@ 96 hours) 2,065 300 

CADM - - - 

Emond 3,452 5,836 (@ 96 hours) 5,836 1000 

CADM - - - 

Emond 9,522 16,050 (@ 96 hours) 16,050 3000 

CADM - - - 

Emond 30,657 51,918 (@ 96 hours) 51,918 10,000 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 0.138 0.224 (@ 79 hours) 0.223 0.1 

CADM - - - 

Emond 4.04 6.56 (@ 78 hours) 6.44 3 

CADM - - - 

Emond 13.3 21.5 (@ 78 hours) 21.0 10 

CADM - - - 

Emond 39.3 63.5 (@ 78 hours) 61.5 30 

CADM - - - 

Emond 129 208 (@ 78 hours) 200 100 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-122 DRAFT—DO NOT CITE OR QUOTE 

Emond 384 618 (@ 77 hours) 590 300 

CADM - - - 

Emond 1,270 2,041 (@ 77 hours) 1,942 1000 

CADM - - - 

Emond 3,793 6,094 (@ 77 hours) 5,784 3000 

CADM - - - 

Emond 12,595 20,226 (@ 77 hours) 19,154 10,000 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 0 0.115 (@ 75 hours) 0 

0.1 

CADM - - - 

Emond 2 2.47 (@ 76 hours) 2 

3 

CADM - - - 

Emond 4 6.42 (@ 76 hours) 5 

10 

CADM - - - 

Emond 10 14.1 (@ 76 hours) 12 

30 

CADM - - - 

Emond 22 29.9 (@ 76 hours) 27 

100 

CADM - - - 

Emond 41 51.9 (@ 77 hours) 49 

300 

CADM - - - 

Emond 68 80.2 (@ 1 hours) 77 

1000 

CADM - - - 

Emond 90 98.6 (@ 1 hours) 96 

3000 

CADM - - - 

Emond 104 108 (@ 1 hours) 107 

10,000 

CADM - - - 

 1 

 2 

3 C.3.1.4. Fattore et al. (2000) 

Type: Rat Dose: 20, 200, 2,000 ng/kg-day 

Strain: Sprague Dawley Route: Dietary 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-123 DRAFT—DO NOT CITE OR QUOTE 

Body weight: 7 weeks old (BW 

150g) 

Regime: 13 weeks 

Sex: Female and male Simulation time: 2,184 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 5,282 8,259 (@ 2,160 hours) 6,135 20 

CADM - - - 

Emond 31,761 56,170 (@ 2,160 hours) 35,183 200 

CADM - - - 

Emond 262,030 497,250 (@ 2,160 hours) 287,690 2,000 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 2,448 3,228 (@ 2,164 hours) 3,078 20 

CADM 4,471 5,639 5,639 

Emond 24,136 30,245 (@ 2,164 hours) 28,709 200 

CADM 45,337 56,499 56,499 

Emond 234,170 288,020 (@ 2,164 hours) 272,590 2,000 

CADM 454,031 565,103 565,103 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 890 1,113 (@ 2,166 hours) 1,101 20 

CADM 1,545 1,796 1,756 

Emond 5,355 6,542 (@ 2,165 hours) 6,430 200 

CADM 13,351 15,604 15,292 

Emond 44,176 54,246 (@ 2,165 hours) 53,140 2,000 

CADM 131,259 153,534 150,516 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-124 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 187 242 (@ 2,164 hours) 233 

20 

CADM 261 324 324 

Emond 1,556 1,940 (@ 2,164 hours) 1,850 200 

CADM 2,496 3,084 3,084 

Emond 14,432 17,797 (@ 2,164 hours) 16,891 2,000 

CADM 24,836 30,674 30,674 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 24.9 29.8 (@ 2,164 hours) 28.8 

20 

CADM - - - 

Emond 69.4 76.0 (@ 2,164 hours) 74.7 

200 

CADM - - - 

Emond 104 106 (@ 2,164 hours) 106 

2,000 

CADM - - - 

1 C.3.1.5. Hassoun et al. (1998) 

Type: Mice Dose: 0, 0.45, 1.5, 15, 150 ng/kg-day. 

Background exposure dose (default) = 0.05 

ng/kg-day 

Strain: B6C3F1 Route: Oral gavage 

Body weight: 8 to 9 weeks old 

(BW set to 23g) 

Regime: 5 days/week for 13 weeks 

Sex: Female Simulation 

time: 

2208 hours* (2,184h + 24h post exposure) 

a

No background has been considered here for this simulation 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-125 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 90.5 167 (@ 2,112 hours) 123 

0.321 

CADM - - - 

Emond 240 441 (@ 2,112 hours) 297 

1.07 

CADM - - - 

Emond 1,350 2,753 (@ 2,112 hours) 1,396 10.7 

CADM - - - 

Emond 7,328 19,496 (@ 2,112 hours) 6,587 107 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 19.5 33.0 (@ 2,116 hours) 28.1 

0.321 

CADM 14.8 24.5 23.2 

Emond 66.7 106 (@ 2,116 hours) 87.4 

1.07 

CADM 59.4 91.9 84.2 

Emond 680 966 (@ 2,117 hours) 736 

10.7 

CADM 768 1,000 825 

Emond 6,768 9,000 (@ 2,117 hours) 6,482 107 

CADM 8,343 10,306 7,863 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 58.6 91.9 (@ 2,135 hours) 89.4 

0.321 

CADM 56.5 85.9 82.7 

Emond 156 228 (@ 2,130 hours) 219 

1.07 

CADM 152 210 199 

Emond 884 1,149 (@ 2,124 hours) 1,075 10.7 

CADM 690 815 735 

Emond 4,818 5,946 (@ 2,120 hours) 5,347 107 

CADM 2,770 3,224 2,684 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-126 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 5.97 9.50 (@ 2,117 hours) 8.93 

0.321 

CADM 7.43 11.4 (@ 2,121 hours) 10.9 

Emond 16.9 25.3 (@ 2,116 hours) 23.2 

1.07 

CADM 20.9 29.3 27.7 

Emond 117 158 (@ 2,116 hours) 135 

10.7 

CADM 119 145 127 

Emond 849 1,100 (@ 2,116 hours) 865 107 

CADM 727 875 694 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 0.564 0.885 (@ 2,116 hours) 0.771 0.321 

CADM - - - 

Emond 1.47 2.15 (@ 2,116 hours) 1.83 

1.07 

CADM - - - 

Emond 7.58 9.83 (@ 2,116 hours) 8.07 

10.7 

CADM - - - 

Emond 30.3 35.9 (@ 2,117 hours) 29.8 

107 

CADM - - - 

 1 

 2 

3 C.3.1.6. Hassoun et al. (2000) 

Type: Rat Dose: 0, 3, 10, 22, 46, 100 ng/kg-day (2.14, 7.14, 

15.7, 32.9, and 71.4 ng/kg-day adjusted 

doses) 

Strain: Sprague Dawley Route: Oral gavage 

Body 

weight: 

8 weeks old 

(BW=215g) 

Regime: 5 days/week for 13 weeks 

Sex: Female Simulation time: 2184 hours 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-127 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,068 1,720 (@ 2,112 hours) 1,303 2.14 

CADM - - - 

Emond 2,542 4,246 (@ 2,112 hours) 2,901 7.14 

CADM - - - 

Emond 4,489 7,835 (@ 2,112 hours) 4,947 15.7 

CADM - - - 

Emond 7,718 14,206 (@ 2,112 hours) 8,277 32.9 

CADM - - - 

Emond 13,960 27,367 (@ 2,112 hours) 14,637 71.4 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 267 399 (@ 2,116 hours) 349 

2.14 

CADM - - - 

Emond 888 1,259 (@ 2,117 hours) 1,079 7.14 

CADM - - - 

Emond 1,948 2,689 (@ 2,117 hours) 2,278 15.7 

CADM - - - 

Emond 4,055 5,484 (@ 2,117 hours) 4,607 32.9 

CADM - - - 

Emond 8,775 11,692 (@ 2,117 hours) 9,754 71.4 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 179 243 (@ 2,126 hours) 235 

2.14 

CADM - - - 

Emond 427 553 (@ 2,124 hours) 528 

7.14 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-128 DRAFT—DO NOT CITE OR QUOTE 

Emond 755 958 (@ 2,123 hours) 908 

15.7 

CADM - - - 

Emond 1,299 1,627 (@ 2,122 hours) 1,529 32.9 

CADM - - - 

Emond 2,350 2,928 (@ 2,121 hours) 2,727 71.4 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 27.4 38.9 (@ 2,116 hours) 35.7 

2.14 

CADM - - - 

Emond 76.9 105 (@ 2,116 hours) 93.7 

7.14 

CADM - - - 

Emond 153 205 (@ 2,116 hours) 180 

15.7 

CADM - - - 

Emond 295 390 (@ 2,116 hours) 339 

32.9 

CADM - - - 

Emond 600 785 (@ 2,116 hours) 674 

71.4 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 6.28 8.48 (@ 2,116 hours) 7.67 

2.14 

CADM - - - 

Emond 13.7 17.5 (@ 2,116 hours) 15.7 

7.14 

CADM - - - 

Emond 22.0 27.1 (@ 2,116 hours) 24.4 

15.7 

CADM - - - 

Emond 32.8 39.2 (@ 2,116 hours) 35.6 

32.9 

CADM - - - 

Emond 47.5 55.0 (@ 2,116 hours) 50.6 

71.4 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-129 DRAFT—DO NOT CITE OR QUOTE 

1 C.3.1.7. Kitchin and Woods (1979) 

Type: Rats Dose: 0, 0.6, 2, 4, 20, 60, 200, 600, 2000, 5000, 

20000 ng/kg-day 

Strain: Sprague-Dawley Route: Oral gavage 

Body weight: 200 to 250 g (BW set to 

225 g) 

Regime: Single dose 

Sex: Female Simulation 

time: 

24 hours 

a 2 The CADM model was not run because the dosing duration is lower than the resolution of the model (1 week). 

3 

4 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 46.8 69.5 (@ 0 hours) 18.0 

0.6 

CADM - - - 

Emond 122 232 (@ 0 hours) 57.1 

2 

CADM - - - 

Emond 221 463 (@ 0 hours) 109 

4 

CADM - - - 

Emond 896 2,318 (@ 0 hours) 462 

20 

CADM - - - 

Emond 2,291 6,949 (@ 0 hours) 1,165 60 

CADM - - - 

Emond 6,393 23,185 (@ 0 hours) 3,073 200 

CADM - - - 

Emond 16,676 69,657 (@ 0 hours) 7,345 600 

CADM - - - 

Emond 50,090 232,550 (@ 0 hours) 19,637 2,000 

CADM - - - 

Emond 120,130 581,930 (@ 0 hours) 43,511 5,000 

CADM - - - 

Emond 475,600 2,332,100 (@ 0 hours) 158,970 20,000 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-130 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 3.99 3.81 (@ 4 hours) 1.60 

0.6 

CADM - - - 

Emond 11.7 12.9 (@ 4 hours) 6.01 

2 

CADM - - - 

Emond 23.4 26.3 (@ 4 hours) 13.2 

4 

CADM - - - 

Emond 129 143 (@ 6 hours) 85.2 

20 

CADM - - - 

Emond 422 463 (@ 8 hours) 305 

60 

CADM - - - 

Emond 1,525 1,666 (@ 9 hours) 1,194 200 

CADM - - - 

Emond 4,822 5,258 (@ 10 hours) 3,987 600 

CADM - - - 

Emond 16,606 18,081 (@ 11 hours) 14,296 2,000 

CADM - - - 

Emond 41,973 45,674 (@ 11 hours) 36,821 5,000 

CADM - - - 

Emond 167,820 182,580 (@ 11 hours) 149,280 20,000

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 2.11 3.03 (@ 72 hours) 3.03 

0.6 

CADM - - - 

Emond 5.54 9.57 (@ 72 hours) 9.57 

2 

CADM - - - 

Emond 10.1 18.2 (@ 72 hours) 18.2 

4 

CADM - - - 

Emond 42.1 76.4 (@ 72 hours) 76.4 

20 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-131 DRAFT—DO NOT CITE OR QUOTE 

Emond 110 192 (@ 72 hours) 192 

60 

CADM - - - 

Emond 317 512 (@ 72 hours) 512 

200 

CADM - - - 

Emond 851 1,250 (@ 72 hours) 1,250 600 

CADM - - - 

Emond 2,621 3,481 (@ 58 hours) 3,462 2,000 

CADM - - - 

Emond 6,361 8,049 (@ 45 hours) 7,887 5,000 

CADM - - - 

Emond 25,402 31,187 (@ 35 hours) 29,738 20,000

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 0.429 0.341 (@ 9 hours) 0.331 0.6 

CADM - - - 

Emond 1.18 1.14 (@ 8 hours) 1.09 2 

CADM - - - 

Emond 2.24 2.27 (@ 8 hours) 2.15 4 

CADM - - - 

Emond 10.7 11.3 (@ 8 hours) 10.4 20 

CADM - - - 

Emond 31.8 33.8 (@ 7 hours) 30.3 60 

CADM - - - 

Emond 105 112 (@ 7 hours) 98 

200 

CADM - - - 

Emond 315 337 (@ 7 hours) 288 

600 

CADM - - - 

Emond 1,049 1,123 (@ 7 hours) 945 2,000 

CADM - - - 

Emond 2,621 2,806 (@ 7 hours) 2,343 5,000 

CADM - - - 

Emond 10,469 11,215 (@ 7 hours) 9,299 20,000

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-132 DRAFT—DO NOT CITE OR QUOTE 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 0.284 0.407 (@ 3 hours) 0.238 0.6 

CADM - - - 

Emond 0.728 1.07 (@ 3 hours) 0.476 2 

CADM - - - 

Emond 1.30 1.94 (@ 3 hours) 0.798 4 

CADM - - - 

Emond 4.90 7.74 (@ 2 hours) 2.95 20 

CADM - - - 

Emond 11.2 18.4 (@ 2 hours) 7.03 60 

CADM - - - 

Emond 25.1 40.8 (@ 1 hours) 16.7 200 

CADM - - - 

Emond 45.8 68.2 (@ 1 hours) 33.0 600 

CADM - - - 

Emond 73.3 93.1 (@ 1 hours) 59.1 2,000 

CADM - - - 

Emond 90.9 104 (@ 1 hours) 79.9 

5,000 

CADM - - - 

Emond 106 110 (@ 1 hours) 101 

20,000

CADM - - - 

1 

 2 

3 C.3.1.8. Kociba et al. (1976) 

Type: Rats Dose: 1, 10, 100, 1000 ng/kg-day 

Strain: Sprague-Dawley 

(Spartan) 

Route: Oral gavage 

Body weight: 170–190 g (bw=180g) Regime: 5 days/week for 13 weeks 

Sex: Female Simulation 

time: 

4,368 hours 

(13wk exposed + 13 wk post exposures) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-133 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 398 761 (@ 2,112 hours) 163 0.714 

CADM - - - 

Emond 1,817 4,196 (@ 2,112 hours) 372 7.143 

CADM - - - 

Emond 9,002 26,872 (@ 2,112 hours) 820 71.43 

CADM - - - 

Emond 60,388 226,470 (@ 2,112 hours) 2,072 714.3 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 70.9 140 (@ 2,116 hours) 21.4 0.714 

CADM 89.0 192 12.1 

Emond 595 1,259 (@ 2,117 hours) 62.4 7.143 

CADM 970 2,007 29.0 

Emond 5,391 11,693 (@ 2,117 hours) 183 71.43 

CADM 9,841 20,170 88.0 

Emond 51,476 112,580 (@ 2,117 hours) 670 714.3 

CADM 98,617 201,814 455 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 68.3 114 (@ 2,129 hours) 28.8 0.714 

CADM 120 190 43.0 

Emond 313 553 (@ 2,124 hours) 66.2 7.143 

CADM 456 787 67.0 

Emond 1,552 2,925 (@ 2,121 hours) 148 71.43 

CADM 3,036 5,748 117 

Emond 10,415 21,127 (@ 2,120 hours) 379 714.3 

CADM 28,382 55,013 274 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-134 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 9.03 16.1 (@ 2,116 hours) 3.41 0.714 

CADM 11.5 20.0 3.75 

Emond 53.7 105 (@ 2,116 hours) 8.44 7.143 

CADM 65.3 126 6.22 

Emond 377 785 (@ 2,116 hours) 20.8 71.43 

CADM 553 1,113 12.0 

Emond 3,230 6,961 (@ 2,116 hours) 62.4 714.3 

CADM 5,401 10,967 37.0 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 2.44 4.17 (@ 2,116 hours) 1.02 0.714 

CADM - - - 

Emond 10.1 17.5 (@ 2,116 hours) 2.30 7.143 

CADM - - - 

Emond 33.2 55.0 (@ 2,116 hours) 4.95 71.43 

CADM - - - 

Emond 69.7 98.2 (@ 2,117 hours) 11.7 714.3 

CADM - - - 

1 C.3.1.9. Kociba et al. (1978) Female 

Type: Rats Dose: 0, 1, 10, 100 ng/kg-day 

Strain: Sprague-Dawley 

(Spartan) 

Route: Dietary 

Body weight: 170–190 g (bw=180) Regime: 104 weeks 

Sex: Female Simulation time: 17,472 hours 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-135 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 853 1,058 (@ 17,448 hours) 929 

1 

CADM - - - 

Emond 3,942 5,098 (@ 17,448 hours) 3,943 10 

CADM - - - 

Emond 21,246 31,697 (@ 17,448 hours) 20,441 100 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 192 226 (@ 17,452 hours) 218 

1 

CADM 292 333 333 

Emond 1,618 1,742 (@ 17,452 hours) 1,665 10 

CADM 2,981 3,342 3,342 

Emond 14,892 15,673 (@ 17,452 hours) 14,907 100 

CADM 29,917 33,432 33,432 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 147 165 (@ 17,457 hours) 164 

1 

CADM 196 229 181 

Emond 680 713 (@ 17,454 hours) 706 

10 

CADM 861 1,015 789 

Emond 3,663 3,788 (@ 17,454 hours) 3,731 100 

CADM 6,756 7,939 6,203 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 21.2 24.3 (@ 17,452 hours) 23.8 

1 

CADM 26.0 27.0 27.0 

Emond 131 140 (@ 17,452 hours) 136 

10 

CADM 169 176 176 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-136 DRAFT—DO NOT CITE OR QUOTE 

Emond 989 1,039 (@ 17,452 hours) 994 

100 

CADM 1,546 1,601 1,601 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 5.11 5.77 (@ 17,452 hours) 5.59 

1 

CADM - - - 

Emond 20.0 21.1 (@ 17,452 hours) 20.4 

10 

CADM - - - 

Emond 59.9 61.5 (@ 17,452 hours) 60.1 

100 

CADM - - - 

1 C.3.1.10. Kociba et al. (1978) Male 

Type: Rats Dose: 0, 1, 10, 100 ng/kg-day 

Strain: Sprague-Dawley 

(Spartan) 

Route: Dietary 

Body weight: Body weight 

approximated to be 

250 g 

Regime: 104 weeks 

Sex: Male Simulation time: 17,472 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 860 1,079 (@ 17,448 hours) 938 

1 

CADM - - - 

Emond 3,945 5,153 (@ 17,448 hours) 3,916 10 

CADM - - - 

Emond 21,334 32,658 (@ 17,448 hours) 20,460 100 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-137 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 194 229 (@ 17,452 hours) 221 

1 

CADM - - - 

Emond 1,616 1,723 (@ 17,452 hours) 1,649 10 

CADM - - - 

Emond 14,898 15,671 (@ 17,452 hours) 14,912 100 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 148 167 (@ 17,456 hours) 166 

1 

CADM - - - 

Emond 680 709 (@ 17,454 hours) 703 

10 

CADM - - - 

Emond 3,677 3,803 (@ 17,453 hours) 3,747 100 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 21.4 24.6 (@ 17,452 hours) 24.1 

1 

CADM - - - 

Emond 131 139 (@ 17,452 hours) 134 

10 

CADM - - - 

Emond 991 1,041 (@ 17,452 hours) 995 

100 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 5.15 5.83 (@ 17,452 hours) 5.64 

1 

CADM - - - 

Emond 20.0 21.0 (@ 17,452 hours) 20.3 

10 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-138 DRAFT—DO NOT CITE OR QUOTE 

Emond 60.0 61.5 (@ 17,452 hours) 60.1 

100 

CADM - - - 

1 C.3.1.11. Latchoumycandane and Mathur (2002) 

Type: Rat Dose: 0, 1, 10, 100 ng/kg-day 

Strain: Wistar Route: Mouth pipetting 

Body weight: 45 days old 

(BW set to 200g) 

Regime: 1/day for 45 days 

Sex: Male Simulation 

time: 

1,104 hours (1,080 daily exposure and 24 hours 

before sacrifice) 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 437 754 (@ 1,056 hours) 630 

1 

CADM - - - 

Emond 2,579 4,505 (@ 1,056 hours) 3,274 10 

CADM - - - 

Emond 15,092 29,672 (@ 1,056 hours) 17,698 100 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 79.7 138 (@ 1,060 hours) 128 

1 

CADM 116 217 217 

Emond 911 1,423 (@ 1,060 hours) 1,282 10 

CADM 1,669 2,550 2,550 

Emond 9,650 14,015 (@ 1,061 hours) 12,439 100 

CADM 17,681 25,915 25,915 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 70.7 113 (@ 1,072 hours) 112 

1 

CADM 150 220 220 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-139 DRAFT—DO NOT CITE OR QUOTE 

Emond 420 608 (@ 1,065 hours) 592 

10 

CADM 744 1,009 1,009 

Emond 2,467 3,425 (@ 1,062 hours) 3,273 100 

CADM 5,719 7,866 7,866 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 9.68 15.9 (@ 1,060 hours) 15.2 

1 

CADM 14.0 22.2 22.2 

Emond 77.5 117 (@ 1,060 hours) 108 

10 

CADM 106 157 157 

Emond 651 933 (@ 1,060 hours) 842 

100 

CADM 988 1,439 1,439 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 2.67 4.12 (@ 1,060 hours) 3.85 

1 

CADM - - - 

Emond 13.8 18.8 (@ 1,060 hours) 17.5 

10 

CADM - - - 

Emond 48.8 59.0 (@ 1,060 hours) 56.0 

100 

CADM - - - 

1 C.3.1.12. Li et al. (1997) 

Type: Rats Dose: 0, 3, 10, 30, 100, 300, 1000, 3000, 

10000, 30000 ng/kg/day 

Strain: Sprague-Dawley Route: Gastric intubation 

Body weight: 22 day old, 55 to 58 g 

(BW set to 56.5 g) 

Regime: One dose for one day 

Sex: Female Simulation time: 24 hours 

2 a 3 The CADM model was not run because the dosing duration is lower than the resolution of the model (1 week) 

4 

5 

6 

7 

8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-140 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) Model 

Time-weighted Ave Max Terminal 

Emond 147 259 (@ 1 hours) 98.9 

3 

CADM - - - 

Emond 440 862 (@ 1 hours) 295 

10 

CADM - - - 

Emond 1,156 2,581 (@ 1 hours) 757 

30 

CADM - - - 

Emond 3,232 8,585 (@ 1 hours) 2,026 100 

CADM - - - 

Emond 8,266 25,780 (@ 0 hours) 4,865 300 

CADM - - - 

Emond 23,875 86,088 (@ 0 hours) 12,873 1,000 

CADM - - - 

Emond 66,081 258,670 (@ 0 hours) 33,013 3,000 

CADM - - - 

Emond 212,650 864,770 (@ 0 hours) 100,410 10,000 

CADM - - - 

Emond 649,740 2,633,500 (@ 0 hours) 294,620 30,000 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) Model 

Time-weighted Ave Max Terminal 

Emond 14.7 18.6 (@ 4 hours) 11.9 

3 

CADM - - - 

Emond 55.0 65.2 (@ 5 hours) 47.6 

10 

CADM - - - 

Emond 185 210 (@ 6 hours) 170 

30 

CADM - - - 

Emond 690 768 (@ 7 hours) 666 

100 

CADM - - - 

Emond 2,248 2,473 (@ 8 hours) 2,240 300 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-141 DRAFT—DO NOT CITE OR QUOTE 

Emond 7,938 8,671 (@ 9 hours) 8,094 1,000 

CADM - - - 

Emond 24,474 26,639 (@ 9 hours) 25,267 3,000 

CADM - - - 

Emond 82,349 89,464 (@ 9 hours) 85,597 10,000 

CADM - - - 

Emond 245,610 265,670 (@ 10 hours) 255,390 30,000 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) Model 

Time-weighted Ave Max Terminal 

Emond 8.75 12.7 (@ 24 hours) 12.7 

3 

CADM - - - 

Emond 26.6 38.0 (@ 24 hours) 38.0 

10 

CADM - - - 

Emond 70.8 98.9 (@ 24 hours) 98.9 

30 

CADM - - - 

Emond 202 273 (@ 24 hours) 273 

100 

CADM - - - 

Emond 530 689 (@ 24 hours) 689 

300 

CADM - - - 

Emond 1,573 1,958 (@ 24 hours) 1,958 1,000 

CADM - - - 

Emond 4,433 5,358 (@ 24 hours) 5,358 3,000 

CADM - - - 

Emond 14,428 17,119 (@ 24 hours) 17,119 10,000 

CADM - - - 

Emond 44,361 51,948 (@ 22 hours) 51,898 30,000 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) Model 

Time-weighted Ave Max Terminal 

Emond 1.60 1.70 (@ 8 hours) 1.68 3 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-142 DRAFT—DO NOT CITE OR QUOTE 

Emond 5.33 5.66 (@ 8 hours) 5.56 10 

CADM - - - 

Emond 15.9 16.9 (@ 8 hours) 16.5 30 

CADM - - - 

Emond 52.8 56.2 (@ 7 hours) 54.5 100 

CADM - - - 

Emond 158 169 (@ 7 hours) 163 

300 

CADM - - - 

Emond 525 561 (@ 7 hours) 539 

1,000 

CADM - - - 

Emond 1,574 1,684 (@ 7 hours) 1,611 3,000 

CADM - - - 

Emond 5,240 5,610 (@ 7 hours) 5,360 10,000 

CADM - - - 

Emond 15,758 16,815 (@ 7 hours) 16,041 30,000 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) Model 

Time-weighted Ave Max Terminal 

Emond 1 1.37 (@ 3 hours) 1 

3 

CADM - - - 

Emond 3 4.10 (@ 2 hours) 2 

10 

CADM - - - 

Emond 6 10.5 (@ 2 hours) 5 

30 

CADM - - - 

Emond 16 25.9 (@ 2 hours) 12 

100 

CADM - - - 

Emond 31.25 50.1 (@ 1 hours) 24.58 300 

CADM - - - 

Emond 56.75 79.8 (@ 1 hours) 47.65 1,000 

CADM - - - 

Emond 81.29 98.4 (@ 1 hours) 73.34 3,000 

CADM - - - 

Emond 99.77 108 (@ 1 hours) 95.70 10,000 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-143 DRAFT—DO NOT CITE OR QUOTE 

Emond 108.04 111 (@ 1 hours) 106.23 30,000 

CADM - - - 

1 C.3.1.13. NTP (1982)—Female Rats, Chronic 

Type: Rat Dose: 10, 50 and 500 ng/kg/wk, 

two doses per week 

Strain: Osborne-Mendel Route: Oral gavage 

Body weight 6 weeks old 

(BW set to 250g)

Regime: Biweekly 

Sex: 

Female

Simulation time 17,976 hours (107 weeks)= (104 weeks of 

exposure + 3 weeks observation post-treatment)

a

The CADM model simulates for 104 weeks only (17,472 hours). As a result, the terminal values from the CADM 

model are overestimated compared to the Emond model, which considered an additional 3 weeks post exposure. 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,072 1,719 (@ 17,388 hours) 685 1.4 

CADM - - - 

Emond 3,111 6,054 (@ 17,388 hours) 1,622 7.1 

CADM - - - 

Emond 16,207 45,310 (@ 17,388 hours) 6,253 71 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 263 310 (@ 17,394 hours) 143 1.4 

CADM 15,318 20,170 7,102 

Emond 1,163 1,338 (@ 17,394 hours) 474 7.1 

CADM 30,700 40,353 14,200 

Emond 10,596 12,182 (@ 17,395 hours) 3,134 71 

CADM 30,700 40,353 14,200 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-144 DRAFT—DO NOT CITE OR QUOTE 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 185 200 (@ 17,412 hours) 124 1.4 

CADM 4,655 5,748 2,107 

Emond 537 569 (@ 17,409 hours) 297 7.1 

CADM 9,064 11,224 3,964 

Emond 2,798 2,973 (@ 17,404 hours) 1,173 71 

CADM 17,879 22,172 7,671 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 27.7 31.2 (@ 17,393 hours) 16.9 1.4 

CADM 855 1,113 403 

Emond 98.5 110 (@ 17,393 hours) 46.6 7.1 

CADM 1,695 2,208 787 

Emond 720 814 (@ 17,393 hours) 241 71 

CADM 3,375 4,395 1,556 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 6.34 7.28 (@ 17,392 hours) 4.17 1.4 

CADM - - - 

Emond 16.5 18.5 (@ 17,392 hours) 9.37 7.1 

CADM - - - 

Emond 52.3 56.4 (@ 17,393 hours) 29.1 71 

CADM - - - 

1 C.3.1.14. NTP (1982)—Male Rats, Chronic 

Type: Rat Dose: 10, 50 and 500 ng/kg/wk, 

two doses per week 

Strain: Osborne-Mendel Route: Oral gavage 

Body weight 6 weeks old 

(BW set to 350g)

Regime: Biweekly 

(Simulation has been perform using female BW 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-145 DRAFT—DO NOT CITE OR QUOTE 

Sex: 

Male

Simulation time 17,976 hours (107 weeks)= (104 weeks of 

exposure + 3 weeks observation post-treatment) 

a

The CADM model simulates for 104 weeks only (17,472 hours). As a result, the terminal values from the CADM 

model are overestimated compared to the Emond model, which considered an additional 3 weeks post exposure. 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,072 1,750 (@ 17,388 hours) 681 1.4 

CADM - - - 

Emond 3,116 6,301 (@ 17,388 hours) 1,622 7.1 

CADM - - - 

Emond 16,272 47,951 (@ 17,388 hours) 6,269 71 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 263 306 (@ 17,394 hours) 141 1.4 

CADM - - - 

Emond 1,162 1,334 (@ 17,394 hours) 473 7.1 

CADM - - - 

Emond 10,598 12,170 (@ 17,395 hours) 3,140 71 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 185 199 (@ 17,412 hours) 123 1.4 

CADM - - - 

Emond 538 569 (@ 17,409 hours) 298 7.1 

CADM - - - 

Emond 2,809 2,983 (@ 17,404 hours) 1,185 71 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-146 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 27.7 30.9 (@ 17,393 hours) 16.8 1.4 

CADM - - - 

Emond 98.6 110 (@ 17,393 hours) 46.6 7.1 

CADM - - - 

Emond 721 816 (@ 17,393 hours) 242 71 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 6.33 7.22 (@ 17,392 hours) 4.14 1.4 

CADM - - - 

Emond 16.4 18.4 (@ 17,392 hours) 9.36 7.1 

CADM - - - 

Emond 52.3 56.3 (@ 17,393 hours) 29.1 71 

CADM - - - 

1 C.3.1.15. NTP (1982)—Female Mice, Chronic 

Type: Mice Dose: 40, 200 and 2000ng/kg/wk, 

two doses during the week 

Strain: B6C3F1 Route: Oral gavage 

Body weight 6 weeks old 

(BW set to 23g) 

Regime: Biweekly 

Sex: Female Simulation time 17,976 hours (107 weeks)= (104 weeks of 

exposure + 3 weeks observation post-treatment) 

a

The mice chronic exposure could not be simulated with the CADM model because this model simulates for only 

123 days. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-147 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,064 2,684 (@ 17,220 hours) 569 5.7 

CADM - - - 

Emond 3,184 10,915 (@ 17,388 hours) 1,334 28.6 

CADM - - - 

Emond 17,406 93,992 (@ 17,220 hours) 4,899 286 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 486 587 (@ 17,227 hours) 209 5.7 

CADM - - - 

Emond 2,206 2,629 (@ 17,395 hours) 682 28.6 

CADM - - - 

Emond 20,515 24,353 (@ 17,396 hours) 4,232 286 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 733 789 (@ 17,324 hours) 436 5.7 

CADM - - - 

Emond 2,194 2,337 (@ 17,404 hours) 1,059 28.6 

CADM - - - 

Emond 12,003 12,861 (@ 17,400 hours) 4,151 286 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 91.2 103 (@ 17,225 hours) 48.5 5.7 

CADM - - - 

Emond 325 370 (@ 17,393 hours) 130 28.6 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-148 DRAFT—DO NOT CITE OR QUOTE 

Emond 2,367 2,740 (@ 17,393 hours) 615 286 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 6.13 7.32 (@ 17,225 hours) 3.44 5.7 

CADM - - - 

Emond 16.1 18.9 (@ 17,393 hours) 7.68 28.6 

CADM - - - 

Emond 51.8 67.8 (@ 2 hours) 23.6 

286 

CADM - - - 

1 C.3.1.16. NTP (1982)—Male Mice, Chronic 

Type: Mice Dose: 10, 50 and 500ng/kg/wk, 

two doses during the week 

Strain: B6C3F1 Route: Oral gavage 

Body weight 6 weeks old 

(BW set to 25g) 

Regime: Biweekly 

Sex: Male Simulation time 17,976 hours (107 weeks)= (104 weeks of 

exposure + 3 weeks observation post-treatment) 

a

The mice chronic exposure could not be simulated with the CADM model because this model simulates for only 

123 days. 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 420 842 (@ 17,136 hours) 270 1.4 

CADM - - - 

Emond 1,240 3,302 (@ 17,304 hours) 644 7.1 

CADM - - - 

Emond 6,118 25,730 (@ 17,388 hours) 2,204 71 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-149 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 137 165 (@ 17,142 hours) 76.7 1.4 

CADM - - - 

Emond 599 723 (@ 17,311 hours) 247 7.1 

CADM - - - 

Emond 5,331 6,328 (@ 17,395 hours) 1,382 71 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 289 314 (@ 17,243 hours) 202 1.4 

CADM - - - 

Emond 854 918 (@ 17,407 hours) 496 7.1 

CADM - - - 

Emond 4,217 4,490 (@ 17,402 hours) 1,799 71 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 32.2 36.3 (@ 17,141 hours) 21.1 1.4 

CADM - - - 

Emond 109 123 (@ 17,309 hours) 55.8 7.1 

CADM - - - 

Emond 701 802 (@ 17,393 hours) 235 71 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

 

Emond 2.54 3.04 (@ 17,141 hours) 1.67 1.4 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-150 DRAFT—DO NOT CITE OR QUOTE 

Emond 7.06 8.41 (@ 17,309 hours) 3.87 7.1 

CADM - - - 

Emond 26.8 32.4 (@ 2 hours) 12.1 

71 

CADM - - - 

1 C.3.1.17. NTP (2006) 31 Weeks 

Type: Rat Dose: 0, 3, 10, 22, 46, 100 ng/kg-day 

Strain: Sprague Dawley Route: Oral gavage 

Body 

weight: 

8 weeks old 

(BW=215g) 

Regime: 5 days/weeks for 31 weeks 

Sex: Female and male Simulation time: 5208 hours (31 weeks) 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,284 1,792 (@ 3,960 hours) 1,360 

2.14 CADM - - - 

Emond 2,932 4,356 (@ 3,960 hours) 2,989 7.14 

CADM - - - 

Emond 5,075 7,958 (@ 3,960 hours) 5,039 15.7 

CADM - - - 

Emond 8,629 14,416 (@ 3,960 hours) 8,417 32.9 

CADM - - - 

Emond 15,503 27,738 (@ 5,136 hours) 14,877 71.4 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 341 425 (@ 3,964 hours) 371 

2.14 

CADM - - - 

Emond 1,077 1,312 (@ 4,133 hours) 1,125 7.14 

CADM - - - 

Emond 2,298 2,760 (@ 3,965 hours) 2,336 15.7 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-151 DRAFT—DO NOT CITE OR QUOTE 

Emond 4,698 5,599 (@ 3,965 hours) 4,711 32.9 

CADM - - - 

Emond 10,036 11,910 (@ 5,141 hours) 9,956 71.4 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 220 256 (@ 4,141 hours) 245 

2.14 

CADM - - - 

Emond 502 571 (@ 4,139 hours) 545 

7.14 

CADM - - - 

Emond 868 979 (@ 4,138 hours) 926 

15.7 

CADM - - - 

Emond 1,476 1,657 (@ 4,137 hours) 1,558 32.9 

CADM - - - 

Emond 2,653 2,979 (@ 5,144 hours) 2,776 71.4 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 34.2 41.2 (@ 3,964 hours) 37.6 

2.14 

CADM - - - 

Emond 91.7 109 (@ 4,132 hours) 97.2 

7.14 

CADM - - - 

Emond 178 210 (@ 3,964 hours) 184 

15.7 

CADM - - - 

Emond 339 398 (@ 4,132 hours) 346 

32.9 

CADM - - - 

Emond 683 799 (@ 5,140 hours) 687 

71.4 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-152 DRAFT—DO NOT CITE OR QUOTE 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 7.48 8.84 (@ 3,964 hours) 7.98 

2.14 

CADM - - - 

Emond 15.6 17.9 (@ 4,132 hours) 16.1 

7.14 

CADM - - - 

Emond 24.4 27.5 (@ 3,964 hours) 24.8 

15.7 

CADM - - - 

Emond 35.7 39.6 (@ 3,964 hours) 36.0 

32.9 

CADM - - - 

Emond 50.9 55.4 (@ 5,140 hours) 51.1 

71.4 

CADM - - - 

1 C.3.1.18. NTP (2006) 53 Weeks 

Type: Rat Dose: 0, 3, 10, 22, 46, 100 ng/kg-day 

Strain: Sprague Dawley Route: Oral gavage 

Body 

weight: 

8 weeks old 

(BW=215g) 

Regime: 5 days/weeks for 105 weeks 

Sex: Female and male Simulation time: 8904 hours (53 weeks) 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,354 1,792 (@ 3,960 hours) 1,367 2.14 

CADM - - - 

Emond 3,056 4,359 (@ 8,832 hours) 2,993 7.14 

CADM - - - 

Emond 5,259 7,958 (@ 3,960 hours) 5,052 15.7 

CADM - - - 

Emond 8,918 14,460 (@ 8,832 hours) 8,438 32.9 

CADM - - - 

Emond 16,001 27,846 (@ 8,832 hours) 14,916 71.4 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-153 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 365 425 (@ 3,964 hours) 373 

2.14 

CADM - - - 

Emond 1,138 1,312 (@ 8,837 hours) 1,127 7.14 

CADM - - - 

Emond 2,407 2,760 (@ 3,965 hours) 2,344 15.7 

CADM - - - 

Emond 4,902 5,611 (@ 8,837 hours) 4,726 32.9 

CADM - - - 

Emond 10,443 11,943 (@ 8,837 hours) 9,989 71.4 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 233 256 (@ 8,845 hours) 247 

2.14 

CADM - - - 

Emond 525 572 (@ 8,843 hours) 546 

7.14 

CADM - - - 

Emond 904 979 (@ 8,842 hours) 928 

15.7 

CADM - - - 

Emond 1,533 1,661 (@ 8,841 hours) 1,562 32.9 

CADM - - - 

Emond 2,750 2,987 (@ 8,840 hours) 2,785 71.4 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 36.4 41.2 (@ 3,964 hours) 37.8 

2.14 

CADM - - - 

Emond 96.4 109 (@ 8,836 hours) 97.3 

7.14 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-154 DRAFT—DO NOT CITE OR QUOTE 

Emond 186 210 (@ 8,836 hours) 185 

15.7 

CADM - - - 

Emond 354 399 (@ 8,836 hours) 347 

32.9 

CADM - - - 

Emond 709 802 (@ 8,836 hours) 689 

71.4 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 8.17 9.30 (@ 17,572 hours) 8.43 

2.14 

CADM - - - 

Emond 16.6 18.0 (@ 17,572 hours) 16.2 

7.14 

CADM - - - 

Emond 25.6 27.6 (@ 17,572 hours) 24.9 

15.7 

CADM - - - 

Emond 37.3 39.7 (@ 17,572 hours) 36.2 

32.9 

CADM - - - 

Emond 52.7 55.5 (@ 17,572 hours) 51.2 

71.4 

CADM - - - 

1 C.3.1.19. NTP (2006) 2 Years 

Type: Rat Dose: 0, 3, 10, 22, 46, 100 ng/kg-day 

Strain: Sprague Dawley Route: Oral gavage 

Body 

weight: 

8 weeks old 

(BW=215g) 

Regime: 5 days/weeks for 105 weeks 

Sex: Female and male Simulation time: 17,640 hours* (105 weeks) 

a

The CADM model simulates for 104 weeks only (17,472 hours). As a result, the terminal values from the CADM 

model may be underestimated compared to the Emond model, which considers the full 105 weeks of exposure. 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,408 1,910 (@ 17,568 hours) 1,444 2.14 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-155 DRAFT—DO NOT CITE OR QUOTE 

Emond 3,137 4,389 (@ 17,568 hours) 3,007 7.14 

CADM - - - 

Emond 5,393 8,039 (@ 17,568 hours) 5,079 15.7 

CADM - - - 

Emond 9,129 14,542 (@ 17,568 hours) 8,468 32.9 

CADM - - - 

Emond 16,361 27,991 (@ 17,568 hours) 14,951 71.4 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 385 460 (@ 17,572 hours) 403 

2.14 

CADM 632 715 715 

Emond 1,177 1,320 (@ 17,573 hours) 1,135 7.14 

CADM 2,127 2,387 2,387 

Emond 2,487 2,779 (@ 17,573 hours) 2,361 15.7 

CADM 4,691 5,252 5,252 

Emond 5,051 5,637 (@ 17,573 hours) 4,749 32.9 

CADM 9,822 10,984 10,984 

Emond 10,734 11,976 (@ 17,573 hours) 10,018 71.4 

CADM 21,366 23,880 23,880 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 243 271 (@ 17,581 hours) 261 

2.14 

CADM 302 355 277 

Emond 541 575 (@ 17,579 hours) 549 

7.14 

CADM 667 787 611 

Emond 930 985 (@ 17,578 hours) 934 

15.7 

CADM 1,242 1,463 1,138 

Emond 1,574 1,667 (@ 17,577 hours) 1,568 32.9 

CADM 2,369 2,787 2,173 

Emond 2,821 2,995 (@ 17,576 hours) 2,792 71.4 

CADM 4,890 5,748 4,489 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-156 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 38.1 44.0 (@ 17,572 hours) 40.4 

2.14 

CADM 46.0 48.0 48.0 

Emond 99.5 109 (@ 17,572 hours) 97.9 

7.14 

CADM 125 130 130 

Emond 192 211 (@ 17,572 hours) 186 

15.7 

CADM 257 267 267 

Emond 364 400 (@ 17,572 hours) 348 

32.9 

CADM 520 538 538 

Emond 729 804 (@ 17,572 hours) 691 

71.4 

CADM 1,110 1,149 1,149 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 8.17 9.30 (@ 17,572 hours) 8.43 

2.14 

CADM - - - 

Emond 16.6 18.0 (@ 17,572 hours) 16.2 

7.14 

CADM - - - 

Emond 25.6 27.6 (@ 17,572 hours) 24.9 

15.7 

CADM - - - 

Emond 37.3 39.7 (@ 17,572 hours) 36.2 

32.9 

CADM - - - 

Emond 52.7 55.5 (@ 17,572 hours) 51.2 

71.4 

CADM - - - 

 1 

 2 

3 C.3.1.20. Sewall et al. (1995) 

Type: Rat Dose: 49, 149.8, 490, and 1750 ng/kg every two 

weeks or 3.5, 10.7, 35, and 125 ng/kg-day 

Strain: Sprauge-Dawley Route: Oral gavage 

Body weight: 12 wk old 

(BW set to 250g) 

Regime: Once every 2 weeks for 30 weeks 

Sex: Female Simulation time: 5040 hours 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-157 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,813 7,535 (@ 4,704 hours) 1,587 3.5 

CADM - - - 

Emond 3,916 21,297 (@ 4,704 hours) 3,189 10.7 

CADM - - - 

Emond 9,163 66,137 (@ 4,704 hours) 6,945 35 

CADM - - - 

Emond 24,608 228,370 (@ 4,704 hours) 17,298 125 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 550 901 (@ 4,711 hours) 459 

3.5 

CADM - - - 

Emond 1,605 2,632 (@ 4,712 hours) 1,229 10.7 

CADM - - - 

Emond 5,072 8,350 (@ 4,712 hours) 3,618 35 

CADM - - - 

Emond 17,683 29,256 (@ 4,713 hours) 12,011 125 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 310 383 (@ 4,765 hours) 290 

3.5 

CADM - - - 

Emond 670 827 (@ 4,763 hours) 590 

10.7 

CADM - - - 

Emond 1,569 1,957 (@ 4,760 hours) 1,304 35 

CADM - - - 

Emond 4,217 5,376 (@ 4,757 hours) 3,303 125 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-158 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 51.4 72.5 (@ 4,710 hours) 45.3 

3.5 

CADM - - - 

Emond 130 189 (@ 4,710 hours) 106 

10.7 

CADM - - - 

Emond 364 546 (@ 4,710 hours) 274 

35 

CADM - - - 

Emond 1,164 1,793 (@ 4,710 hours) 824 125 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 10.2 15.8 (@ 2 hours) 9.18 

3.5 

CADM - - - 

Emond 19.8 34.4 (@ 1 hours) 17.0 

10.7 

CADM - - - 

Emond 37.0 63.2 (@ 1 hours) 31.4 

35 

CADM - - - 

Emond 63.1 90.9 (@ 1 hours) 55.2 

125 

CADM - - - 

 1 

 2 

3 C.3.1.21. Smialowicz et al. (2008) 

Type: Mice Dose: 0, 1.5, 15, 150, 450 ng/kg-day 

Strain: B6C3F1 Route: Oral gavage 

Body weight: 13 wk old 

(BW set to 28g) 

Regime: 5 days/week for 13 weeks 

Sex: Female Simulation time: 2184 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-159 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 241 449 (@ 2,112 hours) 307 

1.07 

CADM - - - 

Emond 1,358 2,821 (@ 2,112 hours) 1,460 10.7 

CADM - - - 

Emond 7,385 20,036 (@ 2,112 hours) 6,978 107 

CADM - - - 

Emond 17,438 54,346 (@ 2,112 hours) 15,650 321 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 67.1 107 (@ 2,116 hours) 91.5 

1.07 

CADM 59.0 92.0 88.0 

Emond 683 971 (@ 2,117 hours) 787 

10.7 

CADM 767 1,000 907 

Emond 6,784 9,010 (@ 2,117 hours) 7,043 107 

CADM 8,349 10,306 8,998 

Emond 20,218 26,379 (@ 2,117 hours) 20,405 321 

CADM 25,344 31,006 26,967 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 156 229 (@ 2,130 hours) 225 

1.07 

CADM 151 210 204 

Emond 885 1,155 (@ 2,124 hours) 1,111 10.7 

CADM 689 815 774 

Emond 4,831 5,979 (@ 2,120 hours) 5,591 107 

CADM 2,771 3,224 2,937 

Emond 11,420 14,037 (@ 2,119 hours) 12,920 321 

CADM 6,337 7,509 6,688 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-160 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 17.0 25.5 (@ 2,116 hours) 23.9 

1.07 

CADM 21.0 29.0 29.0 

Emond 117 159 (@ 2,116 hours) 141 

10.7 

CADM 119 145 135 

Emond 852 1,103 (@ 2,116 hours) 923 107 

CADM 727 875 778 

Emond 2,304 2,958 (@ 2,116 hours) 2,419 321 

CADM 1,961 2,370 2,080 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1.48 2.17 (@ 2,116 hours) 1.90 

1.07 

CADM - - - 

Emond 7.60 9.86 (@ 2,116 hours) 8.42 

10.7 

CADM - - - 

Emond 30.3 36.0 (@ 2,117 hours) 31.1 

107 

CADM - - - 

Emond 51.1 58.1 (@ 2,117 hours) 51.8 

321 

CADM - - - 

1 C.3.1.22. Toth et al., 1 Year (1979) 

Type: Mice Dose: 7, 700, 7000 ng/kg/week 

Strain: Swiss/H/Riop Route: Gastric intubation 

Body weight: 10 weeks old (BW= 

27g) 

Regime: 1/week for 52 weeks 

Sex: Female and male Simulation time: 8,736 hours* 

a

According to the protocol in the paper, the mice were exposed for 52 weeks. However, the post exposure treatment 

was for an additional 60–285 days. For this simulation, we modeled 52 weeks because we have already reached the 

maximum when the dosing ends. We did not simulate the scenario using the CADM model because this mice model 

can only simulate for a maximum of 123 days. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-161 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 315 889 (@ 8,568 hours) 308 

1 

CADM - - - 

Emond 7,814 63,673 (@ 7,896 hours) 6,014 100 

CADM - - - 

Emond 50,105 610,490 (@ 8,568 hours) 34,155 1,000 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 94.1 131 (@ 8,575 hours) 91.5 

1 

CADM - - - 

Emond 7,337 10,132 (@ 7,905 hours) 5,669 100 

CADM - - - 

Emond 70,180 97,655 (@ 8,577 hours) 51,986 1,000 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 215 247 (@ 8,613 hours) 230 

1 

CADM - - - 

Emond 5,337 5,912 (@ 8,594 hours) 4,997 100 

CADM - - - 

Emond 34,239 38,825 (@ 8,588 hours) 30,516 1,000 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 23.4 28.4 (@ 8,574 hours) 24.3 

1 

CADM - - - 

Emond 929 1,189 (@ 7,902 hours) 781 

100 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-162 DRAFT—DO NOT CITE OR QUOTE 

Emond 7,564 10,044 (@ 8,574 hours) 5,965 1,000 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1.93 2.65 (@ 8,573 hours) 1.90 

1 

CADM - - - 

Emond 31.8 58.4 (@ 2 hours) 27.7 

100 

CADM - - - 

Emond 78.6 103 (@ 2 hours) 72.7 

1,000 

CADM - - - 

1 C.3.1.23. Van Birgelen (1995) 

Type: Rat Dose: 0, 13.5, 26.4, 46.9, 320, 1024 ng/kgday 

Strain: Sprague Dawley Route: Oral gavage 

Body weight: 150 g Regime: Once per day for 13 weeks 

Sex: Female Simulation time: 2184 hours (13 weeks) 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 3,969 6,098 (@ 2,160 hours) 4,665 13.5 

CADM - - - 

Emond 6,479 10,258 (@ 2,160 hours) 7,457 26.4 

CADM - - - 

Emond 9,968 16,284 (@ 2,160 hours) 11,313 46.9 

CADM - - - 

Emond 47,606 86,065 (@ 2,160 hours) 52,581 320 

CADM - - - 

Emond 137,820 258,910 (@ 2,160 hours) 151,680 1024 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-163 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1,655 2,208 (@ 2,164 hours) 2,107 13.5 

CADM - - - 

Emond 3,228 4,216 (@ 2,164 hours) 4,017 26.4 

CADM - - - 

Emond 5,719 7,366 (@ 2,164 hours) 7,008 46.9 

CADM - - - 

Emond 38,484 47,999 (@ 2,164 hours) 45,537 320 

CADM - - - 

Emond 121,640 150,410 (@ 2,164 hours) 142,510 1024 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 669 843 (@ 2,167 hours) 835 

13.5 

CADM - - - 

Emond 1,092 1,357 (@ 2,166 hours) 1,342 26.4 

CADM - - - 

Emond 1,680 2,071 (@ 2,166 hours) 2,045 46.9 

CADM - - - 

Emond 8,027 9,816 (@ 2,165 hours) 9,639 320 

CADM - - - 

Emond 23,234 28,519 (@ 2,165 hours) 27,954 1024 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 132 173 (@ 2,164 hours) 167 

13.5 

CADM - - - 

Emond 240 308 (@ 2,164 hours) 296 

26.4 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-164 DRAFT—DO NOT CITE OR QUOTE 

Emond 404 513 (@ 2,164 hours) 492 

46.9 

CADM - - - 

Emond 2,437 3,031 (@ 2,164 hours) 2,887 320 

CADM - - - 

Emond 7,521 9,310 (@ 2,164 hours) 8,846 1024 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 19.9 24.2 (@ 2,164 hours) 23.4 

13.5 

CADM - - - 

Emond 29.0 34.3 (@ 2,164 hours) 33.2 

26.4 

CADM - - - 

Emond 38.8 45.0 (@ 2,164 hours) 43.7 

46.9 

CADM - - - 

Emond 79.1 85.2 (@ 2,164 hours) 84.1 

320 

CADM - - - 

Emond 97.5 101 (@ 2,164 hours) 101 

1024 

CADM - - - 

1 C.3.1.24. Vanden Heuvel et al. (1994) 

Type: Rat Dose: 0.05, 0.1, 1, 10, 100, 1000, 10000 ng/kg-day

Strain: Sprague Dawley Route: Oral gavage 

Body weight: 10 weeks old 

(BW 225 to 275g) 

(BW=250g) 

Regime: Single dose 

Sex: Female Simulation time: 24 hours* 

2 a 3 1 week is the minimum that can be simulated with the Aylward model 

4 

5 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 3.13 5.90 (@ 0 hours) 1.50 

0.05 

Aylward - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-165 DRAFT—DO NOT CITE OR QUOTE 

Emond 6.21 11.9 (@ 0 hours) 2.97 

0.1 

Aylward - - - 

Emond 58.0 118 (@ 0 hours) 28.0 

1 

Aylward - - - 

Emond 484 1,183 (@ 0 hours) 234 

10 

Aylward - - - 

Emond 3,569 11,963 (@ 0 hours) 1,622 100 

Aylward - - - 

Emond 26,736 119,860 (@ 0 hours) 9,984 1,000 

Aylward - - - 

Emond 240,660 1,200,300 (@ 0 hours) 72,090 10,000 

Aylward - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg) Model 

Time-weighted Ave Max Terminal 

Emond 0.230 0.311 (@ 3 hours) 0.114 

0.05 

Aylward - - 0.0140 

Emond 0.465 0.624 (@ 3 hours) 0.232 

0.1 

Aylward - - 0.0320 

Emond 5.04 6.34 (@ 4 hours) 2.61 

1 

Aylward - - 0.950 

Emond 59.7 67.9 (@ 5 hours) 34.0 

10 

Aylward - - 52.7 

Emond 733 800 (@ 8 hours) 477 

100 

Aylward - - 1,342 

Emond 8,215 8,918 (@ 10 hours) 5,941 1,000 

Aylward - - 15,967 

Emond 84,520 91,628 (@ 11 hours) 64,335 10,000 

Aylward - - 162,773 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg) Model 

Time-weighted Ave Max Terminal 

Emond 0.137 0.261 (@ 83 hours) 0.259 0.05 

Aylward - - 0.780 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-166 DRAFT—DO NOT CITE OR QUOTE 

Emond 0.272 0.518 (@ 84 hours) 0.515 0.1 

Aylward - - 1.57 

Emond 2.57 4.90 (@ 85 hours) 4.86 

1 

Aylward - - 15.3 

Emond 22.0 41.4 (@ 89 hours) 41.0 

10 

Aylward - - 125 

Emond 170 293 (@ 88 hours) 288 

100 

Aylward - - 739 

Emond 1,354 1,905 (@ 69 hours) 1,824 1,000 

Aylward - - 5,779 

Emond 12,571 15,593 (@ 40 hours) 13,735 10,000 

Aylward - - 55,825 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg) Model 

Time-weighted Ave Max Terminal 

Emond 0.0267 0.028 (@ 9 hours) 0.0272 0.05 

Aylward - - 0.0450 

Emond 0.0534 0.056 (@ 9 hours) 0.0542 0.1 

Aylward - - 0.0900 

Emond 0.532 0.561 (@ 9 hours) 0.531 

1 

Aylward - - 0.900 

Emond 5.29 5.59 (@ 8 hours) 5.02 

10 

Aylward - - 9.00 

Emond 53.0 56.3 (@ 7 hours) 46.1 

100 

Aylward - - 90.0 

Emond 527 562 (@ 7 hours) 424 

1,000 

Aylward - - 900 

Emond 5,258 5,610 (@ 7 hours) 4,082 10,000 

Aylward - - 9,000 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg) Model 

Time-weighted Ave Max Terminal 

Emond 0.0192 0 (@ 4 hours) 0.00963 

0.05 

Aylward - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-167 DRAFT—DO NOT CITE OR QUOTE 

Emond 0.0380 0 (@ 4 hours) 0.0191 

0.1 

Aylward - - - 

Emond 0.351 1 (@ 3 hours) 0.180 

1 

Aylward - - - 

Emond 2.75 4 (@ 3 hours) 1.48 

10 

Aylward - - - 

Emond 16.1 26 (@ 2 hours) 9.48 

100 

Aylward - - - 

Emond 57.7 77 (@ 2 hours) 40.7 

1,000 

Aylward - - - 

Emond 100 107 (@ 2 hours) 90.4 

10,000 

Aylward - - - 

1 C.3.1.25. White et al. (1986) 

Type: Mice Dose: 10, 50, 100, 500, 1000, 2000 ng/kg-day 

Strain: B6C3F1 Route: Oral gavage 

Body weight: 7 weeks old (BW set 

to 23g) 

Regime: 1/day for 14 days 

Sex: Female Simulation time: 336 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 603 1,502 (@ 312 hours) 785 

10 

CADM - - - 

Emond 2,250 6,387 (@ 312 hours) 2,742 50 

CADM - - - 

Emond 3,934 11,970 (@ 312 hours) 4,650 100 

CADM - - - 

Emond 14,772 53,188 (@ 312 hours) 16,394 500 

CADM - - - 

Emond 26,844 102,960 (@ 312 hours) 29,229 1,000 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-168 DRAFT—DO NOT CITE OR QUOTE 

Emond 49,896 201,110 (@ 312 hours) 53,697 2,000 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose

Model 

Time-weighted Ave Max Terminal 

Emond 216 375 (@ 317 hours) 343 

10 

CADM 217 468 (336h) 463 

Emond 1,279 2,164 (@ 317 hours) 1,997 50 

CADM 1,775 3,261 (336h) 3,261 

Emond 2,707 4,525 (@ 317 hours) 4,184 100 

CADM 3,999 6,923 (336h) 6,923 

Emond 14,802 24,165 (@ 317 hours) 22,383 500 

CADM 22,705 36,362 (336h) 36,362 

Emond 30,278 49,034 (@ 317 hours) 45,414 1,000 

CADM 46,309 73,145 (336h) 73,145 

Emond 61,381 98,703 (@ 317 hours) 91,363 2,000 

CADM 93,577 146,695 (336h) 146,695 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 279 507 (@ 336 hours) 507 

10 

CADM 316 537 (336h) 537 

Emond 1,056 1,846 (@ 336 hours) 1,846 50 

CADM 1,029 1,564 (336h) 1,564 

Emond 1,854 3,195 (@ 333 hours) 3,195 100 

CADM 1,662 2,470 (336h) 2,470 

Emond 7,008 11,868 (@ 324 hours) 11,816 500 

CADM 5,711 8,594 (336h) 8,594 

Emond 12,746 21,566 (@ 323 hours) 21,424 1,000 

CADM 10,498 15,993 (336h) 15,993 

Emond 23,691 40,177 (@ 322 hours) 39,843 2,000 

CADM 19,990 30,726 (336h) 30,726 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-169 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 37.7 65.9 (@ 317 hours) 63.8 

10 

CADM 47.9 85.9 (336h) 85.9 

Emond 175 297 (@ 317 hours) 284 

50 

CADM 207 342 (336h) 342 

Emond 338 570 (@ 316 hours) 542 

100 

CADM 388 624 (336h) 624 

Emond 1,597 2,637 (@ 316 hours) 2,480 500 

CADM 1,761 2,754 (336h) 2,754 

Emond 3,137 5,153 (@ 316 hours) 4,830 1,000 

CADM 3,455 5,387 (336h) 5,387 

Emond 6,186 10,118 (@ 316 hours) 9,459 2,000 

CADM 6,836 10,643 (336h) 10,643 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 3.49 5.32 (@ 316 hours) 4.82 

10 

CADM - - - 

Emond 11.4 16.4 (@ 317 hours) 15.1 

50 

CADM - - - 

Emond 18.1 25.1 (@ 317 hours) 23.4 

100 

CADM - - - 

Emond 44.2 56.2 (@ 317 hours) 53.8 

500 

CADM - - - 

Emond 59.3 71.9 (@ 317 hours) 69.7 

1,000 

CADM - - - 

Emond 74.4 86.1 (@ 317 hours) 84.3 

2,000 

CADM - - - 

 1 

 2 

 3 

 4 

 5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-170 DRAFT—DO NOT CITE OR QUOTE 

1 C.3.2. Gestational Studies 

2 C.3.2.1. Bell et al. (2007) 

Type: Rat Dose: 2.4, 8, and 46 ng/kg-day with a 0.03 ng/kg-day 

background 

Strain: Han/Wistar Route: Dietary 

Body weight: 6 weeks 

(BW= 85g) 

Regime: 12 weeks prior to mating, during the two week mating 

period, and during gestation 

Sex: Female Simulation 

time: 

2,352 hr (98 days) prior to gestation + 504 hr (21 days) 

during gestation for a total of 2,856 hours 

a

Time averages are computed during the gestation period only. 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2.43 1,998 4,977,500 2,452 (@ 2,352 

hours) 1,745 

8.03 4,539 11,602,000 5,781 (@ 2,352 

hours) 4,023 

46.03 15,952 41,518,000 22,096 (@ 2,352 

hours) 14,275 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2.43 381 914,700 437 (@ 2,356 hours) 321 

8.03 1,201 2,970,500 1,351 (@ 2,356 

hours) 1,044 

46.03 6,638 16,802,000 7,260 (@ 2,356 

hours) 5,980 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2.43 233 585,680 263 (@ 2,336 hours) 211 

8.03 528 1,365,300 589 (@ 2,335 hours) 487 

46.03 1,851 4,885,900 2,039 (@ 2,334 

hours) 1,739 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-171 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2.43 43.0 94,428 44.5 (@ 2,836 hours) 43.4 

8.03 113 258,160 118 (@ 2,836 hours) 114 

46.03 506 1,204,800 529 (@ 2,836 hours) 509 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2.43 17.2 8,674 39.7 (@ 2,530 hours) 6.53 

8.03 37.7 19,002 86.7 (@ 2,529 hours) 14.4 

46.03 118 59,628 271 (@ 2,527 hours) 45.9 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2.43 8.13 20,295 8.98 (@ 2,356 hours) 7.24 

8.03 16.8 43,248 18.2 (@ 2,356 hours) 15.4 

46.03 42.7 112,990 44.7 (@ 2,356 hours) 40.5 

1 C.3.2.2. Hojo et al. (2002) 

Type: Rat Dose: 20, 60 and 180 ng/kg 

Strain: Sprague Dawley Route: Oral gavage 

Body weight 20 ng/kg BW = 271g 

60 ng/kg BW = 275g 

180 ng/kg BW = 262g 

Regime: Single dose on GD8 

Sex: Female Simulation time 24 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 1,285 177,790 3,534 (@ 192 hours) 402 

60 3,295 452,060 10,477 (@ 192 hours) 1,002 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-172 DRAFT—DO NOT CITE OR QUOTE 

180 8,465 1,114,200 31,887 (@ 192 hours) 2,396 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 128 20,554 144 (@ 198 hours) 43.2 

60 420 72,340 465 (@ 200 hours) 147 

180 1,364 250,820 1,497 (@ 201 hours) 497 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 32.5 17,253 63.0 (@ 281 hours) 49.4 

60 86.4 44,093 161 (@ 284 hours) 124 

180 226 108,730 398 (@ 286 hours) 301 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 10.6 3,054 11.3 (@ 200 hours) 8.67 

60 31.8 8,702 33.8 (@ 199 hours) 23.6 

180 95.0 24,747 101 (@ 199 hours) 63.4 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 15.9 2,334 18.4 (@ 206 hours) 1.64 

60 39.8 5,829 45.7 (@ 205 hours) 4.10 

180 96.3 13,866 110 (@ 203 hours) 9.72 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 4.88 759 7.74 (@ 194 hours) 1.75 

60 11.2 1,848 18.5 (@ 194 hours) 4.26 

180 23.6 4,157 38.5 (@ 193 hours) 9.65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-173 DRAFT—DO NOT CITE OR QUOTE 

1 C.3.2.3. Ikeda et al. (2005) 

Type: Rat Dose: 400 ng/kg single dose and 80 ng/kg weekly 

maintenance dose 

Strain: Sprague Dawley Route: Oral gavage 

Body weight: 10 weeks 

(BW= 250g) 

Regime: Initial single loading dose, 2 weekly maintenance 

doses prior to gestation and 2 weekly maintenance 

doses during gestation 

Sex: Female Simulation 

time: 

504 hr (21 days) prior to gestation + 504 hr (21 days) 

during gestation for a total simulation of 1,008 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

16.5 18,103 18,249,000 80,047 (@ 144 hours) 8,009 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

16.5 7,755 7,817,300 17,016 (@ 150 hours) 2,698 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

16.5 2,087 2,103,900 3,663 (@ 184 hours) 1,028 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

16.5 548 552,590 1,085 (@ 149 hours) 262 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

16.5 45.9 46,290 245 (@ 679 hours) 30.2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-174 DRAFT—DO NOT CITE OR QUOTE 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

16.5 44.0 44,361 63.8 (@ 149 hours) 26.8 

1 C.3.2.4. Kattainen et al. (2001) 

Type: Rat Dose: 30, 100, 300, and 1,000 ng/kg 

Strain: Han/Wistar (Kuopio) 

and Long/Evans 

(Turku/AB) crossing. 

Route: Oral gavage 

Body weight: BW not specified 

(BW set to 190g)* 

Regime: Single dose on GD15 

Sex: Female Simulation 

time: 

24 hours 

a

Derelanko and Hollinger (1995). 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 1,763 151,690 4,703 (@ 336 hours) 632 

100 4,944 423,680 15,679 (@ 336 hours) 1,761 

300 12,712 1,054,600 47,253 (@ 336 hours) 4,327 

1,000 37,039 2,878,700 158,470 (@ 336 hours) 11,429 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 193 19,784 219 (@ 342 hours) 78.9 

100 713 79,889 793 (@ 344 hours) 324 

300 2,298 276,990 2,533 (@ 345 hours) 1,150 

1,000 8,054 1,032,300 8,830 (@ 345 hours) 4,412 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-175 DRAFT—DO NOT CITE OR QUOTE 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 42.8 12,439 82.8 (@ 426 hours) 77.5 

100 123 34,712 230 (@ 431 hours) 217 

300 327 86,670 571 (@ 431 hours) 536 

1,000 981 238,680 1,551 (@ 425 hours) 1,435 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 15.9 2,562 16.9 (@ 343 hours) 14.1 

100 52.7 8,273 56.2 (@ 343 hours) 44.2 

300 158 24,176 168 (@ 343 hours) 125 

1,000 524 78,767 561 (@ 343 hours) 395 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 4.86 828 6.90 (@ 372 hours) 2.53 

100 13.2 2,221 18.2 (@ 372 hours) 6.89 

300 31.5 5,200 42.3 (@ 371 hours) 16.2 

1,000 82.2 12,907 106 (@ 369 hours) 39.6 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 6.58 634 10.7 (@ 338 hours) 2.73 

100 15.8 1,642 26.3 (@ 338 hours) 7.28 

300 31.6 3,538 50.6 (@ 337 hours) 16.3 

1,000 57.1 7,095 80.1 (@ 337 hours) 34.8 

1 C.3.2.5. Keller et al. (2007) 

Type: Mouse Dose: 10, 100, and 1000 ng/kg 

Strain: CBA/J and C3H/HeJ Route: Oral 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-176 DRAFT—DO NOT CITE OR QUOTE 

Body weight: Not specified (24 g 

used in the simulation) 

Regime: Single dose on GD13 

Sex: Female Simulation time: 504 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

10 296 18,384 788 (@ 312 hours) 48.4 

100 2,365 149,060 7,884 (@ 312 hours) 374 

1,000 18,764 1,083,900 78,825 (@ 312 hours) 2,454 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

10 30.6 2,046 39.8 (@ 316 hours) 4.90 

100 371 28,867 421 (@ 319 hours) 62.7 

1,000 4,214 388,320 4,697 (@ 321 hours) 833 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

10 22.4 7,075 41.1 (@ 386 hours) 35.9 

100 188 57,462 333 (@ 396 hours) 291 

1,000 1,591 425,300 2,441 (@ 392 hours) 2,064 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

10 5.57 1,024 5.99 (@ 319 hours) 4.99 

100 54.3 9,170 59.0 (@ 318 hours) 41.9 

1,000 530 79,818 581 (@ 318 hours) 323 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-177 DRAFT—DO NOT CITE OR QUOTE 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

10 2.57 386 3.80 (@ 337 hours) 0.795 

100 21.8 3,109 30.0 (@ 334 hours) 6.42 

1,000 179 22,097 233 (@ 329 hours) 42.6 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

10 1.74 115 3.14 (@ 315 hours) 0.305 

100 11.5 857 23.5 (@ 314 hours) 2.30 

1,000 46.7 4,430 79.8 (@ 314 hours) 13.3 

1 C.3.2.6. Li et al. (2006) 3-Day 

Type: Mouse Dose: 2, 50, and 100 ng/kg-day 

Strain: NIH Route: Oral gavage 

Body weight: 25-28 g (used 27 g in 

the simulation) 

Regime: Daily exposure from GD1 to GD3 

Sex: Female Simulation time: 72 hours 

2 

3 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2 87.5 6,305 216 (@ 48 hours) 75.1 

50 1,564 112,720 4,906 (@ 48 hours) 1,312 

100 2,823 203,490 9,547 (@ 48 hours) 2,313 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2 8.98 647 15.1 (@ 52 hours) 9.10 

50 333 23,971 539 (@ 53 hours) 402 

100 718 51,738 1,156 (@ 53 hours) 888 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-178 DRAFT—DO NOT CITE OR QUOTE 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2 17.0 1,227 31.1 (@ 72 hours) 31.1 

50 315 22,704 548 (@ 72 hours) 548 

100 576 41,460 984 (@ 72 hours) 984 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2 2.29 165 3.51 (@ 55 hours) 3.43 

50 53.6 3,863 82.2 (@ 54 hours) 77.1 

100 105 7,598 162 (@ 53 hours) 150 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2 0.00 0 0.000 (@ 72 hours) 0.00 

50 0.0 0 0.000 (@ 72 hours) 0.00 

100 0.0 0 0.000 (@ 72 hours) 0.00 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

2 0.538 38.8 0.864 (@ 51 hours) 0.498 

50 8.24 594 13.5 (@ 2 hours) 8.16 

100 13.6 981 23.7 (@ 2 hours) 13.6 

 1 

 2 

3 C.3.2.7. Markowski et al. (2001) 

Type: Rat Dose: 20, 60 and 180 ng/kg 

Strain: Holtzman rats Route: Oral gavage 

Body weight: BW not specified 

(BW set to 190g)* 

Regime: Single dose on GD18 

Sex: Female Simulation 

time: 

24 hours 

a

Derelanko and Hollinger (1995). 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-179 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 1,234 71,255 3,029 (@ 408 hours) 471 

60 3,184 184,690 9,096 (@ 408 hours) 1,317 

180 8,152 465,030 27,457 (@ 408 hours) 3,193 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 123 8,315 142 (@ 414 hours) 56.5 

60 409 29,656 459 (@ 415 hours) 213 

180 1,333 103,210 1,478 (@ 416 hours) 790 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 28.0 4,437 55.6 (@ 498 hours) 55.5 

60 74.0 11,462 144 (@ 504 hours) 144 

180 195 28,948 363 (@ 504 hours) 363 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 10.6 1,013 11.3 (@ 415 hours) 10.2 

60 31.7 2,989 33.7 (@ 415 hours) 29.5 

180 94.7 8,834 101 (@ 415 hours) 85.7 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 1.26 157 1.93 (@ 448 hours) 1.43 

60 3.21 395 4.79 (@ 449 hours) 3.63 

180 7.80 943 11.3 (@ 449 hours) 8.69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-180 DRAFT—DO NOT CITE OR QUOTE 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

20 4.75 299 7.61 (@ 410 hours) 2.12 

60 11.0 729 18.2 (@ 410 hours) 5.47 

180 23.2 1,621 38.1 (@ 409 hours) 12.9 

1 C.3.2.8. Mietinnen et al. (2006) 

Type: Rat Dose: 30, 100, 300 and 1000 ng/kg 

Strain: cross-breeding of 

Han/Wistar and LongEvans rats 

Route: Oral gavage 

Body weight: BW 11 weeks 

(BW set to 180g) 

Regime: Single dose on GD15 

Sex: Female Simulation 

time: 

24 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 1,756 151,180 4,641 (@ 336 hours) 721 

100 4,922 422,480 15,471 (@ 336 hours) 1,758 

300 12,657 1,052,000 46,647 (@ 336 hours) 4,994 

1,000 36,874 2,872,800 156,480 (@ 336 hours) 11,423 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 193 19,697 219 (@ 342 hours) 78.8 

100 711 79,610 791 (@ 344 hours) 323 

300 2,293 276,280 2,529 (@ 345 hours) 1,149 

1,000 8,044 1,030,600 8,822 (@ 345 hours) 4,409 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-181 DRAFT—DO NOT CITE OR QUOTE 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 43.1 12,461 82.9 (@ 425 hours) 77.4 

100 124 34,793 231 (@ 430 hours) 217 

300 329 86,906 572 (@ 430 hours) 536 

1,000 988 239,390 1,555 (@ 424 hours) 1,436 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 15.9 2,560 16.9 (@ 343 hours) 14.1 

100 52.7 8,269 56.2 (@ 343 hours) 44.1 

300 158 24,169 168 (@ 343 hours) 125 

1,000 524 78,769 561 (@ 343 hours) 395 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 4.83 824 6.87 (@ 372 hours) 2.52 

100 13.1 2,213 18.1 (@ 372 hours) 6.87 

300 31.3 5,182 42.1 (@ 371 hours) 16.2 

1,000 81.7 12,867 105 (@ 369 hours) 39.5 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

30 6.56 632 10.7 (@ 338 hours) 2.72 

100 15.8 1,639 26.3 (@ 338 hours) 7.27 

300 31.6 3,533 50.5 (@ 337 hours) 16.3 

1,000 57.0 7,090 80.1 (@ 337 hours) 34.8 

1 C.3.2.9. Murray et al. (1979) Gestational Portion 

Type: Rat Dose: 1, 10, and 100 ng/kg-day 

Strain: Sprague Dawley Route: Diet oral dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-182 DRAFT—DO NOT CITE OR QUOTE 

Body weight: 6- to 7 week 

(Bw= 85g) 

Regime: Once per day for 90 days prior to gestation and 

during gestation 

Sex: Female Simulation 

time: 

2160 hr (90 days ) prior gestation + 504 hr (21 

days) for a total simulation of 2664 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

1 897 2,389,400 1,291 (@ 2,160 hours) 926 

10 4,691 12,497,000 6,780 (@ 2,160 hours) 4,708 

100 26,219 69,849,000 42,272 (@ 2,160 hours) 25,849 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

1 129 342,940 186 (@ 2,164 hours) 133 

10 1,271 3,385,700 1,657 (@ 2,164 hours) 1,298 

100 12,492 33,279,000 15,332 (@ 2,164 hours) 12,876 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

1 105 280,460 142 (@ 2,146 hours) 112 

10 551 1,467,700 682 (@ 2,143 hours) 569 

100 3,080 8,204,300 3,682 (@ 2,142 hours) 3,162 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

1 15.4 41,059 21.8 (@ 2,644 hours) 21.4 

10 108 286,920 141 (@ 2,644 hours) 137 

100 847 2,257,100 1,060 (@ 2,644 hours) 1,017 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-183 DRAFT—DO NOT CITE OR QUOTE 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

1 1.77 4,720 21.7 (@ 2,339 hours) 3.54 

10 8.22 21,889 99.8 (@ 2,337 hours) 16.7 

100 37.4 99,722 453 (@ 2,334 hours) 77.0 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

1 3.79 10,101 5.06 (@ 2,163 hours) 3.96 

10 17.1 45,522 20.5 (@ 2,164 hours) 17.6 

100 55.1 146,790 61.0 (@ 2,164 hours) 56.8 

1 C.3.2.10. Murray et al. (1979) Adult Portion 

Type: Rat Dose: 1, 10, and 100 ng/kg-day 

Strain: Sprague Dawley Route: Dietary 

Body weight: BW set to 4.5 g Regime: 120 days 

Sex: Female Simulation time: 2880 hours 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 619 832 (@ 2,856 hours) 785 

1 

CADM - - - 

Emond 3,241 4,181 (@ 2,856 hours) 3,717 10 

CADM - - - 

Emond 18,038 24,433 (@ 2,856 hours) 19,844 100 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-184 DRAFT—DO NOT CITE OR QUOTE 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 128 180 (@ 2,859 hours) 173 

1 

CADM - - - 

Emond 1,273 1,618 (@ 2,860 hours) 1,540 10 

CADM - - - 

Emond 12,601 15,281 (@ 2,860 hours) 14,460 100 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 106 139 (@ 2,865 hours) 138 

1 

CADM - - - 

Emond 556 665 (@ 2,864 hours) 657 

10 

CADM - - - 

Emond 3,095 3,604 (@ 2,862 hours) 3,534 100 

CADM - - - 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 14.8 20.0 (@ 2,860 hours) 19.6 1 

CADM - - - 

Emond 105 130 (@ 2,860 hours) 126 10 

CADM - - - 

Emond 837 1,003 (@ 2,860 hours) 957 100 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 3.77 4.95 (@ 2,859 hours) 4.77 1 

CADM - - - 

Emond 17.1 20.3 (@ 2,859 hours) 19.5 10 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-185 DRAFT—DO NOT CITE OR QUOTE 

Emond 55.3 60.9 (@ 2,860 hours) 59.4 100 

CADM - - - 

1 C.3.2.11. Nohara et al. (2000) 

Type: Rat Dose: 12.5, 50, 200 or 800 ng TCDD/kg 

Strain: Holtzman rats Route: Oral gavage 

Body weight: BW not specified 

(BW set to 190g)* 

Regime: Single dose on GD15 

Sex: Female Simulation 

time: 

24 hours 

a

Derelanko and Hollinger (1995). 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 816 69,459 1,933 (@ 336 hours) 290 

50 2,724 235,070 7,736 (@ 336 hours) 981 

200 8,912 752,170 31,022 (@ 336 hours) 3,110 

800 30,121 2,378,900 125,030 (@ 336 hours) 9,532 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 73.9 7,084 86.2 (@ 341 hours) 28.3 

50 336 35,736 378 (@ 343 hours) 143 

200 1,492 175,300 1,651 (@ 344 hours) 722 

800 6,387 810,340 7,011 (@ 345 hours) 3,449 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 19.7 5,736 38.1 (@ 419 hours) 35.4 

50 67.6 19,362 129 (@ 427 hours) 121 

200 229 62,032 410 (@ 431 hours) 385 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-186 DRAFT—DO NOT CITE OR QUOTE 

800 803 197,830 1,288 (@ 425 hours) 1,194 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 6.63 1,088 7.05 (@ 343 hours) 6.10 

50 26.4 4,212 28.1 (@ 343 hours) 22.9 

200 105 16,259 112 (@ 343 hours) 85.1 

800 420 63,228 449 (@ 343 hours) 319 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 2.25 385 3.26 (@ 371 hours) 1.17 

50 7.43 1,263 10.5 (@ 372 hours) 3.89 

200 22.8 3,802 31.0 (@ 372 hours) 11.8 

800 68.1 10,862 88.5 (@ 369 hours) 33.6 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 3.24 298 5.12 (@ 338 hours) 1.27 

50 9.66 959 16.0 (@ 338 hours) 4.18 

200 24.8 2,695 40.7 (@ 337 hours) 12.2 

800 51.9 6,315 75.0 (@ 337 hours) 30.6 

1 C.3.2.12. Ohsako et al. (2001) 

Type: Rat Dose: 12.5, 50, 200, and 800 ng/kg-day 

Strain: Holtzmann Route: Oral gavage 

Body weight 10 weeks (200g ) Regime: Single dose on GD15 

Sex: Female Simulation time 24 hours 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-187 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 845 63,918 2,016 (@ 360 hours) 304 

50 2,763 212,870 7,928 (@ 360 hours) 1,020 

200 9,022 677,090 31,557 (@ 360 hours) 3,239 

800 30,504 2,148,100 127,220 (@ 360 hours) 9,983 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 76.8 6,595 89.0 (@ 365 hours) 30.1 

50 340 32,557 383 (@ 367 hours) 152 

200 1,504 157,600 1,657 (@ 368 hours) 768 

800 6,426 724,530 7,026 (@ 369 hours) 3,689 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 19.6 4,897 38.4 (@ 446 hours) 36.9 

50 65.8 16,240 128 (@ 455 hours) 124 

200 223 51,709 404 (@ 458 hours) 393 

800 780 165,660 1,270 (@ 453 hours) 1,224 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 6.84 966 7.24 (@ 367 hours) 6.38 

50 26.6 3,693 28.4 (@ 367 hours) 23.7 

200 106 14,210 112 (@ 367 hours) 88.3 

800 421 55,466 449 (@ 367 hours) 334 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 1.69 274 2.50 (@ 397 hours) 1.16 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-188 DRAFT—DO NOT CITE OR QUOTE 

50 5.48 881 7.91 (@ 398 hours) 3.79 

200 16.8 2,629 23.3 (@ 398 hours) 11.4 

800 50.2 7,518 66.4 (@ 396 hours) 32.3 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

12.5 3.34 274 5.25 (@ 362 hours) 1.33 

50 9.76 863 16.1 (@ 362 hours) 4.34 

200 25.0 2,396 40.7 (@ 361 hours) 12.7 

800 52.1 5,566 75.1 (@ 361 hours) 31.7 

 1 

 2 

3 C.3.2.13. Schantz et al. (1995) and Amin et al. (2000) 

Type: Rat Dose: 25 and 100 ng/kg-day 

Strain: Sprague Dawley Route: Oral gavage 

Body weight: BW not specified 

(BW set to 250g) 

Regime: Daily doses from GD 10 - 16 

Sex: Female Simulation time: 384 hours; time averages are calculated 

from the beginning of the dosing 

 4 

 5 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 2,670 384,750 6,800 (@ 360 hours) 3,190 

100 8,341 1,201,700 24,522 (@ 360 hours) 9,706 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 512 73,705 871 (@ 365 hours) 778 

100 2,371 341,460 4,009 (@ 366 hours) 3,662 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-189 DRAFT—DO NOT CITE OR QUOTE 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 169 24,329 307 (@ 384 hours) 307 

100 532 76,559 949 (@ 384 hours) 949 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 45 6,492 76.6 (@ 365 hours) 74 

100 176 25,401 298 (@ 365 hours) 287 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 25 3,628 30.4 (@ 343 hours) 27 

100 74.0 10,655 88.1 (@ 342 hours) 77.8 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 10 1,440 14.4 (@ 364 hours) 13 

100 25 3,628 34.2 (@ 364 hours) 32 

 1 

2 

3 C.3.2.14. Seo et al. (1995) 

Type: Rat Dose: 25 and 100 ng/kg-day 

Strain: Sprague Dawley Route: Oral gavage 

Body weight: BW not specified 

(BW set to 190g) 

Regime: Daily from GD 10 - 16 

Sex: Female Simulation time: 384 hours; time averages are calculated 

from the beginning of the dosing 

 4 

 5 

 6 

 7 

 8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-190 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 2,655 766,430 6,796 (@ 384 hours) 2,748 

100 8,319 2,372,700 24,284 (@ 384 hours) 8,333 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 506 163,400 972 (@ 389 hours) 606 

100 2,358 767,640 4,486 (@ 389 hours) 2,871 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 173 66,734 358 (@ 436 hours) 339 

100 545 207,420 1,105 (@ 433 hours) 1,037 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 45.3 16,124 87.5 (@ 389 hours) 73.6 

100 177 61,908 339 (@ 389 hours) 271 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 24.7 5,826 29.8 (@ 343 hours) 10.6 

100 72.6 16,930 86.6 (@ 342 hours) 30.2 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

25 9.92 2,937 15.4 (@ 388 hours) 11.0 

100 25.1 7,349 36.1 (@ 388 hours) 27.7 

 1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-191 DRAFT—DO NOT CITE OR QUOTE 

1 C.3.2.15. Shi et al. (2007) Gestational Portion 

Type: Rat Dose: 1, 5, 50 and 200 ng/kg 

Strain: Sprague Dawley Route: Oral gavage 

Body weight: BW not specified 

(BW set to 190g)* 

Regime: Single dose on GD14 and GD21 

Sex: Female Simulation time: 504 hours 

a

Derelanko and Hollinger (1995). 

BLOOD CONCENTRATIONS (ng/kg) (Serum lipid adjusted) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

0.143 17.9 9,014 173 (@ 480 hours) 74.7 

0.714 81.1 40,871 840 (@ 480 hours) 329 

7.14 621 312,880 8,016 (@ 480 hours) 2,310 

28.6 1,975 995,020 31,730 (@ 312 hours) 6,960 

LIVER CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

0.143 1.16 583 8.44 (@ 484 hours) 5.63 

0.714 6.87 3,462 46.8 (@ 485 hours) 35.2 

7.14 96.9 48,840 576 (@ 486 hours) 499 

28.6 465 234,480 2,581 (@ 487 hours) 2,328 

FAT CONCENTRATIONS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

0.143 1.31 662 5.66 (@ 504 hours) 5.66 

0.714 6.02 3,032 25.2 (@ 504 hours) 25.2 

7.14 46.9 23,608 188 (@ 504 hours) 188 

28.6 150 75,504 591 (@ 504 hours) 591 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-192 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

0.143 0.229 116 1.08 (@ 487 hours) 1.07 

0.714 1.12 565 5.32 (@ 487 hours) 5.23 

7.14 10.7 5,389 50.8 (@ 487 hours) 49.4 

28.6 41.3 20,788 196 (@ 487 hours) 190 

FETUS (ng/kg) and AUC ((ng/kg) • hr) 

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

0.143 0.103 52.0 0.430 (@ 343 hours) 0.151 

0.714 0.470 237 1.91 (@ 344 hours) 0.681 

7.14 3.53 1,781 13.8 (@ 345 hours) 5.04 

28.6 10.6 5,354 41.0 (@ 345 hours) 15.1 

BOUND LIVER (ng/kg) and AUC ((ng/kg) • hr)

Dose Metric 

(ng/kg-day) 

Adjusted dose Time-weighted Ave Area Under the 

Curve Max Terminal 

0.143 0.0780 39.3 0.566 (@ 483 hours) 0.341 

0.714 0.348 175 2.31 (@ 483 hours) 1.49 

7.14 2.44 1,231 16.0 (@ 314 hours) 9.67 

28.6 6.67 3,360 40.8 (@ 313 hours) 24.8 

1 C.3.2.16. Shi et al. (2007) Adult Portion 

Type: Rat Dose: 1, 5, 50 and 200 ng/kg 

Strain: Sprague Dawley Route: Oral gavage 

Body weight: BW set to 4.5 g Regime: Weekly doses for 11 months 

Sex: Female Simulation time: 8040 hours 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-193 DRAFT—DO NOT CITE OR QUOTE 

BLOOD CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 188 262 (@ 7,561 hours) 210 0.143 

CADM - - - 

Emond 592 844 (@ 7,560 hours) 603 0.714 

CADM - - - 

Emond 2,882 5,023 (@ 7,560 hours) 2,679 7.14 

CADM - - - 

Emond 7,665 16,103 (@ 7,560 hours) 6,825 28.6 

CADM - - - 

LIVER CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 26.1 36.5 (@ 7,564 hours) 29.6 0.143 

CADM - - - 

Emond 118 159 (@ 7,564 hours) 120 0.714 

CADM - - - 

Emond 1,068 1,415 (@ 7,565 hours) 970 7.14 

CADM - - - 

Emond 4,119 5,450 (@ 7,565 hours) 3,574 28.6 

CADM - - - 

FAT CONCENTRATIONS (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 32.5 40.0 (@ 7,583 hours) 36.7 0.143 

CADM - - - 

Emond 102 120 (@ 7,584 hours) 106 0.714 

CADM - - - 

Emond 497 571 (@ 7,584 hours) 475 7.14 

CADM - - - 

Emond 1,322 1,527 (@ 7,584 hours) 1,217 28.6 

CADM - - - 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-194 DRAFT—DO NOT CITE OR QUOTE 

BODY BURDEN (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 3.94 4.99 (@ 7,566 hours) 4.45 0.143 

CADM - - - 

Emond 14.0 17.2 (@ 7,566 hours) 14.5 0.714 

CADM - - - 

Emond 90.8 112 (@ 7,566 hours) 84.4 7.14 

CADM - - - 

Emond 300 374 (@ 7,566 hours) 266 28.6 

CADM - - - 

BOUND LIVER (ng/kg) 

Dose Metric 

(ng/kg-day) 

Adjusted dose 

Model 

Time-weighted Ave Max Terminal 

Emond 1.18 1.60 (@ 7,563 hours) 1.31 0.143 

CADM - - - 

Emond 3.62 4.75 (@ 7,563 hours) 3.70 0.714 

CADM - - - 

Emond 15.6 19.7 (@ 7,564 hours) 14.7 7.14 

CADM - - - 

Emond 33.5 40.7 (@ 7,564 hours) 31.2 28.6 

CADM - - - 

1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-195 DRAFT—DO NOT CITE OR QUOTE 

1 Table C-1. Model input parameters potentially addressed by selected 

2 articles 

3 

Model input parameters potentially addressed 

Articles 

Absorption Desorption Distribution Elimination Kinetics Induction CYP1A1 Interspecies differences Age Differences Aryl hydrocarbon receptor (AhR) Mode of action Partition coefficient 

Aylward et al., 2004 ● ● ● ● ● 

Aylward et al., 2005 ● ● ● ● ● 

Aylward et al., 2009 ● 

Bohonowych and Denison, 2007 ● ● ● 

Boverhof et al., 2005 ● ● 

Connor and Aylward, 2006 ● ● ● 

Heinzl et al., 2007 ● ● 

Irigaray et al., 2005 ● ● 

Kerger et al., 2006 ● ● ● 

Kerger et al., 2007 ● 

Kim et al., 2003 ● 

Korenaga et al., 2007 ● ● 

Korkalainen et al., 2004 ● ● 

Kransler et al., 2007 ● ● 

Maruyama et al., 2002 ● ● ● 

Maruyama et al., 2003 ● ● ● 

Maruyama and Aoki, 2006 ● ● ● 

Millbrath et al., 2009 ● ● ● ● 

Moser and McLachlan, 2002 ● ● 

Mullerova and Kopecky, 2007 ● 

Nadal et al., 2009 ● ● 

Nohara et al., 2006 ● ● 

Olsman et al., 2007 ● 

Saghir et al., 2005 ● ● ● 

Schecter et al., 2003 ● ● 

Staskal et al., 2005 ● ● 

Toyoshiba et al., 2004 ● ● ● 

Wilkes et al., 2009 ● 

a 4 Partition coefficient estimates and CYP parameter value estimates were derived from Wang et al. (1997, 2000) and 

5 Santostefano et al. (1998). 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-196 DRAFT—DO NOT CITE OR QUOTE 

1 C.4. REFERENCES 

2 Amin, S; Moore, RW; Peterson, RE; et al. (2000) Gestational and lactational exposure to TCDD or coplanar PCBs 

3 alters adult expression of saccharin preference behavior in female rats. Neurotoxicol Teratol 22(5):675–682. 

4 Aylward, LL; Brunet, RC; Carrier, G; et al. (2005a) Concentration-dependent TCDD elimination kinetics in 

5 humans: toxicokinetic modeling for moderately to highly exposed adults from Seveso, Italy, and Vienna, Austria, 

6 and impact on dose estimates for the NIOSH cohort. J Exp Anal Environ Epidemiol 15:51–65. 

7 Aylward, LL; Brunet, RC; Starr, TB; et al. (2005b) Exposure reconstruction for the TCDD-exposed NIOSH cohort 

8 using a concentration- and age-dependent model of elimination. Risk Anal 25(4):945–956. 

9 Aylward, LL; Bodner, KM; Collins, JJ; et al. (2009) TCDD exposure estimation for workers at a New Zealand 

10 2,4,5-T manufacturing facility based on serum sampling data. J Expo Sci Environ Epidemiol. 3 June; 

11 doi:10.1038/jes.2009.31. Available online at http://www.nature.com/jes/journal/vaop/ncurrent/full/jes200931a.html.

12 Bell, DR; Clode, S; Fan, MQ; et al. (2007) Toxicity of 2,3,7,8-tetrachlorodibenzo-p-dioxin in the developing male 

13 Wistar(Han) rat. I: No decrease in epididymal sperm count after a single acute dose. Toxicol Sci (1):214–23. 

14 Bohonowych, JE; Denison, MS. (2007) Persistent binding of ligands to the aryl hydrocarbon receptor. 

15 Toxicological Sciences 98(1):99–109. 

16 Boverhof, DR; Burgoon, LD; Tashiro, C; et al. (2005) Temporal and dose-dependent hepatic gene expression 

17 patterns in mice provide new insights into TCDD-mediated hepatotoxicity. Toxicol Sci 85(2):1048–1063. 

18 Cantoni, L; Salmona, M; Rizzardini, M. (1981) Porphyrogenic effect of chronic treatment with 2,3,7,8-

19 tetrachlorodibenzo-p-dioxin in female rats. Dose-effect relationship following urinary excretion of porphyrins. 

20 Toxicol Appl Pharmacol 57:156–163. 

21 Carrier, G; Brunet, RC; Brodeur, J. (1995a) Modeling of the toxicokinetics of polychlorinated dibenzo-p-dioxins 

22 and dibenzofuranes in mammalians, including humans: II kinetics of absorption and disposition of PCDDs/PCDFs. 

23 Toxicol Appl Pharmacol 131(267):276. 

24 Carrier, G; Brunet, RC; Brodeur, J. (1995b) Modeling of the toxicokinetics of polychlorinated dibenzo-p-dioxins 

25 and dibenzofurans in mammalians, including humans. Toxicol Appl Pharmacol 131:253−266. 

26 Chu, I; Valli, VE; Rousseaux, CG. (2007) Combined effects of 2,3,7,8-tetrachlorodibenzo-pdioxin and 

27 polychlorinated biphenyl congeners in rats. Toxicol Environ Chem 89(1):71–87. 

28 Connor, KT; Aylward, LL. (2006) Human response to dioxin: aryl hydrocarbon receptor (AHR) molecular structure, 

29 function, and dose-response data for enzyme induction indicate an impaired human AhR. J Toxicol Environ Health 

30 Part B: Critical Reviews 9(2):147–171. 

31 Crofton, KM; Craft, ES; Hedge, JM; et al. (2005) Thyroid-hormone-disrupting chemicals: evidence for dose32 dependent additivity or synergism. Environ Health Perspect 113(11):1549–1554. 

33 Derelanko, MJ; Hollinger, MA. (1995) CRC Handbook of Toxicology, pp.1–948. New York, NY. 

34 Diliberto, JJ; Burgin, D; Birnbaum, LS. (1997) Role of CYP1A2 in hepatic sequestration of dioxin: studies using 

35 CYP1A2 knock-out mice. Biochem Biophys Res Commun 236(2):431−433. 

36 Emond, C; Birnbaum, LS; DeVito, M. (2004) Physiologically based pharmacokinetic model for developmental 

37 exposures to TCDD in the rat. Toxicol Sci 80(1):115−133. 

38 Emond, C; Michalek, JE; Birnbaum, LS; et al. (2005) Comparison of the use of a physiologically based 

39 pharmacokinetic model and a classical pharmacokinetic model for dioxin exposure assessments. Environ Health 

40 Perspect 113(12):1666−1668. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-197 DRAFT—DO NOT CITE OR QUOTE 

1 Emond, C; Birnbaum, LS; Devito, MJ. (2006) Use of a physiologically based pharmacokinetic model for rats to 

2 study the influence of body fat mass and induction of CYP1A2 on the pharmacokinetics of TCDD. Environ Health 

3 Perspect 114(9):1394−1400. 

4 Fattore, EE; Trossvik, C; Hakansson, H. (2000) Relative potency values derived from hepatic vitamin A reduction in 

5 male and female Sprague–Dawley rats following subchronic dietary exposure to individual polychlorinated dibenzo6 p-dioxin and dibenzofuran congeners and a mixture thereof. Toxicol Appl Pharmacol 165(3):184–194. 

7 Hassoun, EA; Wilt, SC; Devito, MJ; et al. (1998) Induction of oxidative stress in brain tissues of mice after 

8 subchronic exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin. Toxicol Sci 42:23–27. 

9 Hassoun, EA; Li, F; Abushaban, A; et al. (2000) The relative abilities of TCDD and its congeners to induce 

10 oxidative stress in the hepatic and brain tissues of rats after subchronic exposure. Toxicology 145:103−113. 

11 Heinzl, H; Mittlback, M; Edler, L. (2007) On the translation of uncertainty from toxicokinetic to toxicodynamic 

12 models – the TCDD example. Chemosphere 67(9):S365–S374. 

13 Hojo, R; Stern, S; Zareba, G; et al. (2002) Sexually dimorphic behavioral responses to prenatal dioxin exposure. 

14 Ikeda, M; Mitsui, T; Setani, K; et al. (2005) In utero and lactational exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin 

15 in rats disrupts brain sexual differentiation. Toxicol Appl Pharmacol 205(1):98–105. 

16 ILSI (International Life Sciences Institute). (1994) Physiological parameter values for PBPK models. Washington, 

17 DC: Risk Science Institute. 

18 Irigaray, P; Mejean, L; Laurent, F. (2005) Behaviour of dioxin in pig adipocytes. Food Chem Toxicol 

19 43(3):457−460. 

20 Kattainen, H; Tuukkanen, J; Simanainen, U; et al. (2001) In utero/lactational 2,3,7,8-tetrachlorodibenzo-p-dioxin 

21 exposure impairs molar tooth development in rats. Toxicol Appl Pharmacol 174(3):216–224. 

22 Keller, JM; Huet-Hudson, YM; Leamy, LJ. (2007) Qualitative effects of dioxin on molars vary among inbred mouse 

23 strains. Arch Oral Biol 52(5):450–454. 

24 Kerger, BD; Leung, HW; Scott, P; et al. (2006) Age- and concentration-dependent elimination half-life of 2,3,7,8-

25 tetrachlorodibenzo-p-dioxin in Seveso children. Environ Health Perspect 114(10):1596–1602. 

26 Kerger, BD; Leung, HW; Scott, PK; et al. (2007) Refinements on the age-dependent half-life model for estimating 

27 child body burdens of polychlorodibenzodioxins and dibenzofurans. Chemosphere 67(9):S272–S278. 

28 Kim, AH; Kohn, MC; Nyska, A; et al. (2003) Area under the curve as a dose metric for promotional responses 

29 following 2,3,7,8-tetrachlorodibenzo-p-dioxin exposure. Toxicol Appl Pharmacol 191(1):12–21. 

30 Kitchin, KT; Woods, JS. (1979) 2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) effects on hepatic microsomal 

31 cytochrome P-448-mediated enzyme activities. Toxicol Appl Pharmacol 47:537−546. 

32 Kociba, RJ; Keeler, PA; Park, GN; et al. (1976) 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD): results of a 13-week 

33 oral toxicity study in rats. Toxicol Appl Pharmacol 35:553–574. 

34 Kociba, RJ; Keyes, DG; Beyer, JE; et al. (1978) Results of a two-year chronic toxicity and oncogenicity study of 

35 2,3,7,8-tetrachlorodibenzo-p-dioxin in rats. Toxicol Appl Pharmacol 46(2):279–303. 

36 Kociba, RJ; Keyes, DG; Beyer, JE; et al. (1979) Long-term toxicological studies of 2,3,7,8-tetrachlorodibenzo-p37 dioxin (TCDD) in laboratory animals. Ann NY Acad Sci 320: 397–404. 

38 Korenaga, T; Fukusato, T; Ohta, M; et al. (2007) Long-term effects of subcutaneously injected 2,3,7,8-

39 tetrachlorodibenzo-p-dioxin on the liver of rhesus monkeys. Chemosphere 67(9):S399–S404. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-198 DRAFT—DO NOT CITE OR QUOTE 

1 Korkalainen, M; Tuomisto, J; Pohjanvirta, R. (2004) Primary structure and inducibility by 2,3,7,8-

2 tetrachlorodibenzo-p-dioxin (TCDD) of aryl hydrocarbon receptor repressor in a TCDD-sensitive and a TCDD3 resistant rat strain. Biochem Biophys Res Commun 315(1):123–131. 

4 Kransler, KM; McGarrigle, BP; Olson, JR. (2007) Comparative developmental toxicity of 2,3,7,8-

5 tetrachlorodibenzo-p-dioxin in the hamster, rat, and guinea pig. Toxicology 229(3):214–225. 

6 Krishnan, D. (2007) Neurobehavioral and neuroendocrine assessment of rats perinatally exposed to polychlorinated 

7 biphenyls: a possible model for autism. Bowling Green State University. 

8 Krishnan, K. (2008) Physiologically based pharmacokinetic modelling in toxicology. In: Hayes, AW; ed. Principles 

9 and methods of toxicology. 5th ed. New York, NY: CRC Press, pp. 231−291. 

10 Latchoumycandane, C; Mathur, PP. (2002) Effects of vitamin E on reactive oxygen species-mediated 2,3,7,8-

11 tetrachlorodi-benzo-p-dioxin toxicity in rat testis. J Appl Toxicol 22(5):345–351 

12 Latchoumycandane, C; Chitra, KC; Mathur, PP. (2002) The effect of 2,3,7,8-tetrachlorodibenzo-p-dioxin on the 

13 antioxidant system in mitochondrial and microsomal fractions of rat testis. Toxicology 171(2–3):127–135. 

14 Li, B; Liu, H; Dai, L; et al. (2006) The early embryo loss caused by 2,3,7,8-tetrachlorodibenzo-p-dioxin may be 

15 related to the accumulation of this compound in the uterus. Reprod Toxicol 21(3):301–306. 

16 Luecke, RH; Pearce, BA; Wosilait, WD; et al. (2007) Postnatal growth considerations for PBPK modeling. J 

17 Toxicol Environ Health A 70(12):1027–37. 

18 Markowski, VP; Zareba, G; Stern, S; et al. (2001) Altered operant responding for motor reinforcement and the 

19 determination of benchmark doses following perinatal exposure to low-level 2,3,7,8-tetrachlorodibenzo-p-dioxin. 

20 Environ Health Perspect 109(6):621–627. 

21 Maruyama, W; Aoki, Y. (2006) Estimated cancer risk of dioxins to humans using a bioassay and physiologically 

22 based pharmacokinetic model. Toxicol Appl Pharmacol 214(2):188–198. 

23 Maruyama, W; Yoshida, K; Tanaka, T; et al. (2002) Determination of tissue-blood partition coefficients for a 

24 physiological model for humans, and estimation of dioxin concentration in tissues. Chemosphere 46(7):975–985. 

25 Maruyama, W; Yoshida, K; Tanaka, T; et al. (2003) Simulation of dioxin accumulation in human tissues and 

26 analysis of reproductive risk. Chemosphere 53(4):301–313. 

27 Miettinen, HM; Sovari, R; Alaluusua, S; et al. (2006) The effect of perinatal TCDD exposure on caries susceptibility 

28 in rats. Toxicol Sci 91(2):568–575. 

29 Milbrath, MO; Wenger, Y; Chang, CW; et al. (2009) Apparent half-lives of dioxins, furans, and polychlorinated 

30 biphenyls as a function of age, body fat, smoking status, and breast-feeding. Environ Health Perspect 

31 −117(3):417425. 

32 Moser, GA; McLachlan, MS. (2002) Modeling digestive tract absorption and desorption of lipophilic organic 

33 contaminants in humans. Environ Sci Technol 36(15):3318–25. 

34 Mullerova, D; Kopecky, J. (2007) White adipose tissue: storage and effector site for environmental pollutants. 

35 Physiol Res 56(4):375–381. 

36 Murray, FJ; Smith, FA; Nitschke, KD; et al. (1979) Three-generation reproduction study of rats given 2,3,7,8-

37 tetrachlorodibenzo-p-dioxin (TCDD) in the diet. Toxicol Appl Pharmacol 50:241–252. 

38 Murray, TJ; Yang, X; Sherr, D. (2006) Growth of a human mammary tumor cell line is blocked by galangi, a 

39 naturally occurring bioflavonoid, and is accompanied by down-regulation of cyclins D3, E, and A. Breast Cancer 

40 Res 8:R17 (doi:10.1186/bcr1391) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-199 DRAFT—DO NOT CITE OR QUOTE 

1 Nadal, M; Perello, G; Schuhmacher, M; et al. (2008) Concentrations of PCDD/PCDFs in plasma of subjects living 

2 in the vicinity of a hazardous waste incinerator: Follow-up and modeling validation. Chemosphere 73(6):901–906. 

3 Nadal, M; Domingo, JL; Garcia, F; et al. (2009) Levels of PCDD/F in adipose tissue on non-occupationally exposed 

4 subjects living near a hazardous waste incinerator in Catalonia, Spain. Chemosphere 74(11):1471–1476. 

5 NAS (National Academy of Sciences). (2006) Health risks from dioxin and related compounds: evaluation of the 

6 EPA reassessment. Washington, DC: National Academies Press. Available online at 

7 http://www.nap.edu/catalog.php?record_id=11688. 

8 Nohara, K; Fujimaki, H; Tsukumo, S; et al. (2000) The effects of perinatal exposure to low doses of 2,3,7,8-

9 tetrachlorodibenxo-p-dioxin on immune organs of rats. Toxicology 154(1–3):123–133 

10 Nohara, K; Ao, K; Miyamoto, Y; et al. (2006) Comparison of the 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD)-

11 induced CYP1A1 gene expression profile in lymphocytes from mice, rats, and humans: Most potent induction in 

12 humans. Toxicology 225(2–3):204–213. 

13 NTP (National Toxicology Program). (1982) Bioassay of 2,3,7,8-tetrachlorodibenzo-p-dioxin for possible 

14 carcinogenicity (gavage study). Tech. Rept. Ser. No. 201. U.S. Department of Health and Human Services, Public 

15 Health Service, Research Triangle Park, NC. 

16 NTP (National Toxicology Program). (2006) Studies of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in female 

17 Harlan Sprague-Dawley rats (gavage studies) Tech. Rep. Ser. No. 521. U.S. Department of Health and Human 

18 Services, Public Health Service, Research Triangle Park, NC. 

19 O’Flaherty, EJ. (1992) Modeling bone mineral metabolism, with special reference to calcium and lead. 

20 Neurotoxicity 13(4):789–797. 

21 Ohsako, S; Miyabara, Y; Nishimura, N; et al. (2001) Maternal exposure to a low dose of 2,3,7,8-tetrachlorodibenzo22 p-dioxin (TCDD) suppressed the development of reproductive organs of male rats: dose-dependent increase of 

23 mRNA levels of 5alpha-reductase type 2 in contrast to decrease of androgen receptor in the pubertal ventral prostate. 

24 Toxicol Sci 60(1):132–43. 

25 Olsman, H; Engwall, M; Kammann, U; et al. (2007) Relative differences in aryl hydrocarbon receptor-mediated 

26 response for 18 polybrominated and mixed halogenated dibenzo-p-dioxins and -furans in cell lines from four 

27 different species. Environ Toxicol Chem 26(11):2448–2454. 

28 Pelekis, M; Gephart, LA; Lerman, SE. (2001) Physiological-model-based derivation of the adult and child 

29 pharmacokinetic intraspecies uncertainty factors for volatile organic compounds. Reg Toxicol Pharmacol 

30 33(1):12−20. 

31 Saghir, SA; Lebofsky, M; Pinson, DM; et al. (2005) Validation of Haber’s Rule (dose X time = constant) in rats and 

32 mice for monochloroacetic acid and 2,3,7,8-tetrachlorodibenzo-p-dioxin under conditions of kinetic steady state. 

33 Toxicology 215(1–2):48–56. 

34 Santostefano, MJ; Wang, X; Richardson, VM; et al. (1998) A pharmacodynamic analysis of TCDD-induced 

35 cytochrome P450 gene expression in multiple tissues: dose- and time-dependent effects. Toxicol Appl Pharmacol 

36 151:294–310. 

37 Schantz, SL; Seo, BW; Moshtaghian, J; et al. (1996) Effects of gestational and lactational exposure to TCDD or 

38 coplanar PCBs on spatial learning. Neurotoxicol Teratol 18(3):305–313. 

39 Schecter, A; Pavuk, M; Päpke, O; et al. (2003) Dioxin, dibenzofuran, and coplanar PCB levels in Laotian blood and 

40 milk from agent orange-sprayed and nonsprayed areas, 2001. J Toxicol Environ Health Part A: Current Issues 

41 66(21):2067–2075. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 C-200 DRAFT—DO NOT CITE OR QUOTE 

1 Sewall, CH; Flagler, N; Vanden Heuvel, JP; et al. (1995) Alterations in thyroid function in female Sprague-Dawley 

2 rats following chronic treatment with 2,3,7,8-tetrachlorodibenzo-p-dioxin. Toxicol Appl Pharmacol 132:237–244. 

3 Shi, Z; Valdez, K; Ting, A; et al. (2007) Ovarian endocrine disruption underlies premature reproductive senescence 

4 following environmentally relevant chronic exposure to the aryl hydrocarbon receptor agonist 2,3,7,8-

5 tetrachlorodibenzo-p-dioxin. Biol Reprod 76(2):198–202.

6 Smialowicz, RJ; DeVito, MJ; Williams, WC; et al. (2008) Relative potency based on hepatic enzyme induction 

7 predicts immunosuppressive effects of a mixture of PCDDS/PCDFS and PCBS. Toxicol Appl Pharmacol 

8 227(3):477–484. 

9 Staskal, DF; Diliberto, JJ; Devito, MJ; et al. (2005) Inhibition of human and rat CYP1A2 by TCDD and dioxin-like 

10 chemicals. Toxicol Sci 84(2):225–231. 

11 Toth, K; Somfai-Relle, S; Sugár, J; et al. (1979) Carcinogenicity testing of herbicide 2,4,5-trichlorophenoxyethanol 

12 containing dioxin and of pure dioxin in Swiss mice. Nature 278:548–549. 

13 Toyoshiba, H; Walker, NJ; Bailer, AJ; et al. (2004) Evaluation of toxic equivalency factors for induction of 

14 cytochromes P450 CYP1A1 and CYP1A2 enzyme activity by dioxin-like compounds. Toxicol Appl Pharmacol 

15 194(2):156–168. 

16 U.S. EPA (Environmental Protection Agency). (2003) Exposure and human health reassessment of 2,3,7,8-

17 tetrachlorodibenzo-p-dioxin (TCDD) and related compounds [NAS review draft]. Volumes 1−3. National Center 

18 for Environmental Assessment, Washington, DC; EPA/600/P-00/001 Cb, Volume 1. Available online at 

19 http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

20 Van Birgelen, AP; Van der Kolk, J; Fase, KM; et al. (1995) Subchronic dose-response study of 2,3,7,8-

21 tetrachlorodibenzo-p-dioxin in female Sprague-Dawley rats. Toxicol Appl Pharmacol 132:1–13. 

22 Vanden Heuvel, JP; Clark, GC; Tritscher, A; et al. (1994) Accumulation of polychlorinated dibenzo-p-dioxins and 

23 dibenzofurans in liver of control laboratory rats. Fundam Appl Toxicol 23:465–469. 

24 Wang, X; Santostefano, MJ; Evans, MV; et al. (1997) Determination of parameters responsible for pharmacokinetic 

25 behavior of TCDD in female Sprague-Dawley Rats. Toxicol Appl Pharmacol 147:151−168. 

26 Wang, X; Santostefano, MJ; Devito, MJ; et al. (2000) Extrapolation of a PBPK model for dioxins across dosage 

27 regimen, gender, strain, and species. Toxicol Sci 56(1):49–60. 

28 White, KL, Jr; Lysy, HH; McCay, JA; et al. (1986) Modulation of serum complement levels following exposure to 

29 polychlorinated dibenzo-p-dioxins. Toxicol Appl Pharmacol 84:209–219. 

30 Wilkes, JG; Hass, BS; Buzatu, DA; et al. (2008) Modeling and assaying dioxin-like biological effects for both 

31 dioxin-like and certain non-dioxin-like compounds. Toxicol Sci 102(1):187–195. 

 32 
DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX D 

Epidemiological Kinetic Modeling

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-ii —DO NOT CITE OR QUOTE 

CONTENTS—APPENDIX D: Epidemiological Kinetic Modeling 

 1 

2 LIST OF TABLES.....................................................................................................................D-iii

 3 

4 APPENDIX D. EPIDEMIOLOGICAL KINETIC MODELING ............................................ D-1 

5 D.1. BACCARELLI ET AL. (2008) MODELING......................................................... D-1 

6 D.1.1. Input File for Exposure During Pregnancy................................................ D-1 

7 D.1.2. Table of Results for Baccarelli et al. (2008).............................................. D-1 

8 D.2. MOCARELLI ET AL. (2008) MODELING .......................................................... D-2 

9 D.2.1. Input File for Exposure for Pulse to Measurement 0.5 Years After the 

10 Seveso Pulse Dose ..................................................................................... D-2 

11 D.2.2. Input File for Exposure from Pulse to the End of the Critical Window 

12 3.8 Years After the Seveso Pulse Dose...................................................... D-2 

13 D.2.3. Input File for Continuous Exposure for 10 Years...................................... D-3 

14 D.2.4. Tables of Results for Mocarelli et al. (2008) ............................................. D-4 

15 D.3. ALALUUSUA ET AL. (2004) MODELING ......................................................... D-4 

16 D.3.1. Input File for Exposure for Pulse to Measurement 0.5 Years After the 

17 Seveso Pulse Dose ..................................................................................... D-4 

18 D.3.2. Input File for Exposure from Pulse to the End of the Critical Window 

19 2.5 Years After the Seveso Pulse Dose...................................................... D-5 

20 D.3.3. Input File for Continuous Exposure for 5 Years........................................ D-5 

21 D.3.4. Tables of Results for Alaluusua et al. (2004) ............................................ D-6 

22 D.4. ESKANAZI ET AL. (2002) MODELING.............................................................. D-7 

23 D.4.1. Input File for Exposure for Pulse to Measurement 0.5 Years After the 

24 Seveso Pulse Dose ..................................................................................... D-7 

25 D.4.2. Input File for Exposure from Pulse to the End of the Critical Window 

26 6.7 Years After the Seveso Pulse Dose...................................................... D-8 

27 D.4.3. Input File for Continuous Exposure for 13 Years...................................... D-8 

28 D.4.4. Tables of Results for Eskanazi et al. (2002) .............................................. D-9 

29 D.5. REFERENCES...................................................................................................... D-10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-iii —DO NOT CITE OR QUOTE 

LIST OF TABLES 

1 D-1. Estimated continuous intake corresponding to maternal serum concentration in 

2 Figure 2A ........................................................................................................................ D-1 

3 D-2. Estimated maximum intake corresponding to maternal serum concentration in 

4 Figure 2A ........................................................................................................................ D-2 

5 D-3. Matching critical window average after pulse to critical window average for 

6 continuous intake run...................................................................................................... D-4 

7 D-4. Matching critical window peak after pulse to peak critical window concentration 

8 for continuous intake run ................................................................................................ D-4 

9 D-5. Matching critical window average after pulse to critical window average for 

10 continuous intake run...................................................................................................... D-6 

11 D-6. Matching critical window peak after pulse to peak critical window 

12 concentration for continuous intake run ......................................................................... D-7 

13 D-7. Matching critical window average after pulse to critical window average for 

14 continuous intake run...................................................................................................... D-9 

15 D-8. Matching critical window peak after pulse to peak critical window 

16 concentration for continuous intake run ......................................................................... D-9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-1 —DO NOT CITE OR QUOTE 

1 APPENDIX D. EPIDEMIOLOGICAL KINETIC MODELING 

 2 

 3 

4 D.1. BACCARELLI ET AL. (2008) MODELING

5 D.1.1. Input File for Exposure During Pregnancy 

6 CINT = 1 %168 %100 %integration time 

7 %Exposure scenario 

8 EXP_TIME_ON = 0 % delay before begin exposure (HOUR) 

9 EXP_TIME_OFF = 401190 %TIME EXPOSURE STOP (HOUR) 

10 DAY_CYCLE = 24 %TIME 

11 BCK_TIME_ON = 401190 %DELAY BEFORE BACKGROUND EXP (HOUR) 

12 BCK_TIME_OFF = 401190 %TIME OF BACKGROUND EXP STOP (HOUR) 

13 IV_LACK = 401190 

14 IV_PERIOD = 401190 

15 %GESTATION CONTROL 

16 MATTING = 262800 % BEGINNING MATTING (HOUR)at 30 years old 

17 TIMELIMIT = 269184 %SIMULATION LIMIT TIME (HOUR) 

18 TRANSTIME_ON = 264312 % EXCHANGE MOTHER FETUS 1512 HOUR POST 

19 MATTING 

20 %Exposure dose 

21 MSTOT = 0.021 % ng of TCDD /kg of BW 

22 MSTOTBCKGR = 0. %0.1 % ORAL BACKGROUND EXPOSURE DOSE (nG/KG) 

23 DOSEIV = 0. %10 

24 DOSEIVLATE = 0. %10 

 25 

26 % TRANFER MOTHER TO FETUS CLEARANCE 

27 CLPLA_FET = 0.001 % MOTHER TO FETUS TRANFERT CLEARANCE(L/HR) 

 28 

29 D.1.2. Table of Results for Baccarelli et al. (2008) 

30 Table D-1. Estimated continuous intake corresponding to maternal serum 

31 concentration in Figure 2A 

32 

Variable Value Notes 

Infant b-TSH 5 uU/mL BMR 

Maternal lipid adjusted serum 270 ng/kg From Figure 2A 

Intake 0.024 ng/kg-day From Emond model, pregnancy at 30 

years 

 33 

 34 

 35 

 36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-2 —DO NOT CITE OR QUOTE 

1 Table D-2. Estimated maximum intake corresponding to maternal serum 

2 concentration in Figure 2A 

3 

Variable Value Notes 

Infant b-TSH -- -- 

Maternal lipid adjusted serum 309.5 ng/kg Maximum from Figure 2A 

Intake 0.030 ng/kg-day From Emond model, pregnancy at 30 

years 

4 

5 D.2. MOCARELLI ET AL. (2008) MODELING

6 D.2.1. Input File for Exposure for Pulse to Measurement 0.5 Years After the Seveso Pulse 

7 Dose 

8 CINT = 1. % 

9 EXP_TIME_ON = 54312. % Delay before begin exposure (HOUR) 6.2 years 

10 EXP_TIME_OFF = 54335. %324120 % HOUR/YEAR !TIME EXPOSURE STOP 

11 (HOUR) 6.2 years + 23 hours 

12 DAY_CYCLE = 24. % TIME 

13 BCK_TIME_ON = 0. % DELAY BEFORE BACKGROUND EXP (HOUR) 

14 BCK_TIME_OFF = 613200 % TIME OF BACKGROUND EXP STOP (HOUR) 

15 TIMELIMIT = 58692. % half a year (July 1976 until January 1977) past 6.2 years 

16 MSTOTBCKGR = 3.7E-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 17 

18 % oral dose oral dose oral dose 

19 MSTOT = 232.4 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

20 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

21 % oral dose oral dose oral dose 

 22 

23 MEANLIPID = 731 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

24 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 25 

26 %human variable parameter 

27 MALE = 1. 

28 FEMALE = 0. 

29 Y0 = 0. % 0 years old at the beginning of the simulation 

30 

31 D.2.2. Input File for Exposure from Pulse to the End of the Critical Window 3.8 Years 

32 After the Seveso Pulse Dose 

33 CINT = 1. % 

34 EXP_TIME_ON = 54312. % Delay before begin exposure (HOUR) 6.2 years 

35 EXP_TIME_OFF = 54335. %324120 % HOUR/YEAR !TIME EXPOSURE STOP 

36 (HOUR) 6.2 years + 23 hours 

37 DAY_CYCLE = 24. % TIME 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-3 —DO NOT CITE OR QUOTE 

1 BCK_TIME_ON = 0. % DELAY BEFORE BACKGROUND EXP (HOUR) 

2 BCK_TIME_OFF = 613200. % TIME OF BACKGROUND EXP STOP (HOUR) 

3 TIMELIMIT = 87600. % 10 years 

4 MSTOTBCKGR = 3.7e-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 5 

6 % oral dose oral dose oral dose 

7 MSTOT = 232.5 % Serveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

8 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

9 % oral dose oral dose oral dose 

 10 

11 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

12 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 13 

14 %human variable parameter 

15 MALE = 1. 

16 FEMALE = 0. 

17 Y0 = 0. % 0 years old at the beginning of the simulation 

 18 

19 D.2.3. Input File for Continuous Exposure for 10 Years 

20 CINT = 1. % 

21 EXP_TIME_ON = 0. % Delay before begin exposure (HOUR) 

22 EXP_TIME_OFF = 87600. % HOUR/YEAR !TIME EXPOSURE STOP (HOUR) 

23 DAY_CYCLE = 24. % TIME 

24 BCK_TIME_ON = 0. %324120 % DELAY BEFORE BACKGROUND EXP (HOUR) 

25 BCK_TIME_OFF = 613200 %324120 % TIME OF BACKGROUND EXP STOP (HOUR) 

26 TIMELIMIT = 87600. % 10 years 

27 MSTOTBCKGR = 0. %3.35E-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 28 

29 % oral dose oral dose oral dose 

30 MSTOT = 3.903 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

31 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

32 % oral dose oral dose oral dose 

 33 

34 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

35 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 36 

37 %human variable parameter 

38 MALE = 1. 

39 FEMALE = 0. 

40 Y0 = 0. % 0 years old at the beginning of the simulation 

 41 

 42 

 43 

 44 

 45 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-4 —DO NOT CITE OR QUOTE 

1 D.2.4. Tables of Results for Mocarelli et al. (2008) 

 2 

3 Table D-3. Matching critical window average after pulse to critical window 

4 average for continuous intake run 

5 

Person modeled, 

beginning at age 0 

Lipid adjusted 

serum (1976) ng/kg 

from Figure 3E 

Pulse dose, 0.5 

year lag time 

(ng/kg) 

Average lipid 

adjusted serum 

3.8 years after 

incident (ng/kg) 

Continuous intake 

for 10 years 

(ng/kg-day) 

Boy, 1st quartile 68 8.135 57.72 0.008024 

Boy, 4th quartile 733 232.5 580.5 0.2128 

 6 

 7 

8 Table D-4. Matching critical window peak after pulse to peak critical 

9 window concentration for continuous intake run 

10 

Person modeled, 

beginning at age 0 

Lipid adjusted 

serum (1976) ng/kg 

from Figure 3E 

Pulse dose, 0.5 

year lag time 

(ng/kg) 

Peak lipid 

adjusted serum 

after incident 

(ng/kg) 

Continuous intake 

for 10 years 

(ng/kg-day) 

Boy, 1st quartile 68 8.135 248.0 0.03194 

Boy, 4th quartile 733 232.5 6674 3.904 

 11 

 12 

13 D.3. ALALUUSUA ET AL. (2004) MODELING 

14 D.3.1. Input File for Exposure for Pulse to Measurement 0.5 Years After the Seveso Pulse 

15 Dose 

16 CINT = 1. % 

17 EXP_TIME_ON = 21900. % Delay before begin exposure (HOUR) 2.5 years 

18 EXP_TIME_OFF = 21923. % 21900+23 % HOUR/YEAR !TIME EXPOSURE STOP 

19 (HOUR) 2.5 years and 23 hours 

20 DAY_CYCLE = 24. % TIME 

21 BCK_TIME_ON = 0. % DELAY BEFORE BACKGROUND EXP (HOUR) 

22 BCK_TIME_OFF = 613200. % TIME OF BACKGROUND EXP STOP (HOUR) 

23 TIMELIMIT = 26280. % half a year (July 1976 until January 1977) past 2.5 years 

24 MSTOTBCKGR = 3.7e-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 25 

26 % oral dose oral dose oral dose 

27 MSTOT = 24.22 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

28 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

29 % oral dose oral dose oral dose 

 30 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-5 —DO NOT CITE OR QUOTE 

1 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

2 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 3 

4 %human variable parameter 

5 MALE = 1. 

6 FEMALE = 0. 

7 Y0 = 0. % 0 years old at the beginning of the simulation 

8 

9 D.3.2. Input File for Exposure from Pulse to the End of the Critical Window 2.5 Years 

10 After the Seveso Pulse Dose 

11 CINT = 1. % 

12 EXP_TIME_ON = 21900. % Delay before begin exposure (HOUR) 2.5 years 

13 EXP_TIME_OFF = 21923. % 324120 % HOUR/YEAR !TIME EXPOSURE STOP 

14 (HOUR) 2.5 years and 23 hours 

15 DAY_CYCLE = 24. % TIME 

16 BCK_TIME_ON = 0. % 324120 % DELAY BEFORE BACKGROUND EXP (HOUR) 

17 BCK_TIME_OFF = 613200. % 324120 % TIME OF BACKGROUND EXP STOP (HOUR) 

18 TIMELIMIT = 43800. % 5 years 

19 MSTOTBCKGR = 3.7e-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 20 

21 % oral dose oral dose oral dose 

22 MSTOT = 24.22 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

23 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

24 % oral dose oral dose oral dose 

 25 

26 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

27 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 28 

29 %human variable parameter 

30 MALE = 1. 

31 FEMALE = 0. 

32 Y0 = 0. % 0 years old at the beginning of the simulation 

 33 

34 D.3.3. Input File for Continuous Exposure for 5 Years 

35 CINT = 1. % 

36 EXP_TIME_ON = 0. % Delay before begin exposure (HOUR) 

37 EXP_TIME_OFF = 43800. % 324120 % HOUR/YEAR !TIME EXPOSURE STOP (HOUR) 

38 DAY_CYCLE = 24. % TIME 

39 BCK_TIME_ON = 0. % 324120 % DELAY BEFORE BACKGROUND EXP (HOUR) 

40 BCK_TIME_OFF = 613200. % 324120 % TIME OF BACKGROUND EXP STOP (HOUR) 

41 TIMELIMIT = 43800. % End of critical window (5 years) 

42 MSTOTBCKGR = 0. % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 43 

44 % oral dose oral dose oral dose 

45 MSTOT = 0.03486 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-6 —DO NOT CITE OR QUOTE 

1 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

2 % oral dose oral dose oral dose 

 3 

4 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

5 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 6 

7 %human variable parameter 

8 MALE = 1. 

9 FEMALE = 0. 

10 Y0 = 0. % 0 years old at the beginning of the simulation 

 11 

12 D.3.4. Tables of Results for Alaluusua et al. (2004) 

13 Table D-5. Matching critical window average after pulse to critical window 

14 average for continuous intake run 

 15 

Person modeled, 

beginning at age 0 

Lipid adjusted 

serum (1976) ng/kg 

estimated from 

tertile binsa

Pulse dose, 

0.5 year lag 

time (ng/kg)

Average lipid 

adjusted serum 2.5 

years after 

incident (ng/kg) 

Continuous 

intake for 5 

years (ng/kgday) 

Boy, 1st tertile 130 24.22 110.8 0.03486 

Boy, 2nd tertile 383 108.9 322.7 0.1578 

Boy, 3rd tertile 1830 1041 1538 1.511 

Girl, 1st tertile 130 23.03 110.8 0.03211 

Girl, 2nd tertile 383 105.3 324.4 0.1481 

Girl, 3rd tertile 1830 1015 1546 1.427 

Boy and girl, averaged, 

1st tertile 

130 - - 0.03349 

Boy and girl, averaged, 

2nd tertile 

383 - - 0.1530 

Boy and girl, averaged, 

3rd tertile 

1830 - - 1.469 

16 a 17 Mean of tertile bin assuming a lognormal distribution of serum concentrations. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-7 —DO NOT CITE OR QUOTE 

1 Table D-6. Matching critical window peak after pulse to peak critical 

2 window concentration for continuous intake run 

 3 

Person modeled, 

beginning at age 0 

Lipid adjusted 

serum (1976) ng/kg 

estimated from 

tertile bins 

Pulse dose, 

0.5 year lag 

time (ng/kg) 

Peak lipid 

adjusted serum 

after incident 

(ng/kg) 

Continuous 

intake for 5 

years (ng/kgday) 

Boy, 1st tertile 130 24.22 618.8 0.2113 

Boy, 2nd tertile 383 108.9 2700 1.783 

Boy, 3rd tertile 1830 1041 24706 31.35 

Girl, 1st tertile 130 23.02 588.0 0.1882 

Girl, 2nd tertile 383 105.3 2610 1.642 

Girl, 3rd tertile 1830 1015 24113 29.52 

Boy and girl, averaged, 

1st tertile 

130 - - 0.1998 

Boy and girl, averaged, 

2nd tertile 

383 - - 1.713 

Boy and girl, averaged, 

3rd tertile 

1830 - - 30.44 

4 a 5 Mean of tertile bin assuming a lognormal distribution of serum concentrations. 

 6 

7 

8 D.4. ESKANAZI ET AL. (2002) MODELING 

9 D.4.1. Input File for Exposure for Pulse to Measurement 0.5 Years After the Seveso Pulse 

10 Dose 

11 CINT = 1. % 

12 EXP_TIME_ON = 58692. % Delay before begin exposure (HOUR) 6.7 years 

13 EXP_TIME_OFF = 58715. % HOUR/YEAR !TIME EXPOSURE STOP (HOUR) 6.7 years + 

14 23 hours 

15 DAY_CYCLE = 24. % TIME 

16 BCK_TIME_ON = 0. %324120 % DELAY BEFORE BACKGROUND EXP (HOUR) 

17 BCK_TIME_OFF = 613200. %324120 % TIME OF BACKGROUND EXP STOP (HOUR) 

18 TIMELIMIT = 63072. % half a year (July 1976 until January 1977) past 6.7 years 

19 MSTOTBCKGR = 3.7e-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 20 

21 % oral dose oral dose oral dose 

22 MSTOT = 7193 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

23 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

24 % oral dose oral dose oral dose 

 25 

26 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-8 —DO NOT CITE OR QUOTE 

1 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 2 

3 %human variable parameter 

4 MALE = 0. 

5 FEMALE = 1. 

6 Y0 = 0. % 0 years old at the beginning of the simulation 

7 

8 D.4.2. Input File for Exposure from Pulse to the End of the Critical Window 6.7 Years 

9 After the Seveso Pulse Dose 

10 CINT = 1. % 

11 EXP_TIME_ON = 58692. % Delay before begin exposure (HOUR) 6.7 years 

12 EXP_TIME_OFF = 58715. %324120 % HOUR/YEAR !TIME EXPOSURE STOP 

13 (HOUR) 6.7 years + 23 hours 

14 DAY_CYCLE = 24. % TIME 

15 BCK_TIME_ON = 0. %324120 % DELAY BEFORE BACKGROUND EXP (HOUR) 

16 BCK_TIME_OFF = 613200 %324120 % TIME OF BACKGROUND EXP STOP (HOUR) 

17 TIMELIMIT = 113880. % 13 years 

18 MSTOTBCKGR = 3.7e-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 19 

20 % oral dose oral dose oral dose 

21 MSTOT = 7193 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 

22 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

23 % oral dose oral dose oral dose 

 24 

25 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

26 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 27 

28 %human variable parameter 

29 MALE = 0. 

30 FEMALE = 1. 

31 Y0 = 0. % 0 years old at the beginning of the simulation 

 32 

33 D.4.3. Input File for Continuous Exposure for 13 Years 

34 CINT = 1. % 

35 EXP_TIME_ON = 0. % Delay before begin exposure (HOUR) 

36 EXP_TIME_OFF = 113880. %324120 % HOUR/YEAR !TIME EXPOSURE STOP 

37 (HOUR) 13 years 

38 DAY_CYCLE = 24. % TIME 

39 BCK_TIME_ON = 0. %324120 % DELAY BEFORE BACKGROUND EXP (HOUR) 

40 BCK_TIME_OFF = 613200. %324120 % TIME OF BACKGROUND EXP STOP (HOUR) 

41 TIMELIMIT = 113880. % 13 years 

42 MSTOTBCKGR = 0. %3.35E-4 % ORAL BACKGROUND EXPOSURE DOSE (UG/KG) 

 43 

44 % oral dose oral dose oral dose 

45 MSTOT = 166 % Seveso, ORAL DAILY EXPOSURE DOSE (NG/KG) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-9 —DO NOT CITE OR QUOTE 

1 DOSEIV = 0 % 40 %50 %5 %0.5 %0.3 %0.2 %0.1%0.05%0.3 %NG/KG 

2 % oral dose oral dose oral dose 

 3 

4 MEANLIPID = 730 % 711 %664 %778 %468 %671 %730 %662 %592%615%730% 

5 PAS_INDUC= 1 % NON INDUCTION (0) CONTROLE DE L'INDUCTION 

 6 

7 %human variable parameter 

8 MALE = 0. 

9 FEMALE = 1. 

10 Y0 = 0. % 0 years old at the beginning of the simulation 

 11 

12 D.4.4. Tables of Results for Eskanazi et al. (2002) 

13 Table D-7. Matching critical window average after pulse to critical window 

14 average for continuous intake run 

15 

Person modeled, 

beginning at age 0 

Lipid adjusted serum 

(adjusted to 1976-

1977 levels) ng/kg 

from Figure 1A 

Pulse dose, 

0.5 year lag 

time (ng/kg)

Average lipid 

adjusted serum 6.7 

years after incident 

(ng/kg) 

Continuous 

intake for 13 

years (ng/kg-day)

Girl, estrous cycle 

28.5 days 

166 28.40 114.0 0.01660 

Girl, estrous cycle 

29 days 

693 215.5 455.1 0.1224 

Girl, estrous cycle 

29.5 days 

2020 1008 1295 0.5693 

Girl, estrous cycle 

30 days 

8450 7193 5179 4.054 

 16 

17 Table D-8. Matching critical window peak after pulse to peak critical 

18 window concentration for continuous intake run 

19 

Person modeled, 

beginning at age 0 

Lipid adjusted serum 

(adjusted to 1976-

1977 levels) ng/kg 

from Figure 1A 

Pulse dose, 

0.5 year lag 

time (ng/kg) 

Peak lipid 

adjusted serum 

after incident 

(ng/kg) 

Continuous intake 

for 13 years 

(ng/kg-day) 

Girl, estrous cycle 

28.5 days 

166 28.40 838.2 0.1800 

Girl, estrous cycle 

29 days 

693 215.5 6183 3.148 

Girl, estrous cycle 

29.5 days 

2020 1008 28316 20.86 

Girl, estrous cycle 

30 days 

8450 7193 198240 166.6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT D-10 —DO NOT CITE OR QUOTE 

 1 

2 D.5. REFERENCES 

3 Alaluusua, S; Calderara, P; Gerthoux, PM; et al. (2004) Developmental dental aberrations after the dioxin accident 

4 in Seveso. Environ Health Perspect 112(13):1313−1318. 

5 Baccarelli, A; Giacomini, SM; Corbetta, C; et al. (2008) Neonatal thyroid function in Seveso 25 years after maternal 

6 exposure to dioxin. PLoS Med 5(7):e161. 

7 Eskenazi, B; Mocarelli, P; Warner, M; et al. (2002). Serum dioxin concentrations and endometriosis: a cohort study 

8 in Seveso, Italy. Environ Health Perspect 110(7): 629−634. 

9 Mocarelli, P; Gerthoux, PM; Patterson, DG, Jr.; et al. (2008) Dioxin exposure, from infancy through puberty, 

10 produces endocrine disruption and affects human semen quality. Environ Health Perspect 116(1):70−77. 

11 

DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX E 

Noncancer Benchmark Dose Modeling 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-ii —DO NOT CITE OR QUOTE 

CONTENTS—APPENDIX E: Noncancer Benchmark Dose Modeling 

APPENDIX E. NONCANCER BENCHMARK DOSE MODELING ..................................E-1 

E.1. BMDS INPUT TABLES.............................................................................................E-1 

E.1.1. Amin et al. (2000)..........................................................................................E-1 

E.1.2. Bell et al. (2007a)...........................................................................................E-1 

E.1.3. Cantoni et al. (1981) ......................................................................................E-2 

E.1.4. Crofton et al. (2005).......................................................................................E-2 

E.1.5. DeCaprio et al. (1986)....................................................................................E-3 

E.1.6. Hojo et al. (2002) ...........................................................................................E-4 

E.1.7. Kattainen et al. (2001)....................................................................................E-4 

E.1.8. Keller et al. (2007, 2008a, b) .........................................................................E-5 

E.1.9. Kociba et al. (1978)........................................................................................E-5 

E.1.10. Latchoumycandane and Mathur (2002).........................................................E-6 

E.1.11. Li et al. (1997)................................................................................................E-6 

E.1.12. Li et al. (2006)................................................................................................E-6 

E.1.13. Markowski et al. (2001).................................................................................E-7 

E.1.14. Mietinnin et al. (2006) ...................................................................................E-7 

E.1.15. National Toxicology Program (1982)............................................................E-8 

E.1.16. National Toxicology Program (2006)............................................................E-8 

E.1.17. Ohsako et al. (2001).....................................................................................E-10 

E.1.18. Schantz et al. (1996) ....................................................................................E-10 

E.1.19. Shi et al. (2007)............................................................................................E-11 

E.1.20. Smialowicz et al. (2008) ..............................................................................E-11 

E.1.21. Toth et al. (1979)..........................................................................................E-12 

E.1.22. Van Birgelen et al. (1995)............................................................................E-12 

E.1.23. White et al. (1986) .......................................................................................E-13 

E.2. ALTERNATE DOSE: BLOOD SERUM BMDS RESULTS..................................E-14 

E.2.1. Amin et al. (2000): Saccharin Consumed, Female (0.25%) ........................E-14 

E.2.1.1. Summary Table of BMDS Modeling Results .............................E-14 

E.2.1.2. Figure for Selected Model: Linear, Nonconstant Variance.........E-15 

E.2.1.3. Output File for Selected Model: Linear, Nonconstant 

Variance.......................................................................................E-15 

E.2.1.4. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-18 

E.2.1.5. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-18 

E.2.2. Amin et al. (2000): Saccharin Consumed, Female (0.50%) ........................E-21 

E.2.2.1. Summary Table of BMDS Modeling Results .............................E-21 

E.2.2.2. Figure for Selected Model: Linear, Nonconstant Variance.........E-22 

E.2.2.3. Output File for Selected Model: Linear, Nonconstant 

Variance.......................................................................................E-22 

E.2.2.4. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-25 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-iii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

E.2.2.5. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-25 

E.2.3. Amin et al. (2000): Saccharin Preference Ratio, Female (0.25%)...............E-28 

E.2.3.1. Summary Table of BMDS Modeling Results .............................E-28 

E.2.3.2. Figure for Selected Model: Linear, Nonconstant Variance.........E-29 

E.2.3.3. Output File for Selected Model: Linear, Nonconstant 

Variance.......................................................................................E-29 

E.2.3.4. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-32 

E.2.3.5. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-32 

E.2.4. Amin et al. (2000): Saccharin Preference Ratio, Female (0.50%)...............E-35 

E.2.4.1. Summary Table of BMDS Modeling Results .............................E-35 

E.2.4.2. Figure for Selected Model: Linear, Constant Variance...............E-35 

E.2.4.3. Output File for Selected Model: Linear, Constant Variance.......E-36 

E.2.4.4. Figure for Unrestricted Model: Power, Constant Variance, 

Power Unrestricted......................................................................E-38 

E.2.4.5. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted......................................................E-38 

E.2.5. Bell et al. (2007): Balano-Preputial Separation in Male Pups 

(10% extra risk)............................................................................................E-41 

E.2.5.1. Summary Table of BMDS Modeling Results .............................E-41 

E.2.5.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit.............................................................E-42 

E.2.5.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit.............................................................E-42 

E.2.5.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted .................................................................................E-44 

E.2.5.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted .................................................................................E-44 

E.2.6. Bell et al. (2007): Balano-Preputial Separation in Male Pups 

(5% extra risk)..............................................................................................E-46 

E.2.6.1. Summary Table of BMDS Modeling Results .............................E-46 

E.2.6.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit.............................................................E-47 

E.2.6.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit.............................................................E-47 

E.2.6.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted .................................................................................E-49 

E.2.6.5. Output File for Unrestricted Model: Log-Logistic, 

Slope Unrestricted .......................................................................E-49 

E.2.7. Cantoni et al. (1981): Urinary Copro-Porhyrins..........................................E-51 

E.2.7.1. Summary Table of BMDS Modeling Results .............................E-51 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-iv —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

E.2.7.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1....................................................E-52 

E.2.7.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1...............................E-52 

E.2.7.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ................................E-55 

E.2.7.5. Output file for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ................................E-55 

E.2.7.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, 

n Unrestricted ..............................................................................E-58 

E.2.7.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted..............................................................E-58 

E.2.7.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-61 

E.2.7.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted......................................................E-61 

E.2.8. Cantoni et al. (1981): Urinary Porphyrins ...................................................E-64 

E.2.8.1. Summary Table of BMDS Modeling Results .............................E-64 

E.2.8.2. Figure for Selected Model: Exponential (M2), Nonconstant 

Variance, Power Restricted ≥1....................................................E-65 

E.2.8.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1...............................E-65 

E.2.9. Crofton et al. (2005): Serum T4...................................................................E-68 

E.2.9.1. Summary Table of BMDS Modeling Results .............................E-68 

E.2.9.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1....................................................E-69 

E.2.9.3. Output File for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1....................................................E-69 

E.2.9.4. Figure for Unrestricted Model: Exponential (M5), Constant 

Variance, Power Unrestricted......................................................E-72 

E.2.9.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ......................................E-73 

E.2.9.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted .................................................................................E-76 

E.2.9.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted..............................................................E-76 

E.2.9.8. Figure for Unrestricted Model: Power, Constant Variance, 

Power Unrestricted......................................................................E-79 

E.2.9.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted......................................................E-79 

E.2.10. Hojo et al. (2002): DRL Reinforce Per Min ................................................E-82 

E.2.10.1. Summary Table of BMDS Modeling Results .............................E-82 

E.2.10.2. Figure for Selected Model: Exponental (M4) .............................E-83 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-v —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

E.2.10.3. Output File for Selected Model: Exponential (M4) ....................E-83 

E.2.11. Hojo et al. (2002): DRL Response Per Min.................................................E-86 

E.2.11.1. Summary Table of BMDS Modeling Results .............................E-86 

E.2.11.2. Figure for Selected Model: Exponential (M4) ............................E-87 

E.2.11.3. Output File for Selected Model: Exponential (M4) ....................E-87 

E.2.12. Kattainen et al. (2001): 3rd Molar Mesio-Distal Length (Molar 

Development)...............................................................................................E-90 

E.2.12.1. Summary Table of BMDS Modeling Results .............................E-90 

E.2.12.2. Figure for Selected Model: Hill, Nonconstant Variance, n 

Restricted >1, Bound Hit.............................................................E-91 

E.2.12.3. Output File for Selected Model: Hill, Nonconstant Variance, 

n Restricted >1, Bound Hit..........................................................E-91 

E.2.12.4. Figure for Unrestricted Model: Hill, Nonconstant Variance, 

n Unrestricted ..............................................................................E-94 

E.2.12.5. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted..............................................................E-94 

E.2.13. Kattainen et al. (2001): Females 3rd Molar Eruption..................................E-97 

E.2.13.1. Summary Table of BMDS Modeling Results .............................E-97 

E.2.13.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit.............................................................E-97 

E.2.13.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit.............................................................E-98 

E.2.13.4. Figure for Unrestricted Model: Log-Logistic, Unrestricted........E-99 

E.2.13.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-100 

E.2.14. Kattainen et al., 2001: 3rd molar length in pups........................................E-101 

E.2.14.1. Summary Table of BMDS modeling results .............................E-101 

E.2.14.2. Figure for selected model: Hill..................................................E-102 

E.2.14.3. Output for selected model: Hill.................................................E-102 

E.2.14.4. Figure for additional model presented: Hill, unrestricted .........E-105 

E.2.14.5. Output for additional model presented: Hill, unrestricted.........E-105 

E.2.15. Keller et al. (2006): Missing Mandibular Molars in CBA J Mice .............E-108 

E.2.15.1. Summary Table of BMDS Modeling Results ...........................E-108 

E.2.15.2. Figure for Selected Model: Multistage, 1-Degree.....................E-109 

E.2.15.3. Output File for Selected Model: Multistage, 1-Degree.............E-109 

E.2.16. Kociba et al. (1978): Urinary Coproporphyrins, Females (Table 2)..........E-111 

E.2.16.1. Summary Table of BMDS Modeling Results ...........................E-111 

E.2.17. Kociba et al. (1978): Uroporphyrin per Creatinine, Females ....................E-113 

E.2.17.1. Summary Table of BMDS Modeling Results ...........................E-113 

E.2.17.2. Figure for Selected Model: Linear, Constant Variance.............E-114 

E.2.17.3. Output File for Selected Model: Linear, Constant Variance.....E-114 

1 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-vi —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.18. Latchoumycandane and Mathur (2002): Daily Sperm Production............E-117 

E.2.18.1. Summary Table of BMDS Modeling Results ...........................E-117 

E.2.18.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-118 

E.2.18.3. Output File for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-118 

E.2.18.4. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted ...............................................................................E-121 

E.2.18.5. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted............................................................E-121 

E.2.19. Li et al. (1997): Follicle-Stimulating Hormone .........................................E-123 

E.2.19.1. Summary Table of BMDS Modeling Results ...........................E-123 

E.2.19.2. Figure for Selected Model: Power.............................................E-124 

E.2.19.3. Output for Selected Model: Power............................................E-124 

E.2.19.4. Figure for Unrestricted Model: Power, Unrestricted.................E-127 

E.2.19.5. Output for Unrestricted Model: Power, Unrestricted................E-127 

E.2.20. Li et al. (2006): Hormone Levels (Estradiol).............................................E-130 

E.2.20.1. Summary Table of BMDS Modeling Results ...........................E-130 

E.2.20.2. Figure for Selected Model: Linear, Constant Variance.............E-131 

E.2.20.3. Output File for Unrestricted Model: Linear, Constant 

Variance.....................................................................................E-131 

E.2.20.4. Figure for Unrestricted Model: Exponential (M5), Constant 

Variance, Power Unrestricted....................................................E-134 

E.2.20.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ....................................E-134 

E.2.20.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted ...............................................................................E-137 

E.2.20.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted............................................................E-137 

E.2.20.8. Figure for Unrestricted Model: Power, Constant Variance, 

Power Unrestricted....................................................................E-140 

E.2.20.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted....................................................E-140 

E.2.21. Li et al. (2006): Hormone Levels (Progesterone)......................................E-143 

E.2.21.1. Summary Table of BMDS Modeling Results ...........................E-143 

E.2.21.2. Figure for Selected Model: Exponential (M2), Nonconstant 

Variance, Power Restricted ≥1..................................................E-144 

E.2.21.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-144 

E.2.21.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-147 

E.2.21.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-147 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-vii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.21.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-150 

E.2.21.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-150 

E.2.21.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-153 

E.2.21.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-153 

E.2.22. Markowski et al. (2001): FR10 Run Opportunities...................................E-156 

E.2.22.1. Summary Table of BMDS Modeling Results ...........................E-156 

E.2.22.2. Figure for Selected Model: Exponential (M2) ..........................E-156 

E.2.22.3. Output File for Selected Model: Exponential (M2) ..................E-157 

E.2.23. Markowski et al. (2001): FR2 Revolutions................................................E-160 

E.2.23.1. Summary Table of BMDS Modeling Results ...........................E-160 

E.2.23.2. Figure for Selected Model: Exponential (M5) ..........................E-161 

E.2.23.3. Output File for Selected Model: Exponential (M5) ..................E-161 

E.2.23.4. Figure for Unrestricted Model: Power, Unrestricted.................E-164 

E.2.23.5. Output for Unrestricted Model: Power, Unrestricted................E-164 

E.2.24. Markowski et al. (2001): FR5 Run Opp ....................................................E-167 

E.2.24.1. Summary Table of BMDS Modeling Results ...........................E-167 

E.2.24.2. Figure for Selected Model: Hill.................................................E-168 

E.2.24.3. Output File for Selected Model: Hill.........................................E-168 

E.2.24.4. Figure for Unrestricted Model: Power, Unrestricted.................E-171 

E.2.24.5. Output File for Unrestricted Model: Power, Unrestricted.........E-171 

E.2.25. Mietinnin et al. (2006): Cariogenic Lesions in Pups .................................E-174 

E.2.25.1. Summary Table of BMDS Modeling Results ...........................E-174 

E.2.25.2. Figure for Selected Model: Log-Logistic..................................E-174 

E.2.25.3. Output File for Selected Model: Log-Logistic ..........................E-175 

E.2.25.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-176 

E.2.25.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-177 

E.2.26. National Toxicology Program (1982): Male Mice, Toxic Hepatitis..........E-178 

E.2.26.1. Summary Table of BMDS Modeling Results ...........................E-178 

E.2.26.2. Figure for Selected Model: Multistage, 2nd Degree .................E-179 

E.2.26.3. Output File for Selected Model: Multistage, 2nd Degree .........E-179 

E.2.27. National Toxicology Program (2006): Alveolar Metaplasia .....................E-181 

E.2.27.1. Summary Table of BMDS Modeling Results ...........................E-181 

E.2.27.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-182 

E.2.27.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-182 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-viii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.28. National Toxicology Program (2006): Gingival Hyperplasia 

Squamous, 2 Years.....................................................................................E-184 

E.2.28.1. Summary Table of BMDS Modeling Results ...........................E-184 

E.2.28.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-185 

E.2.28.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-185 

E.2.28.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-187 

E.2.28.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-187 

E.2.29. National Toxicology Program (2006): Heart, Cardiomyopathy................E-189 

E.2.29.1. Summary Table of BMDS Modeling Results ...........................E-189 

E.2.29.2. Figure for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0, Bound Hit...........................................................E-189 

E.2.29.3. Output File for Selected Model: Multistage, 2-Degree, 

Betas Restricted ≥0, Bound Hit.................................................E-190 

E.2.30. National Toxicology Program (2006): Hepatocyte Hypertrophy, 2 

Years..........................................................................................................E-191 

E.2.30.1. Summary Table of BMDS Modeling Results ...........................E-191 

E.2.30.2. Figure for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0, Bound Hit...........................................................E-192 

E.2.30.3. Output File for Selected Model: Multistage, 2-Degree, 

Betas Restricted ≥0, Bound Hit.................................................E-193 

E.2.31. National Toxicology Program (2006): Liver, Eosinophilic Focus, 

Multiple......................................................................................................E-194 

E.2.31.1. Summary Table of BMDS Modeling Results ...........................E-194 

E.2.31.2. Figure for Selected Model: Probit.............................................E-195 

E.2.31.3. Output File for Selected Model: Probit .....................................E-195 

E.2.32. National Toxicology Program (2006): Liver, Fatty Change, Diffuse........E-197 

E.2.32.1. Summary Table of BMDS Modeling Results ...........................E-197 

E.2.32.2. Figure for Selected Model: Weibull, Power Restricted ≥1 .......E-198 

E.2.32.3. Output File for Selected Model: Weibull, Power 

Restricted ≥1..............................................................................E-198 

E.2.33. National Toxicology Program (2006): Liver Necrosis..............................E-200 

E.2.33.1. Summary Table of BMDS Modeling Results ...........................E-200 

E.2.33.2. Figure for Selected Model: Log-Probit .....................................E-200 

E.2.33.3. Output File for Selected Model: Log-Probit .............................E-201 

E.2.34. National Toxicology Program (2006): Liver, Pigmentation......................E-202 

E.2.34.1. Summary Table of BMDS Modeling Results ...........................E-202 

E.2.34.2. Figure for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-203 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-ix —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.34.3. Output File for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-203 

E.2.35. National Toxicology Program (2006): Liver, Toxic Hepatopathy ............E-205 

E.2.35.1. Summary Table of BMDS Modeling Results ...........................E-205 

E.2.35.2. Figure for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0, Bound Hit...........................................................E-205 

E.2.35.3. Output File for Selected Model: Multistage, 2-Degree, 

Betas Restricted ≥0, Bound Hit.................................................E-206 

E.2.35.4. Figure for Unrestricted Model: Multistage, 2-Degree, Betas 

Unrestricted ...............................................................................E-208 

E.2.35.5. Output File for Unrestricted Model: Multistage, 2-Degree, 

Betas Unrestricted .....................................................................E-208 

E.2.36. National Toxicology Program (2006): Lung, Alveolar to Bronchiolar 

Epithelial Metaplasia (Alveolar Epithelium, Metaplasia, Bronchiolar) ....E-210 

E.2.36.1. Summary Table of BMDS Modeling Results ...........................E-210 

E.2.36.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-211 

E.2.36.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-211 

E.2.37. National Toxicology Program (2006): Oval Cell Hyperplasia, 2 

Years..........................................................................................................E-213 

E.2.37.1. Summary Table of BMDS Modeling Results ...........................E-213 

E.2.37.2. Figure for Selected Model: Probit.............................................E-213 

E.2.37.3. Output File for Selected Model: Probit .....................................E-214 

E.2.38. National Toxicology Program (2006): Toxic Hepatopathy.......................E-215 

E.2.38.1. Summary Table of BMDS Modeling Results ...........................E-215 

E.2.38.2. Figure for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0, Bound Hit...........................................................E-216 

E.2.38.3. Output File for Selected Model: Multistage, 2-Degree, 

Betas Restricted ≥0, Bound Hit.................................................E-216 

E.2.38.4. Figure for Unrestricted Model: Multistage, 2-Degree, 

Betas Unrestricted .....................................................................E-218 

E.2.38.5. Output File for Unrestricted Model: Multistage, 2-Degree, 

Betas Unrestricted .....................................................................E-218 

E.2.39. Ohsako et al. (2001): Anogenital Distance in Male Pups..........................E-220 

E.2.39.1. Summary Table of BMDS Modeling Results ...........................E-220 

E.2.39.2. Figure for Selected Model: Hill.................................................E-221 

E.2.39.3. Output File for Selected Model: Hill.........................................E-221 

E.2.39.4. Figure for Unrestricted Model: Hill, Unrestricted.....................E-224 

E.2.39.5. Output File for Unrestricted Model: Hill, Unrestricted.............E-224 

E.2.40. Schantz et al. (1996): Maze Errors Per Block, Female..............................E-227 

E.2.40.1. Summary Table of BMDS Modeling Results ...........................E-227 

E.2.40.2. Figure for Selected Model: Linear, Constant Variance.............E-228 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-x —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.40.3. Output File for Selected Model: Linear, Constant Variance.....E-228 

E.2.40.4. Figure for Unrestricted Model: Power, Constant Variance, 

Power Unrestricted....................................................................E-231 

E.2.40.5. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted....................................................E-231 

E.2.41. Shi et al. (2007): Estradiol .........................................................................E-234 

E.2.41.1. Summary Table of BMDS Modeling Results ...........................E-234 

E.2.41.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1..................................................E-235 

E.2.41.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-235 

E.2.41.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-238 

E.2.41.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-238 

E.2.41.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, 

n Unrestricted ............................................................................E-241 

E.2.41.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-241 

E.2.41.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-244 

E.2.41.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-244 

E.2.42. Smialowicz et al. (2008): PFC per 10^6 Cells...........................................E-247 

E.2.42.1. Summary Table of BMDS Modeling Results ...........................E-247 

E.2.42.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-248 

E.2.42.3. Output File for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-248 

E.2.42.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-251 

E.2.42.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-251 

E.2.42.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-254 

E.2.42.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-254 

E.2.42.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-257 

E.2.42.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-257 

E.2.43. Smialowicz et al. (2008): PFC per Spleen.................................................E-260 

E.2.43.1. Summary Table of BMDS Modeling Results ...........................E-260 

E.2.43.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-261 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xi —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.43.3. Output File for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-261 

E.2.43.4. Figure for UnrestrictedModel: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-264 

E.2.43.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-264 

E.2.43.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-267 

E.2.43.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-267 

E.2.43.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-270 

E.2.43.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-270 

E.2.44. Toth et al. (1978): Amyloidosis.................................................................E-273 

E.2.44.1. Summary Table of BMDS Modeling Results ...........................E-273 

E.2.44.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-274 

E.2.44.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-274 

E.2.44.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-276 

E.2.44.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-276 

E.2.44.6. Figure for Unrestricted Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-278 

E.2.44.7. Output File for Unrestricted Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-278 

E.2.45. Toth et al. (1978): Skin Lesions.................................................................E-280 

E.2.45.1. Summary Table of BMDS Modeling Results ...........................E-280 

E.2.45.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-281 

E.2.45.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1..............................................................................E-281 

E.2.45.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-283 

E.2.45.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-283 

E.2.46. Van Birgelen et al. (1995a): Hepatic Retinol.............................................E-285 

E.2.46.1. Summary Table of BMDS Modeling Results ...........................E-285 

E.2.46.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1..................................................E-287 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.46.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-287 

E.2.46.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-290 

E.2.46.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-290 

E.2.46.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, 

n Unrestricted ............................................................................E-293 

E.2.46.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-293 

E.2.46.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-296 

E.2.46.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-296 

E.2.47. Van Birgelen et al. (1995a): Hepatic Retinol Palmitate ............................E-299 

E.2.47.1. Summary Table of BMDS Modeling Results ...........................E-299 

E.2.47.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1..................................................E-300 

E.2.47.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-300 

E.2.47.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-303 

E.2.47.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-303 

E.2.47.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-306 

E.2.47.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-306 

E.2.47.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-309 

E.2.47.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-309 

E.2.48. Van Birgelen et al. (1995a): Plasma FT4...................................................E-312 

E.2.48.1. Summary Table of BMDS Modeling Results ...........................E-312 

E.2.48.2. Figure for Selected Model: Exponential (M2), Nonconstant 

Variance, Power Restricted ≥1..................................................E-313 

E.2.48.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-314 

E.2.48.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-316 

E.2.48.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-317 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xiii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.2.48.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, 

n Unrestricted ............................................................................E-319 

E.2.48.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-320 

E.2.48.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-322 

E.2.48.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-322 

E.2.49. Van Birgelen et al. (1995a): Plasma TT4 ..................................................E-325 

E.2.49.1. Summary Table of BMDS Modeling Results ...........................E-325 

E.2.49.2. Figure for Selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-327 

E.2.49.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-327 

E.2.49.4. Figure for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ....................................E-330 

E.2.49.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ....................................E-330 

E.2.49.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted ...............................................................................E-333 

E.2.49.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted............................................................E-333 

E.2.49.8. Figure for Unrestricted Model: Power, Constant Variance, 

Power Unrestricted....................................................................E-336 

E.2.49.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted....................................................E-336 

E.2.50. White et al. (1986): CH50..........................................................................E-338 

E.2.50.1. Summary Table of BMDS Modeling Results ...........................E-338 

E.2.50.2. Figure for Selected Model: Hill, Nonconstant Variance, n 

Restricted >1, Bound Hit...........................................................E-340 

E.2.50.3. Output File for Selected Model: Hill, Nonconstant 

Variance, n Restricted >1, Bound Hit .......................................E-340 

E.2.50.4. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-343 

E.2.50.5. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-343 

E.3. ADMINISTERED DOSE BMDS RESULTS.........................................................E-346 

E.3.1. Amin et al. (2000): Saccharin Consumed, Female (0.25%) ......................E-346 

E.3.1.1. Summary Table of BMDS Modeling Results ...........................E-346 

E.3.1.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-347 

E.3.1.3. Output file for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-347 

E.3.2. Amin et al. (2000): Saccharin Consumed, Female (0.50%) ......................E-349 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xiv —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.2.1. Summary Table of BMDS Modeling Results ...........................E-349 

E.3.2.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-350 

E.3.2.3. Output File for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-350 

E.3.3. Amin et al. (2000): Saccharin Preference Ratio, Female (0.25%).............E-353 

E.3.3.1. Summary Table of BMDS Modeling Results ...........................E-353 

E.3.3.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-353 

E.3.3.3. Output File for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-354 

E.3.4. Amin et al. (2000): Saccharin Preference Ratio, Female (0.50%).............E-356 

E.3.4.1. Summary Table of BMDS Modeling Results ...........................E-356 

E.3.4.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-357 

E.3.4.3. Output File for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-357 

E.3.5. Bell et al. (2007): Balano-Preputial Separation in Male Pups (10% 

Extra Risk) .................................................................................................E-359 

E.3.5.1. Summary Table of BMDS modeling results .............................E-359 

E.3.5.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-360 

E.3.5.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-360 

E.3.5.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-362 

E.3.5.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-362 

E.3.6. Bell et al. (2007): Balano-Preputial Separation in Male Pups (5% 

Extra Risk) .................................................................................................E-364 

E.3.6.1. Summary Table of BMDS Modeling Results ...........................E-364 

E.3.6.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-365 

E.3.6.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-365 

E.3.6.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-367 

E.3.6.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-367 

E.3.7. Cantoni et al. (1981): Urinary Copro-Porhyrins........................................E-369 

E.3.7.1. Summary Table of BMDS Modeling Results ...........................E-369 

E.3.7.2. Figure for Selected Model: Probit.............................................E-369 

E.3.7.3. Output File for Selected Model: Probit .....................................E-370 

E.3.8. Cantoni et al. (1981): Urinary Porphyrins .................................................E-371 

E.3.8.1. Summary Table of BMDS Modeling Results ...........................E-371 

E.3.8.2. Figure for Selected Model: Linear, Nonconstant Variance.......E-372 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xv —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.8.3. Output File for Selected Model: Linear, Nonconstant 

Variance.....................................................................................E-373 

E.3.9. Crofton et al. (2005): Serum T4.................................................................E-375 

E.3.9.1. Summary Table of BMDS Modeling Results ...........................E-375 

E.3.9.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1..................................................E-376 

E.3.9.3. Output File for selected Model: Exponential (M4), 

Constant Variance, Power Restricted ≥1...................................E-376 

E.3.10. DeCaprio et al. (1986): Absolute Kidney Weight, Males..........................E-379 

E.3.10.1. Summary Table of BMDS Modeling Results ...........................E-379 

E.3.10.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-380 

E.3.10.3. Output File for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-380 

E.3.11. DeCaprio et al. (1986): Absolute Thymus Weight, Males ........................E-383 

E.3.11.1. Summary Table of BMDS Modeling Results ...........................E-383 

E.3.11.2. Figure for Selected Model: Power, Nonconstant Variance, 

Power Restricted ≥1, Bound Hit................................................E-384 

E.3.11.3. Output File for Selected Model: Power, Nonconstant 

Variance, Power Restricted ≥1, Bound Hit ...............................E-384 

E.3.12. DeCaprio et al. (1986): Body Weight, Females.........................................E-387 

E.3.12.1. Summary Table of BMDS Modeling Results ...........................E-387 

E.3.12.2. Figure for Selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-388 

E.3.12.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-388 

E.3.13. DeCaprio et al. (1986): Body Weight, Males ............................................E-391 

E.3.13.1. Summary Table of BMDS Modeling Results ...........................E-391 

E.3.13.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-392 

E.3.13.3. Output File for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-392 

E.3.14. DeCaprio et al. (1986): Relative Brain Weight, Males..............................E-395 

E.3.14.1. Summary Table of BMDS Modeling Results ...........................E-395 

E.3.14.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1..................................................E-396 

E.3.14.3. Output File for Selected Model: Exponential (M4), 

Constant Variance, Power Restricted ≥1...................................E-396 

E.3.15. DeCaprio et al. (1986): Relative Liver Weight, Females ..........................E-399 

E.3.15.1. Summary Table of BMDS Modeling Results ...........................E-399 

E.3.15.2. Figure for Selected Model: Exponential (M2), Nonconstant 

Variance, Power Restricted ≥1..................................................E-400 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xvi —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.15.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-400 

E.3.16. DeCaprio et al. (1986): Relative Liver Weight, Males..............................E-403 

E.3.16.1. Summary Table of BMDS Modeling Results ...........................E-403 

E.3.16.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1..................................................E-404 

E.3.16.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-404 

E.3.17. DeCaprio et al. (1986): Relative Thymus Weight, Males .........................E-407 

E.3.17.1. Summary Table of BMDS Modeling Results ...........................E-407 

E.3.17.2. Figure for selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-408 

E.3.17.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-408 

E.3.18. Hojo et al. (2002): DRL Reinforce per Min ..............................................E-411 

E.3.18.1. Summary Table of BMDS Modeling Results ...........................E-411 

E.3.18.2. Figure for Selected Model: Linear, Constant Variance.............E-412 

E.3.18.3. Output File for Selected Model: Linear, Constant Variance.....E-412 

E.3.19. Hojo et al. (2002): DRL Response per Min...............................................E-415 

E.3.19.1. Summary Table of BMDS Modeling Results ...........................E-415 

E.3.19.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1..................................................E-416 

E.3.19.3. Output File for Selected Model: Exponential (M4), 

Constant Variance, Power Restricted ≥1...................................E-416 

E.3.20. Kattainen et al. (2001): 3rd Molar Mesio-Distal Length (Molar 

Development).............................................................................................E-419 

E.3.20.1. Summary Table of BMDS Modeling Results ...........................E-419 

E.3.20.2. Figure for Selected Model: Hill, Nonconstant Variance, n 

Restricted >1, Bound Hit...........................................................E-420 

E.3.20.3. Output File for Selected Model: Hill, Nonconstant 

Variance, n Restricted >1, Bound Hit .......................................E-420 

E.3.21. Kattainen et al. (2001): Females 3rd Molar Eruption................................E-423 

E.3.21.1. Summary Table of BMDS Modeling Results ...........................E-423 

E.3.21.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-424 

E.3.21.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-424 

E.3.22. Keller et al. (2006): Missing Mandibular Molars in CBA J Mice .............E-426 

E.3.22.1. Summary Table of BMDS Modeling Results ...........................E-426 

E.3.22.2. Figure for Selected Model: Multistage, 1-Degree, Betas 

Restricted ≥0..............................................................................E-427 

E.3.22.3. Output File for Selected Model: Multistage, 1-Degree, 

Betas Restricted ≥0....................................................................E-427 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xvii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.23. Kociba et al. (1978): Urinary Coproporphyrins, Females (Table 2)..........E-429 

E.3.23.1. Summary Table of BMDS Modeling Results ...........................E-429 

E.3.23.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1..................................................E-430 

E.3.23.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-430 

E.3.24. Kociba et al. (1978): Uroporphyrin per Creatinine, Females ....................E-433 

E.3.24.1. Summary Table of BMDS Modeling Results ...........................E-433 

E.3.24.2. Figure for Selected Model: Linear, Constant Variance.............E-434 

E.3.24.3. Output File for Selected Model: Linear, Constant Variance.....E-434 

E.3.25. Latchoumycandane and Mathur (2002): Daily sperm Production.............E-437 

E.3.25.1. Summary Table of BMDS Modeling Results ...........................E-437 

E.3.25.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-438 

E.3.25.3. Output File for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-438 

E.3.26. Li et al. (2006): Hormone Levels (Estradiol).............................................E-441 

E.3.26.1. Summary Table of BMDS Modeling Results ...........................E-441 

E.3.26.2. Figure for Selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-442 

E.3.26.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-442 

E.3.27. Li et al. (2006): Hormone Levels (Progesterone)......................................E-445 

E.3.27.1. Summary Table of BMDS Modeling Results ...........................E-445 

E.3.27.2. Figure for Selected Model: Exponential (M4), Nonconstant 

Variance, Power Restricted ≥1..................................................E-446 

E.3.27.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-446 

E.3.28. Markowski et al. (2001): FR10 Run Opp ..................................................E-449 

E.3.28.1. Summary Table of BMDS Modeling Results ...........................E-449 

E.3.28.2. Figure for Selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-450 

E.3.28.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-450 

E.3.29. Markowski et al. (2001): FR2 Revolutions................................................E-453 

E.3.29.1. Summary Table of BMDS Modeling Results ...........................E-453 

E.3.29.2. Figure for Selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-454 

E.3.29.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-454 

E.3.30. Markowski et al. (2001): FR5 Run Opp ....................................................E-457 

E.3.30.1. Summary Table of BMDS Modeling Results ...........................E-457 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xviii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.30.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-458 

E.3.30.3. Output File for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-458 

E.3.31. Mietinnin et al. (2006): Caries...................................................................E-461 

E.3.31.1. Summary Table of BMDS Modeling Results ...........................E-461 

E.3.31.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-462 

E.3.31.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-462 

E.3.32. National Toxicology Program (1982): Male Mice, Toxic Hepatitis..........E-464 

E.3.32.1. Summary Table of BMDS Modeling Results ...........................E-464 

E.3.32.2. Figure for Selected Model: Logistic..........................................E-464 

E.3.32.3. Output file for Selected Model: Logistic...................................E-465 

E.3.33. National Toxicology Program (2006): Alveolar Metaplasia .....................E-466 

E.3.33.1. Summary Table of BMDS Modeling Results ...........................E-466 

E.3.33.2. Figure for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-467 

E.3.33.3. Output File for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-467 

E.3.34. National Toxicology Program (2006): Gingival Hyperplasia 

Squamous, 2 Years.....................................................................................E-469 

E.3.34.1. Summary Table of BMDS Modeling Results ...........................E-469 

E.3.34.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-470 

E.3.34.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-470 

E.3.34.4. Figure for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-472 

E.3.34.5. Output File for Unrestricted Model: Log-Logistic, Slope 

Unrestricted ...............................................................................E-472 

E.3.35. National Toxicology Program (2006): Heart, Cardiomyopathy................E-474 

E.3.35.1. Summary Table of BMDS Modeling Results ...........................E-474 

E.3.35.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-474 

E.3.35.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-475 

E.3.36. National Toxicology Program (2006): Hepatocyte Hypertrophy, 2 

Years..........................................................................................................E-476 

E.3.36.1. Summary Table of BMDS Modeling Results ...........................E-476 

E.3.36.2. Figure for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-477 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xix —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.36.3. Output File for Selected Model: Log-Logistic, Slope 

Restricted ≥1, Bound Hit...........................................................E-477 

E.3.37. National Toxicology Program (2006): Liver, Eosinophilic Focus, 

Multiple......................................................................................................E-479 

E.3.37.1. Summary Table of BMDS Modeling Results ...........................E-479 

E.3.37.2. Figure for Selected Model: Weibull, Power Restricted ≥1, 

Bound Hit ..................................................................................E-479 

E.3.37.3. Output File for Selected Model: Weibull, Power 

Restricted ≥1, Bound Hit...........................................................E-480 

E.3.38. National Toxicology Program (2006): Liver, Fatty Change, Diffuse........E-481 

E.3.38.1. Summary Table of BMDS Modeling Results ...........................E-481 

E.3.39. Figure for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0 ..............................................................................................E-482 

E.3.40. Output File for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0 ..............................................................................................E-482 

E.3.41. National Toxicology Program (2006): Liver Necrosis..............................E-484 

E.3.41.1. Summary Table of BMDS Modeling Results ...........................E-484 

E.3.41.2. Figure for Selected Model: LogProbit.......................................E-485 

E.3.41.3. Output File for Selected Model: Log-Probit .............................E-485 

E.3.42. National Toxicology Program (2006): Liver, Pigmentation......................E-487 

E.3.42.1. Summary Table of BMDS Modeling Results ...........................E-487 

E.3.42.2. Figure for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-487 

E.3.42.3. Output File for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-488 

E.3.43. National Toxicology Program (2006): Lung, Alveolar to Bronchiolar 

Epithelial Metaplasia (Alveolar Epithelium, Metaplasia, 

Bronchiolar) ...............................................................................................E-489 

E.3.43.1. Summary Table of BMDS Modeling Results ...........................E-489 

E.3.43.2. Figure for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-490 

E.3.43.3. Output File for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-490 

E.3.44. National Toxicology Program (2006): Oval Cell Hyperplasia, 2 

Years..........................................................................................................E-492 

E.3.44.1. Summary Table of BMDS Modeling Results ...........................E-492 

E.3.44.2. Figure for Selected Model: Multistage, 2-Degree, Betas 

Restricted ≥0..............................................................................E-492 

E.3.44.3. Output File for Selected Model: Multistage, 2-Degree, 

Betas Restricted ≥0....................................................................E-493 

E.3.45. National Toxicology Program (2006): Toxic Hepatopathy.......................E-494 

E.3.45.1. Summary Table of BMDS Modeling Results ...........................E-494 

E.3.45.2. Figure for Selected Model: Gamma, Power Restricted ≥1........E-495 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xx —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.45.3. Output file for Selected Model: Gamma, Power 

Restricted ≥1..............................................................................E-495 

E.3.45.4. Figure for Unrestricted Model: Weibull, Power 

Restricted ≥1..............................................................................E-497 

E.3.45.5. Output File for Unrestricted Model: Weibull, Power 

Restricted ≥1..............................................................................E-497 

E.3.46. Ohsako et al. (2001): Anogenital PND120................................................E-499 

E.3.46.1. Summary Table of BMDS Modeling Results ...........................E-499 

E.3.46.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-500 

E.3.46.3. Output File for Selected Model: Hill, Constant Variance, 

n Restricted >1, Bound Hit........................................................E-500 

E.3.47. Schantz et al. (1996): Maze Errors Per Block, Female..............................E-503 

E.3.47.1. Summary Table of BMDS Modeling Results ...........................E-503 

E.3.47.2. Figure for Selected Model: Linear, Constant Variance.............E-504 

E.3.47.3. Output File for Selected Model: Linear, Constant 

Variance.....................................................................................E-504 

E.3.48. Shi et al. (2007): Estradiol .........................................................................E-506 

E.3.48.1. Summary Table of BMDS Modeling Results ...........................E-506 

E.3.48.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-508 

E.3.48.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-508 

E.3.49. Smialowicz et al. (2008): PFC per 10^6 Cells...........................................E-511 

E.3.49.1. Summary Table of BMDS Modeling Results ...........................E-511 

E.3.49.2. Figure for Selected Model: Exponential (M2), Nonconstant 

Variance, Power Restricted ≥1..................................................E-512 

E.3.49.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-512 

E.3.50. Smialowicz et al. (2008): PFC per Spleen.................................................E-515 

E.3.50.1. Summary Table of BMDS Modeling Results ...........................E-515 

E.3.50.2. Figure for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-516 

E.3.50.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-516 

E.3.51. Toth et al. (1978): Amyloidosis.................................................................E-519 

E.3.51.1. Summary Table of BMDS Modeling Results ...........................E-519 

E.3.51.2. Figure for Selected Model: Multistage, 1-Degree, Betas 

Restricted ≥0..............................................................................E-519 

E.3.51.3. Output File for Selected Model: Multistage, 1-Degree, 

Betas Restricted ≥0....................................................................E-519 

E.3.52. Toth et al. (1978): Skin Lesions.................................................................E-521 

E.3.52.1. Summary Table of BMDS Modeling Results ...........................E-521 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xxi —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.52.2. Figure for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-522 

E.3.52.3. Output File for Selected Model: Log-Probit, Slope 

Restricted ≥1..............................................................................E-522 

E.3.53. Van Birgelen et al. (1995a): Hepatic Retinol.............................................E-524 

E.3.53.1. Summary Table of BMDS Modeling Results ...........................E-524 

E.3.53.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-525 

E.3.53.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1.............................E-526 

E.3.53.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-528 

E.3.53.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-529 

E.3.53.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-531 

E.3.53.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-532 

E.3.53.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-534 

E.3.53.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-535 

E.3.54. Van Birgelen et al. (1995a): Hepatic Retinol Palmitate ............................E-537 

E.3.54.1. Summary Table of BMDS Modeling Results ...........................E-537 

E.3.54.2. Figure for Selected Model: Hill, Nonconstant Variance, n 

Unrestricted ...............................................................................E-539 

E.3.54.3. Output File for Selected Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-539 

E.3.54.4. Figure for Unrestricted Model: Linear, Nonconstant 

Variance.....................................................................................E-542 

E.3.54.5. Output File for Unrestricted Model: Linear, Nonconstant 

Variance.....................................................................................E-542 

E.3.54.6. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-545 

E.3.54.7. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-545 

E.3.54.8. Figure for Unrestricted Model: Exponential (M5), Constant 

Variance, Power Unrestricted....................................................E-548 

E.3.54.9. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ....................................E-548 

E.3.55. Van Birgelen et al. (1995a): Plasma FT4...................................................E-551 

E.3.55.1. Summary Table of BMDS Modeling Results ...........................E-551 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-xxii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

1 

E.3.55.2. Figure for Selected Model: Exponential (M2), Nonconstant 

Variance, Power Restricted ≥1..................................................E-552 

E.3.55.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1.............................E-553 

E.3.55.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-555 

E.3.55.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted ..............................E-556 

E.3.55.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-558 

E.3.55.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted............................................................E-559 

E.3.55.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-561 

E.3.55.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted....................................................E-561 

E.3.56. Van Birgelen et al. (1995a): Plasma TT4 ..................................................E-564 

E.3.56.1. Summary Table of BMDS Modeling Results ...........................E-564 

E.3.56.2. Figure for Selected Model: Exponential (M2), Constant 

Variance, Power Restricted ≥1..................................................E-565 

E.3.56.3. Output File for Selected Model: Exponential (M2), 

Constant Variance, Power Restricted ≥1...................................E-566 

E.3.56.4. Figure for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ....................................E-569 

E.3.56.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted ....................................E-569 

E.3.56.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted ...............................................................................E-572 

E.3.56.7. Output File for Unrestricted Model: Hill, constant 

Variance, n Unrestricted............................................................E-572 

E.3.56.8. Figure for Unrestricted Model: Power, Constant Variance, 

Power Unrestricted....................................................................E-575 

E.3.56.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted....................................................E-575 

E.3.57. White et al. (1986): CH50..........................................................................E-578 

E.3.57.1. Summary Table of BMDS Modeling Results ...........................E-578 

E.3.57.2. Figure for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-579 

E.3.57.3. Output File for Selected Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit...........................................................E-579 

E.4. REFERENCES........................................................................................................E-582 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-1 —DO NOT CITE OR QUOTE 

1 APPENDIX E. NONCANCER BENCHMARK DOSE MODELING 

2 

3 

4 E.1. BMDS INPUT TABLES 

5 E.1.1. Amin et al. (2000)

Administered Dose (ng/kg-day) 

0 25 a 100 

Internal Dose (ng/kg blood) b

0 6,800 24,522 

Endpoint (n = 10) (n = 10) (n = 10) 

Saccharin consumed, female (0.25%) 31.67 ± 26.64 24.60 ± 11.98 10.70 ± 5.33 

Saccharin consumed, female (0.50%) 22.40 ± 15.98 11.38 ± 7.66 4.54 ± 3.33 

Saccharin preference ratio, female (0.25%) 82.14 ± 13.35 58.12 ± 33.88 54.87 ± 19.51

Saccharin preference ratio, female (0.50%) 72.73 ± 24.64 44.48 ± 32.85 33.77 ± 24.64

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

6 

7 

8 E.1.2. Bell et al. (2007a) 

Administered Dose (ng/kg-day) 

0 2.4 a 8 46 

Internal Dose (ng/kg blood) b

0 1,998 4,539 15,952 

Endpoint (n = 30) (n = 30) (n = 30) (n = 30) 

Balano-preputial separation, male 

pups 1/30 (3%) 5/30 (17%) 6/30 (20%) 15/30 (50%) 

a LOAEL. 

b

 From the Emond PRPK model described in 3.3. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-2 —DO NOT CITE OR QUOTE 

1 E.1.3. Cantoni et al. (1981) 

Administered Dose (ng/kg-day) 

0 1.43 a 14.3 143 

Internal Dose (ng/kg blood) b

0 1,018 4,868 27,559 

Endpoint (n = 4) (n = 4) (n = 3) (n = 3) 

Urinary coporphyrins 0.74 ± 0.35 1.81 ± 0.83 c 2.73 ± 1.50 d 3.00 ± 2.60 d

Urinary porphyrins 2.27 ± 0.49 5.55 ± 0.85 c 7.62 ± 1.79 c 196.89 ± 63.14 

d

a LOAEL 

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 

d Statistically significant as compared to control (p < 0.01). 

2 

3 

4 E.1.4. Crofton et al. (2005) 

Administered Dose (ng/kg-day) 

0 0.1 3 10 30 a 100 b 300 1,000 3,000 10,000

Internal Dose (ng/kg blood) c

0 11.3 273 773 1,922 51,11 12,624 35,697 98,088 316,540

Endpoint (n = 

14) (n = 6) 

(n = 

12) (n = 6) (n = 6) (n = 6) (n = 6) (n = 6) (n = 6) (n = 4)

Serum T4 

100.00 

± 

15.44 

96.27 

± 

14.98 

98.57 

± 

18.11

99.76 

± 

19.04

93.32 

± 

12.11

70.94 

± 

12.74

62.52 

± 

14.75

52.68 

± 

22.73 

54.66 

± 

19.71

49.15 

± 

11.17

a NOAEL 

b LOAEL 

c From the Emond PRPK model described in 3.3. 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-3 —DO NOT CITE OR QUOTE 

1 E.1.5. DeCaprio et al. (1986)

Administered Dose (ng/kg-day) 

0 0.12 0.61 a 4.9 b 26 

Internal Dose (ng/kg blood) c

n/a n/a n/a n/a n/a 

Endpoint (n = 10) (n = 10) (n = 11) (n = 10) (n = 4) 

Absolute kidney weight, 

males 

5.49 ± 

0.54 5.14 ± 0.38 4.71 ± 0.4 4.3±0.47d - 

Absolute thymus weight, 

males 

0.56 ± 

0.16 0.45 ± 0.07 0.44 ± 0.11 0.35±0.53e 

 - 

Body weight, males 713 ± 

47.43 682 ± 50.6 651 ± 63.02 603±63.25d 433 ± 76 

f

Relative brain weight, 

males 

0.54 ± 

0.05 0.56 ± 0.05 0.6 ± 0.05 0.65±0.05d - 

Relative liver weight, males 4.54 ± 

0.73 4.1 ± 0.44 5.36 ± 2.02 5.63±0.92d - 

Relative thymus weight, 

males 

0.08 ± 

0.02 0.07 ± 0.01 0.07 ± 0.01 0.06±0.01d - 

Administered Dose (ng/kg-day)

0 0.12 0.68 4.86 31 

Internal Dose (ng/kg blood) c

0 n/a n/a n/a n/a 

Endpoint

(n = 8) (n = 10) (n = 9) (n = 10) (n = 4) 

Body weight, females 602 ± 

33.94 583 ± 69.57 570 ± 66 531 ± 44.27 d 351 ± 98 

f

Relative liver weight, 

females 4.3 ± 0.74 4.49 ± 1.11 4.27 ± 0.48 5.54 ± 1.36 

d 

4.3 ± 

0.74 

a NOAEL 

b LOAEL.

c Internal dose not calculated using the Emond PBPK (ginuea pigs). 

d Statistically significant as compared to control (p < 0.05). e Statistically significant as compared to control (p < 0.01). 

f Statistically significant as compared to control (p < 0.001). 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-4 —DO NOT CITE OR QUOTE 

1 E.1.6. Hojo et al. (2002)

Administered Dose (ng/kg-day) 

0 20 a 60 180 

Internal Dose (ng/kg blood) b

0 1,285 3,295 8,465 

Endpoint (n = 5) (n = 5) (n = 6) (n = 5) 

DRL reinforce per min 0.09 ± 0.45 0.54 ± 0.82 1.27 ± 0.54 0.74 ± 0.44 

DRL response per min 18.46 ± 7.99 -0.99 ± 10.96 -4.52 ± 7.19 -0.41 ± 15.23 

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

2 

3 

4 E.1.7. Kattainen et al. (2001) 

Administered Dose (ng/kg-day) 

0 30 a 100 300 1,000 

Internal Dose (ng/kg blood) b

0 1,763 4,944 12,712 37,039 

Endpoint (n = 16) (n = 17) (n = 15) (n = 12) (n = 19) 

3rd molar mesio-distal 

length (molar development) 1.86 ± 0.07 1.58 ± 0.19 c 1.6 ± 0.27 c 1.5 ± 0.22 c 1.35 ± 0.51 c

Females 3rd molar eruption 1/16 (10%) 3/17 (20%) 4/15 (30%) 6/12 (50%) c

13/19 (70%) c

a LOAEL.

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-5 —DO NOT CITE OR QUOTE 

1 E.1.8. Keller et al. (2007, 2008a, b)

Administered Dose (ng/kg-day) 

0 10 a 100 1,000 

Internal Dose (ng/kg blood) b

Endpoint 0 296 2,365 18,764 

Missing mandibular molars in CBA J mice 0/29 (0%) 2/23 (10%) 

6/29 

(20%) 

30/30 

(100%) 

a LOAEL.

b From the Emond PRPK model described in 3.3. 

2 

3 

4 E.1.9. Kociba et al. (1978) 

Administered Dose (ng/kg-day) 

0 1 a 10 b 100 

Internal Dose (ng/kg blood) c

0 853 3,942 21,246 

Endpoint (n = 5) (n = 5) (n = 5) (n = 5) 

Urinary coproporphyrin, 

females 9.8 ± 1.3 8.6 ± 2 16.4 ± 4.7 d

 17.4 ± 4 d 

Uroporphyrin per creatinine, 

females 0.157 ± 0.05 0.143 ± 0.04 0.181 ± 0.05 0.296 ± 0.07d

a NOAEL 

b LOAEL.

c From the Emond PRPK model described in 3.3. 

d Statistically significant as compared to control (p < 0.05). 

5 

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-6 —DO NOT CITE OR QUOTE 

1 E.1.10. Latchoumycandane and Mathur (2002)

Administered Dose (ng/kg-day) 

0 1 a 10 100 

Internal Dose (ng/kg blood) b

0 437 2,579 15,092 

Endpoint (n = 6) (n = 6) (n = 6) (n = 6) 

Daily sperm production 22.19 ± 2.67 15.67 ± 2.65 c 13.65 ± 2.19 c 13.1 ± 3.16 c

a LOAEL.

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 

2 E.1.11. Li et al. (1997) 

Administered Dose (ng/kg-day) 

0 3 a 10 b 30 100 300 1,000 3,000 10,000 30,000 

Internal Dose (ng/kg blood) c

0 147 440 1,156 3,232 8,266 23,875 66,081 212,650 649,740

Endpoint (n = 10) (n =10) (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) (n = 10)

FSH 

23.86 

± 

29.65 

22.16 

± 

48.51 

85.23 

± 

94.33 

73.30 

± 

48.51 

126.14 

± 

159.01 

132.10 

± 

115.89 

116.76 

± 

51.21 

304.26 

± 

153.62 

346.88 

± 

150.93 

455.11 

± 

285.68 

a NOAEL 

b LOAEL.

c From the Emond PRPK model described in 3.3. 

3 

4 

5 E.1.12. Li et al. (2006) 

Administered Dose (ng/kg-day) 

0 2 a 50 100 

Internal Dose (ng/kg blood) b

0 87.5 1,564 2,823 

Endpoint (n = 10) (n = 10) (n = 10) (n = 10) 

Serum estradiol 10. ± 12.48 20 ± 19.97 24.74 ± 15.00 17.90 ± 18.31 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-7 —DO NOT CITE OR QUOTE 

Serum progesterone 65.25 ± 11.10 43.36 ± 40.48 c 27.46 ± 33.30 25.19 ± 

43.756 

a LOAEL.

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.01). 

1 

2 

3 E.1.13. Markowski et al. (2001)

Administered Dose (ng/kg-day) 

0 20 a 60 180 

Internal Dose (ng/kg blood) b

0 1,234 3,184 8,152 

Endpoint (n = 7) (n = 4) (n = 6) (n = 7) 

FR10 run opp 13.29 ± 8.65 11.25 ± 5.56 5.75 ± 3.53 7 ± 6.01 

FR2 revolutions 119.29 ± 69.9 108.5 ± 61 56.5 ± 31.21 68.14 ± 33.23

FR5 run opp 26.14 ± 12.28 23.5 ± 7.04 12.8 ± 6.17 13.14 ± 7.14 

a LOAEL.

b From the Emond PRPK model described in 3.3. 

4 E.1.14. Mietinnin et al. (2006) 

Administered Dose (ng/kg-day) 

0 30 a 100 300 1,000 

Internal Dose (ng/kg blood) b

0 1,756 4,922 12,657 36,874 

Endpoint (n = 42) (n = 29) (n = 15) (n = 24) (n = 32) 

Cariogenic lesions in pups 25/42 

(60%) 

23/29 

(79%) b

19/25 

(76%) 

20/24 

(83%) c

29/32 

(91%) c

a LOAEL.

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-8 —DO NOT CITE OR QUOTE 

1 E.1.15. National Toxicology Program (1982) 

Administered Dose (ng/kg-day) 

0 1.43 a 7.14 71.4 

Internal Dose (ng/kg blood) b

0 420 1,240 6,118 

Endpoint (n = 73) (n = 49) (n = 49) (n = 50) 

Toxic hepatitis, male mice 1/73 (1.4%) 5/49 (10%) 5/49 (6.1%) 44/50 (88%) 

a LOAEL.

b From the Emond PRPK model described in 3.3. 

2 

3 

4 E.1.16. National Toxicology Program (2006) 

Administered Dose (ng/kg-day) 

0 2.14 a 7.14 15.7 32.9 71.4 

Internal Dose (ng/kg blood) b

0 1,408 3,137 5,393 9,128 16,361 

Endpoint (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) 

Alveolar metaplasia 2/53 

(0%) 

19/54 

(40%)c,

33/53 

(60%)c

35/52 

(70%)c

45/53 

(80%)c

46/52 

(90%)c

Gingival hyperplasia 

squamous, 2 years 

1/53 

(2%) 

7/54 

(13%)d

14/53 

(26%)c

13/53 

(25%)c

15/53 

(28%)c

16/53 

(30%)c

Liver, hepatocyte hypertrophy, 

2 years 

0/53 

(0%) 

19/54 

(40%)c,

19/53 

(40%)c

42/53 

(80%)c

41/53 

(80%)c

52/53 

(100%)c

Heart, cardiomyopathy 10/53 

(19%) 

12/54 

(22%) 

22/53c

(42%) 

25/52c

(48%) 

32/53c

(60%) 

36/52c

(69%) 

Liver, eosinophilic focus, 

multiple 

3/53 

(6%) 

8/54 

(15%) 

14/53 

(26%) 

17/53 

(32%) 

22/53 

(42%) 

42/53 

(79%) 

Liver, fatty change, diffuse 0/53 

(0%) 

2/54 

(4%) 

12/53c

(23%) 

17/53c

(32%) 

30/53c

(57%) 

48/53c

(91%) 

Liver, necrosis 1/53 

(2%) 

4/54 

(7%) 

4/53 

(8%) 

8/53d

(15%) 

10/53c

(19%) 

17/53c

(32%) 

Liver, pigmentation 4/53 9/54 34/53c 48/53c 52/53c 53/53c
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-9 —DO NOT CITE OR QUOTE 

Administered Dose (ng/kg-day) 

0 2.14 a 7.14 15.7 32.9 71.4 

Internal Dose (ng/kg blood) b

0 1,408 3,137 5,393 9,128 16,361 

Endpoint (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) 

(8%) (17%) (64%) (91%) (98%) (100%) 

Liver, toxic hepatopathy 0/53 

(0%) 

2/54 

(4%) 

8/53 

(15%) 

30/53 

(57%) 

45/50 

(85%) 

53/53 

(100%) 

Oval cell hyperplasia, 2 years 0/53 

(0%) 

4/54 

(10%)d

3/53 

(10%) 

20/53 

(40%)c

38/53 

(70%)d

53/53 

(100%)c

Lung, alveolar to bronchiolar 

epithelial metaplasia 

(Alveolar epithelium, 

metaplasia, bronchiolar) 

2/53 

(4%) 

19/54 c

(35%) 

33/53c

(62%) 

35/52c

(67%) 

45/53c

(85%) 

46/52c

(89%) 

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.01). 

d Statistically significant as compared to control (p < 0.05). 

1 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-10 —DO NOT CITE OR QUOTE 

1 E.1.17. Ohsako et al. (2001) 

Administered Dose (ng/kg-day) 

0 12.5 a 50 b 200 800 

Internal Dose (ng/kg blood) c

0 845 2,763 9,022 30,504 

Endpoint (n = 12) (n = 10) (n = 10) (n = 10) (n = 12) 

Anogenital PND120 

28.91 ± 

3.54 

28.08 ± 

2.52 

25.31 ± 

3.59 d

26.07 ± 

3.59 e

23.87 ± 

2.36 d

a NOAEL for selected endpoint. 

b LOAEL for selected endpoint. 

c From the Emond PRPK model described in 3.3. 

d Statistically significant as compared to control (p < 0.01). e Statistically significant as compared to control (p < 0.05). 

2 

3 

4 E.1.18. Schantz et al. (1996) 

Administered Dose (ng/kg-day) 

0 25 100 

Internal Dose (ng/kg blood) a

0 6,800 24,522 

Endpoint (n = 10) (n = 10) (n = 10) 

Maze errors per block 3.55 ± 0.64 2.76 ± 0.81 b 2.34 ± 0.81 c

a From the Emond PRPK model described in 3.3. 

b Statistically significant as compared to control (p < 0.05). c Statistically significant as compared to control (p < 0.001). 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-11 —DO NOT CITE OR QUOTE 

1 E.1.19. Shi et al. (2007) 

Administered Dose (ng/kg-day) 

0 0.143 a 0.714 b 7.14 28.6 

Internal Dose (ng/kg blood) c

0 188 592 2,882 7,665 

Endpoint (n = 10) (n = 10) (n = 10) (n = 10) (n = 10) 

Serum estradiol 

102.86 ± 

41.41 

86.19 ± 

19.58 

63.33 ± 

29.36 d

48.1 ± 

18.82 d

38.57 ± 

22.59 d

a NOAEL. 

b LOAEL. 

c From the Emond PRPK model described in 3.3. 

d Statistically significant as compared to control (p < 0.05). 

2 

3 

4 E.1.20. Smialowicz et al. (2008) 

Administered Dose (ng/kg-day) 

0 1.07 a 10.7 107 321 

Internal Dose (ng/kg blood) b

0 241 1,358 7,385 17,438 

Endpoint (n = 15) (n = 14) (n = 15) (n = 15) (n = 8) 

PFC per 106 Cells 1491 ± 716 1129±171c 945 ± 516 c 677 ± 465 c 161 ± 117 c

PFC per spleen 27.8 ± 13.4 21 ± 13.6 c 17.6 ± 9.4 c 12.6 ± 8.7 c 3 ± 3.1 c

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-12 —DO NOT CITE OR QUOTE 

1 E.1.21. Toth et al. (1979) 

Administered Dose (ng/kg-day) 

0 1 a 100 1,000 

Internal Dose (ng/kg blood) b

0 316 7,814 50,105 

Endpoint (n =38) (n = 44) (n = 44) (n = 43) 

Amyloidosis 0/38 (0%) 5/44 (11%) 10/44 (23%) 17/43 (40%)

Skin Lesions 0/38 (0%) 5/44 (11%) 13/44 (30%) 25/43 (58%)

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

2 

3 

4 E.1.22. Van Birgelen et al. (1995) 

Administered Dose (ng/kg-day) 

0 14 a 26 47 320 1,024 

Internal Dose (ng/kg blood) b

0 3,969 6,479 9,968 47,606 137,820 

Endpoint n = 8 n = 8 n = 8 n = 8 n = 8 n = 8 

Hepatic retinol 14.9 ± 8.77 8.4 ± 3.39 c 8.2 ± 2.26 c 5.1 ± 0.85 c 2.2 ± 0.85 c 0.6 ± 0.57 c

Hepatic retinol palmitate 472 ± 

271.53 94 ± 67.88 c 107 ± 76.37 c 74 ± 39.6 c 22 ± 22.63 c 3 ± 2.83 c

Plasma FT4 23.4 ± 3.11 24.5 ± 5.66 22.4 ± 2.83 19.3 ± 9.33 16.3 ± 4.24 c 10.3 ± 4.81 c

Plasma TT4 40.9 ± 6.79 41.4 ± 5.37 41.4 ± 6.51 32.3 ± 7.35 c 33.6 ± 6.22 c 25.5 ± 7.64 c

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-13 —DO NOT CITE OR QUOTE 

1 E.1.23. White et al. (1986) 

Administered Dose (ng/kg-day) 

0 10 a 50 100 500 1,000 2,000 

Internal Dose (ng/kg blood) b

0 602 2,250 3,934 14,772 26,844 49,896 

Endpoint (n = 8) (n = 8) (n = 8) (n = 8) (n = 8) (n = 8) (n = 8) 

CH50 91 ± 14.14 54 ± 8.5 c 63 ± 11c 56 ± 26 c 41 ± 17 c 32 ± 17 c 17 ± 17 c

a LOAEL. 

b From the Emond PRPK model described in 3.3. 

c Statistically significant as compared to control (p < 0.05). 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-14 —DO NOT CITE OR QUOTE 

1 E.2. ALTERNATE DOSE: BLOOD SERUM BMDS RESULTS 

2 E.2.1. Amin et al. (2000): Saccharin Consumed, Female (0.25%) 

3 E.2.1.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

freedom 

Variance 

p-value a

χ

 2 Test 

statistic

χ 2pvalue

b

AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

Linear c 1 0.00 0.35 0.55 179.21 7.2E+03 4.8E+03 nonconstant 

variance 

Polynomial 1 0.00 0.35 0.55 179.21 7.2E+03 4.8E+03 nonconstant 

variance 

Power 1 0.00 0.35 0.55 179.21 7.2E+03 4.8E+03 nonconstant 

variance, power 

restricted ≥1, 

bound hit 

Power d 0 0.00 0.00 NA 180.86 6.6E+03 2.7E+03 nonconstant 

variance, power 

unrestricted 

Linear 1 0.00 0.00 0.95 191.69 5.3E+03 3.5E+03 constant variance 

Polynomial 1 0.00 0.00 0.95 191.69 5.3E+03 3.5E+03 constant variance 

Power 1 0.00 0.00 0.95 191.69 5.3E+03 3.5E+03 constant variance, 

power restricted 

≥1, bound hit 

Power 0 0.00 0.00 NA 193.68 5.2E+03 1.3E+03 constant variance, 

power 

unrestricted 

4 a 5 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a 

6 constant variance model should be selected. 

b 7 Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

c 8 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix. 

d 9 Alternate model also presented in this appendix. 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-15 —DO NOT CITE OR QUOTE 

1 E.2.1.2. Figure for Selected Model: Linear, Nonconstant Variance 

 5

 10

 15

 20

 25

 30

 35

 40

 45

 50

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:42 11/16 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.2.1.3. Output File for Selected Model: Linear, Nonconstant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_25_s_c.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_25_s_c.plt 

12 Mon Nov 16 13:42:20 2009 

13 ==================================================================== 

14 

15 Rel Male Thymus wt, Tbl 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Signs of the polynomial coefficients are not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 3 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 5.29482 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-16 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 beta_0 = 31.5152 

3 beta_1 = -0.0025051 

4 

5 

6 Asymptotic Correlation Matrix of Parameter Estimates 

7 

8 lalpha rho beta_0 beta_1 

9 

10 lalpha 1 -0.99 -0.029 0.044 

11 

12 rho -0.99 1 0.026 -0.04 

13 

14 beta_0 -0.029 0.026 1 -0.94 

15 

16 beta_1 0.044 -0.04 -0.94 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 lalpha -2.542 1.65042 -5.77677 0.692762 

25 rho 2.40977 0.541752 1.34795 3.47158 

26 beta_0 31.2702 4.19399 23.0501 39.4903 

27 beta_1 -0.00246009 0.000552567 -0.0035431 -0.00137708 

28 

29 

30 

31 Table of Data and Estimated Values of Interest 

32 

33 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

34 ------ --- -------- -------- ----------- ----------- ---------- 

35 

36 0 10 31.7 31.3 20.6 17.8 0.0717 

37 2670 10 24.6 24.7 12 13.4 -0.0253 

38 8341 10 10.7 10.8 5.33 4.91 -0.0363 

39 

40 

41 

42 Model Descriptions for likelihoods calculated 

43 

44 

45 Model A1: Yij = Mu(i) + e(ij) 

46 Var{e(ij)} = Sigma^2 

47 

48 Model A2: Yij = Mu(i) + e(ij) 

49 Var{e(ij)} = Sigma(i)^2 

50 

51 Model A3: Yij = Mu(i) + e(ij) 

52 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

53 Model A3 uses any fixed variance parameters that 

54 were specified by the user 

55 

56 Model R: Yi = Mu + e(i) 

57 Var{e(i)} = Sigma^2 

58 

59 

60 Likelihoods of Interest 

61 

62 Model Log(likelihood) # Param's AIC 

63 A1 -92.841935 4 193.683870 

64 A2 -85.255316 6 182.510632 

65 A3 -85.429148 5 180.858295 

66 fitted -85.605740 4 179.211479 

67 R -98.136607 2 200.273213 

68 

69 

70 Explanation of Tests 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-17 —DO NOT CITE OR QUOTE 

1 

2 Test 1: Do responses and/or variances differ among Dose levels? 

3 (A2 vs. R) 

4 Test 2: Are Variances Homogeneous? (A1 vs A2) 

5 Test 3: Are variances adequately modeled? (A2 vs. A3) 

6 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

7 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

8 

9 Tests of Interest 

10 

11 Test -2*log(Likelihood Ratio) Test df p-value 

12 

13 Test 1 25.7626 4 <.0001 

14 Test 2 15.1732 2 0.0005072 

15 Test 3 0.347663 1 0.5554 

16 Test 4 0.353184 1 0.5523 

17 

18 The p-value for Test 1 is less than .05. There appears to be a 

19 difference between response and/or variances among the dose levels 

20 It seems appropriate to model the data 

21 

22 The p-value for Test 2 is less than .1. A non-homogeneous variance 

23 model appears to be appropriate 

24 

25 The p-value for Test 3 is greater than .1. The modeled variance appears 

26 to be appropriate here 

27 

28 The p-value for Test 4 is greater than .1. The model chosen seems 

29 to adequately describe the data 

30 

31 

32 Benchmark Dose Computation 

33 

34 Specified effect = 1 

35 

36 Risk Type = Estimated standard deviations from the control mean 

37 

38 Confidence level = 0.95 

39 

40 BMD = 7219.69 

41 

42 

43 BMDL = 4809.97 

44 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-18 —DO NOT CITE OR QUOTE 

1 E.2.1.4. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 5

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 25

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 35

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 45

 50

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:42 11/16 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.2.1.5. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_25_s_c.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_25_s_c.plt 

13 Mon Nov 16 13:42:20 2009 

14 ==================================================================== 

15 

16 Rel Male Thymus wt, Tbl 2 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 3 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-19 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 5.29482 

3 rho = 0 

4 control = 31.6727 

5 slope = -0.00381519 

6 power = 0.953851 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho control slope power 

12 

13 lalpha 1 -0.99 0.34 -0.095 -0.061 

14 

15 rho -0.99 1 -0.42 0.11 0.068 

16 

17 control 0.34 -0.42 1 -0.61 -0.56 

18 

19 slope -0.095 0.11 -0.61 1 1 

20 

21 power -0.061 0.068 -0.56 1 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha -2.48291 2.08669 -6.57274 1.60692 

30 rho 2.38455 0.692047 1.02817 3.74094 

31 control 32.99 5.40753 22.3915 43.5886 

32 slope -0.0286289 0.0946744 -0.214187 0.156929 

33 power 0.736753 0.351085 0.0486403 1.42487 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 10 31.7 33 20.6 18.7 -0.223 

43 2670 10 24.6 23.4 12 12.4 0.302 

44 8341 10 10.7 10.8 5.33 4.94 -0.08 

45 

46 Warning: Likelihood for fitted model larger than the Likelihood for model A3. 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-20 —DO NOT CITE OR QUOTE 

1 A1 -92.841935 4 193.683870 

2 A2 -85.255316 6 182.510632 

3 A3 -85.429148 5 180.858295 

4 fitted -85.429148 5 180.858295 

5 R -98.136607 2 200.273213 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 25.7626 4 <.0001 

22 Test 2 15.1732 2 0.0005072 

23 Test 3 0.347663 1 0.5554 

24 Test 4 -8.2423e-013 0 NA 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is less than .1. A non-homogeneous variance 

31 model appears to be appropriate 

32 

33 The p-value for Test 3 is greater than .1. The modeled variance appears 

34 to be appropriate here 

35 

36 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

37 test for fit is not valid 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 6606.37 

49 

50 

51 BMDL = 2702.55 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-21 —DO NOT CITE OR QUOTE 

1 E.2.2. Amin et al. (2000): Saccharin Consumed, Female (0.50%) 

2 E.2.2.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic

χ

 2

pValue

b

AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

linear c 1 <.0001 3.52 0.06 158.58 8.0E+03 5.2E+03 nonconstant 

variance 

polynomial 1 <.0001 3.52 0.06 158.58 8.0E+03 5.2E+03 nonconstant 

variance 

power 1 <.0001 3.52 0.06 158.58 8.0E+03 5.2E+03 nonconstant 

variance, power 

restricted ≥1, 

bound hit 

power d 0 <.0001 0.00 NA 157.06 5.2E+03 9.1E+02 nonconstant 

variance, power 

unrestricted 

3 a 4 Values <0.1 means nonconstant variance model should be selected; values ≥0.1 means a 

5 constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 6 c 7 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d 8 Alternate model also presented in this appendix 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-22 —DO NOT CITE OR QUOTE 

1 E.2.2.2. Figure for Selected Model: Linear, Nonconstant Variance 

 0

 5

 10

 15

 20

 25

 30

 35

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:41 11/16 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.2.2.3. Output File for Selected Model: Linear, Nonconstant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_50_s_c.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_50_s_c.plt 

12 Mon Nov 16 13:41:55 2009 

13 ==================================================================== 

14 

15 Rel Male Thymus wt, Tbl 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Signs of the polynomial coefficients are not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 3 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 4.68512 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-23 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 beta_0 = 20.0674 

3 beta_1 = -0.00199124 

4 

5 

6 Asymptotic Correlation Matrix of Parameter Estimates 

7 

8 lalpha rho beta_0 beta_1 

9 

10 lalpha 1 -0.96 0.019 -0.0016 

11 

12 rho -0.96 1 -0.031 0.015 

13 

14 beta_0 0.019 -0.031 1 -0.96 

15 

16 beta_1 -0.0016 0.015 -0.96 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 lalpha -0.981979 0.982197 -2.90705 0.943092 

25 rho 2.11795 0.401142 1.33173 2.90417 

26 beta_0 18.6205 3.17872 12.3903 24.8507 

27 beta_1 -0.00168815 0.000408035 -0.00248788 -0.000888416 

28 

29 

30 

31 Table of Data and Estimated Values of Interest 

32 

33 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

34 ------ --- -------- -------- ----------- ----------- ---------- 

35 

36 0 10 22.4 18.6 16 13.5 0.872 

37 2670 10 11.4 14.1 7.66 10.1 -0.855 

38 8341 10 4.54 4.54 3.33 3.04 -0.00339 

39 

40 

41 

42 Model Descriptions for likelihoods calculated 

43 

44 

45 Model A1: Yij = Mu(i) + e(ij) 

46 Var{e(ij)} = Sigma^2 

47 

48 Model A2: Yij = Mu(i) + e(ij) 

49 Var{e(ij)} = Sigma(i)^2 

50 

51 Model A3: Yij = Mu(i) + e(ij) 

52 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

53 Model A3 uses any fixed variance parameters that 

54 were specified by the user 

55 

56 Model R: Yi = Mu + e(i) 

57 Var{e(i)} = Sigma^2 

58 

59 

60 Likelihoods of Interest 

61 

62 Model Log(likelihood) # Param's AIC 

63 A1 -83.696404 4 175.392808 

64 A2 -73.511830 6 159.023660 

65 A3 -73.530233 5 157.060467 

66 fitted -75.291848 4 158.583695 

67 R -90.294746 2 184.589492 

68 

69 

70 Explanation of Tests 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-24 —DO NOT CITE OR QUOTE 

1 

2 Test 1: Do responses and/or variances differ among Dose levels? 

3 (A2 vs. R) 

4 Test 2: Are Variances Homogeneous? (A1 vs A2) 

5 Test 3: Are variances adequately modeled? (A2 vs. A3) 

6 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

7 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

8 

9 Tests of Interest 

10 

11 Test -2*log(Likelihood Ratio) Test df p-value 

12 

13 Test 1 33.5658 4 <.0001 

14 Test 2 20.3691 2 <.0001 

15 Test 3 0.0368066 1 0.8479 

16 Test 4 3.52323 1 0.06051 

17 

18 The p-value for Test 1 is less than .05. There appears to be a 

19 difference between response and/or variances among the dose levels 

20 It seems appropriate to model the data 

21 

22 The p-value for Test 2 is less than .1. A non-homogeneous variance 

23 model appears to be appropriate 

24 

25 The p-value for Test 3 is greater than .1. The modeled variance appears 

26 to be appropriate here 

27 

28 The p-value for Test 4 is less than .1. You may want to try a different 

29 model 

30 

31 

32 Benchmark Dose Computation 

33 

34 Specified effect = 1 

35 

36 Risk Type = Estimated standard deviations from the control mean 

37 

38 Confidence level = 0.95 

39 

40 BMD = 8021.29 

41 

42 

43 BMDL = 5183.12 

44 

45 

46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-25 —DO NOT CITE OR QUOTE 

1 E.2.2.4. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 5

 10

 15

 20

 25

 30

 35

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:41 11/16 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.2.2.5. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_50_s_c.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_50_s_c.plt 

13 Mon Nov 16 13:41:56 2009 

14 ==================================================================== 

15 

16 Rel Male Thymus wt, Tbl 2 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 3 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-26 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 4.68512 

3 rho = 0 

4 control = 22.3564 

5 slope = -0.381559 

6 power = 0.42572 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho control slope power 

12 

13 lalpha 1 -0.96 0.34 -0.2 -0.15 

14 

15 rho -0.96 1 -0.47 0.23 0.15 

16 

17 control 0.34 -0.47 1 -0.63 -0.52 

18 

19 slope -0.2 0.23 -0.63 1 0.99 

20 

21 power -0.15 0.15 -0.52 0.99 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha -0.708629 1.298 -3.25267 1.83541 

30 rho 1.96142 0.529653 0.923323 2.99953 

31 control 22.6293 4.48415 13.8405 31.4181 

32 slope -0.50513 0.841243 -2.15394 1.14368 

33 power 0.396043 0.168878 0.0650481 0.727037 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 10 22.4 22.6 16 15 -0.0577 

43 2670 10 11.4 11.1 7.66 7.46 0.105 

44 8341 10 4.54 4.58 3.33 3.12 -0.0475 

45 

46 Degrees of freedom for Test A3 vs fitted <= 0 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-27 —DO NOT CITE OR QUOTE 

1 A1 -83.696404 4 175.392808 

2 A2 -73.511830 6 159.023660 

3 A3 -73.530233 5 157.060467 

4 fitted -73.530233 5 157.060467 

5 R -90.294746 2 184.589492 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 33.5658 4 <.0001 

22 Test 2 20.3691 2 <.0001 

23 Test 3 0.0368066 1 0.8479 

24 Test 4 0 0 NA 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is less than .1. A non-homogeneous variance 

31 model appears to be appropriate 

32 

33 The p-value for Test 3 is greater than .1. The modeled variance appears 

34 to be appropriate here 

35 

36 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

37 test for fit is not valid 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 5186.92 

49 

50 

51 BMDL = 913.947 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-28 —DO NOT CITE OR QUOTE 

1 E.2.3. Amin et al. (2000): Saccharin Preference Ratio, Female (0.25%) 

2 E.2.3.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

linear c 1 0.01 9.51 0.00 227.81 9.2E+03 4.4E+03 nonconstant 

variance 

polynomial 1 0.01 9.51 0.00 227.81 9.2E+03 4.4E+03 nonconstant 

variance 

power 1 0.01 9.51 0.00 227.81 9.2E+03 4.4E+03 nonconstant 

variance, power 

restricted ≥1, 

bound hit 

power d 1 0.01 1.22 0.27 219.52 8.3E+05 error nonconstant 

variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant 

variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

3 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-29 —DO NOT CITE OR QUOTE 

1 E.2.3.2. Figure for Selected Model: Linear, Nonconstant Variance 

 30

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 60

 70

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 90

 0 2000 4000 6000 8000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:41 11/16 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.2.3.3. Output File for Selected Model: Linear, Nonconstant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_25_s_p_f.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_25_s_p_f.plt 

12 Mon Nov 16 13:41:29 2009 

13 ==================================================================== 

14 

15 Rel Male Thymus wt Tbl 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Signs of the polynomial coefficients are not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 3 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 6.34368 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-30 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 beta_0 = 75.4969 

3 beta_1 = -0.00284822 

4 

5 

6 Asymptotic Correlation Matrix of Parameter Estimates 

7 

8 lalpha rho beta_0 beta_1 

9 

10 lalpha 1 -1 0.22 -0.31 

11 

12 rho -1 1 -0.22 0.31 

13 

14 beta_0 0.22 -0.22 1 -0.77 

15 

16 beta_1 -0.31 0.31 -0.77 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 lalpha 3.02282 9.21151 -15.0314 21.077 

25 rho 0.793523 2.21122 -3.54039 5.12744 

26 beta_0 75.1183 6.74307 61.9021 88.3345 

27 beta_1 -0.00274398 0.00127757 -0.00524797 -0.000239995 

28 

29 

30 

31 Table of Data and Estimated Values of Interest 

32 

33 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

34 ------ --- -------- -------- ----------- ----------- ---------- 

35 

36 0 10 82.1 75.1 13.3 25.2 0.883 

37 2670 10 58.1 67.8 33.9 24.2 -1.27 

38 8341 10 54.9 52.2 19.5 21.8 0.383 

39 

40 

41 

42 Model Descriptions for likelihoods calculated 

43 

44 

45 Model A1: Yij = Mu(i) + e(ij) 

46 Var{e(ij)} = Sigma^2 

47 

48 Model A2: Yij = Mu(i) + e(ij) 

49 Var{e(ij)} = Sigma(i)^2 

50 

51 Model A3: Yij = Mu(i) + e(ij) 

52 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

53 Model A3 uses any fixed variance parameters that 

54 were specified by the user 

55 

56 Model R: Yi = Mu + e(i) 

57 Var{e(i)} = Sigma^2 

58 

59 

60 Likelihoods of Interest 

61 

62 Model Log(likelihood) # Param's AIC 

63 A1 -108.574798 4 225.149597 

64 A2 -104.269377 6 220.538754 

65 A3 -105.147952 5 220.295903 

66 fitted -109.902600 4 227.805201 

67 R -112.382522 2 228.765045 

68 

69 

70 Explanation of Tests 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-31 —DO NOT CITE OR QUOTE 

1 

2 Test 1: Do responses and/or variances differ among Dose levels? 

3 (A2 vs. R) 

4 Test 2: Are Variances Homogeneous? (A1 vs A2) 

5 Test 3: Are variances adequately modeled? (A2 vs. A3) 

6 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

7 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

8 

9 Tests of Interest 

10 

11 Test -2*log(Likelihood Ratio) Test df p-value 

12 

13 Test 1 16.2263 4 0.00273 

14 Test 2 8.61084 2 0.0135 

15 Test 3 1.75715 1 0.185 

16 Test 4 9.5093 1 0.002044 

17 

18 The p-value for Test 1 is less than .05. There appears to be a 

19 difference between response and/or variances among the dose levels 

20 It seems appropriate to model the data 

21 

22 The p-value for Test 2 is less than .1. A non-homogeneous variance 

23 model appears to be appropriate 

24 

25 The p-value for Test 3 is greater than .1. The modeled variance appears 

26 to be appropriate here 

27 

28 The p-value for Test 4 is less than .1. You may want to try a different 

29 model 

30 

31 

32 Benchmark Dose Computation 

33 

34 Specified effect = 1 

35 

36 Risk Type = Estimated standard deviations from the control mean 

37 

38 Confidence level = 0.95 

39 

40 BMD = 9167.26 

41 

42 

43 BMDL = 4394.21 

44 

45 

46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-32 —DO NOT CITE OR QUOTE 

1 E.2.3.4. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 30

 40

 50

 60

 70

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 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model

13:41 11/16 2009

Power

2 

3 

4 

5 E.2.3.5. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_25_s_p_f.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_25_s_p_f.plt 

13 Mon Nov 16 13:41:30 2009 

14 ==================================================================== 

15 

16 Rel Male Thymus wt Tbl 2 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 3 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-33 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 6.34368 

3 rho = 0 

4 control = 82.1429 

5 slope = -9.98589 

6 power = 0.111278 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 ( *** The model parameter(s) -power 

12 have been estimated at a boundary point, or have been specified by the user, 

13 and do not appear in the correlation matrix ) 

14 

15 lalpha rho control slope 

16 

17 lalpha 1 -1 -0.26 0.64 

18 

19 rho -1 1 0.27 -0.63 

20 

21 control -0.26 0.27 1 -0.56 

22 

23 slope 0.64 -0.63 -0.56 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 95.0% Wald Confidence Interval 

30 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

31 lalpha 22.273 8.00764 6.57832 37.9677 

32 rho -3.90063 1.89036 -7.60567 -0.195596 

33 control 82.1429 4.00411 74.295 89.9908 

34 slope -25.6494 7.11029 -39.5853 -11.7135 

35 power 0 NA 

36 

37 NA - Indicates that this parameter has hit a bound 

38 implied by some inequality constraint and thus 

39 has no standard error. 

40 

41 

42 

43 Table of Data and Estimated Values of Interest 

44 

45 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

46 ------ --- -------- -------- ----------- ----------- ---------- 

47 

48 0 10 82.1 56.5 13.3 26.3 3.09 

49 2670 10 58.1 56.5 33.9 26.3 0.195 

50 8341 10 54.9 56.5 19.5 26.3 -0.195 

51 

52 

53 

54 Model Descriptions for likelihoods calculated 

55 

56 

57 Model A1: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 

60 Model A2: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma(i)^2 

62 

63 Model A3: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

65 Model A3 uses any fixed variance parameters that 

66 were specified by the user 

67 

68 Model R: Yi = Mu + e(i) 

69 Var{e(i)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-34 —DO NOT CITE OR QUOTE 

1 

2 Likelihoods of Interest 

3 

4 Model Log(likelihood) # Param's AIC 

5 A1 -108.574798 4 225.149597 

6 A2 -104.269377 6 220.538754 

7 A3 -105.147952 5 220.295903 

8 fitted -105.759821 4 219.519641 

9 R -112.382522 2 228.765045 

10 

11 

12 Explanation of Tests 

13 

14 Test 1: Do responses and/or variances differ among Dose levels? 

15 (A2 vs. R) 

16 Test 2: Are Variances Homogeneous? (A1 vs A2) 

17 Test 3: Are variances adequately modeled? (A2 vs. A3) 

18 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

19 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

20 

21 Tests of Interest 

22 

23 Test -2*log(Likelihood Ratio) Test df p-value 

24 

25 Test 1 16.2263 4 0.00273 

26 Test 2 8.61084 2 0.0135 

27 Test 3 1.75715 1 0.185 

28 Test 4 1.22374 1 0.2686 

29 

30 The p-value for Test 1 is less than .05. There appears to be a 

31 difference between response and/or variances among the dose levels 

32 It seems appropriate to model the data 

33 

34 The p-value for Test 2 is less than .1. A non-homogeneous variance 

35 model appears to be appropriate 

36 

37 The p-value for Test 3 is greater than .1. The modeled variance appears 

38 to be appropriate here 

39 

40 The p-value for Test 4 is greater than .1. The model chosen seems 

41 to adequately describe the data 

42 

43 Since the power was estimated to be 0, the BMD is infinite. 

44 Setting BMD = 100*(maximum dose). 

45 

46 Benchmark Dose Computation 

47 

48 Specified effect = 1 

49 

50 Risk Type = Estimated standard deviations from the control mean 

51 

52 Confidence level = 0.95 

53 

54 BMD = 834064 

55 

56 Warning: optimum may not have been found. Bad completion code in Optimization routine. 

57 

58 BMDL computation failed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-35 —DO NOT CITE OR QUOTE 

1 E.2.4. Amin et al. (2000): Saccharin Preference Ratio, Female (0.50%) 

2 E.2.4.1. Summary Table of BMDS Modeling Results 

Saccharin preference ratio, female (0.50%) (Amin et al., 2000) 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

linear c 1 0.56 2.23 0.14 234.25 6.4E+03 4.0E+03 constant variance 

polynomial 1 0.56 2.23 0.14 234.25 6.4E+03 4.0E+03 constant variance 

power 1 0.56 2.23 0.14 234.25 6.4E+03 4.0E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power d 0 0.56 0.00 NA 234.02 2.1E+03 1.3E-05 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

3 

4 

5 

6 E.2.4.2. Figure for Selected Model: Linear, Constant Variance 

 10

 20

 30

 40

 50

 60

 70

 80

 90

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:41 11/16 2009

BMDL BMD

 

Linear

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-36 —DO NOT CITE OR QUOTE 

1 E.2.4.3. Output File for Selected Model: Linear, Constant Variance 

2 

3 

4 ==================================================================== 

5 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\Blood\LinearCV_BMR1_50_s_p_f.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\LinearCV_BMR1_50_s_p_f.plt 

8 Mon Nov 16 13:41:03 2009 

9 ==================================================================== 

10 

11 Rel Male Thymus wt, Tbl 2 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 rho is set to 0 

22 Signs of the polynomial coefficients are not restricted 

23 A constant variance model is fit 

24 

25 Total number of dose groups = 3 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 

32 

33 Default Initial Parameter Values 

34 alpha = 764.602 

35 rho = 0 Specified 

36 beta_0 = 65.8731 

37 beta_1 = -0.00423638 

38 

39 

40 Asymptotic Correlation Matrix of Parameter Estimates 

41 

42 ( *** The model parameter(s) -rho 

43 have been estimated at a boundary point, or have been specified by the user, 

44 and do not appear in the correlation matrix ) 

45 

46 alpha beta_0 beta_1 

47 

48 alpha 1 -4.3e-009 -3.4e-010 

49 

50 beta_0 -4.3e-009 1 -0.73 

51 

52 beta_1 -3.4e-010 -0.73 1 

53 

54 

55 

56 Parameter Estimates 

57 

58 95.0% Wald Confidence Interval 

59 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

60 alpha 741.152 191.365 366.084 1116.22 

61 beta_0 65.8731 7.22637 51.7096 80.0365 

62 beta_1 -0.00423638 0.00142921 -0.00703759 -0.00143517 

63 

64 

65 

66 Table of Data and Estimated Values of Interest 

67 

68 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

69 ------ --- -------- -------- ----------- ----------- ---------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-37 —DO NOT CITE OR QUOTE 

1 

2 0 10 72.7 65.9 24.6 27.2 0.796 

3 2670 10 44.5 54.6 32.9 27.2 -1.17 

4 8341 10 33.8 30.5 24.6 27.2 0.375 

5 

6 

7 

8 Model Descriptions for likelihoods calculated 

9 

10 

11 Model A1: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma^2 

13 

14 Model A2: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma(i)^2 

16 

17 Model A3: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma^2 

19 Model A3 uses any fixed variance parameters that 

20 were specified by the user 

21 

22 Model R: Yi = Mu + e(i) 

23 Var{e(i)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) # Param's AIC 

29 A1 -113.009921 4 234.019841 

30 A2 -112.428886 6 236.857773 

31 A3 -113.009921 4 234.019841 

32 fitted -114.123097 3 234.246193 

33 R -117.976057 2 239.952114 

34 

35 

36 Explanation of Tests 

37 

38 Test 1: Do responses and/or variances differ among Dose levels? 

39 (A2 vs. R) 

40 Test 2: Are Variances Homogeneous? (A1 vs A2) 

41 Test 3: Are variances adequately modeled? (A2 vs. A3) 

42 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

43 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

44 

45 Tests of Interest 

46 

47 Test -2*log(Likelihood Ratio) Test df p-value 

48 

49 Test 1 11.0943 4 0.02552 

50 Test 2 1.16207 2 0.5593 

51 Test 3 1.16207 2 0.5593 

52 Test 4 2.22635 1 0.1357 

53 

54 The p-value for Test 1 is less than .05. There appears to be a 

55 difference between response and/or variances among the dose levels 

56 It seems appropriate to model the data 

57 

58 The p-value for Test 2 is greater than .1. A homogeneous variance 

59 model appears to be appropriate here 

60 

61 

62 The p-value for Test 3 is greater than .1. The modeled variance appears 

63 to be appropriate here 

64 

65 The p-value for Test 4 is greater than .1. The model chosen seems 

66 to adequately describe the data 

67 

68 

69 Benchmark Dose Computation 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-38 —DO NOT CITE OR QUOTE 

1 Specified effect = 1 

2 

3 Risk Type = Estimated standard deviations from the control mean 

4 

5 Confidence level = 0.95 

6 

7 BMD = 6426.26 

8 

9 

10 BMDL = 4028.71 

11 

12 

13 

14 E.2.4.4. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 10

 20

 30

 40

 50

 60

 70

 80

 90

 100

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:41 11/16 2009

BMDL BMD

 

Power

15 

16 

17 

18 E.2.4.5. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

19 

20 

21 ==================================================================== 

22 Power Model. (Version: 2.15; Date: 04/07/2008) 

23 Input Data File: C:\USEPA\BMDS21\AD\Blood\PwrCV_Unrest_BMR1_50_s_p_f.(d) 

24 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\PwrCV_Unrest_BMR1_50_s_p_f.plt 

25 Mon Nov 16 13:41:04 2009 

26 ==================================================================== 

27 

28 Rel Male Thymus wt, Tbl 2 

29 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

30 

31 The form of the response function is: 

32 

33 Y[dose] = control + slope * dose^power 

34 

35 

36 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-39 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 rho is set to 0 

3 The power is not restricted 

4 A constant variance model is fit 

5 

6 Total number of dose groups = 3 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 

13 

14 Default Initial Parameter Values 

15 alpha = 764.602 

16 rho = 0 Specified 

17 control = 72.7273 

18 slope = -3.04504 

19 power = 0.282321 

20 

21 

22 Asymptotic Correlation Matrix of Parameter Estimates 

23 

24 ( *** The model parameter(s) -rho 

25 have been estimated at a boundary point, or have been specified by the user, 

26 and do not appear in the correlation matrix ) 

27 

28 alpha control slope power 

29 

30 alpha 1 -2.2e-008 3.9e-009 1.5e-009 

31 

32 control -2.2e-008 1 -0.3 -0.22 

33 

34 slope 3.9e-009 -0.3 1 0.99 

35 

36 power 1.5e-009 -0.22 0.99 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 95.0% Wald Confidence Interval 

43 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

44 alpha 688.142 177.677 339.9 1036.38 

45 control 72.7273 8.29543 56.4686 88.986 

46 slope -3.04504 8.78405 -20.2615 14.1714 

47 power 0.282321 0.326249 -0.357114 0.921757 

48 

49 

50 

51 Table of Data and Estimated Values of Interest 

52 

53 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

54 ------ --- -------- -------- ----------- ----------- ---------- 

55 

56 0 10 72.7 72.7 24.6 26.2 8.48e-008 

57 2670 10 44.5 44.5 32.9 26.2 -1.25e-008 

58 8341 10 33.8 33.8 24.6 26.2 -3.93e-008 

59 

60 Degrees of freedom for Test A3 vs fitted <= 0 

61 

62 

63 

64 Model Descriptions for likelihoods calculated 

65 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-40 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = Sigma^2 

5 Model A3 uses any fixed variance parameters that 

6 were specified by the user 

7 

8 Model R: Yi = Mu + e(i) 

9 Var{e(i)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) # Param's AIC 

15 A1 -113.009921 4 234.019841 

16 A2 -112.428886 6 236.857773 

17 A3 -113.009921 4 234.019841 

18 fitted -113.009921 4 234.019841 

19 R -117.976057 2 239.952114 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Do responses and/or variances differ among Dose levels? 

25 (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A1 vs A2) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

29 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) Test df p-value 

34 

35 Test 1 11.0943 4 0.02552 

36 Test 2 1.16207 2 0.5593 

37 Test 3 1.16207 2 0.5593 

38 Test 4 0 0 NA 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose levels 

42 It seems appropriate to model the data 

43 

44 The p-value for Test 2 is greater than .1. A homogeneous variance 

45 model appears to be appropriate here 

46 

47 

48 The p-value for Test 3 is greater than .1. The modeled variance appears 

49 to be appropriate here 

50 

51 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

52 test for fit is not valid 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 1 

58 

59 Risk Type = Estimated standard deviations from the control mean 

60 

61 Confidence level = 0.95 

62 

63 BMD = 2054.47 

64 

65 

66 BMDL = 1.26421e-005 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-41 —DO NOT CITE OR QUOTE 

1 

2 E.2.5. Bell et al. (2007): Balano-Preputial Separation in Male Pups (10% extra risk) 

3 E.2.5.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Value a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 2 0.69 0.71 112.07 2.5E+03 1.7E+03 power restricted ≥1, bound 

hit 

logistic 2 2.10 0.35 113.86 5.3E+03 4.1E+03 

log-logistic b 2 0.47 0.79 111.88 2.0E+03 1.2E+03 slope restricted ≥1, 

bound hit 

log-logistic c 1 0.44 0.51 113.86 1806 264.4 slope unrestricted 

log-probit 1 0.54 0.46 113.96 1.8E+03 3.1E+02 slope restricted ≥1 

multistage, 1-

degree 2 0.69 0.71 112.07 2.5E+03 1.7E+03 betas restricted ≥0, bound hit 

probit 2 1.96 0.38 113.65 5.0E+03 3.8E+03 

Weibull 2 0.69 0.71 112.07 2.5E+03 1.7E+03 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-42 —DO NOT CITE OR QUOTE 

1 E.2.5.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:35 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.5.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_BMR2_BPS_d49.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_BMR2_BPS_d49.plt 

12 Sun Nov 29 11:35:46 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is restricted as slope >= 1 

26 

27 Total number of observations = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-43 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0333333 

3 intercept = -9.77382 

4 slope = 1 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -slope 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 background intercept 

14 

15 background 1 -0.48 

16 

17 intercept -0.48 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 background 0.0371259 * * * 

26 intercept -9.77952 * * * 

27 slope 1 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -53.7077 4 

37 Fitted model -53.9377 2 0.460052 2 0.7945 

38 Reduced model -63.9797 1 20.544 3 0.0001309 

39 

40 AIC: 111.875 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0371 1.114 1.000 30 -0.110 

48 1997.8780 0.1349 4.048 5.000 30 0.509 

49 4539.2839 0.2339 7.018 6.000 30 -0.439 

50 15952.0000 0.4940 14.820 15.000 30 0.066 

51 

52 Chi^2 = 0.47 d.f. = 2 P-value = 0.7914 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.1 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 1963.13 

64 

65 BMDL = 1223.41 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-44 —DO NOT CITE OR QUOTE 

1 E.2.5.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:35 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.5.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_Unrest_BMR2_BPS_d49.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_Unrest_BMR2_BPS_d49.plt 

12 Sun Nov 29 11:35:48 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is not restricted 

26 

27 Total number of observations = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-45 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0333333 

3 intercept = -8.67441 

4 slope = 0.877628 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 background intercept slope 

10 

11 background 1 -0.38 0.34 

12 

13 intercept -0.38 1 -1 

14 

15 slope 0.34 -1 1 

16 

17 

18 

19 Parameter Estimates 

20 

21 95.0% Wald Confidence Interval 

22 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

23 background 0.0352883 * * * 

24 intercept -9.31114 * * * 

25 slope 0.948644 * * * 

26 

27 * - Indicates that this value is not calculated. 

28 

29 

30 

31 Analysis of Deviance Table 

32 

33 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

34 Full model -53.7077 4 

35 Fitted model -53.928 3 0.440703 1 0.5068 

36 Reduced model -63.9797 1 20.544 3 0.0001309 

37 

38 AIC: 113.856 

39 

40 

41 Goodness of Fit 

42 Scaled 

43 Dose Est._Prob. Expected Observed Size Residual 

44 ------------------------------------------------------------------------ 

45 0.0000 0.0353 1.059 1.000 30 -0.058 

46 1997.8780 0.1404 4.212 5.000 30 0.414 

47 4539.2839 0.2382 7.145 6.000 30 -0.491 

48 15952.0000 0.4861 14.584 15.000 30 0.152 

49 

50 Chi^2 = 0.44 d.f. = 1 P-value = 0.5076 

51 

52 

53 Benchmark Dose Computation 

54 

55 Specified effect = 0.1 

56 

57 Risk Type = Extra risk 

58 

59 Confidence level = 0.95 

60 

61 BMD = 1806.29 

62 

63 BMDL = 264.35 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-46 —DO NOT CITE OR QUOTE 

1 E.2.6. Bell et al. (2007): Balano-Preputial Separation in Male Pups (5% extra risk) 

2 E.2.6.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2 pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 2 0.69 0.71 112.07 1.2E+03 8.2E+02 power restricted ≥1, bound 

hit 

logistic 2 2.10 0.35 113.86 3.0E+03 2.3E+03 

log-logistic b 2 0.47 0.79 111.88 9.3E+02 5.8E+02 slope restricted ≥1, 

bound hit 

log-logistic c 1 0.44 0.51 113.86 8.2E+02 4.5E+01 slope unrestricted 

log-probit 1 0.54 0.46 113.96 9.5E+02 7.2E+01 slope restricted ≥1 

multistage, 1-

degree 2 0.69 0.71 112.07 1.2E+03 8.2E+02 betas restricted ≥0, bound hit 

probit 2 1.96 0.38 113.65 2.8E+03 2.1E+03 

Weibull 2 0.69 0.71 112.07 1.2E+03 8.2E+02 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-47 —DO NOT CITE OR QUOTE 

1 E.2.6.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:35 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.6.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_BMR1_BPS_d49.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_BMR1_BPS_d49.plt 

12 Sun Nov 29 11:35:45 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is restricted as slope >= 1 

26 

27 Total number of observations = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-48 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0333333 

3 intercept = -9.77382 

4 slope = 1 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -slope 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 background intercept 

14 

15 background 1 -0.48 

16 

17 intercept -0.48 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 background 0.0371259 * * * 

26 intercept -9.77952 * * * 

27 slope 1 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -53.7077 4 

37 Fitted model -53.9377 2 0.460052 2 0.7945 

38 Reduced model -63.9797 1 20.544 3 0.0001309 

39 

40 AIC: 111.875 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0371 1.114 1.000 30 -0.110 

48 1997.8780 0.1349 4.048 5.000 30 0.509 

49 4539.2839 0.2339 7.018 6.000 30 -0.439 

50 15952.0000 0.4940 14.820 15.000 30 0.066 

51 

52 Chi^2 = 0.47 d.f. = 2 P-value = 0.7914 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.05 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 929.901 

64 

65 BMDL = 579.512 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-49 —DO NOT CITE OR QUOTE 

1 E.2.6.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:35 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.6.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_Unrest_BMR1_BPS_d49.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_Unrest_BMR1_BPS_d49.plt 

12 Sun Nov 29 11:35:47 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is not restricted 

26 

27 Total number of observations = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-50 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0333333 

3 intercept = -8.67441 

4 slope = 0.877628 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 background intercept slope 

10 

11 background 1 -0.38 0.34 

12 

13 intercept -0.38 1 -1 

14 

15 slope 0.34 -1 1 

16 

17 

18 

19 Parameter Estimates 

20 

21 95.0% Wald Confidence Interval 

22 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

23 background 0.0352883 * * * 

24 intercept -9.31114 * * * 

25 slope 0.948644 * * * 

26 

27 * - Indicates that this value is not calculated. 

28 

29 

30 

31 Analysis of Deviance Table 

32 

33 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

34 Full model -53.7077 4 

35 Fitted model -53.928 3 0.440703 1 0.5068 

36 Reduced model -63.9797 1 20.544 3 0.0001309 

37 

38 AIC: 113.856 

39 

40 

41 Goodness of Fit 

42 Scaled 

43 Dose Est._Prob. Expected Observed Size Residual 

44 ------------------------------------------------------------------------ 

45 0.0000 0.0353 1.059 1.000 30 -0.058 

46 1997.8780 0.1404 4.212 5.000 30 0.414 

47 4539.2839 0.2382 7.145 6.000 30 -0.491 

48 15952.0000 0.4861 14.584 15.000 30 0.152 

49 

50 Chi^2 = 0.44 d.f. = 1 P-value = 0.5076 

51 

52 

53 Benchmark Dose Computation 

54 

55 Specified effect = 0.05 

56 

57 Risk Type = Extra risk 

58 

59 Confidence level = 0.95 

60 

61 BMD = 821.69 

62 

63 BMDL = 45.4953 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-51 —DO NOT CITE OR QUOTE 

1 E.2.7. Cantoni et al. (1981): Urinary Copro-Porhyrins 

2 E.2.7.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2) 2 0.00 11.91 0.00 32.88 1.8E+04 8.6E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.00 11.91 0.00 32.88 1.8E+04 8.6E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 1 0.00 0.48 0.49 23.46 2.9E+02 9.9E+01 

nonconstant 

variance, power 

restricted ≥1 

exponential (M5) 1 0.00 0.48 0.49 23.46 2.9E+02 9.9E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 1 0.00 0.48 0.49 23.46 2.9E+02 9.9E+01 nonconstant variance, 

power unrestricted 

Hill 1 0.00 0.07 0.79 23.05 2.4E+02 error 

nonconstant variance, 

n restricted >1, bound 

hit 

Hill d 0 0.00 0.00 NA 24.97 1.4E+02 error nonconstant variance, 

n unrestricted 

linear 2 0.00 10.62 0.00 31.59 8.1E+03 1.5E+03 nonconstant variance 

polynomial 2 0.00 10.62 0.00 31.59 8.1E+03 1.5E+03 nonconstant variance 

power 2 0.00 10.62 0.00 31.59 8.1E+03 1.5E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 1 0.00 0.26 0.61 23.23 1.5E+01 2.3E-06 nonconstant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

3 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-52 —DO NOT CITE OR QUOTE 

1 E.2.7.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

-1

 0

 1

 2

 3

 4

 5

 6

 7

 0 5000 10000 15000 20000 25000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:43 11/16 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.7.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_BMR1_urin_copropor.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 13:43:37 2009 

15 ==================================================================== 

16 

17 Figure1-UrinaryCoproporphyrin_3months 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-53 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 4 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 4 

17 -------- -------- 

18 lnalpha -1.50063 

19 rho 2.60979 

20 a 0.704303 

21 b 0.000109864 

22 c 4.47268 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 4 

30 -------- ------- 

31 lnalpha -1.75303 

32 rho 2.63218 

33 a 0.76122 

34 b 0.000438426 

35 c 4.15614 

36 d 1 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 4 0.7414 0.3475 

44 1018 4 1.807 0.8341 

45 4868 4 2.734 1.506 

46 2.756e+004 4 3 2.6 

47 

48 

49 Estimated Values of Interest 

50 

51 Dose Est Mean Est Std Scaled Residual 

52 ------ ---------- --------- ---------------- 

53 0 0.7612 0.2907 -0.1366 

54 1018 1.626 0.7892 0.4589 

55 4868 2.879 1.674 -0.1742 

56 2.756e+004 3.164 1.895 -0.1727 

57 

58 

59 

60 Other models for which likelihoods are calculated: 

61 

62 Model A1: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = Sigma^2 

64 

65 Model A2: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma(i)^2 

67 

68 Model A3: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-54 —DO NOT CITE OR QUOTE 

1 Model R: Yij = Mu + e(i) 

2 Var{e(ij)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) DF AIC 

8 ------- ----------------- ---- ------------ 

9 A1 -12.90166 5 35.80333 

10 A2 -6.203643 8 28.40729 

11 A3 -6.487204 6 24.97441 

12 R -15.73713 2 35.47427 

13 4 -6.729565 5 23.45913 

14 

15 

16 Additive constant for all log-likelihoods = -14.7. This constant added to the 

17 above values gives the log-likelihood including the term that does not 

18 depend on the model parameters. 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 

27 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

28 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) D. F. p-value 

33 -------- ------------------------ ------ -------------- 

34 Test 1 19.07 6 0.004052 

35 Test 2 13.4 3 0.003854 

36 Test 3 0.5671 2 0.7531 

37 Test 6a 0.4847 1 0.4863 

38 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose 

42 levels, it seems appropriate to model the data. 

43 

44 The p-value for Test 2 is less than .1. A non-homogeneous 

45 variance model appears to be appropriate. 

46 

47 The p-value for Test 3 is greater than .1. The modeled 

48 variance appears to be appropriate here. 

49 

50 The p-value for Test 6a is greater than .1. Model 4 seems 

51 to adequately describe the data. 

52 

53 

54 Benchmark Dose Computations: 

55 

56 Specified Effect = 1.000000 

57 

58 Risk Type = Estimated standard deviations from control 

59 

60 Confidence Level = 0.950000 

61 

62 BMD = 294.122 

63 

64 BMDL = 99.3366 

65 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-55 —DO NOT CITE OR QUOTE 

1 E.2.7.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

2 Unrestricted 

-1

 0

 1

 2

 3

 4

 5

 6

 7

 0 5000 10000 15000 20000 25000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:43 11/16 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.7.5. Output file for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

7 Power Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_Unrest_BMR1_urin_copropor.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 13:43:39 2009 

15 ==================================================================== 

16 

17 Figure1-UrinaryCoproporphyrin_3months 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-56 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 4 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 5 

17 -------- -------- 

18 lnalpha -1.50063 

19 rho 2.60979 

20 a 0.704303 

21 b 0.000109864 

22 c 4.47268 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 5 

30 -------- ------- 

31 lnalpha -1.75303 

32 rho 2.63218 

33 a 0.76122 

34 b 0.000438426 

35 c 4.15614 

36 d 1 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 4 0.7414 0.3475 

44 1018 4 1.807 0.8341 

45 4868 4 2.734 1.506 

46 2.756e+004 4 3 2.6 

47 

48 

49 Estimated Values of Interest 

50 

51 Dose Est Mean Est Std Scaled Residual 

52 ------ ---------- --------- ---------------- 

53 0 0.7612 0.2907 -0.1366 

54 1018 1.626 0.7892 0.4589 

55 4868 2.879 1.674 -0.1742 

56 2.756e+004 3.164 1.895 -0.1727 

57 

58 

59 

60 Other models for which likelihoods are calculated: 

61 

62 Model A1: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = Sigma^2 

64 

65 Model A2: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma(i)^2 

67 

68 Model A3: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-57 —DO NOT CITE OR QUOTE 

1 Model R: Yij = Mu + e(i) 

2 Var{e(ij)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) DF AIC 

8 ------- ----------------- ---- ------------ 

9 A1 -12.90166 5 35.80333 

10 A2 -6.203643 8 28.40729 

11 A3 -6.487204 6 24.97441 

12 R -15.73713 2 35.47427 

13 5 -6.729565 5 23.45913 

14 

15 

16 Additive constant for all log-likelihoods = -14.7. This constant added to the 

17 above values gives the log-likelihood including the term that does not 

18 depend on the model parameters. 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 

27 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

28 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) D. F. p-value 

33 -------- ------------------------ ------ -------------- 

34 Test 1 19.07 6 0.004052 

35 Test 2 13.4 3 0.003854 

36 Test 3 0.5671 2 0.7531 

37 Test 7a 0.4847 1 0.4863 

38 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose 

42 levels, it seems appropriate to model the data. 

43 

44 The p-value for Test 2 is less than .1. A non-homogeneous 

45 variance model appears to be appropriate. 

46 

47 The p-value for Test 3 is greater than .1. The modeled 

48 variance appears to be appropriate here. 

49 

50 The p-value for Test 7a is greater than .1. Model 5 seems 

51 to adequately describe the data. 

52 

53 

54 Benchmark Dose Computations: 

55 

56 Specified Effect = 1.000000 

57 

58 Risk Type = Estimated standard deviations from control 

59 

60 Confidence Level = 0.950000 

61 

62 BMD = 294.122 

63 

64 BMDL = 99.3366 

65 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-58 —DO NOT CITE OR QUOTE 

1 E.2.7.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

-1

 0

 1

 2

 3

 4

 5

 6

 7

 0 5000 10000 15000 20000 25000

Mean Response

dose

Hill Model

13:43 11/16 2009

BMD

Hill

2 

3 

4 

5 E.2.7.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_urin_copropor.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_urin_copropor.plt 

12 Mon Nov 16 13:43:40 2009 

13 ==================================================================== 

14 

15 Figure1-UrinaryCoproporphyrin_3months 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Power parameter is not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

27 

28 Total number of dose groups = 4 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 0.90039 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-59 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 intercept = 0.741372 

3 v = 2.25875 

4 n = 0.0266478 

5 k = 8454.34 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho intercept v n k 

11 

12 lalpha 1 -0.62 -0.53 -0.013 0.027 -0.0092 

13 

14 rho -0.62 1 0.43 -0.2 -0.017 -0.051 

15 

16 intercept -0.53 0.43 1 -0.081 0.032 0.011 

17 

18 v -0.013 -0.2 -0.081 1 -0.88 0.96 

19 

20 n 0.027 -0.017 0.032 -0.88 1 -0.92 

21 

22 k -0.0092 -0.051 0.011 0.96 -0.92 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha -1.78758 0.616312 -2.99553 -0.579633 

31 rho 2.64296 0.750855 1.17131 4.11461 

32 intercept 0.759014 0.14058 0.483483 1.03455 

33 v 3.18202 2.82949 -2.36368 8.72772 

34 n 0.739248 0.896737 -1.01832 2.49682 

35 k 3317.45 9482.63 -15268.2 21903.1 

36 

37 

38 

39 Table of Data and Estimated Values of Interest 

40 

41 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

42 ------ --- -------- -------- ----------- ----------- ---------- 

43 

44 0 4 0.741 0.759 0.348 0.284 -0.124 

45 1018 4 1.81 1.7 0.834 0.822 0.27 

46 4868 4 2.73 2.57 1.51 1.43 0.224 

47 2.756e+004 4 3 3.39 2.6 2.05 -0.38 

48 

49 Warning: Likelihood for fitted model larger than the Likelihood for model A3. 

50 

51 

52 

53 Model Descriptions for likelihoods calculated 

54 

55 

56 Model A1: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma^2 

58 

59 Model A2: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = Sigma(i)^2 

61 

62 Model A3: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

64 Model A3 uses any fixed variance parameters that 

65 were specified by the user 

66 

67 Model R: Yi = Mu + e(i) 

68 Var{e(i)} = Sigma^2 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-60 —DO NOT CITE OR QUOTE 

1 Likelihoods of Interest 

2 

3 Model Log(likelihood) # Param's AIC 

4 A1 -12.901663 5 35.803325 

5 A2 -6.203643 8 28.407287 

6 A3 -6.487204 6 24.974409 

7 fitted -6.487204 6 24.974409 

8 R -15.737135 2 35.474269 

9 

10 

11 Explanation of Tests 

12 

13 Test 1: Do responses and/or variances differ among Dose levels? 

14 (A2 vs. R) 

15 Test 2: Are Variances Homogeneous? (A1 vs A2) 

16 Test 3: Are variances adequately modeled? (A2 vs. A3) 

17 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

18 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

19 

20 Tests of Interest 

21 

22 Test -2*log(Likelihood Ratio) Test df p-value 

23 

24 Test 1 19.067 6 0.004052 

25 Test 2 13.396 3 0.003854 

26 Test 3 0.567122 2 0.7531 

27 Test 4 -1.9007e-013 0 NA 

28 

29 The p-value for Test 1 is less than .05. There appears to be a 

30 difference between response and/or variances among the dose levels 

31 It seems appropriate to model the data 

32 

33 The p-value for Test 2 is less than .1. A non-homogeneous variance 

34 model appears to be appropriate 

35 

36 The p-value for Test 3 is greater than .1. The modeled variance appears 

37 to be appropriate here 

38 

39 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

40 test for fit is not valid 

41 

42 

43 Benchmark Dose Computation 

44 

45 Specified effect = 1 

46 

47 Risk Type = Estimated standard deviations from the control mean 

48 

49 Confidence level = 0.95 

50 

51 BMD = 143.414 

52 

53 

54 BMDL computation failed. 

55 

56 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-61 —DO NOT CITE OR QUOTE 

1 E.2.7.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

-1

 0

 1

 2

 3

 4

 5

 6

 7

 0 5000 10000 15000 20000 25000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:43 11/16 2009

BMDLBMD

 

Power

2 

3 

4 

5 E.2.7.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_urin_copropor.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Pwr_Unrest_BMR1_urin_copropor.plt 

13 Mon Nov 16 13:43:39 2009 

14 ==================================================================== 

15 

16 Figure1-UrinaryCoproporphyrin_3months 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 4 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-62 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 0.90039 

3 rho = 0 

4 control = 0.741372 

5 slope = 0.226515 

6 power = 0.224935 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho control slope power 

12 

13 lalpha 1 -0.62 -0.53 -0.03 0.024 

14 

15 rho -0.62 1 0.43 0.052 -0.16 

16 

17 control -0.53 0.43 1 -0.15 0.086 

18 

19 slope -0.03 0.052 -0.15 1 -0.98 

20 

21 power 0.024 -0.16 0.086 -0.98 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha -1.78125 0.617808 -2.99213 -0.570369 

30 rho 2.64332 0.744947 1.18325 4.10339 

31 control 0.75678 0.139979 0.482426 1.03113 

32 slope 0.123953 0.145639 -0.161493 0.4094 

33 power 0.304254 0.135074 0.0395142 0.568993 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 4 0.741 0.757 0.348 0.284 -0.109 

43 1018 4 1.81 1.78 0.834 0.877 0.0705 

44 4868 4 2.73 2.4 1.51 1.3 0.515 

45 2.756e+004 4 3 3.54 2.6 2.18 -0.493 

46 

47 

48 

49 Model Descriptions for likelihoods calculated 

50 

51 

52 Model A1: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = Sigma^2 

54 

55 Model A2: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma(i)^2 

57 

58 Model A3: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

60 Model A3 uses any fixed variance parameters that 

61 were specified by the user 

62 

63 Model R: Yi = Mu + e(i) 

64 Var{e(i)} = Sigma^2 

65 

66 

67 Likelihoods of Interest 

68 

69 Model Log(likelihood) # Param's AIC 

70 A1 -12.901663 5 35.803325 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-63 —DO NOT CITE OR QUOTE 

1 A2 -6.203643 8 28.407287 

2 A3 -6.487204 6 24.974409 

3 fitted -6.617381 5 23.234762 

4 R -15.737135 2 35.474269 

5 

6 

7 Explanation of Tests 

8 

9 Test 1: Do responses and/or variances differ among Dose levels? 

10 (A2 vs. R) 

11 Test 2: Are Variances Homogeneous? (A1 vs A2) 

12 Test 3: Are variances adequately modeled? (A2 vs. A3) 

13 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

14 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

15 

16 Tests of Interest 

17 

18 Test -2*log(Likelihood Ratio) Test df p-value 

19 

20 Test 1 19.067 6 0.004052 

21 Test 2 13.396 3 0.003854 

22 Test 3 0.567122 2 0.7531 

23 Test 4 0.260353 1 0.6099 

24 

25 The p-value for Test 1 is less than .05. There appears to be a 

26 difference between response and/or variances among the dose levels 

27 It seems appropriate to model the data 

28 

29 The p-value for Test 2 is less than .1. A non-homogeneous variance 

30 model appears to be appropriate 

31 

32 The p-value for Test 3 is greater than .1. The modeled variance appears 

33 to be appropriate here 

34 

35 The p-value for Test 4 is greater than .1. The model chosen seems 

36 to adequately describe the data 

37 

38 

39 Benchmark Dose Computation 

40 

41 Specified effect = 1 

42 

43 Risk Type = Estimated standard deviations from the control mean 

44 

45 Confidence level = 0.95 

46 

47 BMD = 15.247 

48 

49 

50 BMDL = 2.31222e-006 

51 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-64 —DO NOT CITE OR QUOTE 

1 

2 E.2.8. Cantoni et al. (1981): Urinary Porphyrins 

3 E.2.8.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2)

c 2 <0.0001 16.12 0.00 55.46 2.1E+03 1.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 <0.0001 16.12 0.00 55.46 2.1E+03 1.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 <0.0001 17.85 <0.0001 59.19 1.4E+02 8.0E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 <0.0001 17.74 N/A 61.08 1.6E+02 8.0E+01 nonconstant variance, 

power restricted ≥1 

Hill 0 <.0001 18.86 NA 62.20 3.4E+03 1.8E+03 nonconstant variance, n 

restricted >1 

linear 2 <.0001 17.85 0.00 57.19 1.4E+02 8.0E+01 nonconstant variance 

polynomial 1 <.0001 16.63 <.0001 57.97 1.9E+02 8.9E+01 nonconstant variance 

power 1 <.0001 17.74 <.0001 59.08 1.6E+02 8.0E+01 nonconstant variance, 

power restricted ≥1 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

4 

5 

6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-65 —DO NOT CITE OR QUOTE 

1 E.2.8.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 50

 100

 150

 200

 250

 300

 350

 0 5000 10000 15000 20000 25000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

13:28 11/16 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.8.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_BMR1_Urinary_porphyrins.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 13:28:56 2009 

15 ==================================================================== 

16 

17 Table 1, dose converted to ng per kg per day 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-66 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 4 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 2 

17 -------- -------- 

18 lnalpha -3.57509 

19 rho 2.23456 

20 a 2.1565 

21 b 3.49686e-008 

22 c 91300.7 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 2 

30 -------- ------- 

31 lnalpha -4.64559 

32 rho 3.18357 

33 a 2.32146 

34 b 2.51372e-009 

35 c 838302 

36 d 1.04944 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 4 2.27 0.49 

44 1018 4 5.55 0.85 

45 4868 3 7.62 1.79 

46 2.756e+004 3 196.9 63.14 

47 

48 

49 Estimated Values of Interest 

50 

51 Dose Est Mean Est Std Scaled Residual 

52 ------ ---------- --------- ---------------- 

53 0 3.579 1.262 -2.074 

54 1018 4.152 1.445 1.936 

55 4868 7.281 2.411 0.2437 

56 2.756e+004 199.5 49.25 -0.09069 

57 

58 

59 

60 Other models for which likelihoods are calculated: 

61 

62 Model A1: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = Sigma^2 

64 

65 Model A2: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma(i)^2 

67 

68 Model A3: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-67 —DO NOT CITE OR QUOTE 

1 Model R: Yij = Mu + e(i) 

2 Var{e(ij)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) DF AIC 

8 ------- ----------------- ---- ------------ 

9 A1 -51.42175 5 112.8435 

10 A2 -15.31211 8 46.62422 

11 A3 -15.66963 6 43.33925 

12 R -68.75058 2 141.5012 

13 2 -23.73172 4 55.46344 

14 

15 

16 Additive constant for all log-likelihoods = -12.87. This constant added to the 

17 above values gives the log-likelihood including the term that does not 

18 depend on the model parameters. 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

27 

28 

29 Tests of Interest 

30 

31 Test -2*log(Likelihood Ratio) D. F. p-value 

32 -------- ------------------------ ------ -------------- 

33 Test 1 106.9 6 < 0.0001 

34 Test 2 72.22 3 < 0.0001 

35 Test 3 0.715 2 0.6994 

36 Test 4 16.12 2 0.0003153 

37 

38 

39 The p-value for Test 1 is less than .05. There appears to be a 

40 difference between response and/or variances among the dose 

41 levels, it seems appropriate to model the data. 

42 

43 The p-value for Test 2 is less than .1. A non-homogeneous 

44 variance model appears to be appropriate. 

45 

46 The p-value for Test 3 is greater than .1. The modeled 

47 variance appears to be appropriate here. 

48 

49 The p-value for Test 4 is less than .1. Model 2 may not adequately 

50 describe the data; you may want to consider another model. 

51 

52 

53 Benchmark Dose Computations: 

54 

55 Specified Effect = 1.000000 

56 

57 Risk Type = Estimated standard deviations from control 

58 

59 Confidence Level = 0.950000 

60 

61 BMD = 2070.13 

62 

63 BMDL = 1521.05 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-68 —DO NOT CITE OR QUOTE 

1 E.2.9. Crofton et al. (2005): Serum T4 

2 E.2.9.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2) 8 0.76 44.20 <0.0001 516.36 6.3E+04 3.4E+04 constant variance, 

power restricted ≥1 

exponential (M3) 8 0.76 44.20 <0.0001 516.36 6.3E+04 3.4E+04 constant variance, 

power restricted ≥1 

exponential (M4)

c 7 0.76 2.29 0.94 476.45 2.9E+03 1.7E+03 constant variance, 

power restricted ≥1 

exponential (M5) 6 0.76 2.08 0.91 478.23 3.2E+03 1.7E+03 constant variance, 

power restricted ≥1 

exponential (M5) d 6 0.76 2.08 0.91 478.23 3.2E+03 1.7E+03 constant variance, 

power unrestricted 

Hill 6 0.76 1.29 0.97 477.45 3.2E+03 1.7E+03 constant variance, n 

restricted >1 

Hill d 6 0.76 1.29 0.97 477.45 3.2E+03 1.7E+03 constant variance, n 

unrestricted 

linear 8 0.76 50.31 <.0001 522.46 1.3E+05 9.7E+04 constant variance 

polynomial 8 0.76 50.31 <.0001 522.46 1.3E+05 9.7E+04 constant variance 

power 8 0.76 50.31 <.0001 522.46 1.3E+05 9.7E+04 

constant variance, 

power restricted ≥1, 

bound hit 

power d 7 0.76 16.95 0.02 491.10 1.4E+03 1.8E+02 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

3 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-69 —DO NOT CITE OR QUOTE 

1 E.2.9.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

2 ≥1 

 20

 40

 60

 80

 100

 120

 0 50000 100000 150000 200000 250000 300000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

15:13 11/16 2009

BMDLBMD

 

Exponential

3 

4 

5 

6 E.2.9.3. Output File for Selected Model: Exponential (M4), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\ExpConstVar_BMR1_SerumT4.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 15:13:33 2009 

15 ==================================================================== 

16 

17 0 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-70 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 rho is set to 0. 

4 A constant variance model is fit. 

5 

6 Total number of dose groups = 10 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 4 

18 -------- -------- 

19 lnalpha 5.47437 

20 rho(S) 0 

21 a 104.999 

22 b 1.16502e-005 

23 c 0.445764 

24 d 1 

25 

26 (S) = Specified 

27 

28 

29 

30 Parameter Estimates 

31 

32 Variable Model 4 

33 -------- ------- 

34 lnalpha 5.50322 

35 rho 0 

36 a 99.7846 

37 b 0.000149614 

38 c 0.533127 

39 d 1.19797 

40 

41 

42 Table of Stats From Input Data 

43 

44 Dose N Obs Mean Obs Std Dev 

45 ----- --- ---------- ------------- 

46 0 14 100 15.44 

47 11.15 6 96.27 14.98 

48 269.2 12 98.57 18.11 

49 763 6 99.76 19.04 

50 1905 6 93.32 12.11 

51 5104 6 70.94 12.74 

52 1.271e+004 6 62.52 14.75 

53 3.617e+004 6 52.68 22.73 

54 9.965e+004 6 54.66 19.71 

55 3.215e+005 4 49.15 11.15 

56 

57 

58 Estimated Values of Interest 

59 

60 Dose Est Mean Est Std Scaled Residual 

61 ------ ---------- --------- ---------------- 

62 0 100.3 15.69 -0.07977 

63 11.15 100.3 15.69 -0.6232 

64 269.2 98.58 15.69 -0.0008246 

65 763 95.52 15.69 0.6615 

66 1905 89.21 15.69 0.6428 

67 5104 76.04 15.69 -0.7955 

68 1.271e+004 60.7 15.69 0.2839 

69 3.617e+004 52.85 15.69 -0.02601 

70 9.965e+004 52.53 15.69 0.3323 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-71 —DO NOT CITE OR QUOTE 

1 3.215e+005 52.53 15.69 -0.432 

2 

3 

4 

5 Other models for which likelihoods are calculated: 

6 

7 Model A1: Yij = Mu(i) + e(ij) 

8 Var{e(ij)} = Sigma^2 

9 

10 Model A2: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma(i)^2 

12 

13 Model A3: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

15 

16 Model R: Yij = Mu + e(i) 

17 Var{e(ij)} = Sigma^2 

18 

19 

20 Likelihoods of Interest 

21 

22 Model Log(likelihood) DF AIC 

23 ------- ----------------- ---- ------------ 

24 A1 -233.0774 11 488.1549 

25 A2 -230.2028 20 500.4056 

26 A3 -233.0774 11 488.1549 

27 R -268.4038 2 540.8076 

28 4 -234.2238 4 476.4476 

29 

30 

31 Additive constant for all log-likelihoods = -66.16. This constant added to the 

32 above values gives the log-likelihood including the term that does not 

33 depend on the model parameters. 

34 

35 

36 Explanation of Tests 

37 

38 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

39 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

40 Test 3: Are variances adequately modeled? (A2 vs. A3) 

41 

42 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

43 

44 

45 Tests of Interest 

46 

47 Test -2*log(Likelihood Ratio) D. F. p-value 

48 -------- ------------------------ ------ -------------- 

49 Test 1 76.4 18 < 0.0001 

50 Test 2 5.749 9 0.7647 

51 Test 3 5.749 9 0.7647 

52 Test 6a 2.293 7 0.9419 

53 

54 

55 The p-value for Test 1 is less than .05. There appears to be a 

56 difference between response and/or variances among the dose 

57 levels, it seems appropriate to model the data. 

58 

59 The p-value for Test 2 is greater than .1. A homogeneous 

60 variance model appears to be appropriate here. 

61 

62 The p-value for Test 3 is greater than .1. The modeled 

63 variance appears to be appropriate here. 

64 

65 The p-value for Test 6a is greater than .1. Model 4 seems 

66 to adequately describe the data. 

67 

68 

69 Benchmark Dose Computations: 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-72 —DO NOT CITE OR QUOTE 

1 Specified Effect = 1.000000 

2 

3 Risk Type = Estimated standard deviations from control 

4 

5 Confidence Level = 0.950000 

6 

7 BMD = 2860.82 

8 

9 BMDL = 1670.13 

10 

11 

12 E.2.9.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

13 Unrestricted 

 20

 40

 60

 80

 100

 120

 0 50000 100000 150000 200000 250000 300000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

15:13 11/16 2009

BMDL BMD

 

Exponential

14 

15 

16 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-73 —DO NOT CITE OR QUOTE 

1 E.2.9.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

2 Unrestricted 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\AD\Blood\ExpConstVar_Unrest_BMR1_SerumT4.(d) 

8 Gnuplot Plotting File: 

9 Mon Nov 16 15:13:40 2009 

10 ==================================================================== 

11 

12 0 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 rho is set to 0. 

35 A constant variance model is fit. 

36 

37 Total number of dose groups = 10 

38 Total number of records with missing values = 0 

39 Maximum number of iterations = 250 

40 Relative Function Convergence has been set to: 1e-008 

41 Parameter Convergence has been set to: 1e-008 

42 

43 MLE solution provided: Exact 

44 

45 

46 Initial Parameter Values 

47 

48 Variable Model 5 

49 -------- -------- 

50 lnalpha 5.47437 

51 rho(S) 0 

52 a 104.999 

53 b 1.16502e-005 

54 c 0.445764 

55 d 1 

56 

57 (S) = Specified 

58 

59 

60 

61 Parameter Estimates 

62 

63 Variable Model 5 

64 -------- ------- 

65 lnalpha 5.50322 

66 rho 0 

67 a 99.7846 

68 b 0.000149614 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-74 —DO NOT CITE OR QUOTE 

1 c 0.533127 

2 d 1.19797 

3 

4 

5 Table of Stats From Input Data 

6 

7 Dose N Obs Mean Obs Std Dev 

8 ----- --- ---------- ------------- 

9 0 14 100 15.44 

10 11.15 6 96.27 14.98 

11 269.2 12 98.57 18.11 

12 763 6 99.76 19.04 

13 1905 6 93.32 12.11 

14 5104 6 70.94 12.74 

15 1.271e+004 6 62.52 14.75 

16 3.617e+004 6 52.68 22.73 

17 9.965e+004 6 54.66 19.71 

18 3.215e+005 4 49.15 11.15 

19 

20 

21 Estimated Values of Interest 

22 

23 Dose Est Mean Est Std Scaled Residual 

24 ------ ---------- --------- ---------------- 

25 0 99.78 15.67 0.0512 

26 11.15 99.76 15.67 -0.5465 

27 269.2 98.8 15.67 -0.05054 

28 763 96.45 15.67 0.5173 

29 1905 90.5 15.67 0.4419 

30 5104 75.78 15.67 -0.7573 

31 1.271e+004 58.58 15.67 0.616 

32 3.617e+004 53.22 15.67 -0.08476 

33 9.965e+004 53.2 15.67 0.2291 

34 3.215e+005 53.2 15.67 -0.5174 

35 

36 

37 

38 Other models for which likelihoods are calculated: 

39 

40 Model A1: Yij = Mu(i) + e(ij) 

41 Var{e(ij)} = Sigma^2 

42 

43 Model A2: Yij = Mu(i) + e(ij) 

44 Var{e(ij)} = Sigma(i)^2 

45 

46 Model A3: Yij = Mu(i) + e(ij) 

47 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

48 

49 Model R: Yij = Mu + e(i) 

50 Var{e(ij)} = Sigma^2 

51 

52 

53 Likelihoods of Interest 

54 

55 Model Log(likelihood) DF AIC 

56 ------- ----------------- ---- ------------ 

57 A1 -233.0774 11 488.1549 

58 A2 -230.2028 20 500.4056 

59 A3 -233.0774 11 488.1549 

60 R -268.4038 2 540.8076 

61 5 -234.1158 5 478.2316 

62 

63 

64 Additive constant for all log-likelihoods = -66.16. This constant added to the 

65 above values gives the log-likelihood including the term that does not 

66 depend on the model parameters. 

67 

68 

69 Explanation of Tests 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-75 —DO NOT CITE OR QUOTE 

1 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

2 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

3 Test 3: Are variances adequately modeled? (A2 vs. A3) 

4 

5 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

6 

7 

8 Tests of Interest 

9 

10 Test -2*log(Likelihood Ratio) D. F. p-value 

11 -------- ------------------------ ------ -------------- 

12 Test 1 76.4 18 < 0.0001 

13 Test 2 5.749 9 0.7647 

14 Test 3 5.749 9 0.7647 

15 Test 7a 2.077 6 0.9125 

16 

17 

18 The p-value for Test 1 is less than .05. There appears to be a 

19 difference between response and/or variances among the dose 

20 levels, it seems appropriate to model the data. 

21 

22 The p-value for Test 2 is greater than .1. A homogeneous 

23 variance model appears to be appropriate here. 

24 

25 The p-value for Test 3 is greater than .1. The modeled 

26 variance appears to be appropriate here. 

27 

28 The p-value for Test 7a is greater than .1. Model 5 seems 

29 to adequately describe the data. 

30 

31 

32 Benchmark Dose Computations: 

33 

34 Specified Effect = 1.000000 

35 

36 Risk Type = Estimated standard deviations from control 

37 

38 Confidence Level = 0.950000 

39 

40 BMD = 3175.08 

41 

42 BMDL = 1706.36 

43 

44 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-76 —DO NOT CITE OR QUOTE 

1 E.2.9.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 20

 40

 60

 80

 100

 120

 0 50000 100000 150000 200000 250000 300000

Mean Response

dose

Hill Model with 0.95 Confidence Level

15:13 11/16 2009

BMDL BMD

 

Hill

2 

3 

4 

5 E.2.9.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\HillConstVar_Unrest_BMR1_SerumT4.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\HillConstVar_Unrest_BMR1_SerumT4.plt 

12 Mon Nov 16 15:13:42 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 Power parameter is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 10 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-77 —DO NOT CITE OR QUOTE 

1 alpha = 276.969 

2 rho = 0 Specified 

3 intercept = 99.999 

4 v = -50.854 

5 n = 1.5549 

6 k = 4585.23 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 ( *** The model parameter(s) -rho 

12 have been estimated at a boundary point, or have been specified by the user, 

13 and do not appear in the correlation matrix ) 

14 

15 alpha intercept v n k 

16 

17 alpha 1 1.9e-009 -2e-008 -1.1e-008 1.1e-008 

18 

19 intercept 1.9e-009 1 -0.58 -0.3 -0.2 

20 

21 v -2e-008 -0.58 1 0.6 -0.36 

22 

23 n -1.1e-008 -0.3 0.6 1 -0.34 

24 

25 k 1.1e-008 -0.2 -0.36 -0.34 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 alpha 242.825 40.4708 163.504 322.146 

34 intercept 99.3375 2.66145 94.1212 104.554 

35 v -46.4797 5.51009 -57.2793 -35.6801 

36 n 1.85655 0.927361 0.0389606 3.67415 

37 k 4564.01 1406.15 1808 7320.02 

38 

39 

40 

41 Table of Data and Estimated Values of Interest 

42 

43 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

44 ------ --- -------- -------- ----------- ----------- ---------- 

45 

46 0 14 100 99.3 15.4 15.6 0.159 

47 11.15 6 96.3 99.3 15 15.6 -0.483 

48 269.2 12 98.6 99.1 18.1 15.6 -0.116 

49 763 6 99.8 97.7 19 15.6 0.321 

50 1905 6 93.3 91.7 12.1 15.6 0.26 

51 5104 6 70.9 73.7 12.7 15.6 -0.433 

52 1.271e+004 6 62.5 58.9 14.8 15.6 0.568 

53 3.617e+004 6 52.7 53.8 22.7 15.6 -0.181 

54 9.965e+004 6 54.7 53 19.7 15.6 0.26 

55 3.215e+005 4 49.1 52.9 11.1 15.6 -0.479 

56 

57 

58 

59 Model Descriptions for likelihoods calculated 

60 

61 

62 Model A1: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = Sigma^2 

64 

65 Model A2: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma(i)^2 

67 

68 Model A3: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma^2 

70 Model A3 uses any fixed variance parameters that 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-78 —DO NOT CITE OR QUOTE 

1 were specified by the user 

2 

3 Model R: Yi = Mu + e(i) 

4 Var{e(i)} = Sigma^2 

5 

6 

7 Likelihoods of Interest 

8 

9 Model Log(likelihood) # Param's AIC 

10 A1 -233.077445 11 488.154889 

11 A2 -230.202783 20 500.405566 

12 A3 -233.077445 11 488.154889 

13 fitted -233.724271 5 477.448543 

14 R -268.403817 2 540.807634 

15 

16 

17 Explanation of Tests 

18 

19 Test 1: Do responses and/or variances differ among Dose levels? 

20 (A2 vs. R) 

21 Test 2: Are Variances Homogeneous? (A1 vs A2) 

22 Test 3: Are variances adequately modeled? (A2 vs. A3) 

23 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

24 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

25 

26 Tests of Interest 

27 

28 Test -2*log(Likelihood Ratio) Test df p-value 

29 

30 Test 1 76.4021 18 <.0001 

31 Test 2 5.74932 9 0.7647 

32 Test 3 5.74932 9 0.7647 

33 Test 4 1.29365 6 0.972 

34 

35 The p-value for Test 1 is less than .05. There appears to be a 

36 difference between response and/or variances among the dose levels 

37 It seems appropriate to model the data 

38 

39 The p-value for Test 2 is greater than .1. A homogeneous variance 

40 model appears to be appropriate here 

41 

42 

43 The p-value for Test 3 is greater than .1. The modeled variance appears 

44 to be appropriate here 

45 

46 The p-value for Test 4 is greater than .1. The model chosen seems 

47 to adequately describe the data 

48 

49 

50 Benchmark Dose Computation 

51 

52 Specified effect = 1 

53 

54 Risk Type = Estimated standard deviations from the control mean 

55 

56 Confidence level = 0.95 

57 

58 BMD = 3156.67 

59 

60 BMDL = 1668.07 

61 

62 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-79 —DO NOT CITE OR QUOTE 

1 E.2.9.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 20

 40

 60

 80

 100

 120

 0 50000 100000 150000 200000 250000 300000

Mean Response

dose

Power Model with 0.95 Confidence Level

15:13 11/16 2009

BMDLBMD

 

Power

2 

3 

4 

5 E.2.9.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

6 

7 

8 ==================================================================== 

9 Power Model. (Version: 2.15; Date: 04/07/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\PowerConstVar_Unrest_BMR1_SerumT4.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\PowerConstVar_Unrest_BMR1_SerumT4.plt 

12 Mon Nov 16 15:13:43 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = control + slope * dose^power 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 The power is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 10 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-80 —DO NOT CITE OR QUOTE 

1 alpha = 276.969 

2 rho = 0 Specified 

3 control = 99.999 

4 slope = -0.28302 

5 power = 0.42875 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha control slope power 

15 

16 alpha 1 3e-010 -1.9e-010 -1.9e-010 

17 

18 control 3e-010 1 -0.73 -0.62 

19 

20 slope -1.9e-010 -0.73 1 0.98 

21 

22 power -1.9e-010 -0.62 0.98 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 301.804 50.3007 203.217 400.392 

31 control 103.499 3.94867 95.76 111.239 

32 slope -3.01678 1.68354 -6.31645 0.282886 

33 power 0.242881 0.0442912 0.156071 0.32969 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 14 100 103 15.4 17.4 -0.754 

43 11.15 6 96.3 98.1 15 17.4 -0.256 

44 269.2 12 98.6 91.8 18.1 17.4 1.36 

45 763 6 99.8 88.4 19 17.4 1.6 

46 1905 6 93.3 84.6 12.1 17.4 1.23 

47 5104 6 70.9 79.5 12.7 17.4 -1.21 

48 1.271e+004 6 62.5 73.6 14.8 17.4 -1.56 

49 3.617e+004 6 52.7 64.9 22.7 17.4 -1.72 

50 9.965e+004 6 54.7 54.1 19.7 17.4 0.077 

51 3.215e+005 4 49.1 37.9 11.1 17.4 1.3 

52 

53 

54 

55 Model Descriptions for likelihoods calculated 

56 

57 

58 Model A1: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma^2 

60 

61 Model A2: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma(i)^2 

63 

64 Model A3: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 Model A3 uses any fixed variance parameters that 

67 were specified by the user 

68 

69 Model R: Yi = Mu + e(i) 

70 Var{e(i)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-81 —DO NOT CITE OR QUOTE 

1 

2 

3 Likelihoods of Interest 

4 

5 Model Log(likelihood) # Param's AIC 

6 A1 -233.077445 11 488.154889 

7 A2 -230.202783 20 500.405566 

8 A3 -233.077445 11 488.154889 

9 fitted -241.552045 4 491.104090 

10 R -268.403817 2 540.807634 

11 

12 

13 Explanation of Tests 

14 

15 Test 1: Do responses and/or variances differ among Dose levels? 

16 (A2 vs. R) 

17 Test 2: Are Variances Homogeneous? (A1 vs A2) 

18 Test 3: Are variances adequately modeled? (A2 vs. A3) 

19 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

20 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

21 

22 Tests of Interest 

23 

24 Test -2*log(Likelihood Ratio) Test df p-value 

25 

26 Test 1 76.4021 18 <.0001 

27 Test 2 5.74932 9 0.7647 

28 Test 3 5.74932 9 0.7647 

29 Test 4 16.9492 7 0.01773 

30 

31 The p-value for Test 1 is less than .05. There appears to be a 

32 difference between response and/or variances among the dose levels 

33 It seems appropriate to model the data 

34 

35 The p-value for Test 2 is greater than .1. A homogeneous variance 

36 model appears to be appropriate here 

37 

38 

39 The p-value for Test 3 is greater than .1. The modeled variance appears 

40 to be appropriate here 

41 

42 The p-value for Test 4 is less than .1. You may want to try a different 

43 model 

44 

45 

46 Benchmark Dose Computation 

47 

48 Specified effect = 1 

49 

50 Risk Type = Estimated standard deviations from the control mean 

51 

52 Confidence level = 0.95 

53 

54 BMD = 1350.28 

55 

56 

57 BMDL = 182.329 

58 

59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-82 —DO NOT CITE OR QUOTE 

1 

2 E.2.10. Hojo et al. (2002): DRL Reinforce Per Min 

3 E.2.10.1. Summary Table of BMDS Modeling Results 

Model a

Degrees 

of 

Freedom 

χ 2pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

Hill 0 NA 6.465 1.320E+03 4.017E-04 

linear 2 0.009 9.126 1.070E+04 4.762E+03 

polynomial 2 0.009 9.126 1.070E+04 4.762E+03 

power 2 0.009 9.126 1.070E+04 4.762E+03 power bound hit 

exponential (M2) 2 0.007 9.614 1.284E+04 6.859E+03 

exponential (M3) 1 0.001 12.870 2.720E+08 1.522E+05 

exponential (M4) c 1 0.054 5.490 1.041E+03 4.944E+00 

exponential (M5) 0 N/A 6.465 1.367E+03 1.245E+01 

a

 Constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

4 

5 

6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-83 —DO NOT CITE OR QUOTE 

1 E.2.10.2. Figure for Selected Model: Exponental (M4) 

2 

-0.5

 0

 0.5

 1

 1.5

 2

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

10:23 01/12 2010

BMDL BMD

 

Exponential

3 

4 Hojo et al., 2002: DRL reinforce per min 

5 

6 

7 E.2.10.3. Output File for Selected Model: Exponential (M4) 

8 Hojo et al., 2002: DRL reinforce per min

9 ==================================================================== 

10 Exponential Model. (Version: 1.61; Date: 7/24/2009) 

11 Input Data File: C:\1\Blood\21_Hojo_2002_DRL_rein_min_exp_ExpCV_1.(d) 

12 Gnuplot Plotting File: 

13 Tue Jan 12 10:23:58 2010 

14 ==================================================================== 

15 

16 Table 5, values adjusted by a constant to allow exponential model 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function by Model: 

20 Model 2: Y[dose] = a * exp{sign * b * dose} 

21 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

22 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

23 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

24 

25 Note: Y[dose] is the median response for exposure = dose; 

26 sign = +1 for increasing trend in data; 

27 sign = -1 for decreasing trend. 

28 

29 Model 2 is nested within Models 3 and 4. 

30 Model 3 is nested within Model 5. 

31 Model 4 is nested within Model 5. 

32 

33 

34 Dependent variable = Mean 

35 Independent variable = Dose 

36 Data are assumed to be distributed: normally 

37 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

38 rho is set to 0. 

39 A constant variance model is fit. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-84 —DO NOT CITE OR QUOTE 

1 

2 Total number of dose groups = 4 

3 Total number of records with missing values = 0 

4 Maximum number of iterations = 250 

5 Relative Function Convergence has been set to: 1e-008 

6 Parameter Convergence has been set to: 1e-008 

7 

8 MLE solution provided: Exact 

9 

10 

11 Initial Parameter Values 

12 

13 Variable Model 4 

14 -------- -------- 

15 lnalpha -1.29672 

16 rho(S) 0 

17 a 0.0817 

18 b 0.000197777 

19 c 16.3733 

20 d 1 

21 

22 (S) = Specified 

23 

24 

25 

26 Parameter Estimates 

27 

28 Variable Model 4 

29 -------- ------- 

30 lnalpha -1.11954 

31 rho 0 

32 a 0.054752 

33 b 0.000895762 

34 c 18.2107 

35 d 1 

36 

37 

38 Table of Stats From Input Data 

39 

40 Dose N Obs Mean Obs Std Dev 

41 ----- --- ---------- ------------- 

42 0 5 0.086 0.448 

43 1285 5 0.536 0.821 

44 3295 6 1.274 0.54 

45 8465 5 0.737 0.443 

46 

47 

48 Estimated Values of Interest 

49 

50 Dose Est Mean Est Std Scaled Residual 

51 ------ ---------- --------- ---------------- 

52 0 0.05475 0.5713 0.1223 

53 1285 0.6991 0.5713 -0.6381 

54 3295 0.9478 0.5713 1.398 

55 8465 0.9966 0.5713 -1.016 

56 

57 

58 

59 Other models for which likelihoods are calculated: 

60 

61 Model A1: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 

64 Model A2: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma(i)^2 

66 

67 Model A3: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

69 

70 Model R: Yij = Mu + e(i) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-85 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma^2 

2 

3 

4 Likelihoods of Interest 

5 

6 Model Log(likelihood) DF AIC 

7 ------- ----------------- ---- ------------ 

8 A1 3.11555 5 3.7689 

9 A2 4.489557 8 7.020886 

10 A3 3.11555 5 3.7689 

11 R -2.435087 2 8.870174 

12 4 1.255168 4 5.489665 

13 

14 

15 Additive constant for all log-likelihoods = -19.3. This constant added to the 

16 above values gives the log-likelihood including the term that does not 

17 depend on the model parameters. 

18 

19 

20 Explanation of Tests 

21 

22 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

23 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

24 Test 3: Are variances adequately modeled? (A2 vs. A3) 

25 

26 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

27 

28 

29 Tests of Interest 

30 

31 Test -2*log(Likelihood Ratio) D. F. p-value 

32 -------- ------------------------ ------ -------------- 

33 Test 1 13.85 6 0.03137 

34 Test 2 2.748 3 0.4321 

35 Test 3 2.748 3 0.4321 

36 Test 6a 3.721 1 0.05374 

37 

38 

39 The p-value for Test 1 is less than .05. There appears to be a 

40 difference between response and/or variances among the dose 

41 levels, it seems appropriate to model the data. 

42 

43 The p-value for Test 2 is greater than .1. A homogeneous 

44 variance model appears to be appropriate here. 

45 

46 The p-value for Test 3 is greater than .1. The modeled 

47 variance appears to be appropriate here. 

48 

49 The p-value for Test 6a is less than .1. Model 4 may not adequately 

50 describe the data; you may want to consider another model. 

51 

52 

53 Benchmark Dose Computations: 

54 

55 Specified Effect = 1.000000 

56 

57 Risk Type = Estimated standard deviations from control 

58 

59 Confidence Level = 0.950000 

60 

61 BMD = 1040.67 

62 

63 BMDL = 4.94408
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-86 —DO NOT CITE OR QUOTE 

1 

2 E.2.11. Hojo et al. (2002): DRL Response Per Min 

3 E.2.11.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2) 2 0.30 1.13 0.57 122.98 1.1E+03 error constant variance, 

power restricted ≥1 

exponential (M3) 2 0.30 1.13 0.57 122.98 1.1E+03 error constant variance, 

power restricted ≥1 

exponential (M4)

c 1 0.30 0.50 0.48 124.36 8.4E+02 5.6E+01 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.30 0.50 N/A 126.35 2.0E+03 4.9E+01 constant variance, 

power restricted ≥1 

Hill 0 0.30 0.50 NA 126.35 2.9E+03 3.2E-11 constant variance, n 

restricted >1 

linear 2 0.30 11.00 0.00 132.86 3.7E+04 1.7E+04 constant variance 

polynomial 2 0.30 11.00 0.00 132.86 3.7E+04 1.7E+04 constant variance 

power 2 0.30 11.00 0.00 132.86 3.7E+04 1.7E+04 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-87 —DO NOT CITE OR QUOTE 

1 E.2.11.2. Figure for Selected Model: Exponential (M4) 

-10

 0

 10

 20

 30

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

10:25 01/12 2010

BMDL BMD

 

Exponential

2 

3 

4 Hojo et al., 2002: DRL response per min 

5 

6 

7 E.2.11.3. Output File for Selected Model: Exponential (M4) 

8 Hojo et al., 2002: DRL response per min 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.61; Date: 7/24/2009) 

12 Input Data File: C:\1\Blood\23_Hojo_2002_DRL_resp_min_exp_ExpCV_1.(d) 

13 Gnuplot Plotting File: 

14 Tue Jan 12 10:25:21 2010 

15 ==================================================================== 

16 

17 Table 5, values adjusted by a constant to allow exponential model 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 

38 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

39 rho is set to 0. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-88 —DO NOT CITE OR QUOTE 

1 A constant variance model is fit. 

2 

3 Total number of dose groups = 4 

4 Total number of records with missing values = 0 

5 Maximum number of iterations = 250 

6 Relative Function Convergence has been set to: 1e-008 

7 Parameter Convergence has been set to: 1e-008 

8 

9 MLE solution provided: Exact 

10 

11 

12 Initial Parameter Values 

13 

14 Variable Model 4 

15 -------- -------- 

16 lnalpha 4.51689 

17 rho(S) 0 

18 a 24.6362 

19 b 0.00047963 

20 c 0.0184785 

21 d 1 

22 

23 (S) = Specified 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 4 

30 -------- ------- 

31 lnalpha 4.54096 

32 rho 0 

33 a 23.4674 

34 b 0.00203802 

35 c 0.101322 

36 d 1 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 5 23.46 7.986 

44 1285 5 4.013 10.96 

45 3295 6 0.478 7.194 

46 8465 5 4.594 15.23 

47 

48 

49 Estimated Values of Interest 

50 

51 Dose Est Mean Est Std Scaled Residual 

52 ------ ---------- --------- ---------------- 

53 0 23.47 9.684 -0.001011 

54 1285 3.914 9.684 0.02275 

55 3295 2.403 9.684 -0.487 

56 8465 2.378 9.684 0.5117 

57 

58 

59 

60 Other models for which likelihoods are calculated: 

61 

62 Model A1: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = Sigma^2 

64 

65 Model A2: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma(i)^2 

67 

68 Model A3: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-89 —DO NOT CITE OR QUOTE 

1 Model R: Yij = Mu + e(i) 

2 Var{e(ij)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) DF AIC 

8 ------- ----------------- ---- ------------ 

9 A1 -57.92733 5 125.8547 

10 A2 -56.09669 8 128.1934 

11 A3 -57.92733 5 125.8547 

12 R -64.49611 2 132.9922 

13 4 -58.18012 4 124.3602 

14 

15 

16 Additive constant for all log-likelihoods = -19.3. This constant added to the 

17 above values gives the log-likelihood including the term that does not 

18 depend on the model parameters. 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 

27 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

28 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) D. F. p-value 

33 -------- ------------------------ ------ -------------- 

34 Test 1 16.8 6 0.01005 

35 Test 2 3.661 3 0.3004 

36 Test 3 3.661 3 0.3004 

37 Test 6a 0.5056 1 0.4771 

38 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose 

42 levels, it seems appropriate to model the data. 

43 

44 The p-value for Test 2 is greater than .1. A homogeneous 

45 variance model appears to be appropriate here. 

46 

47 The p-value for Test 3 is greater than .1. The modeled 

48 variance appears to be appropriate here. 

49 

50 The p-value for Test 6a is greater than .1. Model 4 seems 

51 to adequately describe the data. 

52 

53 

54 Benchmark Dose Computations: 

55 

56 Specified Effect = 1.000000 

57 

58 Risk Type = Estimated standard deviations from control 

59 

60 Confidence Level = 0.950000 

61 

62 BMD = 301.607 

63 

64 BMDL = 7.54952 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-90 —DO NOT CITE OR QUOTE 

E.2.12. Kattainen et al. (2001): 3rd 1 Molar Mesio-Distal Length (Molar Development) 

2 E.2.12.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2) 3 <0.0001 38.96 <0.0001 -

122.90 6.4E+04 3.8E+04 nonconstant variance, power restricted ≥1 

exponential (M3) 3 <0.0001 38.96 <0.0001 -

122.90 6.4E+04 3.8E+04 nonconstant variance, power restricted ≥1 

exponential (M4) 2 <0.0001 79.12 <0.0001 -80.75 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 13.81 0.00 -

146.06 8.5E+02 5.1E+02 nonconstant variance, power restricted ≥1 

Hill c 2 <.0001 8.72 0.01 -

151.15 6.3E+02 3.4E+02 

nonconstant variance, 

n restricted >1, bound 

hit 

Hill d 1 <.0001 2.92 0.09 -

154.95 3.0E+00 2.9E-02 nonconstant variance, n unrestricted 

linear 3 <.0001 39.59 <.0001 -

122.28 7.4E+04 4.7E+04 nonconstant variance 

polynomial 2 <.0001 36.61 <.0001 -

123.26 3.0E+04 1.4E+04 nonconstant variance 

power 3 <.0001 39.59 <.0001 -

122.28 7.4E+04 4.7E+04 

nonconstant variance, 

power restricted ≥1, 

bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-91 —DO NOT CITE OR QUOTE 

1 E.2.12.2. Figure for Selected Model: Hill, Nonconstant Variance, n Restricted >1, Bound Hit 

 1.1

 1.2

 1.3

 1.4

 1.5

 1.6

 1.7

 1.8

 1.9

 0 20000 40000 60000 80000 100000 120000 140000 160000

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:14 11/16 2009

BMDLBMD

 

Hill

2 

3 

4 

5 E.2.12.3. Output File for Selected Model: Hill, Nonconstant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_BMR1_3rd_molar.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_BMR1_3rd_molar.plt 

13 Mon Nov 16 13:14:09 2009 

14 ==================================================================== 

15 

16 Figure 3 female only 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter restricted to be greater than 1 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-92 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = -2.37155 

3 rho = 0 

4 intercept = 1.85591 

5 v = -0.507874 

6 n = 0.825979 

7 k = 4284.51 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -n 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 lalpha rho intercept v k 

17 

18 lalpha 1 -0.98 -0.16 0.84 -0.37 

19 

20 rho -0.98 1 0.2 -0.79 0.39 

21 

22 intercept -0.16 0.2 1 -0.31 -0.11 

23 

24 v 0.84 -0.79 -0.31 1 -0.48 

25 

26 k -0.37 0.39 -0.11 -0.48 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence Interval 

33 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

34 lalpha 3.34591 1.40451 0.593124 6.0987 

35 rho -14.3329 2.62142 -19.4708 -9.19505 

36 intercept 1.8548 0.0159016 1.82364 1.88597 

37 v -0.441028 0.0588146 -0.556302 -0.325753 

38 n 1 NA 

39 k 3764.75 1228.49 1356.95 6172.54 

40 

41 NA - Indicates that this parameter has hit a bound 

42 implied by some inequality constraint and thus 

43 has no standard error. 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 16 1.86 1.85 0.0661 0.0637 0.0692 

53 4703 17 1.58 1.61 0.185 0.176 -0.767 

54 1.568e+004 15 1.6 1.5 0.265 0.293 1.28 

55 4.725e+004 12 1.5 1.45 0.221 0.378 0.527 

56 1.585e+005 19 1.35 1.42 0.515 0.423 -0.783 

57 

58 

59 

60 Model Descriptions for likelihoods calculated 

61 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-93 —DO NOT CITE OR QUOTE 

1 Model A3 uses any fixed variance parameters that 

2 were specified by the user 

3 

4 Model R: Yi = Mu + e(i) 

5 Var{e(i)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) # Param's AIC 

11 A1 56.758717 6 -101.517434 

12 A2 85.856450 10 -151.712901 

13 A3 84.934314 7 -155.868628 

14 fitted 80.574735 5 -151.149469 

15 R 45.373551 2 -86.747101 

16 

17 

18 Explanation of Tests 

19 

20 Test 1: Do responses and/or variances differ among Dose levels? 

21 (A2 vs. R) 

22 Test 2: Are Variances Homogeneous? (A1 vs A2) 

23 Test 3: Are variances adequately modeled? (A2 vs. A3) 

24 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

25 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

26 

27 Tests of Interest 

28 

29 Test -2*log(Likelihood Ratio) Test df p-value 

30 

31 Test 1 80.9658 8 <.0001 

32 Test 2 58.1955 4 <.0001 

33 Test 3 1.84427 3 0.6053 

34 Test 4 8.71916 2 0.01278 

35 

36 The p-value for Test 1 is less than .05. There appears to be a 

37 difference between response and/or variances among the dose levels 

38 It seems appropriate to model the data 

39 

40 The p-value for Test 2 is less than .1. A non-homogeneous variance 

41 model appears to be appropriate 

42 

43 The p-value for Test 3 is greater than .1. The modeled variance appears 

44 to be appropriate here 

45 

46 The p-value for Test 4 is less than .1. You may want to try a different 

47 model 

48 

49 

50 Benchmark Dose Computation 

51 

52 Specified effect = 1 

53 

54 Risk Type = Estimated standard deviations from the control mean 

55 

56 Confidence level = 0.95 

57 

58 BMD = 634.985 

59 

60 BMDL = 335.879 

61 

62 

63 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-94 —DO NOT CITE OR QUOTE 

1 E.2.12.4. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 1.1

 1.2

 1.3

 1.4

 1.5

 1.6

 1.7

 1.8

 1.9

 0 20000 40000 60000 80000 100000 120000 140000 160000

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:14 11/16 2009

BMDBMDL

 

Hill

2 

3 

4 

5 E.2.12.5. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_3rd_molar.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_3rd_molar.plt 

12 Mon Nov 16 13:14:09 2009 

13 ==================================================================== 

14 

15 Figure 3 female only 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Power parameter is not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

27 

28 Total number of dose groups = 5 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = -2.37155 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-95 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 intercept = 1.85591 

3 v = -0.507874 

4 n = 0.825979 

5 k = 4284.51 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho intercept v n k 

11 

12 lalpha 1 -0.98 -0.18 0.18 -0.28 -0.011 

13 

14 rho -0.98 1 0.22 -0.18 0.29 0.012 

15 

16 intercept -0.18 0.22 1 -0.026 -0.058 0.0019 

17 

18 v 0.18 -0.18 -0.026 1 0.52 -0.96 

19 

20 n -0.28 0.29 -0.058 0.52 1 -0.71 

21 

22 k -0.011 0.012 0.0019 -0.96 -0.71 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha 3.21867 1.42224 0.431136 6.00621 

31 rho -14.0858 2.68326 -19.3449 -8.82671 

32 intercept 1.85564 0.016023 1.82424 1.88705 

33 v -2.44363 2.81206 -7.95516 3.06791 

34 n 0.196843 0.0500689 0.0987096 0.294976 

35 k 2.75627e+008 2.27948e+009 -4.19207e+009 4.74332e+009 

36 

37 

38 

39 Table of Data and Estimated Values of Interest 

40 

41 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

42 ------ --- -------- -------- ----------- ----------- ---------- 

43 

44 0 16 1.86 1.86 0.0661 0.0643 0.0163 

45 4703 17 1.58 1.6 0.185 0.18 -0.597 

46 1.568e+004 15 1.6 1.54 0.265 0.234 0.856 

47 4.725e+004 12 1.5 1.48 0.221 0.316 0.259 

48 1.585e+005 19 1.35 1.4 0.515 0.471 -0.465 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-96 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 56.758717 6 -101.517434 

4 A2 85.856450 10 -151.712901 

5 A3 84.934314 7 -155.868628 

6 fitted 83.472636 6 -154.945271 

7 R 45.373551 2 -86.747101 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 80.9658 8 <.0001 

24 Test 2 58.1955 4 <.0001 

25 Test 3 1.84427 3 0.6053 

26 Test 4 2.92336 1 0.08731 

27 

28 The p-value for Test 1 is less than .05. There appears to be a 

29 difference between response and/or variances among the dose levels 

30 It seems appropriate to model the data 

31 

32 The p-value for Test 2 is less than .1. A non-homogeneous variance 

33 model appears to be appropriate 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is less than .1. You may want to try a different 

39 model 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 2.96451 

51 

52 BMDL = 0.0287389 

53 

54 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-97 —DO NOT CITE OR QUOTE 

1 

E.2.13. Kattainen et al. (2001): Females 3rd 2 Molar Eruption 

3 E.2.13.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 pValue a AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

logistic 3 0.360 88.508 7.290E+03 5.273E+03 

log-logistic b 3 0.982 85.227 1.896E+03 1.050E+03 slope bound hit 

log-probit, 

unrestricted 2 0.941 87.181 1.641E+03 1.895E+02 slope unrestricted 

probit 3 0.379 88.352 6.958E+03 5.177E+03 

multistage, 4-

degree 3 0.781 86.155 3.195E+03 2.076E+03 final ß=0 

log-logistic, 

unrestricted c 2 0.949 87.162 1.527E+03 1.456E+02 slope unrestricted 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model, BMDS output presented in this appendix 

c

 Alternate model, BMDS output also presented in this appendix 

4 

5 

6 

7 E.2.13.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 0 5000 10000 15000 20000 25000 30000 35000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

10:26 01/12 2010

BMDL BMD

 

Log-Logistic

8 

9 

10 Kattainen et al., 2001: 3rd molar eruption in pups 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-98 —DO NOT CITE OR QUOTE 

1 E.2.13.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

2 Kattainen et al., 2001: 3rd molar eruption in pups 

3 

4 ==================================================================== 

5 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

6 Input Data File: C:\1\Blood\24_Katt_2001_3molar_erup_LogLogistic_BMR1.(d) 

7 Gnuplot Plotting File: C:\1\Blood\24_Katt_2001_3molar_erup_LogLogistic_BMR1.plt 

8 Tue Jan 12 10:26:06 2010 

9 ==================================================================== 

10 

11 Figure 2 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

17 

18 

19 Dependent variable = DichEff 

20 Independent variable = Dose 

21 Slope parameter is restricted as slope >= 1 

22 

23 Total number of observations = 5 

24 Total number of records with missing values = 0 

25 Maximum number of iterations = 250 

26 Relative Function Convergence has been set to: 1e-008 

27 Parameter Convergence has been set to: 1e-008 

28 

29 

30 

31 User has chosen the log transformed model 

32 

33 

34 Default Initial Parameter Values 

35 background = 0.0625 

36 intercept = -9.748 

37 slope = 1 

38 

39 

40 Asymptotic Correlation Matrix of Parameter Estimates 

41 

42 ( *** The model parameter(s) -slope 

43 have been estimated at a boundary point, or have been specified by the user, 

44 and do not appear in the correlation matrix ) 

45 

46 background intercept 

47 

48 background 1 -0.53 

49 

50 intercept -0.53 1 

51 

52 

53 

54 Parameter Estimates 

55 

56 95.0% Wald Confidence Interval 

57 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

58 background 0.0699182 * * * 

59 intercept -9.74484 * * * 

60 slope 1 * * * 

61 

62 * - Indicates that this value is not calculated. 

63 

64 

65 

66 Analysis of Deviance Table 

67 

68 Model Log(likelihood) # Param's Deviance Test d.f. P-value 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-99 —DO NOT CITE OR QUOTE 

1 Full model -40.5286 5 

2 Fitted model -40.6136 2 0.170098 3 0.9823 

3 Reduced model -50.7341 1 20.411 4 0.0004142 

4 

5 AIC: 85.2273 

6 

7 

8 Goodness of Fit 

9 Scaled 

10 Dose Est._Prob. Expected Observed Size Residual 

11 ------------------------------------------------------------------------ 

12 0.0000 0.0699 1.119 1.000 16 -0.116 

13 1763.4151 0.1570 2.669 3.000 17 0.220 

14 4943.6112 0.2788 4.182 4.000 15 -0.105 

15 12712.0000 0.4670 5.604 6.000 12 0.229 

16 37039.0000 0.7066 13.426 13.000 19 -0.215 

17 

18 Chi^2 = 0.17 d.f. = 3 P-value = 0.9820 

19 

20 

21 Benchmark Dose Computation 

22 

23 Specified effect = 0.1 

24 

25 Risk Type = Extra risk 

26 

27 Confidence level = 0.95 

28 

29 BMD = 1896.22 

30 

31 BMDL = 1049.96 

32 

33 

34 

35 E.2.13.4. Figure for Unrestricted Model: Log-Logistic, Unrestricted 

 0

 0.2

 0.4

 0.6

 0.8

 0 5000 10000 15000 20000 25000 30000 35000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

10:26 01/12 2010

BMDL BMD

 

Log-Logistic

36 

37 

38 Kattainen et al., 2001: 3rd molar eruption in pups 

39 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-100 —DO NOT CITE OR QUOTE 

1 E.2.13.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

2 Kattainen et al., 2001: 3rd molar eruption in pups 

3 ==================================================================== 

4 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

5 Input Data File: C:\1\Blood\24_Katt_2001_3molar_erup_LogLogistic_Unrest_BMR1.(d) 

6 Gnuplot Plotting File: C:\1\Blood\24_Katt_2001_3molar_erup_LogLogistic_Unrest_BMR1.plt 

7 Tue Jan 12 10:26:07 2010 

8 ==================================================================== 

9 

10 Figure 2 

11 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

12 

13 The form of the probability function is: 

14 

15 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

16 

17 

18 Dependent variable = DichEff 

19 Independent variable = Dose 

20 Slope parameter is not restricted 

21 

22 Total number of observations = 5 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 

29 

30 User has chosen the log transformed model 

31 

32 

33 Default Initial Parameter Values 

34 background = 0.0625 

35 intercept = -8.7855 

36 slope = 0.902051 

37 

38 

39 Asymptotic Correlation Matrix of Parameter Estimates 

40 

41 background intercept slope 

42 

43 background 1 -0.43 0.38 

44 

45 intercept -0.43 1 -0.99 

46 

47 slope 0.38 -0.99 1 

48 

49 

50 

51 Parameter Estimates 

52 

53 95.0% Wald Confidence Interval 

54 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

55 background 0.0630017 * * * 

56 intercept -8.87185 * * * 

57 slope 0.910471 * * * 

58 

59 * - Indicates that this value is not calculated. 

60 

61 

62 

63 Analysis of Deviance Table 

64 

65 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

66 Full model -40.5286 5 

67 Fitted model -40.5812 3 0.105153 2 0.9488 

68 Reduced model -50.7341 1 20.411 4 0.0004142 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-101 —DO NOT CITE OR QUOTE 

1 

2 AIC: 87.1623 

3 

4 Goodness of Fit 

5 Scaled 

6 Dose Est._Prob. Expected Observed Size Residual 

7 ------------------------------------------------------------------------ 

8 0.0000 0.0630 1.008 1.000 16 -0.008 

9 1763.4151 0.1684 2.862 3.000 17 0.089 

10 4943.6112 0.2922 4.383 4.000 15 -0.218 

11 12712.0000 0.4692 5.630 6.000 12 0.214 

12 37039.0000 0.6903 13.117 13.000 19 -0.058 

13 

14 Chi^2 = 0.10 d.f. = 2 P-value = 0.9491 

15 

16 Benchmark Dose Computation 

17 

18 Specified effect = 0.1 

19 Risk Type = Extra risk 

20 Confidence level = 0.95 

21 BMD = 1526.84 

22 BMDL = 145.591 

23 

24 

25 E.2.14. Kattainen et al., 2001: 3rd molar length in pups 

26 E.2.14.1. Summary Table of BMDS modeling results 

Model a

Degrees 

of 

Freedom 

χ

 2

 pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) 3 <0.0001 -

124.869 1.319E+04 7.850E+03 

exponential (M3) 3 <0.0001 -

124.869 1.319E+04 7.850E+03 power bound hit 

exponential (M4) 2 0.002 -

147.122 3.351E+02 2.001E+02 

exponential (M5) 2 0.002 -

147.122 3.351E+02 2.001E+02 power bound hit 

Hill c 2 0.022 -

152.241 2.477E+02 1.328E+02 n lower bound hit 

linear 3 <.0001 -

124.026 1.567E+04 1.009E+04 

polynomial 4 <.0001 -84.747 error error 

power 3 <.0001 -

124.026 1.567E+04 1.009E+04 power bound hit 

Hill, unrestricted d 1 <.0001 -78.747 2.007E+05 error n unrestricted 

a

 Non-constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

d

 Alternate model, BMDS output also presented in this appendix 

27 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-102 —DO NOT CITE OR QUOTE 

1 E.2.14.2. Figure for selected model: Hill 

 1.1

 1.2

 1.3

 1.4

 1.5

 1.6

 1.7

 1.8

 1.9

 0 5000 10000 15000 20000 25000 30000 35000

Mean Response

dose

Hill Model with 0.95 Confidence Level

10:26 01/12 2010

BMDLBMD

 

Hill

2 

3 

4 Kattainen et al., 2001: 3rd molar length in pups 

5 

6 

7 E.2.14.3. Output for selected model: Hill 

8 Kattainen et al., 2001: 3rd molar length in pups 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\1\Blood\25_Katt_2001_3molar_length_Hill_1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\25_Katt_2001_3molar_length_Hill_1.plt 

13 Tue Jan 12 10:26:49 2010 

14 ==================================================================== 

15 

16 Figure 3 female only 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter restricted to be greater than 1 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 lalpha = -2.37155 

39 rho = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-103 —DO NOT CITE OR QUOTE 

1 intercept = 1.85591 

2 v = -0.507874 

3 n = 0.845971 

4 k = 1606.5 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -n 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 lalpha rho intercept v k 

14 

15 lalpha 1 -0.98 -0.16 0.84 -0.38 

16 

17 rho -0.98 1 0.2 -0.79 0.4 

18 

19 intercept -0.16 0.2 1 -0.3 -0.11 

20 

21 v 0.84 -0.79 -0.3 1 -0.52 

22 

23 k -0.38 0.4 -0.11 -0.52 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 95.0% Wald Confidence Interval 

30 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

31 lalpha 3.31075 1.40399 0.558982 6.06253 

32 rho -14.2656 2.6274 -19.4152 -9.11596 

33 intercept 1.85483 0.0159478 1.82357 1.88609 

34 v -0.45369 0.0620284 -0.575263 -0.332116 

35 n 1 NA 

36 k 1512.49 494.187 543.903 2481.08 

37 

38 NA - Indicates that this parameter has hit a bound 

39 implied by some inequality constraint and thus 

40 has no standard error. 

41 

42 

43 

44 Table of Data and Estimated Values of Interest 

45 

46 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

47 ------ --- -------- -------- ----------- ----------- ---------- 

48 

49 0 16 1.86 1.85 0.0661 0.0639 0.0674 

50 1763 17 1.58 1.61 0.185 0.175 -0.789 

51 4944 15 1.6 1.51 0.265 0.28 1.22 

52 1.271e+004 12 1.5 1.45 0.221 0.371 0.51 

53 3.704e+004 19 1.35 1.42 0.515 0.432 -0.716 

54 

55 

56 

57 Model Descriptions for likelihoods calculated 

58 

59 

60 Model A1: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 

63 Model A2: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma(i)^2 

65 

66 Model A3: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

68 Model A3 uses any fixed variance parameters that 

69 were specified by the user 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-104 —DO NOT CITE OR QUOTE 

1 Model R: Yi = Mu + e(i) 

2 Var{e(i)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) # Param's AIC 

8 A1 56.758717 6 -101.517434 

9 A2 85.856450 10 -151.712901 

10 A3 84.934314 7 -155.868628 

11 fitted 81.120729 5 -152.241459 

12 R 45.373551 2 -86.747101 

13 

14 

15 Explanation of Tests 

16 

17 Test 1: Do responses and/or variances differ among Dose levels? 

18 (A2 vs. R) 

19 Test 2: Are Variances Homogeneous? (A1 vs A2) 

20 Test 3: Are variances adequately modeled? (A2 vs. A3) 

21 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

22 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

23 

24 Tests of Interest 

25 

26 Test -2*log(Likelihood Ratio) Test df p-value 

27 

28 Test 1 80.9658 8 <.0001 

29 Test 2 58.1955 4 <.0001 

30 Test 3 1.84427 3 0.6053 

31 Test 4 7.62717 2 0.02207 

32 

33 The p-value for Test 1 is less than .05. There appears to be a 

34 difference between response and/or variances among the dose levels 

35 It seems appropriate to model the data 

36 

37 The p-value for Test 2 is less than .1. A non-homogeneous variance 

38 model appears to be appropriate 

39 

40 The p-value for Test 3 is greater than .1. The modeled variance appears 

41 to be appropriate here 

42 

43 The p-value for Test 4 is less than .1. You may want to try a different 

44 model 

45 

46 

47 Benchmark Dose Computation 

48 

49 Specified effect = 1 

50 

51 Risk Type = Estimated standard deviations from the control mean 

52 

53 Confidence level = 0.95 

54 

55 BMD = 247.728 

56 

57 BMDL = 132.818 

58 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-105 —DO NOT CITE OR QUOTE 

1 E.2.14.4. Figure for additional model presented: Hill, unrestricted 

 1.1

 1.2

 1.3

 1.4

 1.5

 1.6

 1.7

 1.8

 1.9

 0 5000 10000 15000 20000 25000 30000 35000

Mean Response

dose

Hill Model

10:26 01/12 2010

Hill

2 

3 

4 Kattainen et al., 2001: 3rd molar length in pups 

5 

6 

7 E.2.14.5. Output for additional model presented: Hill, unrestricted 

8 Kattainen et al., 2001: 3rd molar length in pups 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\1\Blood\25_Katt_2001_3molar_length_Hill_Unrest_1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\25_Katt_2001_3molar_length_Hill_Unrest_1.plt 

13 Tue Jan 12 10:26:49 2010 

14 ==================================================================== 

15 

16 Figure 3 female only 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 lalpha = -2.37155 

39 rho = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-106 —DO NOT CITE OR QUOTE 

1 intercept = 1.85591 

2 v = -0.507874 

3 n = 0.845971 

4 k = 1606.5 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 lalpha rho intercept v n k 

10 

11 lalpha NA NA NA NA NA NA 

12 

13 rho NA NA NA NA NA NA 

14 

15 intercept NA NA 1 NA 0.00038 0.00013 

16 

17 v NA NA NA NA NA NA 

18 

19 n NA NA 0.00038 NA 1 -1.1 

20 

21 k NA NA 0.00013 NA -1.1 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha 7.01946 NA NA NA 

30 rho -20.2971 NA NA NA 

31 intercept 1.57098 NA NA NA 

32 v 4.02956 NA NA NA 

33 n 13.2039 NA NA NA 

34 k 240356 NA NA NA 

35 

36 At least some variance estimates are negative. 

37 THIS USUALLY MEANS THE MODEL HAS NOT CONVERGED! 

38 Try again from another starting point. 

39 

40 

41 

42 Table of Data and Estimated Values of Interest 

43 

44 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

45 ------ --- -------- -------- ----------- ----------- ---------- 

46 

47 0 16 1.86 1.57 0.0661 0.342 3.34 

48 1763 17 1.58 1.57 0.185 0.342 0.0747 

49 4944 15 1.6 1.57 0.265 0.342 0.284 

50 1.271e+004 12 1.5 1.57 0.221 0.342 -0.68 

51 3.704e+004 19 1.35 1.57 0.515 0.342 -2.85 

52 

53 

54 

55 Model Descriptions for likelihoods calculated 

56 

57 

58 Model A1: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma^2 

60 

61 Model A2: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma(i)^2 

63 

64 Model A3: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

66 Model A3 uses any fixed variance parameters that 

67 were specified by the user 

68 

69 Model R: Yi = Mu + e(i) 

70 Var{e(i)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-107 —DO NOT CITE OR QUOTE 

1 

2 

3 Likelihoods of Interest 

4 

5 Model Log(likelihood) # Param's AIC 

6 A1 56.758717 6 -101.517434 

7 A2 85.856450 10 -151.712901 

8 A3 84.934314 7 -155.868628 

9 fitted 45.373551 6 -78.747101 

10 R 45.373551 2 -86.747101 

11 

12 

13 Explanation of Tests 

14 

15 Test 1: Do responses and/or variances differ among Dose levels? 

16 (A2 vs. R) 

17 Test 2: Are Variances Homogeneous? (A1 vs A2) 

18 Test 3: Are variances adequately modeled? (A2 vs. A3) 

19 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

20 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

21 

22 Tests of Interest 

23 

24 Test -2*log(Likelihood Ratio) Test df p-value 

25 

26 Test 1 80.9658 8 <.0001 

27 Test 2 58.1955 4 <.0001 

28 Test 3 1.84427 3 0.6053 

29 Test 4 79.1215 1 <.0001 

30 

31 The p-value for Test 1 is less than .05. There appears to be a 

32 difference between response and/or variances among the dose levels 

33 It seems appropriate to model the data 

34 

35 The p-value for Test 2 is less than .1. A non-homogeneous variance 

36 model appears to be appropriate 

37 

38 The p-value for Test 3 is greater than .1. The modeled variance appears 

39 to be appropriate here 

40 

41 The p-value for Test 4 is less than .1. You may want to try a different 

42 model 

43 

44 

45 Benchmark Dose Computation 

46 

47 Specified effect = 1 

48 

49 Risk Type = Estimated standard deviations from the control mean 

50 

51 Confidence level = 0.95 

52 

53 BMD = 200720 

54 

55 

56 BMDL computation failed. 

57 

58 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-108 —DO NOT CITE OR QUOTE 

1 E.2.15. Keller et al. (2006): Missing Mandibular Molars in CBA J Mice 

2 E.2.15.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2

 pValue a AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

gamma 1 0.105 52.510 1.844E+03 4.959E+02 

logistic 2 0.334 49.984 1.692E+03 1.220E+03 

log-logistic 1 0.105 52.524 2.210E+03 1.330E+03 

log-probit, 

unrestricted 1 0.105 52.524 2.119E+03 1.336E+03 slope unrestricted 

multistage, 1-

degree b 3 0.255 50.434 6.014E+02 4.203E+02 

multistage, 2-

degree 1 0.122 51.394 1.057E+03 5.324E+02 

multistage, 3-

degree 1 0.150 50.855 9.452E+02 5.285E+02 

probit 2 0.342 49.905 1.614E+03 1.132E+03 

Weibull 1 0.108 52.221 1.514E+03 5.160E+02 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model, BMDS output presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-109 —DO NOT CITE OR QUOTE 

1 

2 E.2.15.2. Figure for Selected Model: Multistage, 1-Degree 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 5000 10000 15000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

10:27 01/12 2010

BMDL BMD

 

Multistage

3 

4 

5 Keller et al., 2007: Missing molars

6 

7 

8 E.2.15.3. Output File for Selected Model: Multistage, 1-Degree 

9 Keller et al., 2007: Missing molars 

10 ==================================================================== 

11 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

12 Input Data File: C:\1\Blood\26_Keller_2007_mand_molars_Multi1_1.(d) 

13 Gnuplot Plotting File: C:\1\Blood\26_Keller_2007_mand_molars_Multi1_1.plt 

14 Tue Jan 12 10:27:33 2010 

15 ==================================================================== 

16 

17 Table 1 using mandibular molars only 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the probability function is: 

21 

22 P[response] = background + (1-background)*[1-EXP( 

23 -beta1*dose^1)] 

24 

25 The parameter betas are restricted to be positive 

26 

27 

28 Dependent variable = DichEff 

29 Independent variable = Dose 

30 

31 Total number of observations = 4 

32 Total number of records with missing values = 0 

33 Total number of parameters in model = 2 

34 Total number of specified parameters = 0 

35 Degree of polynomial = 1 

36 

37 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-110 —DO NOT CITE OR QUOTE 

1 Parameter Convergence has been set to: 1e-008 

2 

3 

4 

5 Default Initial Parameter Values 

6 Background = 0 

7 Beta(1) = 5.51735e+015 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -Background 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 Beta(1) 

17 

18 Beta(1) 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0 * * * 

27 Beta(1) 0.000175192 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -21.5798 4 

37 Fitted model -24.2169 1 5.27424 3 0.1528 

38 Reduced model -71.326 1 99.4926 3 <.0001 

39 

40 AIC: 50.4338 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0000 0.000 0.000 29 0.000 

48 296.0903 0.0506 1.163 2.000 23 0.797 

49 2364.8010 0.3392 9.837 6.000 29 -1.505 

50 18764.0000 0.9626 28.879 30.000 30 1.079 

51 

52 Chi^2 = 4.06 d.f. = 3 P-value = 0.2547 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.1 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 601.401 

64 

65 BMDL = 420.296 

66 

67 BMDU = 862.599 

68 

69 Taken together, (420.296, 862.599) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-111 —DO NOT CITE OR QUOTE 

1 

2 E.2.16. Kociba et al. (1978): Urinary Coproporphyrins, Females (Table 2) 

3 E.2.16.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2) 2 0.03 18.65 <0.0001 82.98 1.3E+04 7.4E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.03 18.65 <0.0001 82.98 1.3E+04 7.4E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.03 7.49 0.01 73.82 8.6E+02 4.0E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.03 0.72 N/A 69.05 3.4E+03 8.7E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.03 0.72 N/A 69.05 3.4E+03 8.7E+02 nonconstant variance, 

power unrestricted 

Hill 0 0.03 0.72 NA 69.05 3.0E+03 error nonconstant variance, n 

restricted >1 

Hill 0 0.03 0.72 NA 69.05 3.0E+03 error nonconstant variance, n 

unrestricted 

linear 2 0.03 17.90 0.00 82.23 9.9E+03 2.1E+03 nonconstant variance 

polynomial 2 0.03 17.90 0.00 82.23 9.9E+03 2.1E+03 nonconstant variance 

power 2 0.03 17.90 0.00 82.23 9.9E+03 2.1E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 1 0.03 12.36 0.00 78.69 6.3E+02 5.6E-06 nonconstant variance, 

power unrestricted 

exponential (M2) 2 0.03 11.60 0.00 81.00 1.4E+04 9.5E+03 constant variance, power 

restricted ≥1 

exponential (M3) 2 0.03 11.60 0.00 81.00 1.4E+04 9.5E+03 constant variance, power 

restricted ≥1 

exponential (M4) c 1 0.03 4.05 0.04 75.44 1.4E+03 6.5E+02 constant variance, power 

restricted ≥1 

exponential (M5) 0 0.03 0.41 N/A 73.80 3.5E+03 8.8E+02 constant variance, power 

restricted ≥1 

exponential (M5) d 0 0.03 0.41 N/A 73.80 3.5E+03 8.8E+02 constant variance, power 

unrestricted 

Hill 0 0.03 0.41 NA 73.80 3.3E+03 error constant variance, n 

restricted >1 

Hill d 0 0.03 0.41 NA 73.80 3.3E+03 error constant variance, n 

unrestricted 

linear 2 0.03 11.02 0.00 80.41 1.1E+04 7.3E+03 constant variance 

polynomial 2 0.03 11.02 0.00 80.41 1.1E+04 7.3E+03 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-112 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

power 2 0.03 11.02 0.00 80.41 1.1E+04 7.3E+03 constant variance, power 

restricted ≥1, bound hit 

power d 1 0.03 7.99 0.00 79.38 2.5E+03 1.9E+02 constant variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-113 —DO NOT CITE OR QUOTE 

1 E.2.17. Kociba et al. (1978): Uroporphyrin per Creatinine, Females 

2 E.2.17.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.49 1.09 0.58 -93.46 7.6E+03 5.3E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.49 1.09 0.58 -93.46 7.6E+03 5.3E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.49 0.97 0.32 -91.57 5.7E+03 1.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.49 0.51 N/A -90.03 4.0E+03 2.0E+03 nonconstant variance, 

power restricted ≥1 

Hill 0 0.49 0.51 NA -90.03 4.1E+03 2.0E+03 nonconstant variance, n 

restricted >1 

linear 2 0.49 0.98 0.61 -93.57 5.9E+03 3.7E+03 nonconstant variance 

polynomial 2 0.49 0.98 0.61 -93.57 5.9E+03 3.7E+03 nonconstant variance 

power 1 0.49 0.97 0.33 -91.58 6.3E+03 3.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M2) 2 0.49 0.56 0.75 -93.83 9.0E+03 6.9E+03 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.49 0.56 0.75 -93.83 9.0E+03 6.9E+03 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.49 0.46 0.50 -91.93 6.7E+03 2.2E+03 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.49 0.20 N/A -90.19 4.2E+03 2.3E+03 constant variance, 

power restricted ≥1 

linear c 2 0.49 0.46 0.79 -93.93 7.2E+03 5.1E+03 constant variance 

polynomial 2 0.49 0.46 0.79 -93.93 7.2E+03 5.1E+03 constant variance 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-114 —DO NOT CITE OR QUOTE 

1 E.2.17.2. Figure for Selected Model: Linear, Constant Variance 

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 5000 10000 15000 20000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:40 11/16 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.2.17.3. Output File for Selected Model: Linear, Constant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: 

11 C:\USEPA\BMDS21\AD\Blood\LinearConstVar_BMR1_Females_uroporphyrin_per_creatinine.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AD\Blood\LinearConstVar_BMR1_Females_uroporphyrin_per_creatinine.plt 

14 Mon Nov 16 13:40:10 2009 

15 ==================================================================== 

16 

17 Table 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 rho is set to 0 

28 Signs of the polynomial coefficients are not restricted 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-115 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 0.0030385 

4 rho = 0 Specified 

5 beta_0 = 0.149139 

6 beta_1 = 6.92935e-006 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 ( *** The model parameter(s) -rho 

12 have been estimated at a boundary point, or have been specified by the user, 

13 and do not appear in the correlation matrix ) 

14 

15 alpha beta_0 beta_1 

16 

17 alpha 1 -5.8e-012 2.2e-011 

18 

19 beta_0 -5.8e-012 1 -0.6 

20 

21 beta_1 2.2e-011 -0.6 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 alpha 0.00248773 0.000786688 0.000945846 0.00402961 

30 beta_0 0.149139 0.0139684 0.121762 0.176517 

31 beta_1 6.92935e-006 1.29185e-006 4.39737e-006 9.46132e-006 

32 

33 

34 

35 Table of Data and Estimated Values of Interest 

36 

37 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

38 ------ --- -------- -------- ----------- ----------- ---------- 

39 

40 0 5 0.157 0.149 0.05 0.0499 0.352 

41 852.5 5 0.143 0.155 0.037 0.0499 -0.54 

42 3942 5 0.181 0.176 0.053 0.0499 0.204 

43 2.125e+004 5 0.296 0.296 0.074 0.0499 -0.0161 

44 

45 

46 

47 Model Descriptions for likelihoods calculated 

48 

49 

50 Model A1: Yij = Mu(i) + e(ij) 

51 Var{e(ij)} = Sigma^2 

52 

53 Model A2: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma(i)^2 

55 

56 Model A3: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma^2 

58 Model A3 uses any fixed variance parameters that 

59 were specified by the user 

60 

61 Model R: Yi = Mu + e(i) 

62 Var{e(i)} = Sigma^2 

63 

64 

65 Likelihoods of Interest 

66 

67 Model Log(likelihood) # Param's AIC 

68 A1 50.195349 5 -90.390697 

69 A2 51.400051 8 -86.800103 

70 A3 50.195349 5 -90.390697 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-116 —DO NOT CITE OR QUOTE 

1 fitted 49.963861 3 -93.927722 

2 R 41.049755 2 -78.099510 

3 

4 

5 Explanation of Tests 

6 

7 Test 1: Do responses and/or variances differ among Dose levels? 

8 (A2 vs. R) 

9 Test 2: Are Variances Homogeneous? (A1 vs A2) 

10 Test 3: Are variances adequately modeled? (A2 vs. A3) 

11 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

12 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

13 

14 Tests of Interest 

15 

16 Test -2*log(Likelihood Ratio) Test df p-value 

17 

18 Test 1 20.7006 6 0.002076 

19 Test 2 2.40941 3 0.4919 

20 Test 3 2.40941 3 0.4919 

21 Test 4 0.462975 2 0.7934 

22 

23 The p-value for Test 1 is less than .05. There appears to be a 

24 difference between response and/or variances among the dose levels 

25 It seems appropriate to model the data 

26 

27 The p-value for Test 2 is greater than .1. A homogeneous variance 

28 model appears to be appropriate here 

29 

30 

31 The p-value for Test 3 is greater than .1. The modeled variance appears 

32 to be appropriate here 

33 

34 The p-value for Test 4 is greater than .1. The model chosen seems 

35 to adequately describe the data 

36 

37 

38 Benchmark Dose Computation 

39 

40 Specified effect = 1 

41 

42 Risk Type = Estimated standard deviations from the control mean 

43 

44 Confidence level = 0.95 

45 

46 BMD = 7197.95 

47 

48 

49 BMDL = 5116.98 

50 

51 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-117 —DO NOT CITE OR QUOTE 

1 E.2.18. Latchoumycandane and Mathur (2002): Daily Sperm Production 

2 E.2.18.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.85 19.80 <0.0001 94.90 1.2E+04 5.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.85 19.80 <0.0001 94.90 1.2E+04 5.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.85 0.16 0.69 77.26 1.0E+02 3.9E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.85 0.16 0.69 77.26 1.0E+02 3.9E+01 nonconstant variance, 

power restricted ≥1 

Hill 1 0.85 0.00 0.95 77.10 6.3E+01 6.2E+00 nonconstant variance, n 

restricted >1, bound hit 

Hill 0 0.85 0.00 NA 79.10 5.1E+01 1.7E-05 nonconstant variance, n 

unrestricted 

linear 2 0.85 20.13 <.0001 95.23 1.3E+04 7.3E+03 nonconstant variance 

polynomial 1 0.85 9.62 0.00 86.72 1.4E+03 7.9E+02 nonconstant variance 

power 2 0.85 20.13 <.0001 95.23 1.3E+04 7.3E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.85 20.71 <0.0001 93.82 9.6E+03 5.2E+03 constant variance, power 

restricted ≥1 

exponential (M3) 2 0.85 20.71 <0.0001 93.82 9.6E+03 5.2E+03 constant variance, power 

restricted ≥1 

exponential (M4) d 1 0.85 0.15 0.70 75.26 1.1E+02 4.4E+01 constant variance, power 

restricted ≥1 

exponential (M5) 0 0.85 0.15 N/A 77.26 1.6E+02 4.4E+01 constant variance, power 

restricted ≥1 

Hill, rextricted c 1 0.85 0.00 0.98 118.11 3.40E+02 1.51E-02 

constant variance, n 

restricted >1, bound 

hit 

Hill, unrestricted d 0 0.85 0.00 NA 120.11 3.32E+02 8.77E-03 constant variance, n 

unrestricted 

linear 2 0.85 21.13 <.0001 94.24 1.1E+04 6.7E+03 constant variance 

polynomial 1 0.85 11.01 0.00 86.13 1.1E+03 7.1E+02 constant variance 

power 2 0.85 21.13 <.0001 94.24 1.1E+04 6.7E+03 constant variance, power 

restricted ≥1, bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-118 —DO NOT CITE OR QUOTE 

1 

2 E.2.18.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 5

 10

 15

 20

 25

 30

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Hill Model with 0.95 Confidence Level

10:15 11/27 2009

BMDL BMD

 

Hill

3 

4 

5 

6 E.2.18.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

7 Hit 

8 

9 

10 ==================================================================== 

11 Hill Model. (Version: 2.14; Date: 06/26/2008) 

12 Input Data File: C:\Usepa\Bmds2\Data\HilTCDSet.(d) 

13 Gnuplot Plotting File: C:\Usepa\Bmds2\Data\HilTCDSet.plt 

14 Fri Nov 27 10:15:04 2009 

15 ==================================================================== 

16 

17 BMDS Model Run 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

23 

24 

25 Dependent variable = m_sperm 

26 Independent variable = DOSE 

27 rho is set to 0 

28 Power parameter restricted to be greater than 1 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-119 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 43.3822 

4 rho = 0 Specified 

5 intercept = 22.19 

6 v = -9.09 

7 n = 1.93174 

8 k = 304.417 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -rho -n 

14 have been estimated at a boundary point, or have been specified by 

15 the user, 

16 and do not appear in the correlation matrix ) 

17 

18 alpha intercept v k 

19 

20 alpha 1 6.6e-010 -7.3e-008 6.3e-008 

21 

22 intercept 6.6e-010 1 -0.75 -0.23 

23 

24 v -7.3e-008 -0.75 1 -0.24 

25 

26 k 6.3e-008 -0.23 -0.24 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence 

33 Interval 

34 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. 

35 Limit 

36 alpha 36.1524 10.4363 15.6976 

37 56.6072 

38 intercept 22.1894 2.45468 17.3783 

39 27.0005 

40 v -9.16864 3.2083 -15.4568 -

41 2.88049 

42 n 1 NA 

43 k 178.32 300.643 -410.929 

44 767.569 

45 

46 NA - Indicates that this parameter has hit a bound 

47 implied by some inequality constraint and thus 

48 has no standard error. 

49 

50 

51 

52 Table of Data and Estimated Values of Interest 

53 

54 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

55 ------ --- -------- -------- ----------- ----------- ---------- 

56 

57 0 6 22.2 22.2 6.54 6.01 0.000252 

58 436.7 6 15.7 15.7 6.49 6.01 -0.00371 

59 2579 6 13.7 13.6 5.36 6.01 0.0148 

60 1.509e+004 6 13.1 13.1 7.74 6.01 -0.0113 

61 

62 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-120 —DO NOT CITE OR QUOTE 

1 

2 Model Descriptions for likelihoods calculated 

3 

4 

5 Model A1: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 

8 Model A2: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma(i)^2 

10 

11 Model A3: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma^2 

13 Model A3 uses any fixed variance parameters that 

14 were specified by the user 

15 

16 Model R: Yi = Mu + e(i) 

17 Var{e(i)} = Sigma^2 

18 

19 

20 Likelihoods of Interest 

21 

22 Model Log(likelihood) # Param's AIC 

23 A1 -55.052739 5 120.105478 

24 A2 -54.653533 8 125.307067 

25 A3 -55.052739 5 120.105478 

26 fitted -55.052919 4 118.105839 

27 R -58.755106 2 121.510213 

28 

29 

30 Explanation of Tests 

31 

32 Test 1: Do responses and/or variances differ among Dose levels? 

33 (A2 vs. R) 

34 Test 2: Are Variances Homogeneous? (A1 vs A2) 

35 Test 3: Are variances adequately modeled? (A2 vs. A3) 

36 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

37 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

38 

39 Tests of Interest 

40 

41 Test -2*log(Likelihood Ratio) Test df p-value 

42 

43 Test 1 8.20315 6 0.2236 

44 Test 2 0.798411 3 0.8498 

45 Test 3 0.798411 3 0.8498 

46 Test 4 0.000361116 1 0.9848 

47 

48 The p-value for Test 1 is greater than .05. There may not be a 

49 diffence between responses and/or variances among the dose levels 

50 Modelling the data with a dose/response curve may not be appropriate 

51 

52 The p-value for Test 2 is greater than .1. A homogeneous variance 

53 model appears to be appropriate here 

54 

55 

56 The p-value for Test 3 is greater than .1. The modeled variance appears 

57 to be appropriate here 

58 

59 The p-value for Test 4 is greater than .1. The model chosen seems 

60 to adequately describe the data 

61 

62 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-121 —DO NOT CITE OR QUOTE 

1 Benchmark Dose Computation 

2 

3 Specified effect = 1 

4 

5 Risk Type = Estimated standard deviations from the control mean 

6 

7 Confidence level = 0.95 

8 

9 BMD = 339.732 

10 

11 BMDL = 0.015111 

12 

13 

14 E.2.18.4. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 10000 20000 30000 40000 50000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

07:51 11/27 2009

BMDL BMD

 

Log-Logistic

15 

16 

17 

18 E.2.18.5. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 

19 

20 

21 ==================================================================== 

22 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

23 Input Data File: C:\Usepa\Bmds2\Data\LogTcdSet.(d) 

24 Gnuplot Plotting File: C:\Usepa\Bmds2\Data\LogTcdSet.plt 

25 Fri Nov 27 07:51:12 2009 

26 ==================================================================== 

27 

28 BMDS Model Run 

29 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

30 

31 The form of the probability function is: 

32 

33 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

34 

35 

36 Dependent variable = r_skin 

37 Independent variable = DOSE 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-122 —DO NOT CITE OR QUOTE 

1 Slope parameter is not restricted 

2 

3 Total number of observations = 4 

4 Total number of records with missing values = 0 

5 Maximum number of iterations = 250 

6 Relative Function Convergence has been set to: 1e-008 

7 Parameter Convergence has been set to: 1e-008 

8 

9 

10 

11 User has chosen the log transformed model 

12 

13 

14 Default Initial Parameter Values 

15 background = 0 

16 intercept = -4.78342 

17 slope = 0.469549 

18 

19 

20 Asymptotic Correlation Matrix of Parameter Estimates 

21 

22 ( *** The model parameter(s) -background 

23 have been estimated at a boundary point, or have been specified by 

24 the user, 

25 and do not appear in the correlation matrix ) 

26 

27 intercept slope 

28 

29 intercept 1 -0.98 

30 

31 slope -0.98 1 

32 

33 

34 

35 Parameter Estimates 

36 

37 95.0% Wald Confidence 

38 Interval 

39 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. 

40 Limit 

41 background 0 * * * 

42 intercept -4.84059 * * * 

43 slope 0.475472 * * * 

44 

45 * - Indicates that this value is not calculated. 

46 

47 

48 

49 Analysis of Deviance Table 

50 

51 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

52 Full model -71.5177 4 

53 Fitted model -71.5376 2 0.0398444 2 0.9803 

54 Reduced model -95.8498 1 48.6642 3 <.0001 

55 

56 AIC: 147.075 

57 

58 

59 Goodness of Fit 

60 Scaled 

61 Dose Est._Prob. Expected Observed Size Residual 

62 ------------------------------------------------------------------------ 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-123 —DO NOT CITE OR QUOTE 

1 0.0000 0.0000 0.000 0.000 38 0.000 

2 316.0000 0.1087 4.784 5.000 44 0.105 

3 4714.0000 0.3060 13.464 13.000 44 -0.152 

4 50105.0000 0.5756 24.753 25.000 43 0.076 

5 

6 Chi^2 = 0.04 d.f. = 2 P-value = 0.9803 

7 

8 

9 Benchmark Dose Computation 

10 

11 Specified effect = 0.1 

12 

13 Risk Type = Extra risk 

14 

15 Confidence level = 0.95 

16 

17 BMD = 259.682 

18 

19 BMDL = 31.788 

20 

21 

22 E.2.19. Li et al. (1997): Follicle-Stimulating Hormone 

23 E.2.19.1. Summary Table of BMDS Modeling Results 

24 

Model a

Degrees 

of 

Freedom 

χ 2 pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) 8 <0.0001 1095.433 2.898E+05 2.286E+05 

exponential (M3) 8 <0.0001 1095.433 2.898E+05 2.286E+05 power bound hit 

exponential (M4) 7 <0.0001 1059.480 1.891E+04 5.471E+03 

exponential (M5) 6 <0.0001 1066.195 6.118E+04 4.729E+02 

Hill 7 <.0001 1056.455 2.993E+03 1.081E+03 n lower bound hit 

linear 8 <.0001 1077.819 1.109E+05 7.503E+04 

polynomial 9 <.0001 1155.670 error error 

power c 8 <.0001 1077.819 1.109E+05 7.503E+04 power bound hit 

Hill, unrestricted 6 0.001 1039.476 1.206E+02 error n unrestricted 

power, unrestricted

d 7 0.002 1037.471 1.078E+02 1.353E+01 power unrestricted 

a

 Non-constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

d

 Alternate model, BMDS output also presented in this appendix 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-124 —DO NOT CITE OR QUOTE 

1 E.2.19.2. Figure for Selected Model: Power 

 0

 100

 200

 300

 400

 500

 600

 700

 0 100000 200000 300000 400000 500000 600000

Mean Response

dose

Power Model with 0.95 Confidence Level

10:32 01/12 2010

BMDL BMD

 

Power

2 

3 

4 Li et al., 1997: FSH 

5 

6 

7 E.2.19.3. Output for Selected Model: Power 

8 Li et al., 1997: FSH 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\1\Blood\72_Li_1997_FSH_Power_BMR1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\72_Li_1997_FSH_Power_BMR1.plt 

13 Tue Jan 12 10:32:04 2010 

14 ==================================================================== 

15 

16 Figure 3: FSH in female S-D rats 24hr after dosing, 22 day old rats 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is restricted to be greater than or equal to 1 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 10 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 lalpha = 9.8191 

39 rho = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-125 —DO NOT CITE OR QUOTE 

1 control = 22.1591 

2 slope = 8.17907 

3 power = 0.293959 

4 

5 

6 Asymptotic Correlation Matrix of Parameter Estimates 

7 

8 ( *** The model parameter(s) -power 

9 have been estimated at a boundary point, or have been specified by the user, 

10 and do not appear in the correlation matrix ) 

11 

12 lalpha rho control slope 

13 

14 lalpha 1 -0.99 -0.29 -0.035 

15 

16 rho -0.99 1 0.2 0.035 

17 

18 control -0.29 0.2 1 -0.36 

19 

20 slope -0.035 0.035 -0.36 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 lalpha 3.49167 1.22596 1.08884 5.89451 

29 rho 1.27289 0.242042 0.798492 1.74728 

30 control 87.5089 12.9454 62.1364 112.881 

31 slope 0.000889717 0.000166742 0.000562908 0.00121653 

32 power 1 NA 

33 

34 NA - Indicates that this parameter has hit a bound 

35 implied by some inequality constraint and thus 

36 has no standard error. 

37 

38 

39 

40 Table of Data and Estimated Values of Interest 

41 

42 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

43 ------ --- -------- -------- ----------- ----------- ---------- 

44 

45 0 10 23.9 87.5 29.6 98.7 -2.04 

46 146.5 10 22.2 87.6 48.5 98.8 -2.1 

47 440.1 10 85.2 87.9 94.3 99 -0.0854 

48 1156 10 73.3 88.5 48.5 99.4 -0.485 

49 3232 10 126 90.4 159 101 1.12 

50 8266 10 132 94.9 116 104 1.13 

51 2.388e+004 10 117 109 51.2 113 0.224 

52 6.608e+004 10 304 146 154 137 3.65 

53 2.127e+005 10 347 277 151 205 1.08 

54 6.497e+005 10 455 666 286 359 -1.85 

55 

56 

57 

58 Model Descriptions for likelihoods calculated 

59 

60 

61 Model A1: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 

64 Model A2: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma(i)^2 

66 

67 Model A3: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

69 Model A3 uses any fixed variance parameters that 

70 were specified by the user 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-126 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yi = Mu + e(i) 

3 Var{e(i)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) # Param's AIC 

9 A1 -535.687163 11 1093.374327 

10 A2 -496.367061 20 1032.734122 

11 A3 -502.709623 12 1029.419246 

12 fitted -534.909723 4 1077.819445 

13 R -574.835246 2 1153.670492 

14 

15 

16 Explanation of Tests 

17 

18 Test 1: Do responses and/or variances differ among Dose levels? 

19 (A2 vs. R) 

20 Test 2: Are Variances Homogeneous? (A1 vs A2) 

21 Test 3: Are variances adequately modeled? (A2 vs. A3) 

22 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

23 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

24 

25 Tests of Interest 

26 

27 Test -2*log(Likelihood Ratio) Test df p-value 

28 

29 Test 1 156.936 18 <.0001 

30 Test 2 78.6402 9 <.0001 

31 Test 3 12.6851 8 0.1232 

32 Test 4 64.4002 8 <.0001 

33 

34 The p-value for Test 1 is less than .05. There appears to be a 

35 difference between response and/or variances among the dose levels 

36 It seems appropriate to model the data 

37 

38 The p-value for Test 2 is less than .1. A non-homogeneous variance 

39 model appears to be appropriate 

40 

41 The p-value for Test 3 is greater than .1. The modeled variance appears 

42 to be appropriate here 

43 

44 The p-value for Test 4 is less than .1. You may want to try a different 

45 model 

46 

47 

48 Benchmark Dose Computation 

49 

50 Specified effect = 1 

51 

52 Risk Type = Estimated standard deviations from the control mean 

53 

54 Confidence level = 0.95 

55 

56 BMD = 110907 

57 

58 

59 BMDL = 75025.9 

60 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-127 —DO NOT CITE OR QUOTE 

1 E.2.19.4. Figure for Unrestricted Model: Power, Unrestricted 

 0

 100

 200

 300

 400

 500

 600

 700

 0 100000 200000 300000 400000 500000 600000

Mean Response

dose

Power Model with 0.95 Confidence Level

10:32 01/12 2010

BMDBMDL

 

Power

2 

3 

4 Li et al., 1997: FSH 

5 

6 

7 E.2.19.5. Output for Unrestricted Model: Power, Unrestricted 

8 Li et al., 1997: FSH 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\1\Blood\72_Li_1997_FSH_Power_Unrest_BMR1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\72_Li_1997_FSH_Power_Unrest_BMR1.plt 

13 Tue Jan 12 10:32:11 2010 

14 ==================================================================== 

15 

16 Figure 3: FSH in female S-D rats 24hr after dosing, 22 day old rats 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 10 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 lalpha = 9.8191 

39 rho = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-128 —DO NOT CITE OR QUOTE 

1 control = 22.1591 

2 slope = 8.17907 

3 power = 0.293959 

4 

5 

6 Asymptotic Correlation Matrix of Parameter Estimates 

7 

8 lalpha rho control slope power 

9 

10 lalpha 1 -0.99 -0.69 -0.17 0.26 

11 

12 rho -0.99 1 0.65 0.13 -0.23 

13 

14 control -0.69 0.65 1 -0.12 0.029 

15 

16 slope -0.17 0.13 -0.12 1 -0.97 

17 

18 power 0.26 -0.23 0.029 -0.97 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 lalpha 3.6735 1.12114 1.4761 5.8709 

27 rho 1.17908 0.221492 0.744961 1.61319 

28 control 15.8235 6.8753 2.34812 29.2988 

29 slope 7.68345 2.90499 1.98976 13.3771 

30 power 0.30464 0.0336473 0.238692 0.370587 

31 

32 

33 

34 Table of Data and Estimated Values of Interest 

35 

36 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

37 ------ --- -------- -------- ----------- ----------- ---------- 

38 

39 0 10 23.9 15.8 29.6 32 0.795 

40 146.5 10 22.2 50.9 48.5 63.7 -1.43 

41 440.1 10 85.2 64.9 94.3 73.5 0.875 

42 1156 10 73.3 81.7 48.5 84.1 -0.315 

43 3232 10 126 106 159 98.1 0.652 

44 8266 10 132 136 116 114 -0.102 

45 2.388e+004 10 117 181 51.2 135 -1.52 

46 6.608e+004 10 304 242 154 160 1.24 

47 2.127e+005 10 347 338 151 194 0.139 

48 6.497e+005 10 455 469 286 236 -0.187 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-129 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 -535.687163 11 1093.374327 

4 A2 -496.367061 20 1032.734122 

5 A3 -502.709623 12 1029.419246 

6 fitted -513.735602 5 1037.471204 

7 R -574.835246 2 1153.670492 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 156.936 18 <.0001 

24 Test 2 78.6402 9 <.0001 

25 Test 3 12.6851 8 0.1232 

26 Test 4 22.052 7 0.002489 

27 

28 The p-value for Test 1 is less than .05. There appears to be a 

29 difference between response and/or variances among the dose levels 

30 It seems appropriate to model the data 

31 

32 The p-value for Test 2 is less than .1. A non-homogeneous variance 

33 model appears to be appropriate 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is less than .1. You may want to try a different 

39 model 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 107.761 

51 

52 

53 BMDL = 13.5336

54 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-130 —DO NOT CITE OR QUOTE 

1 

2 E.2.20. Li et al. (2006): Hormone Levels (Estradiol) 

3 E.2.20.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.44 4.95 0.08 271.02 7.7E+03 2.8E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.44 4.95 0.08 271.02 7.7E+03 2.8E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.44 0.34 0.56 268.41 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.44 0.34 N/A 270.41 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.44 0.34 N/A 270.41 error error nonconstant variance, 

power unrestricted 

Hill 1 0.44 0.34 0.56 268.41 error error nonconstant variance, n 

restricted >1 

linear 2 0.44 4.87 0.09 270.95 8.7E+03 2.7E+03 nonconstant variance 

polynomial 2 0.44 4.87 0.09 270.95 8.7E+03 2.7E+03 nonconstant variance 

power 2 0.44 4.87 0.09 270.95 8.7E+03 2.7E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 2 0.44 0.34 0.84 266.41 2.8E+05 error nonconstant variance, 

power unrestricted 

exponential (M2) 2 0.44 3.72 0.16 269.03 7.8E+03 3.1E+03 constant variance, power 

restricted ≥1 

exponential (M3) 2 0.44 3.72 0.16 269.03 7.8E+03 3.1E+03 constant variance, power 

restricted ≥1 

exponential (M4) 1 0.44 0.91 0.34 268.21 error error constant variance, power 

restricted ≥1 

exponential (M5) 0 0.44 0.91 N/A 270.21 error error constant variance, power 

restricted ≥1 

exponential (M5) d 0 0.44 0.91 N/A 270.21 error error constant variance, power 

unrestricted 

Hill 0 0.44 0.91 NA 270.21 error error constant variance, n 

restricted >1 

Hill d 0 0.44 0.96 NA 270.26 5.1E+15 5.1E+15 constant variance, n 

unrestricted 

linear c 2 0.44 3.65 0.16 268.95 8.8E+03 3.0E+03 constant variance 

polynomial 2 0.44 3.65 0.16 268.95 8.8E+03 3.0E+03 constant variance 

power 2 0.44 3.65 0.16 268.95 8.8E+03 3.0E+03 constant variance, power 

restricted ≥1, bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-131 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

power d 1 0.44 0.96 0.33 268.27 5.2E+13 error constant variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.2.20.2. Figure for Selected Model: Linear, Constant Variance 

 0

 5

 10

 15

 20

 25

 30

 35

 0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:50 11/16 2009

BMDL BMD

 

Linear

4 

5 

6 

7 E.2.20.3. Output File for Unrestricted Model: Linear, Constant Variance 

8 

9 

10 ==================================================================== 

11 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\LinearConst_BMR1_Li_Estradiol_3d.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\LinearConst_BMR1_Li_Estradiol_3d.plt 

14 Mon Nov 16 13:50:03 2009 

15 ==================================================================== 

16 

17 Figure 3, 3-day estradiol 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-132 —DO NOT CITE OR QUOTE 

1 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

2 

3 

4 Dependent variable = Mean 

5 Independent variable = Dose 

6 rho is set to 0 

7 Signs of the polynomial coefficients are not restricted 

8 A constant variance model is fit 

9 

10 Total number of dose groups = 4 

11 Total number of records with missing values = 0 

12 Maximum number of iterations = 250 

13 Relative Function Convergence has been set to: 1e-008 

14 Parameter Convergence has been set to: 1e-008 

15 

16 

17 

18 Default Initial Parameter Values 

19 alpha = 267.211 

20 rho = 0 Specified 

21 beta_0 = 16.1706 

22 beta_1 = 0.00183421 

23 

24 

25 Asymptotic Correlation Matrix of Parameter Estimates 

26 

27 ( *** The model parameter(s) -rho 

28 have been estimated at a boundary point, or have been specified by the user, 

29 and do not appear in the correlation matrix ) 

30 

31 alpha beta_0 beta_1 

32 

33 alpha 1 2.7e-011 6.4e-013 

34 

35 beta_0 2.7e-011 1 -0.69 

36 

37 beta_1 6.4e-013 -0.69 1 

38 

39 

40 

41 Parameter Estimates 

42 

43 95.0% Wald Confidence Interval 

44 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

45 alpha 263.435 58.9058 147.981 378.888 

46 beta_0 16.1706 3.55948 9.19411 23.147 

47 beta_1 0.00183421 0.00220486 -0.00248724 0.00615566 

48 

49 

50 

51 Table of Data and Estimated Values of Interest 

52 

53 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

54 ------ --- -------- -------- ----------- ----------- ---------- 

55 

56 0 10 10.2 16.2 12.2 16.2 -1.17 

57 87.49 10 19.9 16.3 20 16.2 0.697 

58 1564 10 24.7 19 14.6 16.2 1.11 

59 2823 10 18.1 21.3 17.6 16.2 -0.635 

60 

61 

62 

63 Model Descriptions for likelihoods calculated 

64 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-133 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma^2 

4 Model A3 uses any fixed variance parameters that 

5 were specified by the user 

6 

7 Model R: Yi = Mu + e(i) 

8 Var{e(i)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) # Param's AIC 

14 A1 -129.653527 5 269.307054 

15 A2 -128.294657 8 272.589314 

16 A3 -129.653527 5 269.307054 

17 fitted -131.476105 3 268.952210 

18 R -131.819169 2 267.638338 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Do responses and/or variances differ among Dose levels? 

24 (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A1 vs A2) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

28 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) Test df p-value 

33 

34 Test 1 7.04902 6 0.3163 

35 Test 2 2.71774 3 0.4372 

36 Test 3 2.71774 3 0.4372 

37 Test 4 3.64516 2 0.1616 

38 

39 The p-value for Test 1 is greater than .05. There may not be a 

40 diffence between responses and/or variances among the dose levels 

41 Modelling the data with a dose/response curve may not be appropriate 

42 

43 The p-value for Test 2 is greater than .1. A homogeneous variance 

44 model appears to be appropriate here 

45 

46 

47 The p-value for Test 3 is greater than .1. The modeled variance appears 

48 to be appropriate here 

49 

50 The p-value for Test 4 is greater than .1. The model chosen seems 

51 to adequately describe the data 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 1 

57 

58 Risk Type = Estimated standard deviations from the control mean 

59 

60 Confidence level = 0.95 

61 

62 BMD = 8848.86 

63 

64 

65 BMDL = 2963.62 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-134 —DO NOT CITE OR QUOTE 

1 E.2.20.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

2 Unrestricted 

 0

 5

 10

 15

 20

 25

 30

 35

 0 500 1000 1500 2000 2500

Mean Response

dose

Exponential_beta Model 5

13:50 11/16 2009

BMD

Exponential

3 

4 

5 

6 E.2.20.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

7 Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\ExpConst_Unrest_BMR1_Li_Estradiol_3d.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 13:50:07 2009 

15 ==================================================================== 

16 

17 Figure 3, 3-day estradiol 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-135 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 rho is set to 0. 

4 A constant variance model is fit. 

5 

6 Total number of dose groups = 4 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 5 

18 -------- -------- 

19 lnalpha 5.48268 

20 rho(S) 0 

21 a 9.65979 

22 b 0.000592388 

23 c 2.68754 

24 d 1 

25 

26 (S) = Specified 

27 

28 

29 

30 Parameter Estimates 

31 

32 Variable Model 5 

33 -------- ------- 

34 lnalpha 5.50531 

35 rho 0 

36 a 10.1682 

37 b 0.0192802 

38 c 2.10526 

39 d 1.3399 

40 

41 NC = No Convergence 

42 

43 

44 Table of Stats From Input Data 

45 

46 Dose N Obs Mean Obs Std Dev 

47 ----- --- ---------- ------------- 

48 0 10 10.17 12.18 

49 87.49 10 19.91 19.97 

50 1564 10 24.72 14.55 

51 2823 10 18.09 17.6 

52 

53 

54 Estimated Values of Interest 

55 

56 Dose Est Mean Est Std Scaled Residual 

57 ------ ---------- --------- ---------------- 

58 0 10.17 15.68 2.254e-007 

59 87.49 19.91 15.68 -2.355e-007 

60 1564 21.41 15.68 0.669 

61 2823 21.41 15.68 -0.669 

62 

63 

64 

65 Other models for which likelihoods are calculated: 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-136 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

5 

6 Model R: Yij = Mu + e(i) 

7 Var{e(ij)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) DF AIC 

13 ------- ----------------- ---- ------------ 

14 A1 -129.6535 5 269.3071 

15 A2 -128.2947 8 272.5893 

16 A3 -129.6535 5 269.3071 

17 R -131.8192 2 267.6383 

18 5 -130.1062 5 270.2123 

19 

20 

21 Additive constant for all log-likelihoods = -36.76. This constant added to the 

22 above values gives the log-likelihood including the term that does not 

23 depend on the model parameters. 

24 

25 

26 Explanation of Tests 

27 

28 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

29 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

30 Test 3: Are variances adequately modeled? (A2 vs. A3) 

31 

32 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

33 

34 

35 Tests of Interest 

36 

37 Test -2*log(Likelihood Ratio) D. F. p-value 

38 -------- ------------------------ ------ -------------- 

39 Test 1 7.049 6 0.3163 

40 Test 2 2.718 3 0.4372 

41 Test 3 2.718 3 0.4372 

42 Test 7a 0.9053 0 N/A 

43 

44 

45 The p-value for Test 1 is greater than .05. There may not be a 

46 diffence between responses and/or variances among the dose levels 

47 Modelling the data with a dose/response curve may not be appropriate. 

48 

49 The p-value for Test 2 is greater than .1. A homogeneous 

50 variance model appears to be appropriate here. 

51 

52 The p-value for Test 3 is greater than .1. The modeled 

53 variance appears to be appropriate here. 

54 

55 Degrees of freedom for Test 7a are less than or equal to 0. 

56 The Chi-Square test for fit is not valid. 

57 

58 

59 Benchmark Dose Computations: 

60 

61 Specified Effect = 1.000000 

62 

63 Risk Type = Estimated standard deviations from control 

64 

65 Confidence Level = 0.950000 

66 

67 BMD = Not_Computed 

68 

69 BMDL = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-137 —DO NOT CITE OR QUOTE 

1 

2 E.2.20.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 0

 5

 10

 15

 20

 25

 30

 35

 0 1e+015 2e+015 3e+015 4e+015 5e+015

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:50 11/16 2009

BMDBMDL

 

Hill

3 

4 

5 

6 E.2.20.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\HillConst_Unrest_BMR1_Li_Estradiol_3d.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AD\Blood\HillConst_Unrest_BMR1_Li_Estradiol_3d.plt 

14 Mon Nov 16 13:50:08 2009 

15 ==================================================================== 

16 

17 Figure 3, 3-day estradiol 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 rho is set to 0 

28 Power parameter is not restricted 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-138 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 alpha = 267.211 

5 rho = 0 Specified 

6 intercept = 10.1682 

7 v = 14.5566 

8 n = 0.0272301 

9 k = 109.605 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -rho 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 alpha intercept v n k 

19 

20 alpha 1 9.3e-007 NA 0.00038 NA 

21 

22 intercept 9.3e-007 1 NA 0.047 NA 

23 

24 v NA NA NA NA NA 

25 

26 n 0.00038 0.047 NA 1 NA 

27 

28 k NA NA NA NA NA 

29 

30 

31 NA - This parameter's variance has been estimated as zero or less. 

32 THE MODEL HAS PROBABLY NOT CONVERGED!!! 

33 

34 

35 

36 Parameter Estimates 

37 

38 95.0% Wald Confidence Interval 

39 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

40 alpha 246.316 NA NA NA 

41 intercept 10.168 NA NA NA 

42 v 23.0562 NA NA NA 

43 n 0.030228 NA NA NA 

44 k 68005.7 NA NA NA 

45 

46 At least some variance estimates are negative. 

47 THIS USUALLY MEANS THE MODEL HAS NOT CONVERGED! 

48 Try again from another starting point. 

49 

50 

51 

52 Table of Data and Estimated Values of Interest 

53 

54 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

55 ------ --- -------- -------- ----------- ----------- ---------- 

56 

57 0 10 10.2 10.2 12.2 15.7 4.22e-005 

58 87.49 10 19.9 20.5 20 15.7 -0.127 

59 1564 10 24.7 21 14.6 15.7 0.743 

60 2823 10 18.1 21.1 17.6 15.7 -0.615 

61 

62 Degrees of freedom for Test A3 vs fitted <= 0 

63 

64 

65 

66 Model Descriptions for likelihoods calculated 

67 

68 

69 Model A1: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-139 —DO NOT CITE OR QUOTE 

1 

2 Model A2: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma(i)^2 

4 

5 Model A3: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 Model A3 uses any fixed variance parameters that 

8 were specified by the user 

9 

10 Model R: Yi = Mu + e(i) 

11 Var{e(i)} = Sigma^2 

12 

13 

14 Likelihoods of Interest 

15 

16 Model Log(likelihood) # Param's AIC 

17 A1 -129.653527 5 269.307054 

18 A2 -128.294657 8 272.589314 

19 A3 -129.653527 5 269.307054 

20 fitted -130.132269 5 270.264537 

21 R -131.819169 2 267.638338 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Do responses and/or variances differ among Dose levels? 

27 (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A1 vs A2) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

31 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

32 

33 Tests of Interest 

34 

35 Test -2*log(Likelihood Ratio) Test df p-value 

36 

37 Test 1 7.04902 6 0.3163 

38 Test 2 2.71774 3 0.4372 

39 Test 3 2.71774 3 0.4372 

40 Test 4 0.957483 0 NA 

41 

42 The p-value for Test 1 is greater than .05. There may not be a 

43 diffence between responses and/or variances among the dose levels 

44 Modelling the data with a dose/response curve may not be appropriate 

45 

46 The p-value for Test 2 is greater than .1. A homogeneous variance 

47 model appears to be appropriate here 

48 

49 

50 The p-value for Test 3 is greater than .1. The modeled variance appears 

51 to be appropriate here 

52 

53 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

54 test for fit is not valid 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 1 

60 

61 Risk Type = Estimated standard deviations from the control mean 

62 

63 Confidence level = 0.95 

64 

65 BMD = 5.11313e+015 

66 

67 BMDL = 5.11313e+015 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-140 —DO NOT CITE OR QUOTE 

1 

2 E.2.20.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

-5

 0

 5

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 15

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 25

 30

 35

 40

 0 500 1000 1500 2000 2500

Mean Response

dose

Power Model

13:50 11/16 2009

Power

3 

4 

5 

6 E.2.20.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\PowerConst_Unrest_BMR1_Li_Estradiol_3d.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AD\Blood\PowerConst_Unrest_BMR1_Li_Estradiol_3d.plt 

14 Mon Nov 16 13:50:08 2009 

15 ==================================================================== 

16 

17 Figure 3, 3-day estradiol 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = control + slope * dose^power 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 rho is set to 0 

28 The power is not restricted 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-141 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 alpha = 267.211 

5 rho = 0 Specified 

6 control = 10.1682 

7 slope = 10.1311 

8 power = 0.00388985 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -rho 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 alpha control slope power 

18 

19 alpha 1 3.9e-009 -6.4e-009 1.1e-008 

20 

21 control 3.9e-009 1 -0.4 0.038 

22 

23 slope -6.4e-009 -0.4 1 -0.91 

24 

25 power 1.1e-008 0.038 -0.91 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 alpha 246.319 55.0786 138.367 354.271 

34 control 10.1675 4.96274 0.440676 19.8943 

35 slope 9.71449 12.3808 -14.5514 33.9803 

36 power 0.0151875 0.171197 -0.320352 0.350727 

37 

38 

39 

40 Table of Data and Estimated Values of Interest 

41 

42 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

43 ------ --- -------- -------- ----------- ----------- ---------- 

44 

45 0 10 10.2 10.2 12.2 15.7 0.000148 

46 87.49 10 19.9 20.6 20 15.7 -0.132 

47 1564 10 24.7 21 14.6 15.7 0.744 

48 2823 10 18.1 21.1 17.6 15.7 -0.612 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-142 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 -129.653527 5 269.307054 

4 A2 -128.294657 8 272.589314 

5 A3 -129.653527 5 269.307054 

6 fitted -130.132565 4 268.265130 

7 R -131.819169 2 267.638338 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 7.04902 6 0.3163 

24 Test 2 2.71774 3 0.4372 

25 Test 3 2.71774 3 0.4372 

26 Test 4 0.958076 1 0.3277 

27 

28 The p-value for Test 1 is greater than .05. There may not be a 

29 diffence between responses and/or variances among the dose levels 

30 Modelling the data with a dose/response curve may not be appropriate 

31 

32 The p-value for Test 2 is greater than .1. A homogeneous variance 

33 model appears to be appropriate here 

34 

35 

36 The p-value for Test 3 is greater than .1. The modeled variance appears 

37 to be appropriate here 

38 

39 The p-value for Test 4 is greater than .1. The model chosen seems 

40 to adequately describe the data 

41 

42 

43 Benchmark Dose Computation 

44 

45 Specified effect = 1 

46 

47 Risk Type = Estimated standard deviations from the control mean 

48 

49 Confidence level = 0.95 

50 

51 BMD = 5.21395e+013 

52 

53 

54 BMDL computation failed. 

55 

56 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-143 —DO NOT CITE OR QUOTE 

1 E.2.21. Li et al. (2006): Hormone Levels (Progesterone) 

2 E.2.21.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2)

c 2 0.00 14.72 0.00 327.86 2.0E+03 7.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.00 14.72 0.00 327.86 2.0E+03 7.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.00 0.60 0.44 315.74 8.3E+00 1.4E-02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.00 0.60 N/A 317.74 2.0E+01 3.5E-02 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 0 0.00 0.60 N/A 317.74 2.0E+01 3.5E-02 nonconstant variance, 

power unrestricted 

Hill 1 0.00 0.60 0.44 315.73 9.0E-01 6.3E-03 nonconstant variance, n 

restricted >1, bound hit 

Hill d 0 0.00 0.62 NA 317.75 1.9E-01 error nonconstant variance, n 

unrestricted 

linear 2 0.00 15.21 0.00 328.35 2.4E+03 1.3E+03 nonconstant variance 

polynomial 2 0.00 15.21 0.00 328.35 2.4E+03 1.3E+03 nonconstant variance 

power 2 0.00 15.21 0.00 328.35 2.4E+03 1.4E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 1 0.00 0.55 0.46 315.69 1.4E-39 1.4E-39 nonconstant variance, 

power unrestricted 

exponential (M2) 2 0.00 2.22 0.33 327.49 2.8E+03 1.1E+03 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.00 2.22 0.33 327.49 2.8E+03 1.1E+03 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.00 0.02 0.88 327.29 2.0E+02 8.3E-01 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.00 0.02 0.88 327.29 2.0E+02 7.8E-01 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.00 0.02 0.88 327.29 2.0E+02 7.8E-01 constant variance, 

power unrestricted 

Hill 0 0.00 0.02 NA 329.29 1.3E+02 1.6E-09 constant variance, n 

restricted >1 

Hill 0 0.00 0.00 NA 329.27 5.5E+02 1.0E-03 constant variance, n 

unrestricted 

linear 2 0.00 2.72 0.26 327.99 2.9E+03 1.7E+03 constant variance 

polynomial 2 0.00 2.72 0.26 327.99 2.9E+03 1.7E+03 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-144 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

power 2 0.00 2.72 0.26 327.99 2.9E+03 1.7E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power 1 0.00 0.02 0.90 327.28 8.1E+02 2.8E-12 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.2.21.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

4 Restricted ≥1 

-10

 0

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 30

 40

 50

 60

 70

 80

 0 500 1000 1500 2000 2500

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

13:48 11/16 2009

BMDL BMD

 

Exponential

5 

6 

7 

8 E.2.21.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_BMR1_Li_Progesterone_3d.(d) 

15 Gnuplot Plotting File: 

16 Mon Nov 16 13:48:35 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-145 —DO NOT CITE OR QUOTE 

1 ==================================================================== 

2 

3 Figure 4, 3-day progesterone 

4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

5 

6 The form of the response function by Model: 

7 Model 2: Y[dose] = a * exp{sign * b * dose} 

8 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

9 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

10 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

11 

12 Note: Y[dose] is the median response for exposure = dose; 

13 sign = +1 for increasing trend in data; 

14 sign = -1 for decreasing trend. 

15 

16 Model 2 is nested within Models 3 and 4. 

17 Model 3 is nested within Model 5. 

18 Model 4 is nested within Model 5. 

19 

20 

21 Dependent variable = Mean 

22 Independent variable = Dose 

23 Data are assumed to be distributed: normally 

24 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

25 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

26 

27 Total number of dose groups = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 MLE solution provided: Exact 

34 

35 

36 Initial Parameter Values 

37 

38 Variable Model 2 

39 -------- -------- 

40 lnalpha 15.2703 

41 rho -2.36741 

42 a 68.5132 

43 b 0.00136853 

44 c 0.350182 

45 d 1 

46 

47 

48 

49 Parameter Estimates 

50 

51 Variable Model 2 

52 -------- ------- 

53 lnalpha 19.9572 

54 rho -3.64854 

55 a 65.2616 

56 b 0.0274418 

57 c 0.490738 

58 d 1.59344 

59 

60 

61 Table of Stats From Input Data 

62 

63 Dose N Obs Mean Obs Std Dev 

64 ----- --- ---------- ------------- 

65 0 10 65.25 11.1 

66 87.49 10 43.36 40.48 

67 1564 10 27.46 33.3 

68 2823 10 25.19 43.75 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-146 —DO NOT CITE OR QUOTE 

1 Estimated Values of Interest 

2 

3 Dose Est Mean Est Std Scaled Residual 

4 ------ ---------- --------- ---------------- 

5 0 55.31 28.9 1.088 

6 87.49 53.54 29.21 -1.102 

7 1564 30.93 34.87 -0.314 

8 2823 19.36 40.57 0.4542 

9 

10 

11 

12 Other models for which likelihoods are calculated: 

13 

14 Model A1: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma^2 

16 

17 Model A2: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma(i)^2 

19 

20 Model A3: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

22 

23 Model R: Yij = Mu + e(i) 

24 Var{e(ij)} = Sigma^2 

25 

26 

27 Likelihoods of Interest 

28 

29 Model Log(likelihood) DF AIC 

30 ------- ----------------- ---- ------------ 

31 A1 -159.6327 5 329.2653 

32 A2 -151.8128 8 319.6255 

33 A3 -152.5679 6 317.1358 

34 R -163.9025 2 331.805 

35 2 -159.928 4 327.856 

36 

37 

38 Additive constant for all log-likelihoods = -36.76. This constant added to the 

39 above values gives the log-likelihood including the term that does not 

40 depend on the model parameters. 

41 

42 

43 Explanation of Tests 

44 

45 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

46 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

47 Test 3: Are variances adequately modeled? (A2 vs. A3) 

48 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

49 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) D. F. p-value 

54 -------- ------------------------ ------ -------------- 

55 Test 1 24.18 6 0.000484 

56 Test 2 15.64 3 0.001344 

57 Test 3 1.51 2 0.4699 

58 Test 4 14.72 2 0.0006361 

59 

60 

61 The p-value for Test 1 is less than .05. There appears to be a 

62 difference between response and/or variances among the dose 

63 levels, it seems appropriate to model the data. 

64 

65 The p-value for Test 2 is less than .1. A non-homogeneous 

66 variance model appears to be appropriate. 

67 

68 The p-value for Test 3 is greater than .1. The modeled 

69 variance appears to be appropriate here. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-147 —DO NOT CITE OR QUOTE 

1 The p-value for Test 4 is less than .1. Model 2 may not adequately 

2 describe the data; you may want to consider another model. 

3 

4 

5 Benchmark Dose Computations: 

6 

7 Specified Effect = 1.000000 

8 

9 Risk Type = Estimated standard deviations from control 

10 

11 Confidence Level = 0.950000 

12 

13 BMD = 1988.62 

14 

15 BMDL = 712.505 

16 

17 

18 E.2.21.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

19 Unrestricted 

-10

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 10

 20

 30

 40

 50

 60

 70

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 0 500 1000 1500 2000 2500

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:48 11/16 2009

BMDL BMD

 

Exponential

20 

21 

22 

23 E.2.21.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

24 Power Unrestricted 

25 

26 

27 ==================================================================== 

28 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

29 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_Unrest_BMR1_Li_Progesterone_3d.(d) 

30 Gnuplot Plotting File: 

31 Mon Nov 16 13:48:36 2009 

32 ==================================================================== 

33 

34 Figure 4, 3-day progesterone 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-148 —DO NOT CITE OR QUOTE 

1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

2 

3 The form of the response function by Model: 

4 Model 2: Y[dose] = a * exp{sign * b * dose} 

5 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

6 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

7 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

8 

9 Note: Y[dose] is the median response for exposure = dose; 

10 sign = +1 for increasing trend in data; 

11 sign = -1 for decreasing trend. 

12 

13 Model 2 is nested within Models 3 and 4. 

14 Model 3 is nested within Model 5. 

15 Model 4 is nested within Model 5. 

16 

17 

18 Dependent variable = Mean 

19 Independent variable = Dose 

20 Data are assumed to be distributed: normally 

21 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

22 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

23 

24 Total number of dose groups = 4 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 MLE solution provided: Exact 

31 

32 

33 Initial Parameter Values 

34 

35 Variable Model 5 

36 -------- -------- 

37 lnalpha 15.2703 

38 rho -2.36741 

39 a 68.5132 

40 b 0.00136853 

41 c 0.350182 

42 d 1 

43 

44 

45 

46 Parameter Estimates 

47 

48 Variable Model 5 

49 -------- ------- 

50 lnalpha 19.9572 

51 rho -3.64854 

52 a 65.2616 

53 b 0.0274418 

54 c 0.490738 

55 d 1.59344 

56 

57 

58 Table of Stats From Input Data 

59 

60 Dose N Obs Mean Obs Std Dev 

61 ----- --- ---------- ------------- 

62 0 10 65.25 11.1 

63 87.49 10 43.36 40.48 

64 1564 10 27.46 33.3 

65 2823 10 25.19 43.75 

66 

67 

68 Estimated Values of Interest 

69 

70 Dose Est Mean Est Std Scaled Residual 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-149 —DO NOT CITE OR QUOTE 

1 ------ ---------- --------- ---------------- 

2 0 65.26 10.55 -0.003266 

3 87.49 32.61 37.4 0.909 

4 1564 32.03 38.65 -0.3733 

5 2823 32.03 38.65 -0.5591 

6 

7 

8 

9 Other models for which likelihoods are calculated: 

10 

11 Model A1: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma^2 

13 

14 Model A2: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma(i)^2 

16 

17 Model A3: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

19 

20 Model R: Yij = Mu + e(i) 

21 Var{e(ij)} = Sigma^2 

22 

23 

24 Likelihoods of Interest 

25 

26 Model Log(likelihood) DF AIC 

27 ------- ----------------- ---- ------------ 

28 A1 -159.6327 5 329.2653 

29 A2 -151.8128 8 319.6255 

30 A3 -152.5679 6 317.1358 

31 R -163.9025 2 331.805 

32 5 -152.8697 6 317.7393 

33 

34 

35 Additive constant for all log-likelihoods = -36.76. This constant added to the 

36 above values gives the log-likelihood including the term that does not 

37 depend on the model parameters. 

38 

39 

40 Explanation of Tests 

41 

42 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

43 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

44 Test 3: Are variances adequately modeled? (A2 vs. A3) 

45 

46 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

47 

48 

49 Tests of Interest 

50 

51 Test -2*log(Likelihood Ratio) D. F. p-value 

52 -------- ------------------------ ------ -------------- 

53 Test 1 24.18 6 0.000484 

54 Test 2 15.64 3 0.001344 

55 Test 3 1.51 2 0.4699 

56 Test 7a 0.6035 0 N/A 

57 

58 

59 The p-value for Test 1 is less than .05. There appears to be a 

60 difference between response and/or variances among the dose 

61 levels, it seems appropriate to model the data. 

62 

63 The p-value for Test 2 is less than .1. A non-homogeneous 

64 variance model appears to be appropriate. 

65 

66 The p-value for Test 3 is greater than .1. The modeled 

67 variance appears to be appropriate here. 

68 

69 Degrees of freedom for Test 7a are less than or equal to 0. 

70 The Chi-Square test for fit is not valid. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-150 —DO NOT CITE OR QUOTE 

1 

2 

3 Benchmark Dose Computations: 

4 

5 Specified Effect = 1.000000 

6 

7 Risk Type = Estimated standard deviations from control 

8 

9 Confidence Level = 0.950000 

10 

11 BMD = 19.9163 

12 

13 BMDL = 0.03489 

14 

15 

16 E.2.21.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

-10

 0

 10

 20

 30

 40

 50

 60

 70

 80

 0 500 1000 1500 2000 2500

Mean Response

dose

Hill Model

13:48 11/16 2009

BMD

Hill

17 

18 

19 

20 E.2.21.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

21 

22 

23 ==================================================================== 

24 Hill Model. (Version: 2.14; Date: 06/26/2008) 

25 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_Li_Progesterone_3d.(d) 

26 Gnuplot Plotting File: 

27 C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_Li_Progesterone_3d.plt 

28 Mon Nov 16 13:48:37 2009 

29 ==================================================================== 

30 

31 Figure 4, 3-day progesterone 

32 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

33 

34 The form of the response function is: 

35 

36 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-151 —DO NOT CITE OR QUOTE 

1 

2 

3 Dependent variable = Mean 

4 Independent variable = Dose 

5 Power parameter is not restricted 

6 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

7 

8 Total number of dose groups = 4 

9 Total number of records with missing values = 0 

10 Maximum number of iterations = 250 

11 Relative Function Convergence has been set to: 1e-008 

12 Parameter Convergence has been set to: 1e-008 

13 

14 

15 

16 Default Initial Parameter Values 

17 lalpha = 7.08699 

18 rho = 0 

19 intercept = 65.2507 

20 v = -40.059 

21 n = 4.4725 

22 k = 80.0627 

23 

24 

25 Asymptotic Correlation Matrix of Parameter Estimates 

26 

27 lalpha rho intercept v n k 

28 

29 lalpha 1 -1 -0.17 0.84 6e-008 1.1e-008 

30 

31 rho -1 1 0.19 -0.82 -5.6e-008 -1e-008 

32 

33 intercept -0.17 0.19 1 -0.43 1e-008 1.9e-009 

34 

35 v 0.84 -0.82 -0.43 1 1.4e-009 2.6e-010 

36 

37 n 6e-008 -5.6e-008 1e-008 1.4e-009 1 1.1 

38 

39 k 1.1e-008 -1e-008 1.9e-009 2.6e-010 1.1 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 95.0% Wald Confidence Interval 

46 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

47 lalpha 19.8437 5.41703 9.22649 30.4609 

48 rho -3.62235 1.35086 -6.27 -0.974711 

49 intercept 65.2507 3.33016 58.7237 71.7777 

50 v -33.2448 7.73875 -48.4125 -18.0772 

51 n 5.43075 5.32553e+006 -1.04378e+007 1.04378e+007 

52 k 0.22398 1.45115e+006 -2.84421e+006 2.84421e+006 

53 

54 

55 

56 Table of Data and Estimated Values of Interest 

57 

58 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

59 ------ --- -------- -------- ----------- ----------- ---------- 

60 

61 0 10 65.3 65.3 11.1 10.5 -7.47e-007 

62 87.49 10 43.4 32 40.5 38.3 0.939 

63 1564 10 27.5 32 33.3 38.3 -0.375 

64 2823 10 25.2 32 43.7 38.3 -0.563 

65 

66 Degrees of freedom for Test A3 vs fitted <= 0 

67 

68 

69 

70 Model Descriptions for likelihoods calculated 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-152 —DO NOT CITE OR QUOTE 

1 

2 

3 Model A1: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = Sigma^2 

5 

6 Model A2: Yij = Mu(i) + e(ij) 

7 Var{e(ij)} = Sigma(i)^2 

8 

9 Model A3: Yij = Mu(i) + e(ij) 

10 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

11 Model A3 uses any fixed variance parameters that 

12 were specified by the user 

13 

14 Model R: Yi = Mu + e(i) 

15 Var{e(i)} = Sigma^2 

16 

17 

18 Likelihoods of Interest 

19 

20 Model Log(likelihood) # Param's AIC 

21 A1 -159.632675 5 329.265349 

22 A2 -151.812765 8 319.625529 

23 A3 -152.567898 6 317.135795 

24 fitted -152.876553 6 317.753105 

25 R -163.902499 2 331.804998 

26 

27 

28 Explanation of Tests 

29 

30 Test 1: Do responses and/or variances differ among Dose levels? 

31 (A2 vs. R) 

32 Test 2: Are Variances Homogeneous? (A1 vs A2) 

33 Test 3: Are variances adequately modeled? (A2 vs. A3) 

34 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

35 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

36 

37 Tests of Interest 

38 

39 Test -2*log(Likelihood Ratio) Test df p-value 

40 

41 Test 1 24.1795 6 0.000484 

42 Test 2 15.6398 3 0.001344 

43 Test 3 1.51027 2 0.4699 

44 Test 4 0.61731 0 NA 

45 

46 The p-value for Test 1 is less than .05. There appears to be a 

47 difference between response and/or variances among the dose levels 

48 It seems appropriate to model the data 

49 

50 The p-value for Test 2 is less than .1. A non-homogeneous variance 

51 model appears to be appropriate 

52 

53 The p-value for Test 3 is greater than .1. The modeled variance appears 

54 to be appropriate here 

55 

56 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

57 test for fit is not valid 

58 

59 

60 Benchmark Dose Computation 

61 

62 Specified effect = 1 

63 

64 Risk Type = Estimated standard deviations from the control mean 

65 

66 Confidence level = 0.95 

67 

68 BMD = 0.19442 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-153 —DO NOT CITE OR QUOTE 

1 BMDL computation failed. 

2 

3 

4 E.2.21.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

-10

 0

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 30

 40

 50

 60

 70

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 0 500 1000 1500 2000 2500

Mean Response

dose

Power Model with 0.95 Confidence Level

13:48 11/16 2009

BMDBMDL

 

Power

5 

6 

7 

8 E.2.21.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

9 Unrestricted 

10 

11 

12 ==================================================================== 

13 Power Model. (Version: 2.15; Date: 04/07/2008) 

14 Input Data File: C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_Li_Progesterone_3d.(d) 

15 Gnuplot Plotting File: 

16 C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_Li_Progesterone_3d.plt 

17 Mon Nov 16 13:48:37 2009 

18 ==================================================================== 

19 

20 Figure 4, 3-day progesterone 

21 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

22 

23 The form of the response function is: 

24 

25 Y[dose] = control + slope * dose^power 

26 

27 

28 Dependent variable = Mean 

29 Independent variable = Dose 

30 The power is not restricted 

31 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

32 

33 Total number of dose groups = 4 

34 Total number of records with missing values = 0 

35 Maximum number of iterations = 250 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-154 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 lalpha = 7.08699 

8 rho = 0 

9 control = 65.2507 

10 slope = -9.66956 

11 power = 0.178886 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 lalpha rho control slope power 

17 

18 lalpha 1 -1 -0.17 0.57 0.15 

19 

20 rho -1 1 0.19 -0.55 -0.13 

21 

22 control -0.17 0.19 1 -0.22 0.02 

23 

24 slope 0.57 -0.55 -0.22 1 0.84 

25 

26 power 0.15 -0.13 0.02 0.84 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence Interval 

33 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

34 lalpha 20.0647 5.5864 9.11557 31.0139 

35 rho -3.67315 1.39112 -6.39969 -0.946614 

36 control 65.2739 3.34327 58.7212 71.8266 

37 slope -30.3669 13.1525 -56.1453 -4.58852 

38 power 0.0117985 0.0472043 -0.0807202 0.104317 

39 

40 

41 

42 Table of Data and Estimated Values of Interest 

43 

44 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

45 ------ --- -------- -------- ----------- ----------- ---------- 

46 

47 0 10 65.3 65.3 11.1 10.6 -0.00695 

48 87.49 10 43.4 33.3 40.5 36.5 0.876 

49 1564 10 27.5 32.2 33.3 38.8 -0.382 

50 2823 10 25.2 31.9 43.7 39.3 -0.541 

51 

52 

53 

54 Model Descriptions for likelihoods calculated 

55 

56 

57 Model A1: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 

60 Model A2: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma(i)^2 

62 

63 Model A3: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

65 Model A3 uses any fixed variance parameters that 

66 were specified by the user 

67 

68 Model R: Yi = Mu + e(i) 

69 Var{e(i)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-155 —DO NOT CITE OR QUOTE 

1 

2 Likelihoods of Interest 

3 

4 Model Log(likelihood) # Param's AIC 

5 A1 -159.632675 5 329.265349 

6 A2 -151.812765 8 319.625529 

7 A3 -152.567898 6 317.135795 

8 fitted -152.844599 5 315.689197 

9 R -163.902499 2 331.804998 

10 

11 

12 Explanation of Tests 

13 

14 Test 1: Do responses and/or variances differ among Dose levels? 

15 (A2 vs. R) 

16 Test 2: Are Variances Homogeneous? (A1 vs A2) 

17 Test 3: Are variances adequately modeled? (A2 vs. A3) 

18 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

19 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

20 

21 Tests of Interest 

22 

23 Test -2*log(Likelihood Ratio) Test df p-value 

24 

25 Test 1 24.1795 6 0.000484 

26 Test 2 15.6398 3 0.001344 

27 Test 3 1.51027 2 0.4699 

28 Test 4 0.553402 1 0.4569 

29 

30 The p-value for Test 1 is less than .05. There appears to be a 

31 difference between response and/or variances among the dose levels 

32 It seems appropriate to model the data 

33 

34 The p-value for Test 2 is less than .1. A non-homogeneous variance 

35 model appears to be appropriate 

36 

37 The p-value for Test 3 is greater than .1. The modeled variance appears 

38 to be appropriate here 

39 

40 The p-value for Test 4 is greater than .1. The model chosen seems 

41 to adequately describe the data 

42 

43 

44 Benchmark Dose Computation 

45 

46 Specified effect = 1 

47 

48 Risk Type = Estimated standard deviations from the control mean 

49 

50 Confidence level = 0.95 

51 

52 BMD = 1.42955e-039 

53 

54 

55 BMDL = 1.42955e-039 

56 

57 

58 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-156 —DO NOT CITE OR QUOTE 

1 E.2.22. Markowski et al. (2001): FR10 Run Opportunities 

2 E.2.22.1. Summary Table of BMDS Modeling Results 

Model a

Degrees 

of 

Freedom 

χ

 2

 pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) c 2 0.304 117.151 6.769E+03 2.281E+03 

exponential (M3) 2 0.304 117.151 6.769E+03 2.281E+03 power bound hit 

exponential (M4) 1 0.370 117.574 2.732E+03 1.151E+01 

exponential (M5) 0 N/A 118.918 1.834E+03 9.541E-03 

Hill 0 NA 118.918 1.428E+03 1.932E-04 

linear 2 0.226 117.744 8.734E+03 4.535E+03 

polynomial 2 0.226 117.744 8.734E+03 4.535E+03 

power 2 0.226 117.744 8.734E+03 4.535E+03 power bound hit 

a

 Non-constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

3 

4 E.2.22.2. Figure for Selected Model: Exponential (M2) 

 0

 5

 10

 15

 20

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

10:28 01/12 2010

BMDL BMD

 

Exponential

5 

6 Markowski et al., 2001: FR10 run opportunities 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-157 —DO NOT CITE OR QUOTE 

1 E.2.22.3. Output File for Selected Model: Exponential (M2) 

2 Markowski et al., 2001: FR10 run opportunities 

3 ==================================================================== 

4 Exponential Model. (Version: 1.61; Date: 7/24/2009) 

5 Input Data File: C:\1\Blood\33_Markowski_2001_FR10_run_opp_ExpCV_BMR1.(d) 

6 Gnuplot Plotting File: 

7 Tue Jan 12 10:28:14 2010 

8 ==================================================================== 

9 

10 Table 3 

11 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

12 

13 The form of the response function by Model: 

14 Model 2: Y[dose] = a * exp{sign * b * dose} 

15 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

16 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

17 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

18 

19 Note: Y[dose] is the median response for exposure = dose; 

20 sign = +1 for increasing trend in data; 

21 sign = -1 for decreasing trend. 

22 

23 Model 2 is nested within Models 3 and 4. 

24 Model 3 is nested within Model 5. 

25 Model 4 is nested within Model 5. 

26 

27 

28 Dependent variable = Mean 

29 Independent variable = Dose 

30 Data are assumed to be distributed: normally 

31 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

32 rho is set to 0. 

33 A constant variance model is fit. 

34 

35 Total number of dose groups = 4 

36 Total number of records with missing values = 0 

37 Maximum number of iterations = 250 

38 Relative Function Convergence has been set to: 1e-008 

39 Parameter Convergence has been set to: 1e-008 

40 

41 MLE solution provided: Exact 

42 

43 

44 Initial Parameter Values 

45 

46 Variable Model 2 

47 -------- -------- 

48 lnalpha 3.5321 

49 rho(S) 0 

50 a 6.7793 

51 b 7.36629e-005 

52 c 0 

53 d 1 

54 

55 (S) = Specified 

56 

57 

58 

59 Parameter Estimates 

60 

61 Variable Model 2 

62 -------- ------- 

63 lnalpha 3.63129 

64 rho 0 

65 a 12.2912 

66 b 0.00010238 

67 c 0 

68 d 1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-158 —DO NOT CITE OR QUOTE 

1 

2 

3 Table of Stats From Input Data 

4 

5 Dose N Obs Mean Obs Std Dev 

6 ----- --- ---------- ------------- 

7 0 7 13.29 8.65 

8 1234 4 11.25 5.56 

9 3184 6 5.75 3.53 

10 8152 7 7 6.01 

11 

12 

13 Estimated Values of Interest 

14 

15 Dose Est Mean Est Std Scaled Residual 

16 ------ ---------- --------- ---------------- 

17 0 12.29 6.145 0.43 

18 1234 10.83 6.145 0.1359 

19 3184 8.872 6.145 -1.245 

20 8152 5.335 6.145 0.7168 

21 

22 

23 

24 Other models for which likelihoods are calculated: 

25 

26 Model A1: Yij = Mu(i) + e(ij) 

27 Var{e(ij)} = Sigma^2 

28 

29 Model A2: Yij = Mu(i) + e(ij) 

30 Var{e(ij)} = Sigma(i)^2 

31 

32 Model A3: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

34 

35 Model R: Yij = Mu + e(i) 

36 Var{e(ij)} = Sigma^2 

37 

38 

39 Likelihoods of Interest 

40 

41 Model Log(likelihood) DF AIC 

42 ------- ----------------- ---- ------------ 

43 A1 -54.38526 5 118.7705 

44 A2 -51.88568 8 119.7714 

45 A3 -54.38526 5 118.7705 

46 R -57.45429 2 118.9086 

47 2 -55.57543 3 117.1509 

48 

49 

50 Additive constant for all log-likelihoods = -22.05. This constant added to the 

51 above values gives the log-likelihood including the term that does not 

52 depend on the model parameters. 

53 

54 

55 Explanation of Tests 

56 

57 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

58 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

59 Test 3: Are variances adequately modeled? (A2 vs. A3) 

60 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

61 

62 

63 Tests of Interest 

64 

65 Test -2*log(Likelihood Ratio) D. F. p-value 

66 -------- ------------------------ ------ -------------- 

67 Test 1 11.14 6 0.08423 

68 Test 2 4.999 3 0.1719 

69 Test 3 4.999 3 0.1719 

70 Test 4 2.38 2 0.3042 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-159 —DO NOT CITE OR QUOTE 

1 

2 

3 The p-value for Test 1 is greater than .05. There may not be a 

4 diffence between responses and/or variances among the dose levels 

5 Modelling the data with a dose/response curve may not be appropriate. 

6 

7 The p-value for Test 2 is greater than .1. A homogeneous 

8 variance model appears to be appropriate here. 

9 

10 The p-value for Test 3 is greater than .1. The modeled 

11 variance appears to be appropriate here. 

12 

13 The p-value for Test 4 is greater than .1. Model 2 seems 

14 to adequately describe the data. 

15 

16 

17 Benchmark Dose Computations: 

18 

19 Specified Effect = 1.000000 

20 

21 Risk Type = Estimated standard deviations from control 

22 

23 Confidence Level = 0.950000 

24 

25 BMD = 6769.45 

26 

27 BMDL = 2280.85 

28 

29 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-160 —DO NOT CITE OR QUOTE 

1 E.2.23. Markowski et al. (2001): FR2 Revolutions 

2 E.2.23.1. Summary Table of BMDS Modeling Results 

Model a

Degrees 

of 

Freedom 

χ

 2

 pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

power, unrestricted 1 0.053 216.124 1.570E+04 3.350E+02 power unrestricted 

exponential (M2) 2 0.236 217.220 6.704E+03 2.553E+03 

exponential (M3) 2 0.236 217.220 6.704E+03 2.553E+03 power bound hit 

exponential (M4) 1 0.262 217.588 2.702E+03 1.655E+01 

exponential (M5) c 0 N/A 218.532 1.922E+03 7.384E+02 

Hill 1 0.654 216.532 1.458E+03 4.757E+02 n lower bound hit 

linear 2 0.180 217.765 8.361E+03 4.426E+03 

polynomial 2 0.180 217.765 8.361E+03 4.426E+03 

Hill, unrestricted 1 0.654 216.532 1.458E+03 error n unrestricted 

power, unrestricted

d 1 0.161 218.297 4.538E+03 8.152E-12 power unrestricted 

a

 Constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

d

 Alternate model, BMDS output also presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-161 —DO NOT CITE OR QUOTE 

1 E.2.23.2. Figure for Selected Model: Exponential (M5) 

 0

 50

 100

 150

 200

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:52 01/13 2010

BMDL BMD

 

Exponential

2 

3 

4 Markowski et al., 2001: FR2 revolutions 

5 

6 

7 E.2.23.3. Output File for Selected Model: Exponential (M5) 

8 Markowski et al., 2001: FR2 revolutions 

9 ==================================================================== 

10 Exponential Model. (Version: 1.61; Date: 7/24/2009) 

11 Input Data File: C:\1\Blood\34_Markowski_2001_FR2_rev_ExpCV_1.(d) 

12 Gnuplot Plotting File: 

13 Wed Jan 13 14:52:52 2010 

14 ==================================================================== 

15 

16 Table 3 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function by Model: 

20 Model 2: Y[dose] = a * exp{sign * b * dose} 

21 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

22 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

23 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

24 

25 Note: Y[dose] is the median response for exposure = dose; 

26 sign = +1 for increasing trend in data; 

27 sign = -1 for decreasing trend. 

28 

29 Model 2 is nested within Models 3 and 4. 

30 Model 3 is nested within Model 5. 

31 Model 4 is nested within Model 5. 

32 

33 

34 Dependent variable = Mean 

35 Independent variable = Dose 

36 Data are assumed to be distributed: normally 

37 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

38 rho is set to 0. 

39 A constant variance model is fit. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-162 —DO NOT CITE OR QUOTE 

1 

2 Total number of dose groups = 4 

3 Total number of records with missing values = 0 

4 Maximum number of iterations = 250 

5 Relative Function Convergence has been set to: 1e-008 

6 Parameter Convergence has been set to: 1e-008 

7 

8 MLE solution provided: Exact 

9 

10 

11 Initial Parameter Values 

12 

13 Variable Model 5 

14 -------- -------- 

15 lnalpha 7.68046 

16 rho(S) 0 

17 a 125.255 

18 b 0.000305547 

19 c 0.429602 

20 d 1 

21 

22 (S) = Specified 

23 

24 

25 

26 Parameter Estimates 

27 

28 Variable Model 5 

29 -------- ------- 

30 lnalpha 7.68885 

31 rho 0 

32 a 119.29 

33 b 0.000585299 

34 c 0.526177 

35 d 4.76993 

36 

37 

38 Table of Stats From Input Data 

39 

40 Dose N Obs Mean Obs Std Dev 

41 ----- --- ---------- ------------- 

42 0 7 119.3 69.9 

43 1234 4 108.5 61 

44 3184 6 56.5 31.21 

45 8152 7 68.14 33.23 

46 

47 

48 Estimated Values of Interest 

49 

50 Dose Est Mean Est Std Scaled Residual 

51 ------ ---------- --------- ---------------- 

52 0 119.3 46.73 -1.267e-006 

53 1234 108.5 46.73 2.704e-006 

54 3184 62.77 46.73 -0.3285 

55 8152 62.77 46.73 0.3042 

56 

57 

58 

59 Other models for which likelihoods are calculated: 

60 

61 Model A1: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 

64 Model A2: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma(i)^2 

66 

67 Model A3: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

69 

70 Model R: Yij = Mu + e(i) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-163 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma^2 

2 

3 

4 Likelihoods of Interest 

5 

6 Model Log(likelihood) DF AIC 

7 ------- ----------------- ---- ------------ 

8 A1 -104.1655 5 218.331 

9 A2 -101.1402 8 218.2803 

10 A3 -104.1655 5 218.331 

11 R -107.5993 2 219.1985 

12 5 -104.2662 5 218.5323 

13 

14 

15 Additive constant for all log-likelihoods = -22.05. This constant added to the 

16 above values gives the log-likelihood including the term that does not 

17 depend on the model parameters. 

18 

19 

20 Explanation of Tests 

21 

22 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

23 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

24 Test 3: Are variances adequately modeled? (A2 vs. A3) 

25 

26 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

27 

28 

29 Tests of Interest 

30 

31 Test -2*log(Likelihood Ratio) D. F. p-value 

32 -------- ------------------------ ------ -------------- 

33 Test 1 12.92 6 0.04435 

34 Test 2 6.051 3 0.1092 

35 Test 3 6.051 3 0.1092 

36 Test 7a 0.2013 0 N/A 

37 

38 

39 The p-value for Test 1 is less than .05. There appears to be a 

40 difference between response and/or variances among the dose 

41 levels, it seems appropriate to model the data. 

42 

43 The p-value for Test 2 is greater than .1. A homogeneous 

44 variance model appears to be appropriate here. 

45 

46 The p-value for Test 3 is greater than .1. The modeled 

47 variance appears to be appropriate here. 

48 

49 Degrees of freedom for Test 7a are less than or equal to 0. 

50 The Chi-Square test for fit is not valid. 

51 

52 

53 Benchmark Dose Computations: 

54 

55 Specified Effect = 1.000000 

56 

57 Risk Type = Estimated standard deviations from control 

58 

59 Confidence Level = 0.950000 

60 

61 BMD = 1921.95 

62 

63 BMDL = 738.412 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-164 —DO NOT CITE OR QUOTE 

1 E.2.23.4. Figure for Unrestricted Model: Power, Unrestricted 

 0

 50

 100

 150

 200

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:52 01/13 2010

BMDL BMD

 

Power

2 

3 

4 Markowski et al., 2001: FR2 revolutions 

5 

6 

7 E.2.23.5. Output for Unrestricted Model: Power, Unrestricted 

8 Markowski et al., 2001: FR2 revolutions 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\1\Blood\34_Markowski_2001_FR2_rev_PowerCV_Unrest_1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\34_Markowski_2001_FR2_rev_PowerCV_Unrest_1.plt 

13 Wed Jan 13 14:52:55 2010 

14 ==================================================================== 

15 

16 Table 3 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 The power is not restricted 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 alpha = 2598.74 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-165 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 control = 119.29 

3 slope = -0.0418736 

4 power = 0.825655 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -rho 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 alpha control slope power 

14 

15 alpha 1 3.2e-009 -4.2e-009 -2.8e-009 

16 

17 control 3.2e-009 1 -0.39 -0.28 

18 

19 slope -4.2e-009 -0.39 1 0.99 

20 

21 power -2.8e-009 -0.28 0.99 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 alpha 2350.46 678.52 1020.59 3680.33 

30 control 120.079 18.0799 84.6433 155.515 

31 slope -3.33162 10.4368 -23.7875 17.1242 

32 power 0.318007 0.351246 -0.370423 1.00644 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 7 119 120 69.9 48.5 -0.0431 

42 1234 4 109 88 61 48.5 0.844 

43 3184 6 56.5 76.8 31.2 48.5 -1.02 

44 8152 7 68.1 61.7 33.2 48.5 0.353 

45 

46 

47 

48 Model Descriptions for likelihoods calculated 

49 

50 

51 Model A1: Yij = Mu(i) + e(ij) 

52 Var{e(ij)} = Sigma^2 

53 

54 Model A2: Yij = Mu(i) + e(ij) 

55 Var{e(ij)} = Sigma(i)^2 

56 

57 Model A3: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 Model A3 uses any fixed variance parameters that 

60 were specified by the user 

61 

62 Model R: Yi = Mu + e(i) 

63 Var{e(i)} = Sigma^2 

64 

65 

66 Likelihoods of Interest 

67 

68 Model Log(likelihood) # Param's AIC 

69 A1 -104.165520 5 218.331040 

70 A2 -101.140174 8 218.280349 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-166 —DO NOT CITE OR QUOTE 

1 A3 -104.165520 5 218.331040 

2 fitted -105.148400 4 218.296799 

3 R -107.599268 2 219.198536 

4 

5 

6 Explanation of Tests 

7 

8 Test 1: Do responses and/or variances differ among Dose levels? 

9 (A2 vs. R) 

10 Test 2: Are Variances Homogeneous? (A1 vs A2) 

11 Test 3: Are variances adequately modeled? (A2 vs. A3) 

12 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

13 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

14 

15 Tests of Interest 

16 

17 Test -2*log(Likelihood Ratio) Test df p-value 

18 

19 Test 1 12.9182 6 0.04435 

20 Test 2 6.05069 3 0.1092 

21 Test 3 6.05069 3 0.1092 

22 Test 4 1.96576 1 0.1609 

23 

24 The p-value for Test 1 is less than .05. There appears to be a 

25 difference between response and/or variances among the dose levels 

26 It seems appropriate to model the data 

27 

28 The p-value for Test 2 is greater than .1. A homogeneous variance 

29 model appears to be appropriate here 

30 

31 

32 The p-value for Test 3 is greater than .1. The modeled variance appears 

33 to be appropriate here 

34 

35 The p-value for Test 4 is greater than .1. The model chosen seems 

36 to adequately describe the data 

37 

38 

39 Benchmark Dose Computation 

40 

41 Specified effect = 1 

42 

43 Risk Type = Estimated standard deviations from the control mean 

44 

45 Confidence level = 0.95 

46 

47 BMD = 4538.4 

48 

49 

50 BMDL = 8.15173e-012 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-167 —DO NOT CITE OR QUOTE 

1 E.2.24. Markowski et al. (2001): FR5 Run Opp 

2 E.2.24.1. Summary Table of BMDS Modeling Results 

Model a

Degrees 

of 

Freedom 

χ

 2

 pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) 2 0.205 133.194 4.012E+03 1.927E+03 

exponential (M3) 2 0.205 133.194 4.012E+03 1.927E+03 power bound hit 

exponential (M4) 1 0.253 133.335 1.710E+03 5.425E+02 

exponential (M5) 1 0.212 133.587 1.757E+03 5.030E+02 power bound hit 

Hill c 1 0.939 132.032 1.366E+03 7.212E+02 n lower bound hit 

linear 2 0.122 134.230 5.715E+03 3.500E+03 

polynomial 2 0.122 134.230 5.715E+03 3.500E+03 

power 2 0.122 134.230 5.715E+03 3.500E+03 power bound hit 

Hill, unrestricted 1 0.939 132.032 1.366E+03 6.598E+02 n unrestricted 

power, unrestricted

d 1 0.134 134.272 2.109E+03 8.152E-12 power unrestricted 

a

 Constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

d

 Alternate model, BMDS output also presented in this appendix 

3 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-168 —DO NOT CITE OR QUOTE 

1 E.2.24.2. Figure for Selected Model: Hill 

 5

 10

 15

 20

 25

 30

 35

 40

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Hill Model with 0.95 Confidence Level

10:29 01/12 2010

BMDL BMD

 

Hill

2 

3 

4 Markowski et al., 2001: FR5 run opportunities 

5 

6 

7 E.2.24.3. Output File for Selected Model: Hill 

8 Markowski et al., 2001: FR5 run opportunities 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\1\Blood\35_Markowski_2001_FR5_run_opp_HillCV_BMR1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\35_Markowski_2001_FR5_run_opp_HillCV_BMR1.plt 

13 Tue Jan 12 10:29:45 2010 

14 ==================================================================== 

15 

16 Table 3 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter restricted to be greater than 1 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 alpha = 77.4849 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-169 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 intercept = 26.14 

3 v = -13.34 

4 n = 2.78062 

5 k = 1968.39 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho -n 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha intercept v k 

15 

16 alpha 1 -1.9e-010 1.7e-008 1.8e-008 

17 

18 intercept -1.9e-010 1 -0.81 -0.51 

19 

20 v 1.7e-008 -0.81 1 0.36 

21 

22 k 1.8e-008 -0.51 0.36 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 64.5863 18.6445 28.0438 101.129 

31 intercept 26.14 3.03753 20.1865 32.0935 

32 v -13.1569 3.7676 -20.5413 -5.77257 

33 n 18 NA 

34 k 1332.5 165.441 1008.24 1656.76 

35 

36 NA - Indicates that this parameter has hit a bound 

37 implied by some inequality constraint and thus 

38 has no standard error. 

39 

40 

41 

42 Table of Data and Estimated Values of Interest 

43 

44 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

45 ------ --- -------- -------- ----------- ----------- ---------- 

46 

47 0 7 26.1 26.1 12.3 8.04 -3.13e-008 

48 1234 4 23.5 23.5 7.04 8.04 -1.71e-008 

49 3184 6 12.8 13 6.17 8.04 -0.0558 

50 8152 7 13.1 13 7.14 8.04 0.0517 

51 

52 

53 

54 Model Descriptions for likelihoods calculated 

55 

56 

57 Model A1: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 

60 Model A2: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma(i)^2 

62 

63 Model A3: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 Model A3 uses any fixed variance parameters that 

66 were specified by the user 

67 

68 Model R: Yi = Mu + e(i) 

69 Var{e(i)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-170 —DO NOT CITE OR QUOTE 

1 

2 Likelihoods of Interest 

3 

4 Model Log(likelihood) # Param's AIC 

5 A1 -62.013133 5 134.026266 

6 A2 -59.839035 8 135.678070 

7 A3 -62.013133 5 134.026266 

8 fitted -62.016025 4 132.032049 

9 R -67.530040 2 139.060081 

10 

11 

12 Explanation of Tests 

13 

14 Test 1: Do responses and/or variances differ among Dose levels? 

15 (A2 vs. R) 

16 Test 2: Are Variances Homogeneous? (A1 vs A2) 

17 Test 3: Are variances adequately modeled? (A2 vs. A3) 

18 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

19 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

20 

21 Tests of Interest 

22 

23 Test -2*log(Likelihood Ratio) Test df p-value 

24 

25 Test 1 15.382 6 0.01748 

26 Test 2 4.3482 3 0.2262 

27 Test 3 4.3482 3 0.2262 

28 Test 4 0.00578335 1 0.9394 

29 

30 The p-value for Test 1 is less than .05. There appears to be a 

31 difference between response and/or variances among the dose levels 

32 It seems appropriate to model the data 

33 

34 The p-value for Test 2 is greater than .1. A homogeneous variance 

35 model appears to be appropriate here 

36 

37 

38 The p-value for Test 3 is greater than .1. The modeled variance appears 

39 to be appropriate here 

40 

41 The p-value for Test 4 is greater than .1. The model chosen seems 

42 to adequately describe the data 

43 

44 

45 Benchmark Dose Computation 

46 

47 Specified effect = 1 

48 

49 Risk Type = Estimated standard deviations from the control mean 

50 

51 Confidence level = 0.95 

52 

53 BMD = 1366.29 

54 

55 BMDL = 721.238 

56 

57 

58 

59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-171 —DO NOT CITE OR QUOTE 

1 E.2.24.4. Figure for Unrestricted Model: Power, Unrestricted 

 5

 10

 15

 20

 25

 30

 35

 40

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

10:29 01/12 2010

BMDL BMD

 

Power

2 

3 

4 Markowski et al., 2001: FR5 run opportunities 

5 

6 

7 E.2.24.5. Output File for Unrestricted Model: Power, Unrestricted 

8 Markowski et al., 2001: FR5 run opportunities 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\1\Blood\35_Markowski_2001_FR5_run_opp_PowerCV_Unrest_BMR1.(d) 

12 Gnuplot Plotting File: 

13 C:\1\Blood\35_Markowski_2001_FR5_run_opp_PowerCV_Unrest_BMR1.plt 

14 Tue Jan 12 10:29:46 2010 

15 ==================================================================== 

16 

17 Table 3 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = control + slope * dose^power 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 rho is set to 0 

28 The power is not restricted 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 

37 

38 

39 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-172 —DO NOT CITE OR QUOTE 

1 alpha = 77.4849 

2 rho = 0 Specified 

3 control = 26.14 

4 slope = -0.00843066 

5 power = 0.845567 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha control slope power 

15 

16 alpha 1 -2e-008 -1e-008 -1.3e-008 

17 

18 control -2e-008 1 -0.43 -0.34 

19 

20 slope -1e-008 -0.43 1 0.99 

21 

22 power -1.3e-008 -0.34 0.99 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 70.905 20.4685 30.7875 111.023 

31 control 26.3577 3.12942 20.2242 32.4913 

32 slope -0.41863 1.06088 -2.49792 1.66066 

33 power 0.392134 0.282163 -0.160895 0.945164 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 7 26.1 26.4 12.3 8.42 -0.0684 

43 1234 4 23.5 19.5 7.04 8.42 0.942 

44 3184 6 12.8 16.5 6.17 8.42 -1.07 

45 8152 7 13.1 12.1 7.14 8.42 0.342 

46 

47 

48 

49 Model Descriptions for likelihoods calculated 

50 

51 

52 Model A1: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = Sigma^2 

54 

55 Model A2: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma(i)^2 

57 

58 Model A3: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma^2 

60 Model A3 uses any fixed variance parameters that 

61 were specified by the user 

62 

63 Model R: Yi = Mu + e(i) 

64 Var{e(i)} = Sigma^2 

65 

66 

67 Likelihoods of Interest 

68 

69 Model Log(likelihood) # Param's AIC 

70 A1 -62.013133 5 134.026266 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-173 —DO NOT CITE OR QUOTE 

1 A2 -59.839035 8 135.678070 

2 A3 -62.013133 5 134.026266 

3 fitted -63.136095 4 134.272189 

4 R -67.530040 2 139.060081 

5 

6 

7 Explanation of Tests 

8 

9 Test 1: Do responses and/or variances differ among Dose levels? 

10 (A2 vs. R) 

11 Test 2: Are Variances Homogeneous? (A1 vs A2) 

12 Test 3: Are variances adequately modeled? (A2 vs. A3) 

13 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

14 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

15 

16 Tests of Interest 

17 

18 Test -2*log(Likelihood Ratio) Test df p-value 

19 

20 Test 1 15.382 6 0.01748 

21 Test 2 4.3482 3 0.2262 

22 Test 3 4.3482 3 0.2262 

23 Test 4 2.24592 1 0.134 

24 

25 The p-value for Test 1 is less than .05. There appears to be a 

26 difference between response and/or variances among the dose levels 

27 It seems appropriate to model the data 

28 

29 The p-value for Test 2 is greater than .1. A homogeneous variance 

30 model appears to be appropriate here 

31 

32 

33 The p-value for Test 3 is greater than .1. The modeled variance appears 

34 to be appropriate here 

35 

36 The p-value for Test 4 is greater than .1. The model chosen seems 

37 to adequately describe the data 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 2109.29 

49 

50 

51 BMDL = 8.15175e-012
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-174 —DO NOT CITE OR QUOTE 

1 E.2.25. Mietinnin et al. (2006): Cariogenic Lesions in Pups 

2 E.2.25.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2

 pValue a AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

gamma 3 0.410 162.281 2.689E+03 1.494E+03 power bound hit 

logistic 3 0.371 162.518 3.248E+03 1.937E+03 

log-logistic b 3 0.603 161.291 1.129E+03 4.091E+02 slope bound hit 

log-probit, 

unrestricted 2 0.732 161.972 5.141E+01 error slope unrestricted 

multistage, 4-

degree 3 0.410 162.281 2.689E+03 1.494E+03 final ß=0 

probit 3 0.350 162.656 3.596E+03 2.284E+03 

Weibull 3 0.410 162.281 2.689E+03 1.494E+03 power bound hit 

log-logistic, 

unrestricted c 2 0.728 161.983 3.912E+01 error slope unrestricted 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model, BMDS output presented in this appendix 

c

 Alternate model, BMDS output also presented in this appendix 

3 

4 E.2.25.2. Figure for Selected Model: Log-Logistic 

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1

 0 5000 10000 15000 20000 25000 30000 35000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

10:30 01/12 2010

BMDL BMD

 

Log-Logistic

5 

6 Mietinnen et al., 2006: Cariogenic lesions in pups 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-175 —DO NOT CITE OR QUOTE 

1 E.2.25.3. Output File for Selected Model: Log-Logistic 

2 Mietinnen et al., 2006: Cariogenic lesions in pups 

3 ==================================================================== 

4 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

5 Input Data File: C:\1\Blood\36_Miet_06_carc_lesions_LogLogistic_1.(d) 

6 Gnuplot Plotting File: C:\1\Blood\36_Miet_06_carc_lesions_LogLogistic_1.plt 

7 Tue Jan 12 10:30:32 2010 

8 ==================================================================== 

9 

10 Table 2 converting the percentage into the number of animals, and control is Control II from the 

11 study. Dose is in ng per kg and is from Table 1 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

17 

18 

19 Dependent variable = DichEff 

20 Independent variable = Dose 

21 Slope parameter is restricted as slope >= 1 

22 

23 Total number of observations = 5 

24 Total number of records with missing values = 0 

25 Maximum number of iterations = 250 

26 Relative Function Convergence has been set to: 1e-008 

27 Parameter Convergence has been set to: 1e-008 

28 

29 

30 

31 User has chosen the log transformed model 

32 

33 

34 Default Initial Parameter Values 

35 background = 0.595238 

36 intercept = -9.1668 

37 slope = 1 

38 

39 

40 Asymptotic Correlation Matrix of Parameter Estimates 

41 

42 ( *** The model parameter(s) -slope 

43 have been estimated at a boundary point, or have been specified by the user, 

44 and do not appear in the correlation matrix ) 

45 

46 background intercept 

47 

48 background 1 -0.66 

49 

50 intercept -0.66 1 

51 

52 

53 

54 Parameter Estimates 

55 

56 95.0% Wald Confidence Interval 

57 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

58 background 0.644146 * * * 

59 intercept -9.22611 * * * 

60 slope 1 * * * 

61 

62 * - Indicates that this value is not calculated. 

63 

64 

65 

66 Analysis of Deviance Table 

67 

68 Model Log(likelihood) # Param's Deviance Test d.f. P-value 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-176 —DO NOT CITE OR QUOTE 

1 Full model -77.6769 5 

2 Fitted model -78.6457 2 1.93773 3 0.5854 

3 Reduced model -83.2067 1 11.0597 4 0.0259 

4 

5 AIC: 161.291 

6 

7 

8 Goodness of Fit 

9 Scaled 

10 Dose Est._Prob. Expected Observed Size Residual 

11 ------------------------------------------------------------------------ 

12 0.0000 0.6441 27.054 25.000 42 -0.662 

13 1755.6399 0.6966 20.201 23.000 29 1.131 

14 4922.4989 0.7603 19.007 19.000 25 -0.003 

15 12657.0000 0.8416 20.197 20.000 24 -0.110 

16 36874.0000 0.9231 29.540 29.000 32 -0.359 

17 

18 Chi^2 = 1.86 d.f. = 3 P-value = 0.6025 

19 

20 

21 Benchmark Dose Computation 

22 

23 Specified effect = 0.1 

24 

25 Risk Type = Extra risk 

26 

27 Confidence level = 0.95 

28 

29 BMD = 1128.77 

30 

31 BMDL = 409.065 

32 

33 

34 

35 

36 E.2.25.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1

 0 5000 10000 15000 20000 25000 30000 35000

Fraction Affected

dose

Log-Logistic Model

10:30 01/12 2010

Log-Logistic

37 

38 

39 Mietinnen et al., 2006: Cariogenic lesions in pups 

40 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-177 —DO NOT CITE OR QUOTE 

1 

2 E.2.25.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

3 Mietinnen et al., 2006: Cariogenic lesions in pups 

4 ==================================================================== 

5 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

6 Input Data File: C:\1\Blood\36_Miet_06_carc_lesions_LogLogistic_Unrest_1.(d) 

7 Gnuplot Plotting File: C:\1\Blood\36_Miet_06_carc_lesions_LogLogistic_Unrest_1.plt 

8 Tue Jan 12 10:30:33 2010 

9 ==================================================================== 

10 

11 Table 2 converting the percentage into the number of animals, and control is Control II from the 

12 study. Dose is in ng per kg and is from Table 1 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the probability function is: 

16 

17 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

18 

19 

20 Dependent variable = DichEff 

21 Independent variable = Dose 

22 Slope parameter is not restricted 

23 

24 Total number of observations = 5 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 User has chosen the log transformed model 

33 

34 

35 Default Initial Parameter Values 

36 background = 0.595238 

37 intercept = -3.69546 

38 slope = 0.442957 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 background intercept slope 

44 

45 background 1 -0.34 0.24 

46 

47 intercept -0.34 1 -0.99 

48 

49 slope 0.24 -0.99 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 background 0.597745 * * * 

58 intercept -3.90353 * * * 

59 slope 0.465358 * * * 

60 

61 * - Indicates that this value is not calculated. 

62 

63 

64 

65 Analysis of Deviance Table 

66 

67 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

68 Full model -77.6769 5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-178 —DO NOT CITE OR QUOTE 

1 Fitted model -77.9913 3 0.62887 2 0.7302 

2 Reduced model -83.2067 1 11.0597 4 0.0259 

3 

4 AIC: 161.983 

5 

6 

7 Goodness of Fit 

8 Scaled 

9 Dose Est._Prob. Expected Observed Size Residual 

10 ------------------------------------------------------------------------ 

11 0.0000 0.5977 25.105 25.000 42 -0.033 

12 1755.6399 0.7566 21.941 23.000 29 0.458 

13 4922.4989 0.8042 20.104 19.000 25 -0.557 

14 12657.0000 0.8474 20.338 20.000 24 -0.192 

15 36874.0000 0.8910 28.512 29.000 32 0.277 

16 

17 Chi^2 = 0.63 d.f. = 2 P-value = 0.7282 

18 

19 

20 Benchmark Dose Computation 

21 

22 Specified effect = 0.1 

23 

24 Risk Type = Extra risk 

25 

26 Confidence level = 0.95 

27 

28 BMD = 39.1207 

29 

30 Benchmark dose computation failed. Lower limit includes zero. 

31 

32 

33 E.2.26. National Toxicology Program (1982): Male Mice, Toxic Hepatitis 

34 E.2.26.1. Summary Table of BMDS Modeling Results 

Model Degrees of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) 

Model 

Notes 

gamma 1 4.92 0.03 113.10 2.1E+03 1.1E+03 

power 

restricted 

≥1 

logistic b 2 4.77 0.09 110.35 1.7E+03 1.3E+03 

log-logistic 1 4.93 0.03 113.09 2.1E+03 1.2E+03 

slope 

restricted 

≥1 

log-probit 1 4.89 0.03 113.11 1.9E+03 1.3E+03 

slope 

restricted 

≥1 

multistage 2-

degree 1 6.04 0.01 113.71 1.3E+03 7.0E+02 

betas 

restricted 

≥0 

probit 2 4.99 0.08 110.51 1.5E+03 1.2E+03 

Weibull 1 5.00 0.03 113.04 2.2E+03 9.3E+02 

power 

restricted 

≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-179 —DO NOT CITE OR QUOTE 

1 

E.2.26.2. Figure for Selected Model: Multistage, 2nd 2 Degree 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 1000 2000 3000 4000 5000 6000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

13:20 11/16 2009

BMDL BMD

 

Multistage

3 

4 

5 

E.2.26.3. Output File for Selected Model: Multistage, 2nd 6 Degree 

7 

8 

9 ==================================================================== 

10 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\Multistage_BMR2_Toxic_hepatitis.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\Multistage_BMR2_Toxic_hepatitis.plt 

13 Sun Nov 29 13:16:19 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background + (1-background)*[1-EXP( 

22 -beta1*dose^1-beta2*dose^2)] 

23 

24 The parameter betas are restricted to be positive 

25 

26 

27 Dependent variable = DichEff 

28 Independent variable = Dose 

29 

30 Total number of observations = 4 

31 Total number of records with missing values = 0 

32 Total number of parameters in model = 3 

33 Total number of specified parameters = 0 

34 Degree of polynomial = 2 

35 

36 

37 Maximum number of iterations = 250 

38 Relative Function Convergence has been set to: 1e-008 

39 Parameter Convergence has been set to: 1e-008 

40 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-180 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 Background = 0.0298369 

5 Beta(1) = 0 

6 Beta(2) = 5.57954e-008 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 Background Beta(1) Beta(2) 

12 

13 Background 1 -0.8 0.74 

14 

15 Beta(1) -0.8 1 -0.97 

16 

17 Beta(2) 0.74 -0.97 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 Background 0.0286224 * * * 

26 Beta(1) 1.97711e-005 * * * 

27 Beta(2) 5.00241e-008 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -51.0633 4 

37 Fitted model -53.8523 3 5.57784 1 0.01819 

38 Reduced model -121.743 1 141.358 3 <.0001 

39 

40 AIC: 113.705 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0286 2.089 1.000 73 -0.765 

48 420.0366 0.0451 2.211 5.000 49 1.920 

49 1239.6134 0.1223 5.991 3.000 49 -1.304 

50 6117.5662 0.8676 43.381 44.000 50 0.258 

51 

52 Chi^2 = 6.04 d.f. = 1 P-value = 0.0140 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.1 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 1267.05 

64 

65 BMDL = 698.659 

66 

67 BMDU = 1628.68 

68 

69 Taken together, (698.659, 1628.68) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-181 —DO NOT CITE OR QUOTE 

1 

2 E.2.27. National Toxicology Program (2006): Alveolar Metaplasia 

3 E.2.27.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 13.37 0.01 320.09 2.7E+02 2.3E+02 power restricted ≥1, bound 

hit 

gamma 4 13.37 0.01 320.09 5.4E+02 4.6E+02 power restricted ≥1, bound 

hit 

logistic 4 33.08 0.00 343.28 6.8E+02 5.8E+02 

logistic 4 33.08 0.00 343.28 1.3E+03 1.1E+03 

log-logistic 3 1.32 0.72 312.56 1.8E+02 9.8E+01 slope restricted ≥1 

log-logistic b 3 1.32 0.72 312.56 3.6E+02 2.1E+02 slope restricted ≥1 

log-probit 3 1.44 0.70 312.68 2.2E+02 7.4E+01 slope restricted ≥1 

log-probit 3 1.44 0.70 312.68 3.8E+02 1.5E+02 slope restricted ≥1 

multistage, 2-

degree 4 13.37 0.01 320.09 2.7E+02 2.3E+02 betas restricted ≥0, bound hit 

multistage, 2-

degree 4 13.37 0.01 320.09 5.4E+02 4.6E+02 betas restricted ≥0, bound hit 

probit 4 35.22 0.00 347.07 7.2E+02 6.2E+02 

probit 4 35.22 0.00 347.07 1.4E+03 1.2E+03 

Weibull 4 13.37 0.01 320.09 2.7E+02 2.3E+02 power restricted ≥1, bound 

hit 

Weibull 4 13.37 0.01 320.09 5.4E+02 4.6E+02 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-182 —DO NOT CITE OR QUOTE 

1 E.2.27.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

13:20 11/16 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.27.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR2_Alveolar_metaplasia.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR2_Alveolar_metaplasia.plt 

13 Mon Nov 16 13:20:58 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

22 

23 

24 Dependent variable = DichEff 

25 Independent variable = Dose 

26 Slope parameter is restricted as slope >= 1 

27 

28 Total number of observations = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 User has chosen the log transformed model 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-183 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 background = 0.0377358 

4 intercept = -8.78161 

5 slope = 1.1228 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 background intercept slope 

11 

12 background 1 -0.13 0.1 

13 

14 intercept -0.13 1 -1 

15 

16 slope 0.1 -1 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 background 0.0373474 * * * 

25 intercept -8.85134 * * * 

26 slope 1.13159 * * * 

27 

28 * - Indicates that this value is not calculated. 

29 

30 

31 

32 Analysis of Deviance Table 

33 

34 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

35 Full model -152.615 6 

36 Fitted model -153.279 3 1.32714 3 0.7227 

37 Reduced model -216.802 1 128.374 5 <.0001 

38 

39 AIC: 312.558 

40 

41 

42 Goodness of Fit 

43 Scaled 

44 Dose Est._Prob. Expected Observed Size Residual 

45 ------------------------------------------------------------------------ 

46 0.0000 0.0373 1.979 2.000 53 0.015 

47 1408.4504 0.3682 19.881 19.000 54 -0.249 

48 3137.0446 0.5807 30.777 33.000 53 0.619 

49 5392.9593 0.7162 37.244 35.000 52 -0.690 

50 9128.8027 0.8197 43.445 45.000 53 0.556 

51 16361.0000 0.8976 46.674 46.000 52 -0.308 

52 

53 Chi^2 = 1.32 d.f. = 3 P-value = 0.7232 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.1 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 357.926 

65 

66 BMDL = 206.635 

67 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-184 —DO NOT CITE OR QUOTE 

1 E.2.28. National Toxicology Program (2006): Gingival Hyperplasia Squamous, 2 Years 

2 E.2.28.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Value a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 10.30 0.04 314.99 4.3E+03 2.8E+03 power restricted ≥1, bound 

hit 

logistic 4 12.16 0.02 318.60 7.7E+03 5.8E+03 

log-logistic b 4 9.26 0.06 313.35 3.2E+03 2.1E+03 slope restricted ≥1, 

bound hit 

log-logistic c 3 1.62 0.66 307.51 3.9E+02 6.9E-03 slope unrestricted 

log-probit 3 1.56 0.67 307.44 4.6E+02 2.6E-02 slope restricted ≥1 

multistage, 1-

degree 4 10.30 0.04 314.99 4.3E+03 2.8E+03 betas restricted ≥0, bound hit 

probit 4 11.97 0.02 318.24 7.3E+03 5.5E+03 

Weibull 4 10.30 0.04 314.99 4.3E+03 2.8E+03 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-185 —DO NOT CITE OR QUOTE 

1 E.2.28.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.1

 0.2

 0.3

 0.4

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:36 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.28.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_BMR2_Ging_Hyp_2yr.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_BMR2_Ging_Hyp_2yr.plt 

12 Sun Nov 29 11:36:25 2009 

13 ==================================================================== 

14 

15 [insert study notes] 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is restricted as slope >= 1 

26 

27 Total number of observations = 6 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-186 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0188679 

3 intercept = -10.0647 

4 slope = 1 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -slope 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 background intercept 

14 

15 background 1 -0.79 

16 

17 intercept -0.79 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 background 0.0671889 * * * 

26 intercept -10.2754 * * * 

27 slope 1 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -149.95 6 

37 Fitted model -154.675 2 9.45083 4 0.05077 

38 Reduced model -162.631 1 25.3627 5 0.0001186 

39 

40 AIC: 313.351 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0672 3.561 1.000 53 -1.405 

48 1408.4504 0.1104 5.961 7.000 54 0.451 

49 3137.0446 0.1582 8.386 14.000 53 2.113 

50 5392.9593 0.2134 11.311 13.000 53 0.566 

51 9128.8027 0.2905 15.395 15.000 53 -0.119 

52 16361.0000 0.4036 21.389 16.000 53 -1.509 

53 

54 Chi^2 = 9.26 d.f. = 4 P-value = 0.0550 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.1 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 3223.25 

66 

67 BMDL = 2054.88 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-187 —DO NOT CITE OR QUOTE 

1 E.2.28.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

 0.2

 0.3

 0.4

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:36 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.28.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_Unrest_BMR2_Ging_Hyp_2yr.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\Nov29\Blood\LogLogistic_Unrest_BMR2_Ging_Hyp_2yr.plt 

13 Sun Nov 29 11:36:27 2009 

14 ==================================================================== 

15 

16 [insert study notes] 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

22 

23 

24 Dependent variable = DichEff 

25 Independent variable = Dose 

26 Slope parameter is not restricted 

27 

28 Total number of observations = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 User has chosen the log transformed model 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-188 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 background = 0.0188679 

4 intercept = -4.87817 

5 slope = 0.424322 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 background intercept slope 

11 

12 background 1 -0.16 0.11 

13 

14 intercept -0.16 1 -0.99 

15 

16 slope 0.11 -0.99 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 background 0.0185138 * * * 

25 intercept -4.42531 * * * 

26 slope 0.373718 * * * 

27 

28 * - Indicates that this value is not calculated. 

29 

30 

31 

32 Analysis of Deviance Table 

33 

34 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

35 Full model -149.95 6 

36 Fitted model -150.753 3 1.60686 3 0.6578 

37 Reduced model -162.631 1 25.3627 5 0.0001186 

38 

39 AIC: 307.507 

40 

41 

42 Goodness of Fit 

43 Scaled 

44 Dose Est._Prob. Expected Observed Size Residual 

45 ------------------------------------------------------------------------ 

46 0.0000 0.0185 0.981 1.000 53 0.019 

47 1408.4504 0.1681 9.078 7.000 54 -0.756 

48 3137.0446 0.2101 11.136 14.000 53 0.966 

49 5392.9593 0.2433 12.893 13.000 53 0.034 

50 9128.8027 0.2792 14.795 15.000 53 0.063 

51 16361.0000 0.3230 17.117 16.000 53 -0.328 

52 

53 Chi^2 = 1.62 d.f. = 3 P-value = 0.6555 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.1 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 388.363 

65 

66 BMDL = 0.00694785 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-189 —DO NOT CITE OR QUOTE 

1 E.2.29. National Toxicology Program (2006): Heart, Cardiomyopathy 

2 E.2.29.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 2.65 0.62 394.49 1.5E+03 1.2E+03 power restricted ≥1, bound 

hit 

logistic 4 6.73 0.15 398.64 2.7E+03 2.2E+03 

log-logistic 3 1.32 0.72 395.20 1.2E+03 7.3E+02 slope restricted ≥1 

log-probit 3 1.11 0.78 394.98 1.3E+03 4.9E+02 slope restricted ≥1 

multistage, 2-

degree b 4 2.65 0.62 394.49 1.5E+03 1.2E+03 betas restricted ≥0, bound hit 

probit 4 6.71 0.15 398.61 2.6E+03 2.2E+03 

Weibull 4 2.65 0.62 394.49 1.5E+03 1.2E+03 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.2.29.2. Figure for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound Hit 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0.8

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

13:37 11/16 2009

BMDL BMD

 

Multistage

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-190 —DO NOT CITE OR QUOTE 

1 

2 E.2.29.3. Output File for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound 

3 Hit 

4 

5 

6 ==================================================================== 

7 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

8 Input Data File: C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Cardiomyopathy.(d) 

9 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Cardiomyopathy.plt 

10 Mon Nov 16 13:37:37 2009 

11 ==================================================================== 

12 

13 0 

14 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

15 

16 The form of the probability function is: 

17 

18 P[response] = background + (1-background)*[1-EXP( 

19 -beta1*dose^1-beta2*dose^2)] 

20 

21 The parameter betas are restricted to be positive 

22 

23 

24 Dependent variable = DichEff 

25 Independent variable = Dose 

26 

27 Total number of observations = 6 

28 Total number of records with missing values = 0 

29 Total number of parameters in model = 3 

30 Total number of specified parameters = 0 

31 Degree of polynomial = 2 

32 

33 

34 Maximum number of iterations = 250 

35 Relative Function Convergence has been set to: 1e-008 

36 Parameter Convergence has been set to: 1e-008 

37 

38 

39 

40 Default Initial Parameter Values 

41 Background = 0.234028 

42 Beta(1) = 6.08803e-005 

43 Beta(2) = 0 

44 

45 

46 Asymptotic Correlation Matrix of Parameter Estimates 

47 

48 ( *** The model parameter(s) -Beta(2) 

49 have been estimated at a boundary point, or have been specified by the user, 

50 and do not appear in the correlation matrix ) 

51 

52 Background Beta(1) 

53 

54 Background 1 -0.69 

55 

56 Beta(1) -0.69 1 

57 

58 

59 

60 Parameter Estimates 

61 

62 95.0% Wald Confidence Interval 

63 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

64 Background 0.196221 * * * 

65 Beta(1) 6.98634e-005 * * * 

66 Beta(2) 0 * * * 

67 

68 * - Indicates that this value is not calculated. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-191 —DO NOT CITE OR QUOTE 

1 

2 

3 

4 Analysis of Deviance Table 

5 

6 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

7 Full model -193.93 6 

8 Fitted model -195.247 2 2.63378 4 0.6209 

9 Reduced model -216.802 1 45.7449 5 <.0001 

10 

11 AIC: 394.493 

12 

13 

14 Goodness of Fit 

15 Scaled 

16 Dose Est._Prob. Expected Observed Size Residual 

17 ------------------------------------------------------------------------ 

18 0.0000 0.1962 10.400 10.000 53 -0.138 

19 1408.4504 0.2715 14.663 12.000 54 -0.815 

20 3137.0446 0.3544 18.784 22.000 53 0.924 

21 5392.9593 0.4485 23.325 25.000 52 0.467 

22 9128.8027 0.5752 30.487 32.000 53 0.420 

23 16361.0000 0.7437 38.673 36.000 52 -0.849 

24 

25 Chi^2 = 2.65 d.f. = 4 P-value = 0.6176 

26 

27 

28 Benchmark Dose Computation 

29 

30 Specified effect = 0.1 

31 

32 Risk Type = Extra risk 

33 

34 Confidence level = 0.95 

35 

36 BMD = 1508.09 

37 

38 BMDL = 1170.08 

39 

40 BMDU = 2325.84 

41 

42 Taken together, (1170.08, 2325.84) is a 90 % two-sided confidence 

43 interval for the BMD 

44 

45 

46 

47 E.2.30. National Toxicology Program (2006): Hepatocyte Hypertrophy, 2 Years 

48 E.2.30.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 5 12.03 0.03 273.88 2.4E+02 2.1E+02 power restricted ≥1, bound 

hit 

gamma 5 12.03 0.03 273.88 5.0E+02 4.3E+02 power restricted ≥1, bound 

hit 

logistic 4 26.14 0.00 297.90 7.4E+02 6.2E+02 

logistic 4 26.14 0.00 297.90 1.4E+03 1.2E+03 

log-logistic 4 14.32 0.01 279.21 3.7E+02 1.8E+02 slope restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-192 —DO NOT CITE OR QUOTE 

log-logistic 4 14.32 0.01 279.21 6.3E+02 3.6E+02 slope restricted ≥1 

log-probit 4 13.74 0.01 278.36 4.3E+02 2.3E+02 slope restricted ≥1 

log-probit 4 13.74 0.01 278.36 6.6E+02 3.9E+02 slope restricted ≥1 

multistage, 2-

degree 5 12.03 0.03 273.88 2.4E+02 2.1E+02 betas restricted ≥0, bound hit 

multistage, 2-

degree b 5 12.03 0.03 273.88 5.0E+02 4.3E+02 betas restricted ≥0, bound hit 

probit 4 28.00 0.00 299.73 7.2E+02 6.2E+02 

probit 4 28.00 0.00 299.73 1.4E+03 1.2E+03 

Weibull 5 12.03 0.03 273.88 2.4E+02 2.1E+02 power restricted ≥1, bound 

hit 

Weibull 5 12.03 0.03 273.88 5.0E+02 4.3E+02 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

1 

2 

3 E.2.30.2. Figure for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

13:27 11/16 2009

BMDLBMD

 

Multistage

4 

5 

6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-193 —DO NOT CITE OR QUOTE 

1 E.2.30.3. Output File for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound 

2 Hit 

3 

4 

5 ==================================================================== 

6 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

7 Input Data File: 

8 C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Hepatocyte_hypertrophy_2years.(d) 

9 Gnuplot Plotting File: 

10 C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Hepatocyte_hypertrophy_2years.plt 

11 Mon Nov 16 13:27:47 2009 

12 ==================================================================== 

13 

14 [insert study notes] 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the probability function is: 

18 

19 P[response] = background + (1-background)*[1-EXP( 

20 -beta1*dose^1-beta2*dose^2)] 

21 

22 The parameter betas are restricted to be positive 

23 

24 

25 Dependent variable = DichEff 

26 Independent variable = Dose 

27 

28 Total number of observations = 6 

29 Total number of records with missing values = 0 

30 Total number of parameters in model = 3 

31 Total number of specified parameters = 0 

32 Degree of polynomial = 2 

33 

34 

35 Maximum number of iterations = 250 

36 Relative Function Convergence has been set to: 1e-008 

37 Parameter Convergence has been set to: 1e-008 

38 

39 

40 

41 Default Initial Parameter Values 

42 Background = 0.117028 

43 Beta(1) = 0.000142077 

44 Beta(2) = 5.42278e-009 

45 

46 

47 Asymptotic Correlation Matrix of Parameter Estimates 

48 

49 ( *** The model parameter(s) -Background -Beta(2) 

50 have been estimated at a boundary point, or have been specified by the user, 

51 and do not appear in the correlation matrix ) 

52 

53 Beta(1) 

54 

55 Beta(1) 1 

56 

57 

58 

59 Parameter Estimates 

60 

61 95.0% Wald Confidence Interval 

62 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

63 Background 0 * * * 

64 Beta(1) 0.00021035 * * * 

65 Beta(2) 0 * * * 

66 

67 * - Indicates that this value is not calculated. 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-194 —DO NOT CITE OR QUOTE 

1 

2 

3 Analysis of Deviance Table 

4 

5 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

6 Full model -129.986 6 

7 Fitted model -135.938 1 11.9043 5 0.03612 

8 Reduced model -219.97 1 179.968 5 <.0001 

9 

10 AIC: 273.876 

11 

12 

13 Goodness of Fit 

14 Scaled 

15 Dose Est._Prob. Expected Observed Size Residual 

16 ------------------------------------------------------------------------ 

17 0.0000 0.0000 0.000 0.000 53 0.000 

18 1408.4504 0.2564 13.846 19.000 54 1.606 

19 3137.0446 0.4831 25.604 19.000 53 -1.815 

20 5392.9593 0.6784 35.955 42.000 53 1.778 

21 9128.8027 0.8534 45.232 41.000 53 -1.643 

22 16361.0000 0.9680 51.303 52.000 53 0.544 

23 

24 Chi^2 = 12.03 d.f. = 5 P-value = 0.0344 

25 

26 

27 Benchmark Dose Computation 

28 

29 Specified effect = 0.1 

30 

31 Risk Type = Extra risk 

32 

33 Confidence level = 0.95 

34 

35 BMD = 500.882 

36 

37 BMDL = 433.488 

38 

39 BMDU = 637.074 

40 

41 Taken together, (433.488, 637.074) is a 90 % two-sided confidence 

42 interval for the BMD 

43 

44 

45 

46 E.2.31. National Toxicology Program (2006): Liver, Eosinophilic Focus, Multiple 

47 E.2.31.1. Summary Table of BMDS Modeling Results 

Model Degrees of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

gamma 3 3.72 0.29 331.90 2.0E+03 1.2E+03 power restricted ≥1 

logistic 4 4.01 0.40 330.40 3.3E+03 2.8E+03 

log-logistic 3 5.29 0.15 333.52 2.3E+03 1.1E+03 slope restricted ≥1 

log-probit 3 5.90 0.12 334.15 2.3E+03 1.2E+03 slope restricted ≥1 

multistage, 2-degree 3 2.69 0.44 330.82 2.0E+03 1.3E+03 betas restricted ≥0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-195 —DO NOT CITE OR QUOTE 

probit b 4 3.62 0.46 329.94 3.1E+03 2.7E+03 

Weibull 3 3.47 0.32 331.63 2.1E+03 1.2E+03 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded

1 

2 

3 E.2.31.2. Figure for Selected Model: Probit 

 0

 0.2

 0.4

 0.6

 0.8

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Probit Model with 0.95 Confidence Level

13:31 11/16 2009

BMDL BMD

 

Probit

4 

5 

6 

7 E.2.31.3. Output File for Selected Model: Probit 

8 

9 

10 ==================================================================== 

11 Probit Model. (Version: 3.1; Date: 05/16/2008) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Probit_BMR2_liver_eosin_focus.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Probit_BMR2_liver_eosin_focus.plt 

14 Mon Nov 16 13:31:29 2009 

15 ==================================================================== 

16 

17 0 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the probability function is: 

21 

22 P[response] = CumNorm(Intercept+Slope*Dose), 

23 

24 where CumNorm(.) is the cumulative normal distribution function 

25 

26 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-196 —DO NOT CITE OR QUOTE 

1 Dependent variable = DichEff 

2 Independent variable = Dose 

3 Slope parameter is not restricted 

4 

5 Total number of observations = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 

12 

13 Default Initial (and Specified) Parameter Values 

14 background = 0 Specified 

15 intercept = -1.28017 

16 slope = 0.000129308 

17 

18 

19 Asymptotic Correlation Matrix of Parameter Estimates 

20 

21 ( *** The model parameter(s) -background 

22 have been estimated at a boundary point, or have been specified by the user, 

23 and do not appear in the correlation matrix ) 

24 

25 intercept slope 

26 

27 intercept 1 -0.77 

28 

29 slope -0.77 1 

30 

31 

32 

33 Parameter Estimates 

34 

35 95.0% Wald Confidence Interval 

36 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

37 intercept -1.23453 0.125131 -1.47978 -0.98928 

38 slope 0.000124995 1.49436e-005 9.57063e-005 0.000154284 

39 

40 

41 

42 Analysis of Deviance Table 

43 

44 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

45 Full model -161.07 6 

46 Fitted model -162.972 2 3.80457 4 0.4331 

47 Reduced model -202.816 1 83.4925 5 <.0001 

48 

49 AIC: 329.944 

50 

51 

52 Goodness of Fit 

53 Scaled 

54 Dose Est._Prob. Expected Observed Size Residual 

55 ------------------------------------------------------------------------ 

56 0.0000 0.1085 5.751 3.000 53 -1.215 

57 1408.4504 0.1449 7.826 8.000 54 0.067 

58 3137.0446 0.1998 10.588 14.000 53 1.172 

59 5392.9593 0.2876 15.242 17.000 53 0.533 

60 9128.8027 0.4628 24.526 22.000 53 -0.696 

61 16361.0000 0.7912 41.932 42.000 53 0.023 

62 

63 Chi^2 = 3.62 d.f. = 4 P-value = 0.4593 

64 

65 

66 Benchmark Dose Computation 

67 

68 Specified effect = 0.1 

69 

70 Risk Type = Extra risk 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-197 —DO NOT CITE OR QUOTE 

1 

2 Confidence level = 0.95 

3 

4 BMD = 3076.08 

5 

6 BMDL = 2679.85 

7 

8 

9 

10 E.2.32. National Toxicology Program (2006): Liver, Fatty Change, Diffuse 

11 E.2.32.1. Summary Table of BMDS Modeling Results 

Model Degrees of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

gamma 4 2.42 0.66 252.35 2.2E+03 1.6E+03 power restricted ≥1 

logistic 4 9.22 0.06 262.13 3.2E+03 2.8E+03 

log-logistic 4 4.36 0.36 254.41 2.3E+03 1.8E+03 slope restricted ≥1 

log-probit 4 4.30 0.37 254.43 2.3E+03 1.8E+03 slope restricted ≥1 

multistage, 2-degree 4 2.03 0.73 252.07 2.0E+03 1.4E+03 betas restricted ≥0 

probit 4 8.50 0.07 260.92 3.1E+03 2.6E+03 

Weibull b 4 2.06 0.72 251.99 2.2E+03 1.6E+03 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-198 —DO NOT CITE OR QUOTE 

1 

2 E.2.32.2. Figure for Selected Model: Weibull, Power Restricted ≥1 

3 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Weibull Model with 0.95 Confidence Level

13:31 11/16 2009

BMDL BMD

 

Weibull

4 

5 

6 

7 E.2.32.3. Output File for Selected Model: Weibull, Power Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Weibull Model using Weibull Model (Version: 2.12; Date: 05/16/2008) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Weibull_BMR2_liver_fatty_change_diff.(d) 

13 Gnuplot Plotting File: 

14 C:\USEPA\BMDS21\AD\Blood\Weibull_BMR2_liver_fatty_change_diff.plt 

15 Mon Nov 16 13:31:55 2009 

16 ==================================================================== 

17 

18 NTP_liver_fatty_change_diffuse 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the probability function is: 

22 

23 P[response] = background + (1-background)*[1-EXP(-slope*dose^power)] 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 Power parameter is restricted as power >=1 

29 

30 Total number of observations = 6 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-199 —DO NOT CITE OR QUOTE 

1 

2 Default Initial (and Specified) Parameter Values 

3 Background = 0.00925926 

4 Slope = 1.61086e-007 

5 Power = 1.69678 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -Background 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 Slope Power 

15 

16 Slope 1 -1 

17 

18 Power -1 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0 NA 

27 Slope 1.01566e-006 1.55672e-006 -2.03545e-006 4.06678e-006 

28 Power 1.50443 0.168998 1.1732 1.83566 

29 

30 NA - Indicates that this parameter has hit a bound 

31 implied by some inequality constraint and thus 

32 has no standard error. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -122.992 6 

40 Fitted model -123.994 2 2.00421 4 0.735 

41 Reduced model -204.846 1 163.708 5 <.0001 

42 

43 AIC: 251.989 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0000 0.000 0.000 53 0.000 

51 1408.4504 0.0539 2.912 2.000 54 -0.550 

52 3137.0446 0.1688 8.949 12.000 53 1.119 

53 5392.9593 0.3415 18.102 17.000 53 -0.319 

54 9128.8027 0.6024 31.929 30.000 53 -0.542 

55 16361.0000 0.8913 47.238 48.000 53 0.336 

56 

57 Chi^2 = 2.06 d.f. = 4 P-value = 0.7243 

58 

59 

60 Benchmark Dose Computation 

61 

62 Specified effect = 0.1 

63 

64 Risk Type = Extra risk 

65 

66 Confidence level = 0.95 

67 

68 BMD = 2158.24 

69 

70 BMDL = 1573.34 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-200 —DO NOT CITE OR QUOTE 

1 

2 

3 E.2.33. National Toxicology Program (2006): Liver Necrosis 

4 E.2.33.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

 pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 0.80 0.94 234.40 4.8E+03 3.5E+03 power restricted ≥1, bound 

hit 

logistic 4 2.75 0.60 236.74 8.2E+03 6.8E+03 

log-logistic 4 0.77 0.94 234.38 4.4E+03 3.1E+03 slope restricted ≥1, bound 

hit 

log-logistic 3 0.75 0.86 236.38 4.3E+03 1.9E+03 slope unrestricted 

log-probit b 3 0.99 0.80 236.60 4.1E+03 1.9E+03 slope unrestricted 

multistage, 2-

degree 4 0.80 0.94 234.40 4.8E+03 3.5E+03 betas restricted ≥0, bound hit 

probit 4 2.38 0.67 236.29 7.7E+03 6.4E+03 

Weibull 4 0.80 0.94 234.40 4.8E+03 3.5E+03 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

5 

6 

7 E.2.33.2. Figure for Selected Model: Log-Probit 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

12:27 11/29 2009

BMDL BMD

 

LogProbit

8 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-201 —DO NOT CITE OR QUOTE 

1 

2 E.2.33.3. Output File for Selected Model: Log-Probit 

3 

4 ==================================================================== 

5 Probit Model. (Version: 3.1; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov29\Blood\LogProbit_BMR2_liver_necrosis.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\Blood\LogProbit_BMR2_liver_necrosis.plt 

8 Sun Nov 29 12:27:13 2009 

9 ==================================================================== 

10 

11 NTP_liver_necrosis 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = Background 

17 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

18 

19 where CumNorm(.) is the cumulative normal distribution function 

20 

21 

22 Dependent variable = DichEff 

23 Independent variable = Dose 

24 Slope parameter is not restricted 

25 

26 Total number of observations = 6 

27 Total number of records with missing values = 0 

28 Maximum number of iterations = 250 

29 Relative Function Convergence has been set to: 1e-008 

30 Parameter Convergence has been set to: 1e-008 

31 

32 

33 

34 User has chosen the log transformed model 

35 

36 

37 Default Initial (and Specified) Parameter Values 

38 background = 0.0188679 

39 intercept = -5.04893 

40 slope = 0.457364 

41 

42 

43 Asymptotic Correlation Matrix of Parameter Estimates 

44 

45 background intercept slope 

46 

47 background 1 -0.59 0.55 

48 

49 intercept -0.59 1 -1 

50 

51 slope 0.55 -1 1 

52 

53 

54 

55 Parameter Estimates 

56 

57 95.0% Wald Confidence Interval 

58 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

59 background 0.0221159 0.0221444 -0.0212863 0.0655182 

60 intercept -5.58721 1.71363 -8.94586 -2.22855 

61 slope 0.517092 0.185108 0.154287 0.879898 

62 

63 

64 

65 Analysis of Deviance Table 

66 

67 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

68 Full model -114.813 6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-202 —DO NOT CITE OR QUOTE 

1 Fitted model -115.299 3 0.972296 3 0.808 

2 Reduced model -127.98 1 26.3331 5 <.0001 

3 

4 AIC: 236.598 

5 

6 

7 Goodness of Fit 

8 Scaled 

9 Dose Est._Prob. Expected Observed Size Residual 

10 ------------------------------------------------------------------------ 

11 0.0000 0.0221 1.172 1.000 53 -0.161 

12 1408.4504 0.0544 2.938 4.000 54 0.637 

13 3137.0446 0.0976 5.174 4.000 53 -0.543 

14 5392.9593 0.1457 7.720 8.000 53 0.109 

15 9128.8027 0.2096 11.106 10.000 53 -0.373 

16 16361.0000 0.3002 15.908 17.000 53 0.327 

17 

18 Chi^2 = 0.99 d.f. = 3 P-value = 0.8048 

19 

20 

21 Benchmark Dose Computation 

22 

23 Specified effect = 0.1 

24 

25 Risk Type = Extra risk 

26 

27 Confidence level = 0.95 

28 

29 BMD = 4132.6 

30 

31 BMDL = 1930.47 

32 

33 

34 

35 E.2.34. National Toxicology Program (2006): Liver, Pigmentation 

36 E.2.34.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 3 2.10 0.55 196.97 1.2E+03 8.2E+02 power restricted ≥1 

logistic 4 5.42 0.25 197.07 1.0E+03 8.4E+02 

log-logistic 3 0.16 0.98 195.53 1.4E+03 1.1E+03 slope restricted ≥1 

log-probit b 3 0.29 0.96 195.53 1.4E+03 1.0E+03 slope restricted ≥1 

multistage, 2-

degree 3 7.47 0.06 199.96 1.0E+03 5.5E+02 betas restricted ≥0 

probit 4 15.44 0.00 200.50 9.4E+02 7.9E+02 

Weibull 3 4.42 0.22 199.01 9.7E+02 6.6E+02 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

37 

38 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-203 —DO NOT CITE OR QUOTE 

1 E.2.34.2. Figure for Selected Model: Log-Probit, Slope Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

13:38 11/16 2009

BMDL BMD

 

LogProbit

2 

3 

4 

5 E.2.34.3. Output File for Selected Model: Log-Probit, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Probit Model. (Version: 3.1; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\LogProbit_BMR2_Pigmentation.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\LogProbit_BMR2_Pigmentation.plt 

12 Mon Nov 16 13:38:02 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = Background 

21 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

22 

23 where CumNorm(.) is the cumulative normal distribution function 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 Slope parameter is not restricted 

29 

30 Total number of observations = 6 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-204 —DO NOT CITE OR QUOTE 

1 User has chosen the log transformed model 

2 

3 

4 Default Initial (and Specified) Parameter Values 

5 background = 0.0754717 

6 intercept = -12.1574 

7 slope = 1.53218 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 background intercept slope 

13 

14 background 1 -0.35 0.33 

15 

16 intercept -0.35 1 -1 

17 

18 slope 0.33 -1 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 background 0.0725493 0.0338874 0.00613127 0.138967 

27 intercept -14.4941 2.03052 -18.4738 -10.5144 

28 slope 1.83177 0.246866 1.34792 2.31562 

29 

30 

31 

32 Analysis of Deviance Table 

33 

34 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

35 Full model -94.6177 6 

36 Fitted model -94.7632 3 0.290885 3 0.9617 

37 Reduced model -210.717 1 232.198 5 <.0001 

38 

39 AIC: 195.526 

40 

41 

42 Goodness of Fit 

43 Scaled 

44 Dose Est._Prob. Expected Observed Size Residual 

45 ------------------------------------------------------------------------ 

46 0.0000 0.0725 3.845 4.000 53 0.082 

47 1408.4504 0.1769 9.552 9.000 54 -0.197 

48 3137.0446 0.6291 33.342 34.000 53 0.187 

49 5392.9593 0.9013 47.771 48.000 53 0.105 

50 9128.8027 0.9874 52.334 52.000 53 -0.412 

51 16361.0000 0.9995 52.974 53.000 53 0.160 

52 

53 Chi^2 = 0.29 d.f. = 3 P-value = 0.9624 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.1 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 1356.93 

65 

66 BMDL = 1041.17 

67 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-205 —DO NOT CITE OR QUOTE 

1 E.2.35. National Toxicology Program (2006): Liver, Toxic Hepatopathy 

2 E.2.35.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 1.90 0.75 185.76 2.4E+03 1.9E+03 power restricted ≥1 

logistic 4 6.59 0.16 191.14 2.7E+03 2.2E+03 

log-logistic 3 3.01 0.39 189.58 2.6E+03 2.1E+03 slope restricted ≥1 

log-probit 3 2.99 0.39 189.58 2.7E+03 2.1E+03 slope restricted ≥1 

multistage, 2-

degree b 5 2.28 0.81 184.08 2.1E+03 1.7E+03 betas restricted ≥0, bound hit 

probit 4 5.60 0.23 189.82 2.5E+03 2.1E+03 

Weibull 4 2.11 0.72 185.79 2.3E+03 1.8E+03 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

3 

4 

5 E.2.35.2. Figure for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:44 11/19 2009

BMDL BMD

 

Multistage

6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-206 —DO NOT CITE OR QUOTE 

1 

2 

3 E.2.35.3. Output File for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound 

4 Hit 

5 

6 

7 ==================================================================== 

8 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

9 Input Data File: C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Toxic_hepatopathy.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Toxic_hepatopathy.plt 

11 Thu Nov 19 11:44:22 2009 

12 ==================================================================== 

13 

14 0 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the probability function is: 

18 

19 P[response] = background + (1-background)*[1-EXP( 

20 -beta1*dose^1-beta2*dose^2)] 

21 

22 The parameter betas are restricted to be positive 

23 

24 

25 Dependent variable = DichEff 

26 Independent variable = Dose 

27 

28 Total number of observations = 6 

29 Total number of records with missing values = 0 

30 Total number of parameters in model = 3 

31 Total number of specified parameters = 0 

32 Degree of polynomial = 2 

33 

34 

35 Maximum number of iterations = 250 

36 Relative Function Convergence has been set to: 1e-008 

37 Parameter Convergence has been set to: 1e-008 

38 

39 

40 

41 Default Initial Parameter Values 

42 Background = 0 

43 Beta(1) = 0 

44 Beta(2) = 3.75131e+011 

45 

46 

47 Asymptotic Correlation Matrix of Parameter Estimates 

48 

49 ( *** The model parameter(s) -Background -Beta(1) 

50 have been estimated at a boundary point, or have been specified by the user, 

51 and do not appear in the correlation matrix ) 

52 

53 Beta(2) 

54 

55 Beta(2) 1 

56 

57 

58 

59 Parameter Estimates 

60 

61 95.0% Wald Confidence Interval 

62 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

63 Background 0 * * * 

64 Beta(1) 0 * * * 

65 Beta(2) 2.3767e-008 * * * 

66 

67 * - Indicates that this value is not calculated. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-207 —DO NOT CITE OR QUOTE 

1 

2 

3 

4 Analysis of Deviance Table 

5 

6 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

7 Full model -89.8076 6 

8 Fitted model -91.0417 1 2.46809 5 0.7813 

9 Reduced model -218.207 1 256.799 5 <.0001 

10 

11 AIC: 184.083 

12 

13 

14 Goodness of Fit 

15 Scaled 

16 Dose Est._Prob. Expected Observed Size Residual 

17 ------------------------------------------------------------------------ 

18 0.0000 0.0000 0.000 0.000 53 0.000 

19 1408.4504 0.0461 2.487 2.000 54 -0.316 

20 3137.0446 0.2086 11.053 8.000 53 -1.032 

21 5392.9593 0.4990 26.449 30.000 53 0.975 

22 9128.8027 0.8620 45.687 45.000 53 -0.274 

23 16361.0000 0.9983 52.909 53.000 53 0.303 

24 

25 Chi^2 = 2.28 d.f. = 5 P-value = 0.8087 

26 

27 

28 Benchmark Dose Computation 

29 

30 Specified effect = 0.1 

31 

32 Risk Type = Extra risk 

33 

34 Confidence level = 0.95 

35 

36 BMD = 2105.48 

37 

38 BMDL = 1698.91 

39 

40 BMDU = 2318.05 

41 

42 Taken together, (1698.91, 2318.05) is a 90 % two-sided confidence 

43 interval for the BMD 

44 

45 

46 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-208 —DO NOT CITE OR QUOTE 

1 E.2.35.4. Figure for Unrestricted Model: Multistage, 2-Degree, Betas Unrestricted 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:22 11/19 2009

BMDL BMD

 

Multistage

2 

3 

4 

5 E.2.35.5. Output File for Unrestricted Model: Multistage, 2-Degree, Betas Unrestricted 

6 

7 

8 ==================================================================== 

9 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Multistage_Unrest_BMR2_Toxic_hepatopathy.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AD\Blood\Multistage_Unrest_BMR2_Toxic_hepatopathy.plt 

13 Thu Nov 19 11:22:30 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background + (1-background)*[1-EXP( 

22 -beta1*dose^1-beta2*dose^2)] 

23 

24 The parameter betas are not restricted 

25 

26 

27 Dependent variable = DichEff 

28 Independent variable = Dose 

29 

30 Total number of observations = 6 

31 Total number of records with missing values = 0 

32 Total number of parameters in model = 3 

33 Total number of specified parameters = 0 

34 Degree of polynomial = 2 

35 

36 

37 Maximum number of iterations = 250 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-209 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 Background = 1 

8 Beta(1) = -6.1241e+015 

9 Beta(2) = 7.17596e+011 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) Beta(2) 

19 

20 Beta(1) 1 -0.92 

21 

22 Beta(2) -0.92 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 Background 0 * * * 

31 Beta(1) -1.36642e-005 * * * 

32 Beta(2) 2.62877e-008 * * * 

33 

34 * - Indicates that this value is not calculated. 

35 

36 

37 

38 Analysis of Deviance Table 

39 

40 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

41 Full model -89.8076 6 

42 Fitted model -90.8336 2 2.05202 4 0.7262 

43 Reduced model -218.207 1 256.799 5 <.0001 

44 

45 AIC: 185.667 

46 

47 

48 Goodness of Fit 

49 Scaled 

50 Dose Est._Prob. Expected Observed Size Residual 

51 ------------------------------------------------------------------------ 

52 0.0000 0.0000 0.000 0.000 53 0.000 

53 1408.4504 0.0324 1.748 2.000 54 0.194 

54 3137.0446 0.1941 10.289 8.000 53 -0.795 

55 5392.9593 0.4989 26.439 30.000 53 0.978 

56 9128.8027 0.8733 46.285 45.000 53 -0.531 

57 16361.0000 0.9989 52.942 53.000 53 0.241 

58 

59 Chi^2 = 1.97 d.f. = 4 P-value = 0.7420 

60 

61 

62 Benchmark Dose Computation 

63 

64 Specified effect = 0.1 

65 

66 Risk Type = Extra risk 

67 

68 Confidence level = 0.95 

69 

70 BMD = 2278.69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-210 —DO NOT CITE OR QUOTE 

1 

2 BMDL = 1743.86 

3 

4 BMDU = 2713.68 

5 

6 Taken together, (1743.86, 2713.68) is a 90 % two-sided confidence 

7 interval for the BMD 

8 

9 

10 

11 E.2.36. National Toxicology Program (2006): Lung, Alveolar to Bronchiolar Epithelial 

12 Metaplasia (Alveolar Epithelium, Metaplasia, Bronchiolar) 

13 E.2.36.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 13.37 0.01 320.09 5.4E+02 4.6E+02 power restricted ≥1, bound 

hit 

logistic 4 33.08 0.00 343.28 1.3E+03 1.1E+03 

log-logistic b 3 1.32 0.72 312.56 3.6E+02 2.1E+02 slope restricted ≥1 

log-probit 3 1.44 0.70 312.68 3.8E+02 1.5E+02 slope restricted ≥1 

multistage, 2-

degree 4 13.37 0.01 320.09 5.4E+02 4.6E+02 betas restricted ≥0, bound hit 

probit 4 35.22 0.00 347.07 1.4E+03 1.2E+03 

Weibull 4 13.37 0.01 320.09 5.4E+02 4.6E+02 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

14 

15 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-211 —DO NOT CITE OR QUOTE 

1 E.2.36.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

13:38 11/16 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.2.36.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR2_Alv_bronch_epith_metapl.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR2_Alv_bronch_epith_metapl.plt 

13 Mon Nov 16 13:38:53 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

22 

23 

24 Dependent variable = DichEff 

25 Independent variable = Dose 

26 Slope parameter is restricted as slope <= 1 

27 

28 Total number of observations = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 User has chosen the log transformed model 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-212 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 background = 0.0377358 

4 intercept = -8.78161 

5 slope = 1.1228 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 background intercept slope 

11 

12 background 1 -0.13 0.1 

13 

14 intercept -0.13 1 -1 

15 

16 slope 0.1 -1 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 background 0.0373474 * * * 

25 intercept -8.85134 * * * 

26 slope 1.13159 * * * 

27 

28 * - Indicates that this value is not calculated. 

29 

30 

31 

32 Analysis of Deviance Table 

33 

34 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

35 Full model -152.615 6 

36 Fitted model -153.279 3 1.32714 3 0.7227 

37 Reduced model -216.802 1 128.374 5 <.0001 

38 

39 AIC: 312.558 

40 

41 

42 Goodness of Fit 

43 Scaled 

44 Dose Est._Prob. Expected Observed Size Residual 

45 ------------------------------------------------------------------------ 

46 0.0000 0.0373 1.979 2.000 53 0.015 

47 1408.4504 0.3682 19.881 19.000 54 -0.249 

48 3137.0446 0.5807 30.777 33.000 53 0.619 

49 5392.9593 0.7162 37.244 35.000 52 -0.690 

50 9128.8027 0.8197 43.445 45.000 53 0.556 

51 16361.0000 0.8976 46.674 46.000 52 -0.308 

52 

53 Chi^2 = 1.32 d.f. = 3 P-value = 0.7232 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.1 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 357.926 

65 

66 BMDL = 206.635 

67 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-213 —DO NOT CITE OR QUOTE 

1 E.2.37. National Toxicology Program (2006): Oval Cell Hyperplasia, 2 Years 

2 E.2.37.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 3 6.94 0.07 199.47 3.7E+03 2.8E+03 power restricted ≥1 

logistic 4 6.40 0.17 196.80 3.3E+03 2.8E+03 

log-logistic 3 8.21 0.04 201.66 3.8E+03 3.1E+03 slope restricted ≥1 

log-probit 3 7.00 0.07 200.12 3.9E+03 3.3E+03 slope restricted ≥1 

multistage, 2-

degree 4 7.05 0.13 197.13 2.5E+03 2.0E+03 betas restricted ≥0 

probit b 4 5.64 0.23 195.45 3.1E+03 2.6E+03 

Weibull 3 6.85 0.08 198.38 3.2E+03 2.3E+03 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.2.37.2. Figure for Selected Model: Probit 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Probit Model with 0.95 Confidence Level

13:21 11/16 2009

BMDL BMD

 

Probit

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-214 —DO NOT CITE OR QUOTE 

1 

2 E.2.37.3. Output File for Selected Model: Probit 

3 

4 

5 ==================================================================== 

6 Probit Model. (Version: 3.1; Date: 05/16/2008) 

7 Input Data File: C:\USEPA\BMDS21\AD\Blood\Probit_BMR2_Oval_cell_hyperplasia.(d) 

8 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Probit_BMR2_Oval_cell_hyperplasia.plt 

9 Mon Nov 16 13:21:57 2009 

10 ==================================================================== 

11 

12 0 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the probability function is: 

16 

17 P[response] = CumNorm(Intercept+Slope*Dose), 

18 

19 where CumNorm(.) is the cumulative normal distribution function 

20 

21 

22 Dependent variable = DichEff 

23 Independent variable = Dose 

24 Slope parameter is not restricted 

25 

26 Total number of observations = 6 

27 Total number of records with missing values = 0 

28 Maximum number of iterations = 250 

29 Relative Function Convergence has been set to: 1e-008 

30 Parameter Convergence has been set to: 1e-008 

31 

32 

33 

34 Default Initial (and Specified) Parameter Values 

35 background = 0 Specified 

36 intercept = -2.29925 

37 slope = 0.000307725 

38 

39 

40 Asymptotic Correlation Matrix of Parameter Estimates 

41 

42 ( *** The model parameter(s) -background 

43 have been estimated at a boundary point, or have been specified by the user, 

44 and do not appear in the correlation matrix ) 

45 

46 intercept slope 

47 

48 intercept 1 -0.87 

49 

50 slope -0.87 1 

51 

52 

53 

54 Parameter Estimates 

55 

56 95.0% Wald Confidence Interval 

57 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

58 intercept -2.18988 0.208022 -2.59759 -1.78216 

59 slope 0.000313001 3.3114e-005 0.000248098 0.000377903 

60 

61 

62 

63 Analysis of Deviance Table 

64 

65 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

66 Full model -92.4898 6 

67 Fitted model -95.7243 2 6.46898 4 0.1668 

68 Reduced model -210.191 1 235.402 5 <.0001 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-215 —DO NOT CITE OR QUOTE 

1 

2 AIC: 195.449 

3 

4 

5 Goodness of Fit 

6 Scaled 

7 Dose Est._Prob. Expected Observed Size Residual 

8 ------------------------------------------------------------------------ 

9 0.0000 0.0143 0.756 0.000 53 -0.876 

10 1408.4504 0.0401 2.168 4.000 54 1.270 

11 3137.0446 0.1135 6.017 3.000 53 -1.306 

12 5392.9593 0.3079 16.317 20.000 53 1.096 

13 9128.8027 0.7478 39.631 38.000 53 -0.516 

14 16361.0000 0.9983 52.911 53.000 53 0.299 

15 

16 Chi^2 = 5.64 d.f. = 4 P-value = 0.2274 

17 

18 

19 Benchmark Dose Computation 

20 

21 Specified effect = 0.1 

22 

23 Risk Type = Extra risk 

24 

25 Confidence level = 0.95 

26 

27 BMD = 3125.6 

28 

29 BMDL = 2640.99 

30 

31 

32 

33 E.2.38. National Toxicology Program (2006): Toxic Hepatopathy 

34 E.2.38.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 1.90 0.75 185.76 2.4E+03 1.9E+03 power restricted ≥1 

logistic 4 6.59 0.16 191.14 2.7E+03 2.2E+03 

log-logistic 3 3.01 0.39 189.58 2.6E+03 2.1E+03 slope restricted ≥1 

log-probit 3 2.99 0.39 189.58 2.7E+03 2.1E+03 slope restricted ≥1 

multistage, 2-

degree b 5 2.28 0.81 184.08 2.1E+03 1.7E+03 betas restricted ≥0, bound hit 

probit 4 5.60 0.23 189.82 2.5E+03 2.1E+03 

Weibull 4 2.11 0.72 185.79 2.3E+03 1.8E+03 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-216 —DO NOT CITE OR QUOTE 

1 E.2.38.2. Figure for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:44 11/19 2009

BMDL BMD

 

Multistage

2 

3 

4 

5 E.2.38.3. Output File for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Toxic_hepatopathy.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Multistage_BMR2_Toxic_hepatopathy.plt 

13 Thu Nov 19 11:44:22 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background + (1-background)*[1-EXP( 

22 -beta1*dose^1-beta2*dose^2)] 

23 

24 The parameter betas are restricted to be positive 

25 

26 

27 Dependent variable = DichEff 

28 Independent variable = Dose 

29 

30 Total number of observations = 6 

31 Total number of records with missing values = 0 

32 Total number of parameters in model = 3 

33 Total number of specified parameters = 0 

34 Degree of polynomial = 2 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-217 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0 

10 Beta(2) = 3.75131e+011 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background -Beta(1) 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(2) 

20 

21 Beta(2) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 0 * * * 

31 Beta(2) 2.3767e-008 * * * 

32 

33 * - Indicates that this value is not calculated. 

34 

35 

36 

37 Analysis of Deviance Table 

38 

39 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

40 Full model -89.8076 6 

41 Fitted model -91.0417 1 2.46809 5 0.7813 

42 Reduced model -218.207 1 256.799 5 <.0001 

43 

44 AIC: 184.083 

45 

46 

47 Goodness of Fit 

48 Scaled 

49 Dose Est._Prob. Expected Observed Size Residual 

50 ------------------------------------------------------------------------ 

51 0.0000 0.0000 0.000 0.000 53 0.000 

52 1408.4504 0.0461 2.487 2.000 54 -0.316 

53 3137.0446 0.2086 11.053 8.000 53 -1.032 

54 5392.9593 0.4990 26.449 30.000 53 0.975 

55 9128.8027 0.8620 45.687 45.000 53 -0.274 

56 16361.0000 0.9983 52.909 53.000 53 0.303 

57 

58 Chi^2 = 2.28 d.f. = 5 P-value = 0.8087 

59 

60 

61 Benchmark Dose Computation 

62 

63 Specified effect = 0.1 

64 

65 Risk Type = Extra risk 

66 

67 Confidence level = 0.95 

68 

69 BMD = 2105.48 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-218 —DO NOT CITE OR QUOTE 

1 BMDL = 1698.91 

2 

3 BMDU = 2318.05 

4 

5 Taken together, (1698.91, 2318.05) is a 90 % two-sided confidence 

6 interval for the BMD 

7 

8 

9 

10 E.2.38.4. Figure for Unrestricted Model: Multistage, 2-Degree, Betas Unrestricted 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:44 11/19 2009

BMDL BMD

 

Multistage

11 

12 

13 

14 E.2.38.5. Output File for Unrestricted Model: Multistage, 2-Degree, Betas Unrestricted 

15 

16 

17 ==================================================================== 

18 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

19 Input Data File: 

20 C:\USEPA\BMDS21\AD\Blood\Multistage_Unrest_BMR2_2nd_Toxic_hepatopathy.(d) 

21 Gnuplot Plotting File: 

22 C:\USEPA\BMDS21\AD\Blood\Multistage_Unrest_BMR2_2nd_Toxic_hepatopathy.plt 

23 Thu Nov 19 11:44:23 2009 

24 ==================================================================== 

25 

26 0 

27 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

28 

29 The form of the probability function is: 

30 

31 P[response] = background + (1-background)*[1-EXP( 

32 -beta1*dose^1-beta2*dose^2)] 

33 

34 The parameter betas are not restricted 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-219 —DO NOT CITE OR QUOTE 

1 Dependent variable = DichEff 

2 Independent variable = Dose 

3 

4 Total number of observations = 6 

5 Total number of records with missing values = 0 

6 Total number of parameters in model = 3 

7 Total number of specified parameters = 0 

8 Degree of polynomial = 2 

9 

10 

11 Maximum number of iterations = 250 

12 Relative Function Convergence has been set to: 1e-008 

13 Parameter Convergence has been set to: 1e-008 

14 

15 

16 

17 Default Initial Parameter Values 

18 Background = 1 

19 Beta(1) = -6.1241e+015 

20 Beta(2) = 7.17596e+011 

21 

22 

23 Asymptotic Correlation Matrix of Parameter Estimates 

24 

25 ( *** The model parameter(s) -Background 

26 have been estimated at a boundary point, or have been specified by the user, 

27 and do not appear in the correlation matrix ) 

28 

29 Beta(1) Beta(2) 

30 

31 Beta(1) 1 -0.92 

32 

33 Beta(2) -0.92 1 

34 

35 

36 

37 Parameter Estimates 

38 

39 95.0% Wald Confidence Interval 

40 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

41 Background 0 * * * 

42 Beta(1) -1.36642e-005 * * * 

43 Beta(2) 2.62877e-008 * * * 

44 

45 * - Indicates that this value is not calculated. 

46 

47 

48 

49 Analysis of Deviance Table 

50 

51 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

52 Full model -89.8076 6 

53 Fitted model -90.8336 2 2.05202 4 0.7262 

54 Reduced model -218.207 1 256.799 5 <.0001 

55 

56 AIC: 185.667 

57 

58 

59 Goodness of Fit 

60 Scaled 

61 Dose Est._Prob. Expected Observed Size Residual 

62 ------------------------------------------------------------------------ 

63 0.0000 0.0000 0.000 0.000 53 0.000 

64 1408.4504 0.0324 1.748 2.000 54 0.194 

65 3137.0446 0.1941 10.289 8.000 53 -0.795 

66 5392.9593 0.4989 26.439 30.000 53 0.978 

67 9128.8027 0.8733 46.285 45.000 53 -0.531 

68 16361.0000 0.9989 52.942 53.000 53 0.241 

69 

70 Chi^2 = 1.97 d.f. = 4 P-value = 0.7420 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-220 —DO NOT CITE OR QUOTE 

1 

2 

3 Benchmark Dose Computation 

4 

5 Specified effect = 0.1 

6 

7 Risk Type = Extra risk 

8 

9 Confidence level = 0.95 

10 

11 BMD = 2278.69 

12 

13 BMDL = 1743.86 

14 

15 BMDU = 2713.68 

16 

17 Taken together, (1743.86, 2713.68) is a 90 % two-sided confidence 

18 interval for the BMD 

19 

20 

21 

22 E.2.39. Ohsako et al. (2001): Anogenital Distance in Male Pups 

23 E.2.39.1. Summary Table of BMDS Modeling Results 

Model a

Degrees 

of 

Freedom 

χ 2 pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) 3 0.092 185.349 2.358E+04 1.529E+04 

exponential (M3) 3 0.092 185.349 2.358E+04 1.529E+04 power bound hit 

exponential (M4) 2 0.190 184.217 2.617E+03 8.029E+02 

exponential (M5) 1 0.092 185.741 2.204E+03 8.487E+02 

Hill c 2 0.261 183.587 3.628E+03 8.053E+02 n lower bound hit 

linear 3 0.086 185.490 2.436E+04 1.638E+04 

polynomial 3 0.086 185.490 2.436E+04 1.638E+04 

power 3 0.086 185.490 2.436E+04 1.638E+04 power bound hit 

Hill, unrestricted d 1 0.106 185.515 4.741E+03 4.517E+02 n unrestricted 

a

 Constant variance model selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model, BMDS output presented in this appendix 

d

 Alternate model, BMDS output also presented in this appendix 

24 

25 

26 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-221 —DO NOT CITE OR QUOTE 

1 E.2.39.2. Figure for Selected Model: Hill 

 22

 24

 26

 28

 30

 32

 0 5000 10000 15000 20000 25000 30000

Mean Response

dose

Hill Model with 0.95 Confidence Level

10:31 01/12 2010

BMDL BMD

 

Hill

2 

3 

4 Ohsako et al., 2001: Ano-genital distance in male pups 

5 

6 

7 E.2.39.3. Output File for Selected Model: Hill 

8 Ohsako et al., 2001: Ano-genital distance in male pups 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\1\Blood\56_Ohsako_2001_anogenital_HillCV_1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\56_Ohsako_2001_anogenital_HillCV_1.plt 

13 Tue Jan 12 10:31:18 2010 

14 ==================================================================== 

15 

16 Figure 7 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter restricted to be greater than 1 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 5 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 alpha = 9.96434 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-222 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 intercept = 28.9146 

3 v = -5.04512 

4 n = 1.64399 

5 k = 2013.5 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho -n 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha intercept v k 

15 

16 alpha 1 4.1e-008 7.2e-008 -1e-007 

17 

18 intercept 4.1e-008 1 -0.53 -0.53 

19 

20 v 7.2e-008 -0.53 1 -0.27 

21 

22 k -1e-007 -0.53 -0.27 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 9.50299 1.82885 5.91851 13.0875 

31 intercept 28.988 0.868025 27.2867 30.6893 

32 v -5.03805 1.23954 -7.4675 -2.6086 

33 n 1 NA 

34 k 2301.52 2261.96 -2131.83 6734.88 

35 

36 NA - Indicates that this parameter has hit a bound 

37 implied by some inequality constraint and thus 

38 has no standard error. 

39 

40 

41 

42 Table of Data and Estimated Values of Interest 

43 

44 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

45 ------ --- -------- -------- ----------- ----------- ---------- 

46 

47 0 12 28.9 29 3.54 3.08 -0.0824 

48 845.3 10 28.1 27.6 2.52 3.08 0.455 

49 2763 10 25.3 26.2 3.59 3.08 -0.953 

50 9022 10 26.1 25 3.59 3.08 1.12 

51 3.05e+004 12 23.9 24.3 2.36 3.08 -0.488 

52 

53 

54 

55 Model Descriptions for likelihoods calculated 

56 

57 

58 Model A1: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma^2 

60 

61 Model A2: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma(i)^2 

63 

64 Model A3: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 Model A3 uses any fixed variance parameters that 

67 were specified by the user 

68 

69 Model R: Yi = Mu + e(i) 

70 Var{e(i)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-223 —DO NOT CITE OR QUOTE 

1 

2 

3 Likelihoods of Interest 

4 

5 Model Log(likelihood) # Param's AIC 

6 A1 -86.449919 6 184.899838 

7 A2 -84.654549 10 189.309098 

8 A3 -86.449919 6 184.899838 

9 fitted -87.793369 4 183.586738 

10 R -95.473923 2 194.947846 

11 

12 

13 Explanation of Tests 

14 

15 Test 1: Do responses and/or variances differ among Dose levels? 

16 (A2 vs. R) 

17 Test 2: Are Variances Homogeneous? (A1 vs A2) 

18 Test 3: Are variances adequately modeled? (A2 vs. A3) 

19 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

20 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

21 

22 Tests of Interest 

23 

24 Test -2*log(Likelihood Ratio) Test df p-value 

25 

26 Test 1 21.6387 8 0.005631 

27 Test 2 3.59074 4 0.4642 

28 Test 3 3.59074 4 0.4642 

29 Test 4 2.6869 2 0.2609 

30 

31 The p-value for Test 1 is less than .05. There appears to be a 

32 difference between response and/or variances among the dose levels 

33 It seems appropriate to model the data 

34 

35 The p-value for Test 2 is greater than .1. A homogeneous variance 

36 model appears to be appropriate here 

37 

38 

39 The p-value for Test 3 is greater than .1. The modeled variance appears 

40 to be appropriate here 

41 

42 The p-value for Test 4 is greater than .1. The model chosen seems 

43 to adequately describe the data 

44 

45 

46 Benchmark Dose Computation 

47 

48 Specified effect = 1 

49 

50 Risk Type = Estimated standard deviations from the control mean 

51 

52 Confidence level = 0.95 

53 

54 BMD = 3628.44 

55 

56 BMDL = 805.33 

57 

58 

59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-224 —DO NOT CITE OR QUOTE 

1 E.2.39.4. Figure for Unrestricted Model: Hill, Unrestricted 

 22

 24

 26

 28

 30

 32

 0 5000 10000 15000 20000 25000 30000

Mean Response

dose

Hill Model with 0.95 Confidence Level

10:31 01/12 2010

BMDL BMD

 

Hill

2 

3 

4 Ohsako et al., 2001: Ano-genital distance in male pups

5 

6 

7 E.2.39.5. Output File for Unrestricted Model: Hill, Unrestricted 

8 Ohsako et al., 2001: Ano-genital distance in male pups 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\1\Blood\56_Ohsako_2001_anogenital_HillCV_Unrest_1.(d) 

12 Gnuplot Plotting File: C:\1\Blood\56_Ohsako_2001_anogenital_HillCV_Unrest_1.plt 

13 Tue Jan 12 10:31:19 2010 

14 ==================================================================== 

15 

16 Figure 7 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter is not restricted 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 5 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 alpha = 9.96434 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-225 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 intercept = 28.9146 

3 v = -5.04512 

4 n = 1.64399 

5 k = 2013.5 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha intercept v n k 

15 

16 alpha 1 1.7e-008 7.5e-008 7.3e-008 -7.2e-008 

17 

18 intercept 1.7e-008 1 -0.0053 -0.0089 -0.14 

19 

20 v 7.5e-008 -0.0053 1 0.98 -0.99 

21 

22 n 7.3e-008 -0.0089 0.98 1 -0.96 

23 

24 k -7.2e-008 -0.14 -0.99 -0.96 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 95.0% Wald Confidence Interval 

31 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

32 alpha 9.49042 1.82643 5.91068 13.0702 

33 intercept 28.9785 0.871908 27.2696 30.6874 

34 v -6.77236 12.034 -30.3585 16.8138 

35 n 0.615459 1.15558 -1.64943 2.88035 

36 k 6361.67 43105.4 -78123.4 90846.7 

37 

38 

39 

40 Table of Data and Estimated Values of Interest 

41 

42 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

43 ------ --- -------- -------- ----------- ----------- ---------- 

44 

45 0 12 28.9 29 3.54 3.08 -0.0718 

46 845.3 10 28.1 27.5 2.52 3.08 0.633 

47 2763 10 25.3 26.4 3.59 3.08 -1.16 

48 9022 10 26.1 25.2 3.59 3.08 0.861 

49 3.05e+004 12 23.9 24.1 2.36 3.08 -0.231 

50 

51 

52 

53 Model Descriptions for likelihoods calculated 

54 

55 

56 Model A1: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma^2 

58 

59 Model A2: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = Sigma(i)^2 

61 

62 Model A3: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = Sigma^2 

64 Model A3 uses any fixed variance parameters that 

65 were specified by the user 

66 

67 Model R: Yi = Mu + e(i) 

68 Var{e(i)} = Sigma^2 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-226 —DO NOT CITE OR QUOTE 

1 Likelihoods of Interest 

2 

3 Model Log(likelihood) # Param's AIC 

4 A1 -86.449919 6 184.899838 

5 A2 -84.654549 10 189.309098 

6 A3 -86.449919 6 184.899838 

7 fitted -87.757640 5 185.515280 

8 R -95.473923 2 194.947846 

9 

10 

11 Explanation of Tests 

12 

13 Test 1: Do responses and/or variances differ among Dose levels? 

14 (A2 vs. R) 

15 Test 2: Are Variances Homogeneous? (A1 vs A2) 

16 Test 3: Are variances adequately modeled? (A2 vs. A3) 

17 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

18 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

19 

20 Tests of Interest 

21 

22 Test -2*log(Likelihood Ratio) Test df p-value 

23 

24 Test 1 21.6387 8 0.005631 

25 Test 2 3.59074 4 0.4642 

26 Test 3 3.59074 4 0.4642 

27 Test 4 2.61544 1 0.1058 

28 

29 The p-value for Test 1 is less than .05. There appears to be a 

30 difference between response and/or variances among the dose levels 

31 It seems appropriate to model the data 

32 

33 The p-value for Test 2 is greater than .1. A homogeneous variance 

34 model appears to be appropriate here 

35 

36 

37 The p-value for Test 3 is greater than .1. The modeled variance appears 

38 to be appropriate here 

39 

40 The p-value for Test 4 is greater than .1. The model chosen seems 

41 to adequately describe the data 

42 

43 

44 Benchmark Dose Computation 

45 

46 Specified effect = 1 

47 

48 Risk Type = Estimated standard deviations from the control mean 

49 

50 Confidence level = 0.95 

51 

52 BMD = 4741.19 

53 

54 BMDL = 451.715 

55 

56 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-227 —DO NOT CITE OR QUOTE 

1 

2 E.2.40. Schantz et al. (1996): Maze Errors Per Block, Female 

3 E.2.40.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

linear 1 0.71 2.38 0.12 19.76 5.1E+03 2.9E+03 nonconstant variance 

polynomial 1 0.71 2.38 0.12 19.76 5.1E+03 2.9E+03 nonconstant variance 

power 1 0.71 2.38 0.12 19.76 5.1E+03 2.9E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 0 0.71 0.00 NA 19.38 1.2E+03 5.4E-08 nonconstant variance, 

power unrestricted 

linear c 1 0.71 1.99 0.16 17.95 5.5E+03 3.6E+03 constant variance 

polynomial 1 0.71 1.99 0.16 17.95 5.5E+03 3.6E+03 constant variance 

power 1 0.71 1.99 0.16 17.95 5.5E+03 3.6E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power d 0 0.71 0.00 NA 17.95 2.0E+03 8.1E-06 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-228 —DO NOT CITE OR QUOTE 

1 E.2.40.2. Figure for Selected Model: Linear, Constant Variance 

 2

 2.5

 3

 3.5

 4

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:42 11/16 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.2.40.3. Output File for Selected Model: Linear, Constant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\LinearConstVar_BMR4_maze_errors.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\LinearConstVar_BMR4_maze_errors.plt 

12 Mon Nov 16 13:42:46 2009 

13 ==================================================================== 

14 

15 Rel Male Thymus wt, Tbl 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 Signs of the polynomial coefficients are not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 3 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-229 —DO NOT CITE OR QUOTE 

1 alpha = 0.569565 

2 rho = 0 Specified 

3 beta_0 = 3.37789 

4 beta_1 = -0.000133906 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -rho 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 alpha beta_0 beta_1 

14 

15 alpha 1 1.5e-010 7.3e-012 

16 

17 beta_0 1.5e-010 1 -0.73 

18 

19 beta_1 7.3e-012 -0.73 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 alpha 0.547839 0.141451 0.270599 0.825079 

28 beta_0 3.37789 0.196469 2.99282 3.76296 

29 beta_1 -0.000133906 3.88571e-005 -0.000210064 -5.77472e-005 

30 

31 

32 

33 Table of Data and Estimated Values of Interest 

34 

35 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

36 ------ --- -------- -------- ----------- ----------- ---------- 

37 

38 0 10 3.55 3.38 0.639 0.74 0.755 

39 2670 10 2.76 3.02 0.806 0.74 -1.11 

40 8341 10 2.34 2.26 0.806 0.74 0.355 

41 

42 

43 

44 Model Descriptions for likelihoods calculated 

45 

46 

47 Model A1: Yij = Mu(i) + e(ij) 

48 Var{e(ij)} = Sigma^2 

49 

50 Model A2: Yij = Mu(i) + e(ij) 

51 Var{e(ij)} = Sigma(i)^2 

52 

53 Model A3: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 Model A3 uses any fixed variance parameters that 

56 were specified by the user 

57 

58 Model R: Yi = Mu + e(i) 

59 Var{e(i)} = Sigma^2 

60 

61 

62 Likelihoods of Interest 

63 

64 Model Log(likelihood) # Param's AIC 

65 A1 -4.976366 4 17.952732 

66 A2 -4.638353 6 21.276707 

67 A3 -4.976366 4 17.952732 

68 fitted -5.973388 3 17.946777 

69 R -10.975997 2 25.951993 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-230 —DO NOT CITE OR QUOTE 

1 

2 Explanation of Tests 

3 

4 Test 1: Do responses and/or variances differ among Dose levels? 

5 (A2 vs. R) 

6 Test 2: Are Variances Homogeneous? (A1 vs A2) 

7 Test 3: Are variances adequately modeled? (A2 vs. A3) 

8 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

9 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

10 

11 Tests of Interest 

12 

13 Test -2*log(Likelihood Ratio) Test df p-value 

14 

15 Test 1 12.6753 4 0.01298 

16 Test 2 0.676025 2 0.7132 

17 Test 3 0.676025 2 0.7132 

18 Test 4 1.99405 1 0.1579 

19 

20 The p-value for Test 1 is less than .05. There appears to be a 

21 difference between response and/or variances among the dose levels 

22 It seems appropriate to model the data 

23 

24 The p-value for Test 2 is greater than .1. A homogeneous variance 

25 model appears to be appropriate here 

26 

27 

28 The p-value for Test 3 is greater than .1. The modeled variance appears 

29 to be appropriate here 

30 

31 The p-value for Test 4 is greater than .1. The model chosen seems 

32 to adequately describe the data 

33 

34 

35 Benchmark Dose Computation 

36 

37 Specified effect = 1 

38 

39 Risk Type = Estimated standard deviations from the control mean 

40 

41 Confidence level = 0.95 

42 

43 BMD = 5527.48 

44 

45 

46 BMDL = 3627.8 

47 

48 

49 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-231 —DO NOT CITE OR QUOTE 

1 E.2.40.4. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 2

 2.5

 3

 3.5

 4

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:42 11/16 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.2.40.5. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

6 

7 

8 ==================================================================== 

9 Power Model. (Version: 2.15; Date: 04/07/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\PwrConstVar_Unrest_BMR6_maze_errors.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AD\Blood\PwrConstVar_Unrest_BMR6_maze_errors.plt 

13 Mon Nov 16 13:42:47 2009 

14 ==================================================================== 

15 

16 Rel Male Thymus wt, Tbl 2 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 The power is not restricted 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 3 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-232 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 alpha = 0.569565 

3 rho = 0 Specified 

4 control = 3.55459 

5 slope = -0.0428676 

6 power = 0.369985 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 ( *** The model parameter(s) -rho 

12 have been estimated at a boundary point, or have been specified by the user, 

13 and do not appear in the correlation matrix ) 

14 

15 alpha control slope power 

16 

17 alpha 1 -6.8e-011 -1.4e-012 -1.6e-013 

18 

19 control -6.8e-011 1 -0.35 -0.28 

20 

21 slope -1.4e-012 -0.35 1 1 

22 

23 power -1.6e-013 -0.28 1 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 95.0% Wald Confidence Interval 

30 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

31 alpha 0.512609 0.132355 0.253198 0.77202 

32 control 3.55459 0.226409 3.11084 3.99834 

33 slope -0.0428676 0.119074 -0.276249 0.190514 

34 power 0.369985 0.311491 -0.240526 0.980496 

35 

36 

37 

38 Table of Data and Estimated Values of Interest 

39 

40 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

41 ------ --- -------- -------- ----------- ----------- ---------- 

42 

43 0 10 3.55 3.55 0.639 0.716 2.62e-010 

44 2670 10 2.76 2.76 0.806 0.716 3.09e-010 

45 8341 10 2.34 2.34 0.806 0.716 3.32e-010 

46 

47 Degrees of freedom for Test A3 vs fitted <= 0 

48 

49 

50 

51 Model Descriptions for likelihoods calculated 

52 

53 

54 Model A1: Yij = Mu(i) + e(ij) 

55 Var{e(ij)} = Sigma^2 

56 

57 Model A2: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma(i)^2 

59 

60 Model A3: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 Model A3 uses any fixed variance parameters that 

63 were specified by the user 

64 

65 Model R: Yi = Mu + e(i) 

66 Var{e(i)} = Sigma^2 

67 

68 

69 Likelihoods of Interest 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-233 —DO NOT CITE OR QUOTE 

1 Model Log(likelihood) # Param's AIC 

2 A1 -4.976366 4 17.952732 

3 A2 -4.638353 6 21.276707 

4 A3 -4.976366 4 17.952732 

5 fitted -4.976366 4 17.952732 

6 R -10.975997 2 25.951993 

7 

8 

9 Explanation of Tests 

10 

11 Test 1: Do responses and/or variances differ among Dose levels? 

12 (A2 vs. R) 

13 Test 2: Are Variances Homogeneous? (A1 vs A2) 

14 Test 3: Are variances adequately modeled? (A2 vs. A3) 

15 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

16 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

17 

18 Tests of Interest 

19 

20 Test -2*log(Likelihood Ratio) Test df p-value 

21 

22 Test 1 12.6753 4 0.01298 

23 Test 2 0.676025 2 0.7132 

24 Test 3 0.676025 2 0.7132 

25 Test 4 1.77636e-015 0 NA 

26 

27 The p-value for Test 1 is less than .05. There appears to be a 

28 difference between response and/or variances among the dose levels 

29 It seems appropriate to model the data 

30 

31 The p-value for Test 2 is greater than .1. A homogeneous variance 

32 model appears to be appropriate here 

33 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi-Square 

39 test for fit is not valid 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 2017.9 

51 

52 

53 BMDL = 8.10578e-006 

54 

55 

56 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-234 —DO NOT CITE OR QUOTE 

1 E.2.41. Shi et al. (2007): Estradiol 

2 E.2.41.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 0.05 11.41 0.01 391.64 3.8E+03 2.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.05 11.41 0.01 391.64 3.8E+03 2.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 2 0.05 0.74 0.69 382.97 4.4E+02 2.0E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.05 0.74 0.69 382.97 4.4E+02 2.0E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 2 0.05 0.74 0.69 382.97 4.4E+02 2.0E+02 nonconstant variance, 

power unrestricted 

Hill 2 0.05 0.05 0.97 382.28 4.0E+02 error nonconstant variance, n 

restricted >1, bound hit 

Hill d 1 0.05 0.02 0.90 384.24 3.9E+02 error nonconstant variance, n 

unrestricted 

linear 3 0.05 14.08 0.00 394.31 5.4E+03 3.7E+03 nonconstant variance 

polynomial 2 0.05 5.06 0.08 387.29 1.8E+03 1.2E+03 nonconstant variance 

power 3 0.05 14.08 0.00 394.31 5.4E+03 3.7E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 2 0.05 1.36 0.51 383.59 3.5E+02 1.8E+01 nonconstant variance, 

power unrestricted 

exponential (M2) 3 0.05 9.37 0.02 392.09 2.8E+03 1.6E+03 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.05 9.37 0.02 392.09 2.8E+03 1.6E+03 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.05 0.61 0.74 385.34 3.3E+02 1.5E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.05 0.61 0.74 385.34 3.3E+02 1.5E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.05 0.61 0.74 385.34 3.3E+02 1.5E+02 constant variance, 

power unrestricted 

Hill 1 0.05 0.26 0.61 386.98 3.1E+02 1.2E+02 constant variance, n 

restricted >1 

Hill 1 0.05 0.26 0.61 386.98 3.1E+02 4.0E+01 constant variance, n 

unrestricted 

linear 3 0.05 12.21 0.01 394.93 4.4E+03 3.2E+03 constant variance 

polynomial 2 0.05 5.39 0.07 390.12 1.4E+03 9.3E+02 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-235 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

power 3 0.05 12.21 0.01 394.93 4.4E+03 3.2E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power 2 0.05 1.66 0.44 386.38 2.3E+02 1.2E+01 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.2.41.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 20

 40

 60

 80

 100

 120

 140

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:45 11/16 2009

BMDL BMD

 

Exponential

5 

6 

7 

8 E.2.41.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_BMR1_Shi_estradiol_17B_conc_PE9.(d) 

15 Gnuplot Plotting File: 

16 Mon Nov 16 13:45:19 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-236 —DO NOT CITE OR QUOTE 

1 ==================================================================== 

2 

3 Figure 4 PE9 only 

4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

5 

6 The form of the response function by Model: 

7 Model 2: Y[dose] = a * exp{sign * b * dose} 

8 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

9 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

10 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

11 

12 Note: Y[dose] is the median response for exposure = dose; 

13 sign = +1 for increasing trend in data; 

14 sign = -1 for decreasing trend. 

15 

16 Model 2 is nested within Models 3 and 4. 

17 Model 3 is nested within Model 5. 

18 Model 4 is nested within Model 5. 

19 

20 

21 Dependent variable = Mean 

22 Independent variable = Dose 

23 Data are assumed to be distributed: normally 

24 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

25 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

26 

27 Total number of dose groups = 5 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 MLE solution provided: Exact 

34 

35 

36 Initial Parameter Values 

37 

38 Variable Model 4 

39 -------- -------- 

40 lnalpha 2.65881 

41 rho 0.913414 

42 a 108 

43 b 0.000503911 

44 c 0.340136 

45 d 1 

46 

47 

48 

49 Parameter Estimates 

50 

51 Variable Model 4 

52 -------- ------- 

53 lnalpha 1.66777 

54 rho 1.15313 

55 a 103.145 

56 b 0.00182735 

57 c 0.418744 

58 d 1 

59 

60 

61 Table of Stats From Input Data 

62 

63 Dose N Obs Mean Obs Std Dev 

64 ----- --- ---------- ------------- 

65 0 10 102.9 41.41 

66 188.3 10 86.19 19.58 

67 592.1 10 63.33 29.36 

68 2882 10 48.1 18.82 

69 7665 10 38.57 22.59 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-237 —DO NOT CITE OR QUOTE 

1 

2 Estimated Values of Interest 

3 

4 Dose Est Mean Est Std Scaled Residual 

5 ------ ---------- --------- ---------------- 

6 0 103.1 33.35 -0.02732 

7 188.3 85.69 29.96 0.05287 

8 592.1 63.51 25.21 -0.02235 

9 2882 43.5 20.27 0.7167 

10 7665 43.19 20.19 -0.7237 

11 

12 

13 

14 Other models for which likelihoods are calculated: 

15 

16 Model A1: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma^2 

18 

19 Model A2: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = Sigma(i)^2 

21 

22 Model A3: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

24 

25 Model R: Yij = Mu + e(i) 

26 Var{e(ij)} = Sigma^2 

27 

28 

29 Likelihoods of Interest 

30 

31 Model Log(likelihood) DF AIC 

32 ------- ----------------- ---- ------------ 

33 A1 -188.3615 6 388.7231 

34 A2 -183.667 10 387.3339 

35 A3 -186.1132 7 386.2263 

36 R -203.3606 2 410.7211 

37 4 -186.4844 5 382.9688 

38 

39 

40 Additive constant for all log-likelihoods = -45.95. This constant added to the 

41 above values gives the log-likelihood including the term that does not 

42 depend on the model parameters. 

43 

44 

45 Explanation of Tests 

46 

47 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

48 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

49 Test 3: Are variances adequately modeled? (A2 vs. A3) 

50 

51 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

52 

53 

54 Tests of Interest 

55 

56 Test -2*log(Likelihood Ratio) D. F. p-value 

57 -------- ------------------------ ------ -------------- 

58 Test 1 39.39 8 < 0.0001 

59 Test 2 9.389 4 0.05208 

60 Test 3 4.892 3 0.1798 

61 Test 6a 0.7425 2 0.6899 

62 

63 

64 The p-value for Test 1 is less than .05. There appears to be a 

65 difference between response and/or variances among the dose 

66 levels, it seems appropriate to model the data. 

67 

68 The p-value for Test 2 is less than .1. A non-homogeneous 

69 variance model appears to be appropriate. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-238 —DO NOT CITE OR QUOTE 

1 The p-value for Test 3 is greater than .1. The modeled 

2 variance appears to be appropriate here. 

3 

4 The p-value for Test 6a is greater than .1. Model 4 seems 

5 to adequately describe the data. 

6 

7 

8 Benchmark Dose Computations: 

9 

10 Specified Effect = 1.000000 

11 

12 Risk Type = Estimated standard deviations from control 

13 

14 Confidence Level = 0.950000 

15 

16 BMD = 444.551 

17 

18 BMDL = 195.249 

19 

20 

21 E.2.41.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

22 Unrestricted 

 20

 40

 60

 80

 100

 120

 140

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:45 11/16 2009

BMDL BMD

 

Exponential

23 

24 

25 

26 E.2.41.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

27 Power Unrestricted 

28 

29 

30 ==================================================================== 

31 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

32 Input Data File: 

33 C:\USEPA\BMDS21\AD\Blood\Exp_Unrest_BMR1_Shi_estradiol_17B_conc_PE9.(d) 

34 Gnuplot Plotting File: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-239 —DO NOT CITE OR QUOTE 

1 Mon Nov 16 13:45:21 2009 

2 ==================================================================== 

3 

4 Figure 4 PE9 only 

5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

6 

7 The form of the response function by Model: 

8 Model 2: Y[dose] = a * exp{sign * b * dose} 

9 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

10 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

11 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

12 

13 Note: Y[dose] is the median response for exposure = dose; 

14 sign = +1 for increasing trend in data; 

15 sign = -1 for decreasing trend. 

16 

17 Model 2 is nested within Models 3 and 4. 

18 Model 3 is nested within Model 5. 

19 Model 4 is nested within Model 5. 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 Data are assumed to be distributed: normally 

25 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 5 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 MLE solution provided: Exact 

35 

36 

37 Initial Parameter Values 

38 

39 Variable Model 5 

40 -------- -------- 

41 lnalpha 2.65881 

42 rho 0.913414 

43 a 108 

44 b 0.000503911 

45 c 0.340136 

46 d 1 

47 

48 

49 

50 Parameter Estimates 

51 

52 Variable Model 5 

53 -------- ------- 

54 lnalpha 1.66777 

55 rho 1.15313 

56 a 103.145 

57 b 0.00182735 

58 c 0.418744 

59 d 1 

60 

61 

62 Table of Stats From Input Data 

63 

64 Dose N Obs Mean Obs Std Dev 

65 ----- --- ---------- ------------- 

66 0 10 102.9 41.41 

67 188.3 10 86.19 19.58 

68 592.1 10 63.33 29.36 

69 2882 10 48.1 18.82 

70 7665 10 38.57 22.59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-240 —DO NOT CITE OR QUOTE 

1 

2 

3 Estimated Values of Interest 

4 

5 Dose Est Mean Est Std Scaled Residual 

6 ------ ---------- --------- ---------------- 

7 0 103.1 33.35 -0.02732 

8 188.3 85.69 29.96 0.05287 

9 592.1 63.51 25.21 -0.02235 

10 2882 43.5 20.27 0.7167 

11 7665 43.19 20.19 -0.7237 

12 

13 

14 

15 Other models for which likelihoods are calculated: 

16 

17 Model A1: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma^2 

19 

20 Model A2: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma(i)^2 

22 

23 Model A3: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

25 

26 Model R: Yij = Mu + e(i) 

27 Var{e(ij)} = Sigma^2 

28 

29 

30 Likelihoods of Interest 

31 

32 Model Log(likelihood) DF AIC 

33 ------- ----------------- ---- ------------ 

34 A1 -188.3615 6 388.7231 

35 A2 -183.667 10 387.3339 

36 A3 -186.1132 7 386.2263 

37 R -203.3606 2 410.7211 

38 5 -186.4844 5 382.9688 

39 

40 

41 Additive constant for all log-likelihoods = -45.95. This constant added to the 

42 above values gives the log-likelihood including the term that does not 

43 depend on the model parameters. 

44 

45 

46 Explanation of Tests 

47 

48 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

49 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

50 Test 3: Are variances adequately modeled? (A2 vs. A3) 

51 

52 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

53 

54 

55 Tests of Interest 

56 

57 Test -2*log(Likelihood Ratio) D. F. p-value 

58 -------- ------------------------ ------ -------------- 

59 Test 1 39.39 8 < 0.0001 

60 Test 2 9.389 4 0.05208 

61 Test 3 4.892 3 0.1798 

62 Test 7a 0.7425 2 0.6899 

63 

64 

65 The p-value for Test 1 is less than .05. There appears to be a 

66 difference between response and/or variances among the dose 

67 levels, it seems appropriate to model the data. 

68 

69 The p-value for Test 2 is less than .1. A non-homogeneous 

70 variance model appears to be appropriate. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-241 —DO NOT CITE OR QUOTE 

1 

2 The p-value for Test 3 is greater than .1. The modeled 

3 variance appears to be appropriate here. 

4 

5 The p-value for Test 7a is greater than .1. Model 5 seems 

6 to adequately describe the data. 

7 

8 

9 Benchmark Dose Computations: 

10 

11 Specified Effect = 1.000000 

12 

13 Risk Type = Estimated standard deviations from control 

14 

15 Confidence Level = 0.950000 

16 

17 BMD = 444.551 

18 

19 BMDL = 195.249 

20 

21 

22 E.2.41.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 20

 40

 60

 80

 100

 120

 140

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Hill Model

13:45 11/16 2009

BMD

Hill

23 

24 

25 

26 E.2.41.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

27 

28 

29 ==================================================================== 

30 Hill Model. (Version: 2.14; Date: 06/26/2008) 

31 Input Data File: 

32 C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_Shi_estradiol_17B_conc_PE9.(d) 

33 Gnuplot Plotting File: 

34 C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_Shi_estradiol_17B_conc_PE9.plt 

35 Mon Nov 16 13:45:22 2009 

36 ==================================================================== 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-242 —DO NOT CITE OR QUOTE 

1 

2 Figure 4 PE9 only 

3 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

4 

5 The form of the response function is: 

6 

7 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

8 

9 

10 Dependent variable = Mean 

11 Independent variable = Dose 

12 Power parameter is not restricted 

13 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

14 

15 Total number of dose groups = 5 

16 Total number of records with missing values = 0 

17 Maximum number of iterations = 250 

18 Relative Function Convergence has been set to: 1e-008 

19 Parameter Convergence has been set to: 1e-008 

20 

21 

22 

23 Default Initial Parameter Values 

24 lalpha = 6.63982 

25 rho = 0 

26 intercept = 102.857 

27 v = -64.2856 

28 n = 1.33525 

29 k = 461.707 

30 

31 

32 Asymptotic Correlation Matrix of Parameter Estimates 

33 

34 lalpha rho intercept v n k 

35 

36 lalpha 1 -1 0.064 -0.095 0.073 0.085 

37 

38 rho -1 1 -0.075 0.096 -0.074 -0.085 

39 

40 intercept 0.064 -0.075 1 -0.61 -0.22 -0.37 

41 

42 v -0.095 0.096 -0.61 1 0.83 -0.4 

43 

44 n 0.073 -0.074 -0.22 0.83 1 -0.52 

45 

46 k 0.085 -0.085 -0.37 -0.4 -0.52 1 

47 

48 

49 

50 Parameter Estimates 

51 

52 95.0% Wald Confidence Interval 

53 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

54 lalpha 1.54702 2.36086 -3.08017 6.17422 

55 rho 1.17907 0.564621 0.0724289 2.2857 

56 intercept 105.265 10.3805 84.9191 125.61 

57 v -70.2058 20.1009 -109.603 -30.8086 

58 n 0.875252 0.64467 -0.388278 2.13878 

59 k 426.676 337.186 -234.197 1087.55 

60 

61 

62 

63 Table of Data and Estimated Values of Interest 

64 

65 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

66 ------ --- -------- -------- ----------- ----------- ---------- 

67 

68 0 10 103 105 41.4 33.7 -0.226 

69 188.3 10 86.2 82.2 19.6 29.2 0.431 

70 592.1 10 63.3 65.2 29.4 25.4 -0.227 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-243 —DO NOT CITE OR QUOTE 

1 2882 10 48.1 46.2 18.8 20.8 0.294 

2 7665 10 38.6 40.2 22.6 19.1 -0.277 

3 

4 

5 

6 Model Descriptions for likelihoods calculated 

7 

8 

9 Model A1: Yij = Mu(i) + e(ij) 

10 Var{e(ij)} = Sigma^2 

11 

12 Model A2: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma(i)^2 

14 

15 Model A3: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

17 Model A3 uses any fixed variance parameters that 

18 were specified by the user 

19 

20 Model R: Yi = Mu + e(i) 

21 Var{e(i)} = Sigma^2 

22 

23 

24 Likelihoods of Interest 

25 

26 Model Log(likelihood) # Param's AIC 

27 A1 -188.361545 6 388.723090 

28 A2 -183.666974 10 387.333947 

29 A3 -186.113162 7 386.226325 

30 fitted -186.121461 6 384.242922 

31 R -203.360558 2 410.721116 

32 

33 

34 Explanation of Tests 

35 

36 Test 1: Do responses and/or variances differ among Dose levels? 

37 (A2 vs. R) 

38 Test 2: Are Variances Homogeneous? (A1 vs A2) 

39 Test 3: Are variances adequately modeled? (A2 vs. A3) 

40 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

41 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

42 

43 Tests of Interest 

44 

45 Test -2*log(Likelihood Ratio) Test df p-value 

46 

47 Test 1 39.3872 8 <.0001 

48 Test 2 9.38914 4 0.05208 

49 Test 3 4.89238 3 0.1798 

50 Test 4 0.0165976 1 0.8975 

51 

52 The p-value for Test 1 is less than .05. There appears to be a 

53 difference between response and/or variances among the dose levels 

54 It seems appropriate to model the data 

55 

56 The p-value for Test 2 is less than .1. A non-homogeneous variance 

57 model appears to be appropriate 

58 

59 The p-value for Test 3 is greater than .1. The modeled variance appears 

60 to be appropriate here 

61 

62 The p-value for Test 4 is greater than .1. The model chosen seems 

63 to adequately describe the data 

64 

65 

66 Benchmark Dose Computation 

67 

68 Specified effect = 1 

69 

70 Risk Type = Estimated standard deviations from the control mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-244 —DO NOT CITE OR QUOTE 

1 

2 Confidence level = 0.95 

3 

4 BMD = 390.413 

5 

6 

7 BMDL computation failed. 

8 

9 

10 E.2.41.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 20

 40

 60

 80

 100

 120

 140

 0 1000 2000 3000 4000 5000 6000 7000 8000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:45 11/16 2009

BMDL BMD

 

Power

11 

12 

13 

14 E.2.41.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

15 Unrestricted 

16 

17 

18 ==================================================================== 

19 Power Model. (Version: 2.15; Date: 04/07/2008) 

20 Input Data File: 

21 C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_Shi_estradiol_17B_conc_PE9.(d) 

22 Gnuplot Plotting File: 

23 C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_Shi_estradiol_17B_conc_PE9.plt 

24 Mon Nov 16 13:45:22 2009 

25 ==================================================================== 

26 

27 Figure 4 PE9 only 

28 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

29 

30 The form of the response function is: 

31 

32 Y[dose] = control + slope * dose^power 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-245 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 The power is not restricted 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 5 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 

12 

13 Default Initial Parameter Values 

14 lalpha = 6.63982 

15 rho = 0 

16 control = 102.857 

17 slope = -2.986 

18 power = 0.343163 

19 

20 

21 Asymptotic Correlation Matrix of Parameter Estimates 

22 

23 lalpha rho control slope power 

24 

25 lalpha 1 -1 0.048 0.17 0.25 

26 

27 rho -1 1 -0.059 -0.17 -0.25 

28 

29 control 0.048 -0.059 1 -0.74 -0.59 

30 

31 slope 0.17 -0.17 -0.74 1 0.98 

32 

33 power 0.25 -0.25 -0.59 0.98 1 

34 

35 

36 

37 Parameter Estimates 

38 

39 95.0% Wald Confidence Interval 

40 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

41 lalpha 1.5482 2.39188 -3.13979 6.23619 

42 rho 1.1846 0.571778 0.0639365 2.30526 

43 control 106.216 10.4574 85.7201 126.712 

44 slope -9.40933 6.9801 -23.0901 4.27142 

45 power 0.221631 0.0746081 0.0754014 0.36786 

46 

47 

48 

49 Table of Data and Estimated Values of Interest 

50 

51 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

52 ------ --- -------- -------- ----------- ----------- ---------- 

53 

54 0 10 103 106 41.4 34.4 -0.309 

55 188.3 10 86.2 76.2 19.6 28.2 1.12 

56 592.1 10 63.3 67.5 29.4 26.3 -0.5 

57 2882 10 48.1 51.2 18.8 22.3 -0.443 

58 7665 10 38.6 37.9 22.6 18.7 0.113 

59 

60 

61 

62 Model Descriptions for likelihoods calculated 

63 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-246 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

3 Model A3 uses any fixed variance parameters that 

4 were specified by the user 

5 

6 Model R: Yi = Mu + e(i) 

7 Var{e(i)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) # Param's AIC 

13 A1 -188.361545 6 388.723090 

14 A2 -183.666974 10 387.333947 

15 A3 -186.113162 7 386.226325 

16 fitted -186.795167 5 383.590334 

17 R -203.360558 2 410.721116 

18 

19 

20 Explanation of Tests 

21 

22 Test 1: Do responses and/or variances differ among Dose levels? 

23 (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A1 vs A2) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

27 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

28 

29 Tests of Interest 

30 

31 Test -2*log(Likelihood Ratio) Test df p-value 

32 

33 Test 1 39.3872 8 <.0001 

34 Test 2 9.38914 4 0.05208 

35 Test 3 4.89238 3 0.1798 

36 Test 4 1.36401 2 0.5056 

37 

38 The p-value for Test 1 is less than .05. There appears to be a 

39 difference between response and/or variances among the dose levels 

40 It seems appropriate to model the data 

41 

42 The p-value for Test 2 is less than .1. A non-homogeneous variance 

43 model appears to be appropriate 

44 

45 The p-value for Test 3 is greater than .1. The modeled variance appears 

46 to be appropriate here 

47 

48 The p-value for Test 4 is greater than .1. The model chosen seems 

49 to adequately describe the data 

50 

51 

52 Benchmark Dose Computation 

53 

54 Specified effect = 1 

55 

56 Risk Type = Estimated standard deviations from the control mean 

57 

58 Confidence level = 0.95 

59 

60 BMD = 346.016 

61 

62 

63 BMDL = 18.2028 

64 

65 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-247 —DO NOT CITE OR QUOTE 

1 E.2.42. Smialowicz et al. (2008): PFC per 10^6 Cells 

2 E.2.42.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 <0.0001 13.24 0.00 892.22 5.8E+03 3.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 639.80 <0.0001 1518.75 6.4E+03 error nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 13.24 0.00 892.22 5.8E+03 3.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 10.69 0.00 891.67 8.4E+03 5.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 2 <0.0001 10.69 0.00 891.67 8.4E+03 5.1E+03 nonconstant variance, 

power unrestricted 

Hill 2 <.0001 9.23 0.01 890.21 8.2E+03 error nonconstant variance, n 

restricted >1, bound hit 

Hill d 1 <.0001 8.09 0.00 891.07 6.0E+03 error nonconstant variance, n 

unrestricted 

linear c 3 <.0001 9.68 0.02 888.66 9.7E+03 7.8E+03 nonconstant variance 

polynomial 2 <.0001 9.28 0.01 890.26 8.4E+03 5.4E+03 nonconstant variance 

power 3 <.0001 9.68 0.02 888.66 9.7E+03 7.8E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 2 <.0001 7.86 0.02 888.84 5.9E+03 1.6E+03 nonconstant variance, 

power unrestricted 

exponential (M2) 3 <0.0001 6.23 0.10 901.90 4.6E+03 2.8E+03 constant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 6.23 0.10 901.90 4.6E+03 2.8E+03 constant variance, 

power restricted ≥1 

exponential (M4) 2 <0.0001 6.23 0.04 903.90 4.6E+03 8.1E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 6.23 0.04 903.90 4.6E+03 8.1E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 6.23 0.04 903.90 4.6E+03 8.1E+02 constant variance, 

power unrestricted 

Hill 2 <.0001 5.53 0.06 903.19 2.0E+03 3.8E+02 constant variance, n 

restricted >1, bound hit 

Hill 1 <.0001 1.55 0.21 901.22 1.1E+03 1.2E+02 constant variance, n 

unrestricted 

linear 3 <.0001 7.92 0.05 903.59 7.6E+03 5.8E+03 constant variance 

polynomial 2 <.0001 6.55 0.04 904.22 5.3E+03 3.3E+03 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-248 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

power 3 <.0001 7.92 0.05 903.59 7.6E+03 5.8E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power 2 <.0001 1.46 0.48 899.13 1.0E+03 1.2E+02 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.2.42.2. Figure for Selected Model: Linear, Nonconstant Variance 

 0

 500

 1000

 1500

 2000

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:47 11/16 2009

BMDL BMD

 

Linear

4 

5 

6 

7 E.2.42.3. Output File for Selected Model: Linear, Nonconstant Variance 

8 

9 

10 ==================================================================== 

11 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_PFC_per_cells.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_PFC_per_cells.plt 

14 Mon Nov 16 13:47:58 2009 

15 ==================================================================== 

16 

17 Anti Response to SRBCs, PFC per 10^6 cells, Table 4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-249 —DO NOT CITE OR QUOTE 

1 

2 The form of the response function is: 

3 

4 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

5 

6 

7 Dependent variable = Mean 

8 Independent variable = Dose 

9 Signs of the polynomial coefficients are not restricted 

10 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

11 

12 Total number of dose groups = 5 

13 Total number of records with missing values = 0 

14 Maximum number of iterations = 250 

15 Relative Function Convergence has been set to: 1e-008 

16 Parameter Convergence has been set to: 1e-008 

17 

18 

19 

20 Default Initial Parameter Values 

21 lalpha = 12.3562 

22 rho = 0 

23 beta_0 = 1213.22 

24 beta_1 = -0.0629452 

25 

26 

27 Asymptotic Correlation Matrix of Parameter Estimates 

28 

29 lalpha rho beta_0 beta_1 

30 

31 lalpha 1 -1 0.081 -0.15 

32 

33 rho -1 1 -0.08 0.15 

34 

35 beta_0 0.081 -0.08 1 -0.9 

36 

37 beta_1 -0.15 0.15 -0.9 1 

38 

39 

40 

41 Parameter Estimates 

42 

43 95.0% Wald Confidence Interval 

44 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

45 lalpha 1.72142 1.91282 -2.02764 5.47047 

46 rho 1.55211 0.2835 0.99646 2.10776 

47 beta_0 1192.68 79.6002 1036.66 1348.69 

48 beta_1 -0.0597519 0.00532318 -0.0701851 -0.0493186 

49 

50 

51 

52 Table of Data and Estimated Values of Interest 

53 

54 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

55 ------ --- -------- -------- ----------- ----------- ---------- 

56 

57 0 15 1.49e+003 1.19e+003 716 577 2 

58 241.3 14 1.13e+003 1.18e+003 171 572 -0.322 

59 1358 15 945 1.11e+003 516 547 -1.18 

60 7385 15 677 751 465 403 -0.715 

61 1.744e+004 8 161 151 117 116 0.251 

62 

63 

64 

65 Model Descriptions for likelihoods calculated 

66 

67 

68 Model A1: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-250 —DO NOT CITE OR QUOTE 

1 Model A2: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = Sigma(i)^2 

3 

4 Model A3: Yij = Mu(i) + e(ij) 

5 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

6 Model A3 uses any fixed variance parameters that 

7 were specified by the user 

8 

9 Model R: Yi = Mu + e(i) 

10 Var{e(i)} = Sigma^2 

11 

12 

13 Likelihoods of Interest 

14 

15 Model Log(likelihood) # Param's AIC 

16 A1 -444.832859 6 901.665718 

17 A2 -425.402825 10 870.805651 

18 A3 -435.489363 7 884.978727 

19 fitted -440.330158 4 888.660316 

20 R -463.753685 2 931.507371 

21 

22 

23 Explanation of Tests 

24 

25 Test 1: Do responses and/or variances differ among Dose levels? 

26 (A2 vs. R) 

27 Test 2: Are Variances Homogeneous? (A1 vs A2) 

28 Test 3: Are variances adequately modeled? (A2 vs. A3) 

29 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

30 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) Test df p-value 

35 

36 Test 1 76.7017 8 <.0001 

37 Test 2 38.8601 4 <.0001 

38 Test 3 20.1731 3 0.0001563 

39 Test 4 9.68159 3 0.02148 

40 

41 The p-value for Test 1 is less than .05. There appears to be a 

42 difference between response and/or variances among the dose levels 

43 It seems appropriate to model the data 

44 

45 The p-value for Test 2 is less than .1. A non-homogeneous variance 

46 model appears to be appropriate 

47 

48 The p-value for Test 3 is less than .1. You may want to consider a 

49 different variance model 

50 

51 The p-value for Test 4 is less than .1. You may want to try a different 

52 model 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 1 

58 

59 Risk Type = Estimated standard deviations from the control mean 

60 

61 Confidence level = 0.95 

62 

63 BMD = 9660.48 

64 

65 

66 BMDL = 7755.63 

67 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-251 —DO NOT CITE OR QUOTE 

1 E.2.42.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

2 Unrestricted 

 0

 500

 1000

 1500

 2000

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:48 11/16 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.42.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

7 Power Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_Unrest_BMR1_PFC_per_cells.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 13:48:00 2009 

15 ==================================================================== 

16 

17 Anti Response to SRBCs, PFC per 10^6 cells, Table 4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-252 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 5 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 5 

17 -------- -------- 

18 lnalpha 3.29848 

19 rho 1.2578 

20 a 1565.55 

21 b 0.000129358 

22 c 0.000102839 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 5 

30 -------- ------- 

31 lnalpha 1.88041 

32 rho 1.53102 

33 a 1200.9 

34 b 9.15015e-005 

35 c 0 

36 d 1.53838 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 15 1491 716 

44 241.3 14 1129 171 

45 1358 15 945 516 

46 7385 15 677 465 

47 1.744e+004 8 161 117 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 1201 583.1 1.927 

55 241.3 1198 581.8 -0.4405 

56 1358 1153 565.3 -1.427 

57 7385 694.8 383.5 -0.1801 

58 1.744e+004 154.3 121.2 0.1566 

59 

60 

61 

62 Other models for which likelihoods are calculated: 

63 

64 Model A1: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 

67 Model A2: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma(i)^2 

69 

70 Model A3: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-253 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

2 

3 Model R: Yij = Mu + e(i) 

4 Var{e(ij)} = Sigma^2 

5 

6 

7 Likelihoods of Interest 

8 

9 Model Log(likelihood) DF AIC 

10 ------- ----------------- ---- ------------ 

11 A1 -444.8329 6 901.6657 

12 A2 -425.4028 10 870.8057 

13 A3 -435.4894 7 884.9787 

14 R -463.7537 2 931.5074 

15 5 -440.8331 5 891.6662 

16 

17 

18 Additive constant for all log-likelihoods = -61.57. This constant added to the 

19 above values gives the log-likelihood including the term that does not 

20 depend on the model parameters. 

21 

22 

23 Explanation of Tests 

24 

25 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 

29 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

30 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) D. F. p-value 

35 -------- ------------------------ ------ -------------- 

36 Test 1 76.7 8 < 0.0001 

37 Test 2 38.86 4 < 0.0001 

38 Test 3 20.17 3 0.0001563 

39 Test 7a 10.69 2 0.004778 

40 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose 

44 levels, it seems appropriate to model the data. 

45 

46 The p-value for Test 2 is less than .1. A non-homogeneous 

47 variance model appears to be appropriate. 

48 

49 The p-value for Test 3 is less than .1. You may want to 

50 consider a different variance model. 

51 

52 The p-value for Test 7a is less than .1. Model 5 may not adequately 

53 describe the data; you may want to consider another model. 

54 

55 

56 Benchmark Dose Computations: 

57 

58 Specified Effect = 1.000000 

59 

60 Risk Type = Estimated standard deviations from control 

61 

62 Confidence Level = 0.950000 

63 

64 BMD = 8379.86 

65 

66 BMDL = 5143.92 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-254 —DO NOT CITE OR QUOTE 

1 E.2.42.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 500

 1000

 1500

 2000

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Mean Response

dose

Hill Model

13:48 11/16 2009

BMD

Hill

2 

3 

4 

5 E.2.42.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_PFC_per_cells.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_PFC_per_cells.plt 

12 Mon Nov 16 13:48:01 2009 

13 ==================================================================== 

14 

15 Anti Response to SRBCs, PFC per 10^6 cells, Table 4 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Power parameter is not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

27 

28 Total number of dose groups = 5 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 12.3562 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-255 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 intercept = 1491 

3 v = -1330 

4 n = 0.478435 

5 k = 4033.79 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho intercept v n k 

11 

12 lalpha 1 -1 0.4 -0.047 -0.39 0.16 

13 

14 rho -1 1 -0.41 0.05 0.39 -0.16 

15 

16 intercept 0.4 -0.41 1 -0.15 -0.77 0.36 

17 

18 v -0.047 0.05 -0.15 1 0.37 -0.95 

19 

20 n -0.39 0.39 -0.77 0.37 1 -0.65 

21 

22 k 0.16 -0.16 0.36 -0.95 -0.65 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha 2.8564 2.65961 -2.35633 8.06913 

31 rho 1.38249 0.391339 0.615484 2.1495 

32 intercept 1309.76 139.641 1036.07 1583.45 

33 v -18748.9 37661.1 -92563.2 55065.4 

34 n 0.659862 0.240194 0.189091 1.13063 

35 k 1.07302e+006 4.27003e+006 -7.29608e+006 9.44213e+006 

36 

37 

38 

39 Table of Data and Estimated Values of Interest 

40 

41 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

42 ------ --- -------- -------- ----------- ----------- ---------- 

43 

44 0 15 1.49e+003 1.31e+003 716 596 1.18 

45 241.3 14 1.13e+003 1.24e+003 171 572 -0.703 

46 1358 15 945 1.08e+003 516 522 -1.02 

47 7385 15 677 633 465 360 0.469 

48 1.744e+004 8 161 149 117 133 0.251 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-256 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 -444.832859 6 901.665718 

4 A2 -425.402825 10 870.805651 

5 A3 -435.489363 7 884.978727 

6 fitted -439.536553 6 891.073107 

7 R -463.753685 2 931.507371 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 76.7017 8 <.0001 

24 Test 2 38.8601 4 <.0001 

25 Test 3 20.1731 3 0.0001563 

26 Test 4 8.09438 1 0.00444 

27 

28 The p-value for Test 1 is less than .05. There appears to be a 

29 difference between response and/or variances among the dose levels 

30 It seems appropriate to model the data 

31 

32 The p-value for Test 2 is less than .1. A non-homogeneous variance 

33 model appears to be appropriate 

34 

35 The p-value for Test 3 is less than .1. You may want to consider a 

36 different variance model 

37 

38 The p-value for Test 4 is less than .1. You may want to try a different 

39 model 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 6049.74 

51 

52 

53 BMDL computation failed. 

54 

55 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-257 —DO NOT CITE OR QUOTE 

1 E.2.42.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 500

 1000

 1500

 2000

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:48 11/16 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.2.42.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_PFC_per_cells.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_PFC_per_cells.plt 

13 Mon Nov 16 13:48:05 2009 

14 ==================================================================== 

15 

16 Anti Response to SRBCs, PFC per 10^6 cells, Table 4 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-258 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 12.3562 

3 rho = 0 

4 control = 1491 

5 slope = -79.8343 

6 power = 0.288026 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho control slope power 

12 

13 lalpha 1 -1 0.39 -0.42 -0.4 

14 

15 rho -1 1 -0.41 0.42 0.4 

16 

17 control 0.39 -0.41 1 -0.81 -0.79 

18 

19 slope -0.42 0.42 -0.81 1 1 

20 

21 power -0.4 0.4 -0.79 1 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha 2.91272 2.64894 -2.2791 8.10454 

30 rho 1.37364 0.389689 0.60986 2.13741 

31 control 1319.7 140.669 1043.99 1595.41 

32 slope -2.80443 6.05405 -14.6701 9.06128 

33 power 0.617853 0.211323 0.203668 1.03204 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 15 1.49e+003 1.32e+003 716 597 1.11 

43 241.3 14 1.13e+003 1.24e+003 171 571 -0.705 

44 1358 15 945 1.08e+003 516 519 -0.992 

45 7385 15 677 631 465 359 0.494 

46 1.744e+004 8 161 149 117 133 0.256 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-259 —DO NOT CITE OR QUOTE 

1 A1 -444.832859 6 901.665718 

2 A2 -425.402825 10 870.805651 

3 A3 -435.489363 7 884.978727 

4 fitted -439.417961 5 888.835922 

5 R -463.753685 2 931.507371 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 76.7017 8 <.0001 

22 Test 2 38.8601 4 <.0001 

23 Test 3 20.1731 3 0.0001563 

24 Test 4 7.85719 2 0.01967 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is less than .1. A non-homogeneous variance 

31 model appears to be appropriate 

32 

33 The p-value for Test 3 is less than .1. You may want to consider a 

34 different variance model 

35 

36 The p-value for Test 4 is less than .1. You may want to try a different 

37 model 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 5856.4 

49 

50 

51 BMDL = 1632.55 

52 

53 

54 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-260 —DO NOT CITE OR QUOTE 

1 E.2.43. Smialowicz et al. (2008): PFC per Spleen 

2 E.2.43.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 0.00 5.76 0.12 377.56 7.4E+03 4.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.00 5.34 0.07 379.14 8.5E+03 4.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.00 5.76 0.12 377.56 7.4E+03 4.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.00 5.34 0.02 381.14 8.5E+03 4.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 1 0.00 5.34 0.02 381.14 8.5E+03 4.9E+03 nonconstant variance, 

power unrestricted 

Hill 2 0.00 4.31 0.12 378.11 8.6E+03 error 

nonconstant variance, 

n restricted >1, bound 

hit 

Hill d 1 0.00 2.66 0.10 378.46 6.6E+03 error nonconstant variance, 

n unrestricted 

linear c 3 0.00 5.72 0.13 377.52 1.1E+04 8.9E+03 nonconstant 

variance 

polynomial 2 0.00 4.49 0.11 378.29 8.9E+03 5.7E+03 nonconstant variance 

power 3 0.00 5.72 0.13 377.52 1.1E+04 8.9E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 2 0.00 2.62 0.27 376.42 6.5E+03 2.1E+03 nonconstant variance, 

power unrestricted 

exponential (M2) 3 0.00 4.38 0.22 391.51 5.8E+03 3.2E+03 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.00 4.38 0.22 391.51 5.8E+03 3.2E+03 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.00 4.38 0.11 393.51 5.8E+03 8.0E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 4.38 0.11 393.51 5.8E+03 8.0E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 4.38 0.11 393.51 5.8E+03 8.0E+02 constant variance, 

power unrestricted 

Hill 2 0.00 3.87 0.14 393.00 2.7E+03 4.0E+02 

constant variance, n 

restricted >1, bound 

hit 

Hill 1 0.00 1.06 0.30 392.19 1.8E+03 1.8E+02 constant variance, n 

unrestricted 

linear 3 0.00 5.59 0.13 392.72 9.0E+03 6.7E+03 constant variance 

polynomial 2 0.00 4.61 0.10 393.74 6.5E+03 3.8E+03 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-261 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

power 3 0.00 5.59 0.13 392.72 9.0E+03 6.7E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power 2 0.00 1.01 0.60 390.14 1.8E+03 1.8E+02 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.2.43.2. Figure for Selected Model: Linear, Nonconstant Variance 

 0

 5

 10

 15

 20

 25

 30

 35

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:45 11/16 2009

BMDL BMD

 

Linear

4 

5 

6 E.2.43.3. Output File for Selected Model: Linear, Nonconstant Variance 

7 

8 

9 ==================================================================== 

10 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_PFC_per_spleen.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Linear_BMR1_PFC_per_spleen.plt 

13 Mon Nov 16 13:45:55 2009 

14 ==================================================================== 

15 

16 Anti Response to SRBCs - PFC x 10 to the 4 per spleen, Table 4 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-262 —DO NOT CITE OR QUOTE 

1 The form of the response function is: 

2 

3 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

4 

5 

6 Dependent variable = Mean 

7 Independent variable = Dose 

8 Signs of the polynomial coefficients are not restricted 

9 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

10 

11 Total number of dose groups = 5 

12 Total number of records with missing values = 0 

13 Maximum number of iterations = 250 

14 Relative Function Convergence has been set to: 1e-008 

15 Parameter Convergence has been set to: 1e-008 

16 

17 

18 

19 Default Initial Parameter Values 

20 lalpha = 4.76607 

21 rho = 0 

22 beta_0 = 22.5956 

23 beta_1 = -0.00117245 

24 

25 

26 Asymptotic Correlation Matrix of Parameter Estimates 

27 

28 lalpha rho beta_0 beta_1 

29 

30 lalpha 1 -0.97 0.031 -0.021 

31 

32 rho -0.97 1 -0.034 0.026 

33 

34 beta_0 0.031 -0.034 1 -0.88 

35 

36 beta_1 -0.021 0.026 -0.88 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 95.0% Wald Confidence Interval 

43 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

44 lalpha 0.491077 0.742891 -0.964962 1.94712 

45 rho 1.47094 0.264097 0.953314 1.98856 

46 beta_0 22.151 1.72621 18.7677 25.5343 

47 beta_1 -0.00110204 0.000118826 -0.00133493 -0.000869145 

48 

49 

50 

51 Table of Data and Estimated Values of Interest 

52 

53 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

54 ------ --- -------- -------- ----------- ----------- ---------- 

55 

56 0 15 27.8 22.2 13.4 12.5 1.75 

57 241.3 14 21 21.9 13.6 12.4 -0.268 

58 1358 15 17.6 20.7 9.4 11.9 -0.998 

59 7385 15 12.6 14 8.7 8.91 -0.614 

60 1.744e+004 8 3 2.93 3.1 2.82 0.0665 

61 

62 

63 

64 Model Descriptions for likelihoods calculated 

65 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-263 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

5 Model A3 uses any fixed variance parameters that 

6 were specified by the user 

7 

8 Model R: Yi = Mu + e(i) 

9 Var{e(i)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) # Param's AIC 

15 A1 -190.565019 6 393.130038 

16 A2 -181.476284 10 382.952569 

17 A3 -181.900030 7 377.800059 

18 fitted -184.760998 4 377.521996 

19 R -204.636496 2 413.272993 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Do responses and/or variances differ among Dose levels? 

25 (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A1 vs A2) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

29 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) Test df p-value 

34 

35 Test 1 46.3204 8 <.0001 

36 Test 2 18.1775 4 0.001139 

37 Test 3 0.84749 3 0.8381 

38 Test 4 5.72194 3 0.126 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose levels 

42 It seems appropriate to model the data 

43 

44 The p-value for Test 2 is less than .1. A non-homogeneous variance 

45 model appears to be appropriate 

46 

47 The p-value for Test 3 is greater than .1. The modeled variance appears 

48 to be appropriate here 

49 

50 The p-value for Test 4 is greater than .1. The model chosen seems 

51 to adequately describe the data 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 1 

57 

58 Risk Type = Estimated standard deviations from the control mean 

59 

60 Confidence level = 0.95 

61 

62 BMD = 11322.2 

63 

64 

65 BMDL = 8948.34 

66 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-264 —DO NOT CITE OR QUOTE 

1 E.2.43.4. Figure for UnrestrictedModel: Exponential (M5), Nonconstant Variance, Power 

2 Unrestricted 

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Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:45 11/16 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.43.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

7 Power Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_Unrest_BMR1_PFC_per_spleen.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 16 13:45:56 2009 

15 ==================================================================== 

16 

17 Anti Response to SRBCs - PFC x 10 to the 4 per spleen, Table 4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-265 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 5 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 5 

17 -------- -------- 

18 lnalpha 0.786146 

19 rho 1.36372 

20 a 29.19 

21 b 0.000129431 

22 c 0.000102775 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 5 

30 -------- ------- 

31 lnalpha 0.52811 

32 rho 1.45744 

33 a 23.1604 

34 b 9.96651e-005 

35 c 6.92509e-030 

36 d 1.23518 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 15 27.8 13.4 

44 241.3 14 21 13.6 

45 1358 15 17.6 9.4 

46 7385 15 12.6 8.7 

47 1.744e+004 8 3 3.1 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 23.16 12.86 1.397 

55 241.3 22.93 12.77 -0.5656 

56 1358 21.28 12.09 -1.18 

57 7385 11.68 7.807 0.4578 

58 1.744e+004 3.2 3.04 -0.1864 

59 

60 

61 

62 Other models for which likelihoods are calculated: 

63 

64 Model A1: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 

67 Model A2: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma(i)^2 

69 

70 Model A3: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-266 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

2 

3 Model R: Yij = Mu + e(i) 

4 Var{e(ij)} = Sigma^2 

5 

6 

7 Likelihoods of Interest 

8 

9 Model Log(likelihood) DF AIC 

10 ------- ----------------- ---- ------------ 

11 A1 -190.565 6 393.13 

12 A2 -181.4763 10 382.9526 

13 A3 -181.9 7 377.8001 

14 R -204.6365 2 413.273 

15 5 -184.5689 6 381.1378 

16 

17 

18 Additive constant for all log-likelihoods = -61.57. This constant added to the 

19 above values gives the log-likelihood including the term that does not 

20 depend on the model parameters. 

21 

22 

23 Explanation of Tests 

24 

25 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 

29 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

30 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) D. F. p-value 

35 -------- ------------------------ ------ -------------- 

36 Test 1 46.32 8 < 0.0001 

37 Test 2 18.18 4 0.001139 

38 Test 3 0.8475 3 0.8381 

39 Test 7a 5.338 1 0.02087 

40 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose 

44 levels, it seems appropriate to model the data. 

45 

46 The p-value for Test 2 is less than .1. A non-homogeneous 

47 variance model appears to be appropriate. 

48 

49 The p-value for Test 3 is greater than .1. The modeled 

50 variance appears to be appropriate here. 

51 

52 The p-value for Test 7a is less than .1. Model 5 may not adequately 

53 describe the data; you may want to consider another model. 

54 

55 

56 Benchmark Dose Computations: 

57 

58 Specified Effect = 1.000000 

59 

60 Risk Type = Estimated standard deviations from control 

61 

62 Confidence Level = 0.950000 

63 

64 BMD = 8460.94 

65 

66 BMDL = 4901.02 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-267 —DO NOT CITE OR QUOTE 

1 E.2.43.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

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Mean Response

dose

Hill Model

13:45 11/16 2009

BMD

Hill

2 

3 

4 

5 E.2.43.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_PFC_per_spleen.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_PFC_per_spleen.plt 

12 Mon Nov 16 13:45:57 2009 

13 ==================================================================== 

14 

15 Anti Response to SRBCs - PFC x 10 to the 4 per spleen, Table 4 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Power parameter is not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

27 

28 Total number of dose groups = 5 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 4.76607 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-268 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 intercept = 27.8 

3 v = -24.8 

4 n = 0.476652 

5 k = 4009.51 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho intercept v n k 

11 

12 lalpha 1 -0.98 0.24 0.03 -0.21 0.019 

13 

14 rho -0.98 1 -0.3 -0.026 0.21 -0.021 

15 

16 intercept 0.24 -0.3 1 0.079 -0.73 0.1 

17 

18 v 0.03 -0.026 0.079 1 0.019 -0.96 

19 

20 n -0.21 0.21 -0.73 0.019 1 -0.28 

21 

22 k 0.019 -0.021 0.1 -0.96 -0.28 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha 0.742099 1.02085 -1.25872 2.74292 

31 rho 1.37015 0.355955 0.67249 2.06781 

32 intercept 25.3072 2.92734 19.5697 31.0447 

33 v -1195.09 4993.33 -10981.8 8591.65 

34 n 0.543247 0.174917 0.200417 0.886078 

35 k 2.57198e+007 2.10767e+008 -3.87375e+008 4.38815e+008 

36 

37 

38 

39 Table of Data and Estimated Values of Interest 

40 

41 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

42 ------ --- -------- -------- ----------- ----------- ---------- 

43 

44 0 15 27.8 25.3 13.4 13.3 0.728 

45 241.3 14 21 23.1 13.6 12.5 -0.629 

46 1358 15 17.6 19.7 9.4 11.2 -0.716 

47 7385 15 12.6 11.2 8.7 7.6 0.691 

48 1.744e+004 8 3 3.03 3.1 3.1 -0.03 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-269 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 -190.565019 6 393.130038 

4 A2 -181.476284 10 382.952569 

5 A3 -181.900030 7 377.800059 

6 fitted -183.230840 6 378.461681 

7 R -204.636496 2 413.272993 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 46.3204 8 <.0001 

24 Test 2 18.1775 4 0.001139 

25 Test 3 0.84749 3 0.8381 

26 Test 4 2.66162 1 0.1028 

27 

28 The p-value for Test 1 is less than .05. There appears to be a 

29 difference between response and/or variances among the dose levels 

30 It seems appropriate to model the data 

31 

32 The p-value for Test 2 is less than .1. A non-homogeneous variance 

33 model appears to be appropriate 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is greater than .1. The model chosen seems 

39 to adequately describe the data 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 6615.87 

51 

52 

53 BMDL computation failed. 

54 

55 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-270 —DO NOT CITE OR QUOTE 

1 E.2.43.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

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Mean Response

dose

Power Model with 0.95 Confidence Level

13:45 11/16 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.2.43.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_PFC_per_spleen.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Power_Unrest_BMR1_PFC_per_spleen.plt 

13 Mon Nov 16 13:45:57 2009 

14 ==================================================================== 

15 

16 Anti Response to SRBCs - PFC x 10 to the 4 per spleen, Table 4 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-271 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 4.76607 

3 rho = 0 

4 control = 27.8 

5 slope = -1.51177 

6 power = 0.286447 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho control slope power 

12 

13 lalpha 1 -0.98 0.25 -0.24 -0.22 

14 

15 rho -0.98 1 -0.3 0.25 0.22 

16 

17 control 0.25 -0.3 1 -0.78 -0.74 

18 

19 slope -0.24 0.25 -0.78 1 1 

20 

21 power -0.22 0.22 -0.74 1 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha 0.746924 1.02058 -1.25337 2.74721 

30 rho 1.36826 0.355827 0.670849 2.06566 

31 control 25.3818 2.96695 19.5666 31.1969 

32 slope -0.124774 0.226126 -0.567972 0.318425 

33 power 0.531205 0.175723 0.186794 0.875617 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 15 27.8 25.4 13.4 13.3 0.705 

43 241.3 14 21 23.1 13.6 12.4 -0.626 

44 1358 15 17.6 19.6 9.4 11.1 -0.704 

45 7385 15 12.6 11.2 8.7 7.6 0.702 

46 1.744e+004 8 3 3.03 3.1 3.1 -0.0313 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-272 —DO NOT CITE OR QUOTE 

1 A1 -190.565019 6 393.130038 

2 A2 -181.476284 10 382.952569 

3 A3 -181.900030 7 377.800059 

4 fitted -183.210067 5 376.420134 

5 R -204.636496 2 413.272993 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 46.3204 8 <.0001 

22 Test 2 18.1775 4 0.001139 

23 Test 3 0.84749 3 0.8381 

24 Test 4 2.62008 2 0.2698 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is less than .1. A non-homogeneous variance 

31 model appears to be appropriate 

32 

33 The p-value for Test 3 is greater than .1. The modeled variance appears 

34 to be appropriate here 

35 

36 The p-value for Test 4 is greater than .1. The model chosen seems 

37 to adequately describe the data 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 6542.48 

49 

50 

51 BMDL = 2072.46 

52 

53 

54 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-273 —DO NOT CITE OR QUOTE 

1 E.2.44. Toth et al. (1978): Amyloidosis 

2 E.2.44.1. Summary Table of BMDS Modeling Results 

Amyloidosis (Toth et al. (1978)) 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Value a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 2 6.45 0.04 149.12 1.1E+04 7.0E+03 power restricted ≥1, bound 

hit 

logistic 2 7.91 0.02 151.34 2.0E+04 1.6E+04 

log-logisticb 2 5.86 0.05 148.27 8.3E+03 4.8E+03 slope restricted ≥1, 

bound hit 

log-logistic c 2 0.20 0.90 140.24 2.7E+02 2.9E+00 slope unrestricted 

log-probit 2 9.94 0.007 153.52 2.2E+04 1.5E+4 slope restricted ≥1, bound 

hit 

log-probit 2 0.28 0.87 140.32 2.7E+02 4.0E+00 slope unrestricted 

multistage 2 6.45 0.04 149.12 1.1E+04 7.0E+03 betas restricted ≥0 

probit 2 7.75 0.02 151.11 1.9E+04 1.5E+04 

Weibull 2 6.45 0.04 149.12 1.1E+04 7.0E+03 power restricted ≥1, bound 

hit 

Weibull 3 0.00 1.00 140.03 2.0E+02 1.9E+00 power unrestricted 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-274 —DO NOT CITE OR QUOTE 

1 

2 E.2.44.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1

3 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 10000 20000 30000 40000 50000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

13:39 11/16 2009

BMDL BMD

 

Log-Logistic

4 

5 

6 

7 E.2.44.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1 

8 

9 ==================================================================== 

10 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR1_Amyloidosis.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR1_Amyloidosis.plt 

14 Mon Nov 16 13:39:45 2009 

15 ==================================================================== 

16 

17 Table 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the probability function is: 

21 

22 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

23 

24 

25 Dependent variable = DichEff 

26 Independent variable = Dose 

27 Slope parameter is restricted as slope >= 1 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-275 —DO NOT CITE OR QUOTE 

1 

2 User has chosen the log transformed model 

3 

4 

5 Default Initial Parameter Values 

6 background = 0 

7 intercept = -10.8548 

8 slope = 1 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -slope 

14 have been estimated at a boundary point, or have been specified by 

15 the user, 

16 and do not appear in the correlation matrix ) 

17 

18 background intercept 

19 

20 background 1 -0.49 

21 

22 intercept -0.49 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence 

29 Interval 

30 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. 

31 Limit 

32 background 0.0699641 * * * 

33 intercept -11.2157 * * * 

34 slope 1 * * * 

35 

36 * - Indicates that this value is not calculated. 

37 

38 

39 

40 Analysis of Deviance Table 

41 

42 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

43 Full model -68.017 4 

44 Fitted model -72.1329 2 8.23187 2 0.01631 

45 Reduced model -82.0119 1 27.99 3 <.0001 

46 

47 AIC: 148.266 

48 

49 

50 Goodness of Fit 

51 Scaled 

52 Dose Est._Prob. Expected Observed Size Residual 

53 ------------------------------------------------------------------------ 

54 0.0000 0.0700 2.659 0.000 38 -1.691 

55 315.4949 0.0739 3.251 5.000 44 1.008 

56 7814.0188 0.1585 6.973 10.000 44 1.250 

57 50105.0000 0.4446 19.117 17.000 43 -0.650 

58 

59 Chi^2 = 5.86 d.f. = 2 P-value = 0.0535 

60 

61 

62 Benchmark Dose Computation 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-276 —DO NOT CITE OR QUOTE 

1 

2 Specified effect = 0.1 

3 

4 Risk Type = Extra risk 

5 

6 Confidence level = 0.95 

7 

8 BMD = 8254.29 

9 

10 BMDL = 4805.18 

11 

12 

13 

14 E.2.44.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

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 0.5

 0.6

 0 10000 20000 30000 40000 50000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

13:39 11/16 2009

BMDL BMD

 

Log-Logistic

15 

16 

17 

18 E.2.44.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

19 

20 

21 ==================================================================== 

22 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

23 Input Data File: C:\USEPA\BMDS21\AD\Blood\LogLogistic_Unrest_BMR1_Amyloidosis.(d) 

24 Gnuplot Plotting File: 

25 C:\USEPA\BMDS21\AD\Blood\LogLogistic_Unrest_BMR1_Amyloidosis.plt 

26 Mon Nov 16 13:39:45 2009 

27 ==================================================================== 

28 

29 Table 2 

30 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

31 

32 The form of the probability function is: 

33 

34 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-277 —DO NOT CITE OR QUOTE 

1 

2 

3 Dependent variable = DichEff 

4 Independent variable = Dose 

5 Slope parameter is not restricted 

6 

7 Total number of observations = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 

14 

15 User has chosen the log transformed model 

16 

17 

18 Default Initial Parameter Values 

19 background = 0 

20 intercept = -3.91243 

21 slope = 0.314588 

22 

23 

24 Asymptotic Correlation Matrix of Parameter Estimates 

25 

26 ( *** The model parameter(s) -background 

27 have been estimated at a boundary point, or have been specified by the user, 

28 and do not appear in the correlation matrix ) 

29 

30 intercept slope 

31 

32 intercept 1 -0.98 

33 

34 slope -0.98 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 95.0% Wald Confidence Interval 

41 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

42 background 0 * * * 

43 intercept -4.01968 * * * 

44 slope 0.326277 * * * 

45 

46 * - Indicates that this value is not calculated. 

47 

48 

49 

50 Analysis of Deviance Table 

51 

52 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

53 Full model -68.017 4 

54 Fitted model -68.1202 2 0.206421 2 0.9019 

55 Reduced model -82.0119 1 27.99 3 <.0001 

56 

57 AIC: 140.24 

58 

59 

60 Goodness of Fit 

61 Scaled 

62 Dose Est._Prob. Expected Observed Size Residual 

63 ------------------------------------------------------------------------ 

64 0.0000 0.0000 0.000 0.000 38 0.000 

65 315.4949 0.1051 4.623 5.000 44 0.186 

66 7814.0188 0.2507 11.029 10.000 44 -0.358 

67 50105.0000 0.3802 16.348 17.000 43 0.205 

68 

69 Chi^2 = 0.20 d.f. = 2 P-value = 0.9028 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-278 —DO NOT CITE OR QUOTE 

1 

2 Benchmark Dose Computation 

3 

4 Specified effect = 0.1 

5 

6 Risk Type = Extra risk 

7 

8 Confidence level = 0.95 

9 

10 BMD = 266.567 

11 

12 BMDL = 2.92895 

13 

14 

15 

16 E.2.44.6. Figure for Unrestricted Model: Log-Probit, Slope Restricted ≥1 

 0

 0.1

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 0 10000 20000 30000 40000 50000

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

13:39 11/16 2009

BMDL BMD

 

LogProbit

17 

18 

19 

20 E.2.44.7. Output File for Unrestricted Model: Log-Probit, Slope Restricted ≥1 

21 

22 

23 ==================================================================== 

24 Probit Model. (Version: 3.1; Date: 05/16/2008) 

25 Input Data File: C:\USEPA\BMDS21\AD\Blood\LogProbit_BMR1_Amyloidosis.(d) 

26 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\LogProbit_BMR1_Amyloidosis.plt 

27 Mon Nov 16 13:39:45 2009 

28 ==================================================================== 

29 

30 Table 2 

31 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

32 

33 The form of the probability function is: 

34 

35 P[response] = Background 

36 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-279 —DO NOT CITE OR QUOTE 

1 

2 where CumNorm(.) is the cumulative normal distribution function 

3 

4 

5 Dependent variable = DichEff 

6 Independent variable = Dose 

7 Slope parameter is not restricted 

8 

9 Total number of observations = 4 

10 Total number of records with missing values = 0 

11 Maximum number of iterations = 250 

12 Relative Function Convergence has been set to: 1e-008 

13 Parameter Convergence has been set to: 1e-008 

14 

15 

16 

17 User has chosen the log transformed model 

18 

19 

20 Default Initial (and Specified) Parameter Values 

21 background = 0 

22 intercept = -2.2812 

23 slope = 0.180958 

24 

25 

26 Asymptotic Correlation Matrix of Parameter Estimates 

27 

28 ( *** The model parameter(s) -background 

29 have been estimated at a boundary point, or have been specified by the user, 

30 and do not appear in the correlation matrix ) 

31 

32 intercept slope 

33 

34 intercept 1 -0.98 

35 

36 slope -0.98 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 95.0% Wald Confidence Interval 

43 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

44 background 0 NA 

45 intercept -2.3225 0.57595 -3.45134 -1.19365 

46 slope 0.185565 0.0628719 0.0623389 0.308792 

47 

48 NA - Indicates that this parameter has hit a bound 

49 implied by some inequality constraint and thus 

50 has no standard error. 

51 

52 

53 

54 Analysis of Deviance Table 

55 

56 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

57 Full model -68.017 4 

58 Fitted model -68.1574 2 0.280896 2 0.869 

59 Reduced model -82.0119 1 27.99 3 <.0001 

60 

61 AIC: 140.315 

62 

63 

64 Goodness of Fit 

65 Scaled 

66 Dose Est._Prob. Expected Observed Size Residual 

67 ------------------------------------------------------------------------ 

68 0.0000 0.0000 0.000 0.000 38 0.000 

69 315.4949 0.1048 4.611 5.000 44 0.192 

70 7814.0188 0.2549 11.216 10.000 44 -0.421 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-280 —DO NOT CITE OR QUOTE 

1 50105.0000 0.3766 16.195 17.000 43 0.253 

2 

3 Chi^2 = 0.28 d.f. = 2 P-value = 0.8704 

4 

5 

6 Benchmark Dose Computation 

7 

8 Specified effect = 0.1 

9 

10 Risk Type = Extra risk 

11 

12 Confidence level = 0.95 

13 

14 BMD = 273.029 

15 

16 BMDL = 4.02007 

17 

18 

19 

20 E.2.45. Toth et al. (1978): Skin Lesions 

21 E.2.45.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Value a AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

gamma 2 6.89 0.03 156.34 5.7E+03 4.1E+03 power restricted ≥1, 

bound hit 

logistic 2 10.70 0.00 161.42 1.4E+04 1.1E+04 

log-logisticb 2 5.09 0.08 153.96 3.5E+03 2.2E+03 slope restricted ≥1, 

bound hit 

log-logisticc 2 0.04 0.95 147.08 2.60E+02 3.18E+01 slope urestricted 

log-probit 2 14.29 <0.001 164.79 1.24E+04 8.31E+03 slope restricted ≥1, 

bound hit 

log-probit 2 0.80 0.67 147.84 3.3E+02 4.5E+01 slope unrestricted ≥1 

multistage 2 6.89 0.03 156.34 5.7E+03 4.1E+03 betas restricted ≥0 

probit 2 10.39 0.01 160.99 1.3E+04 1.0E+04 

Weibull 2 6.89 0.03 156.34 5.7E+03 4.1E+03 power restricted ≥1, 

bound hit 

Weibull 2 0.00 1.00 147.04 2.19E+02 2.08E+01 power unrestricted 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

22 

23 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-281 —DO NOT CITE OR QUOTE 

1 E.2.45.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1 

 0

 0.1

 0.2

 0.3

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 0 10000 20000 30000 40000 50000

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

13:30 11/16 2009

BMDL BMD

 

LogProbit

2 

3 

4 

5 E.2.45.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\A\Blood\LogLogistic_BMR2_Skin_lesion_1yr.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AD\Blood\LogLogistic_BMR2_Skin_lesion_1yr.plt 

13 Mon Nov 16 13:30:07 2009 

14 ==================================================================== 

15 

16 Table 2 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

22 

23 

24 Dependent variable = DichEff 

25 Independent variable = Dose 

26 Slope parameter is restricted as slope >= 1 

27 

28 Total number of observations = 4 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-282 —DO NOT CITE OR QUOTE 

1 

2 

3 User has chosen the log transformed model 

4 

5 

6 Default Initial Parameter Values 

7 background = 0 

8 intercept = -10.252 

9 slope = 1 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -slope 

15 have been estimated at a boundary point, or have been specified by 

16 the user, 

17 and do not appear in the correlation matrix ) 

18 

19 background intercept 

20 

21 background 1 -0.43 

22 

23 intercept -0.43 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 95.0% Wald Confidence 

30 Interval 

31 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. 

32 Limit 

33 background 0.0564295 * * * 

34 intercept -10.3645 * * * 

35 slope 1 * * * 

36 

37 * - Indicates that this value is not calculated. 

38 

39 

40 

41 Analysis of Deviance Table 

42 

43 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

44 Full model -71.5177 4 

45 Fitted model -74.9791 2 6.92292 2 0.03138 

46 Reduced model -95.8498 1 48.6642 3 <.0001 

47 

48 AIC: 153.958 

49 

50 

51 Goodness of Fit 

52 Scaled 

53 Dose Est._Prob. Expected Observed Size Residual 

54 ------------------------------------------------------------------------ 

55 0.0000 0.0564 2.144 0.000 38 -1.508 

56 315.4949 0.0657 2.892 5.000 44 1.283 

57 7814.0188 0.2430 10.690 13.000 44 0.812 

58 50105.0000 0.6343 27.273 25.000 43 -0.720 

59 

60 Chi^2 = 5.09 d.f. = 2 P-value = 0.0783 

61 

62 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-283 —DO NOT CITE OR QUOTE 

1 Benchmark Dose Computation 

2 

3 Specified effect = 0.1 

4 

5 Risk Type = Extra risk 

6 

7 Confidence level = 0.95 

8 

9 BMD = 3523.85 

10 

11 BMDL = 2211.53 

12 

13 

14 

15 E.2.45.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

16 

 0

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 0.7

 0 10000 20000 30000 40000 50000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

07:51 11/27 2009

BMDLBMD

 

Log-Logistic

17 

18 

19 

20 E.2.45.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

21 

22 ==================================================================== 

23 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

24 Input Data File: C:\Usepa\Bmds2\Data\LogTcdSet.(d) 

25 Gnuplot Plotting File: C:\Usepa\Bmds2\Data\LogTcdSet.plt 

26 Fri Nov 27 07:51:12 2009 

27 ==================================================================== 

28 

29 BMDS Model Run 

30 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

31 

32 The form of the probability function is: 

33 

34 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-284 —DO NOT CITE OR QUOTE 

1 

2 Dependent variable = r_skin 

3 Independent variable = DOSE 

4 Slope parameter is not restricted 

5 

6 Total number of observations = 4 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 

13 

14 User has chosen the log transformed model 

15 

16 

17 Default Initial Parameter Values 

18 background = 0 

19 intercept = -4.78342 

20 slope = 0.469549 

21 

22 

23 Asymptotic Correlation Matrix of Parameter Estimates 

24 

25 ( *** The model parameter(s) -background 

26 have been estimated at a boundary point, or have been specified by 

27 the user, 

28 and do not appear in the correlation matrix ) 

29 

30 intercept slope 

31 

32 intercept 1 -0.98 

33 

34 slope -0.98 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 95.0% Wald Confidence 

41 Interval 

42 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. 

43 Limit 

44 background 0 * * * 

45 intercept -4.84059 * * * 

46 slope 0.475472 * * * 

47 

48 * - Indicates that this value is not calculated. 

49 

50 

51 

52 Analysis of Deviance Table 

53 

54 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

55 Full model -71.5177 4 

56 Fitted model -71.5376 2 0.0398444 2 0.9803 

57 Reduced model -95.8498 1 48.6642 3 <.0001 

58 

59 AIC: 147.075 

60 

61 

62 Goodness of Fit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-285 —DO NOT CITE OR QUOTE 

1 Scaled 

2 Dose Est._Prob. Expected Observed Size Residual 

3 ------------------------------------------------------------------------ 

4 0.0000 0.0000 0.000 0.000 38 0.000 

5 316.0000 0.1087 4.784 5.000 44 0.105 

6 4714.0000 0.3060 13.464 13.000 44 -0.152 

7 50105.0000 0.5756 24.753 25.000 43 0.076 

8 

9 Chi^2 = 0.04 d.f. = 2 P-value = 0.9803 

10 

11 

12 Benchmark Dose Computation 

13 

14 Specified effect = 0.1 

15 

16 Risk Type = Extra risk 

17 

18 Confidence level = 0.95 

19 

20 BMD = 259.682 

21 

22 BMDL = 31.788 

23 

24 

25 

26 E.2.46. Van Birgelen et al. (1995a): Hepatic Retinol 

27 E.2.46.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 4 <0.0001 41.09 <0.0001 159.73 4.3E+03 2.3E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 40.44 <0.0001 159.09 3.4E+04 2.4E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 3 <0.0001 20.80 0.00 141.45 1.4E+04 1.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 20.80 0.00 141.45 1.4E+04 1.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 <0.0001 20.80 0.00 141.45 1.4E+04 1.9E+03 nonconstant variance, 

power unrestricted 

Hill 3 <.0001 4.22 0.24 124.86 2.9E+03 error nonconstant variance, n 

restricted >1, bound hit 

Hill d 2 <.0001 2.85 0.24 125.50 2.0E+03 error nonconstant variance, n 

unrestricted 

linear 4 <.0001 58.18 <.0001 176.83 1.0E+05 7.9E+04 nonconstant variance 

polynomial 4 <.0001 58.18 <.0001 176.83 1.0E+05 7.9E+04 nonconstant variance 

power 4 <.0001 58.18 <.0001 176.83 1.0E+05 7.9E+04 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 11.12 0.01 131.77 2.1E+02 7.7E+00 nonconstant variance, 

power unrestricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-286 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 4 <0.0001 3.87 0.42 184.19 3.0E+03 1.9E+03 constant variance, power 

restricted ≥1 

exponential (M3) 4 <0.0001 3.87 0.42 184.19 3.0E+03 1.9E+03 constant variance, power 

restricted ≥1 

exponential (M4) 3 <0.0001 1.84 0.61 184.15 2.7E+03 1.7E+03 constant variance, power 

restricted ≥1 

exponential (M5) 3 <0.0001 1.84 0.61 184.15 2.7E+03 1.7E+03 constant variance, power 

restricted ≥1 

exponential (M5) 3 <0.0001 1.84 0.61 184.15 2.7E+03 1.7E+03 constant variance, power 

unrestricted 

Hill 3 <.0001 1.04 0.79 183.36 2.1E+03 1.1E+03 constant variance, n 

restricted >1, bound hit 

Hill 2 <.0001 0.98 0.61 185.29 1.7E+03 4.0E+01 constant variance, n 

unrestricted 

linear 4 <.0001 25.63 <.0001 205.94 6.8E+04 5.0E+04 constant variance 

polynomial 4 <.0001 25.63 <.0001 205.94 6.8E+04 5.0E+04 constant variance 

power 4 <.0001 25.63 <.0001 205.94 6.8E+04 5.0E+04 constant variance, power 

restricted ≥1, bound hit 

power 3 <.0001 2.28 0.52 184.60 2.1E+02 6.2E+00 constant variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-287 —DO NOT CITE OR QUOTE 

1 E.2.46.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 5

 10

 15

 20

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:28 11/20 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.46.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_hepatic_retinol.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 12:28:01 2009 

15 ==================================================================== 

16 

17 Tbl3, hepatic retinol 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-288 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 4 

17 -------- -------- 

18 lnalpha -1.16065 

19 rho 1.53688 

20 a 15.645 

21 b 4.61687e-005 

22 c 0.0365247 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 4 

30 -------- ------- 

31 lnalpha -0.926841 

32 rho 1.77261 

33 a 11.5052 

34 b 5.20223e-005 

35 c 0.0653036 

36 d 1 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 8 14.9 8.768 

44 3969 8 8.4 3.394 

45 6479 8 8.2 2.263 

46 9968 8 5.1 0.8485 

47 4.761e+004 8 2.2 0.8485 

48 1.378e+005 8 0.6 0.5657 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 11.51 5.483 1.751 

56 3969 9.499 4.627 -0.6719 

57 6479 8.428 4.161 -0.1551 

58 9968 7.154 3.599 -1.614 

59 4.761e+004 1.655 0.9832 1.568 

60 1.378e+005 0.7596 0.4931 -0.9156 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-289 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 -87.1567 7 188.3134 

14 A2 -47.28742 12 118.5748 

15 A3 -55.32422 8 126.6484 

16 R -109.967 2 223.934 

17 4 -65.72639 5 141.4528 

18 

19 

20 Additive constant for all log-likelihoods = -44.11. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 

31 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

32 

33 

34 Tests of Interest 

35 

36 Test -2*log(Likelihood Ratio) D. F. p-value 

37 -------- ------------------------ ------ -------------- 

38 Test 1 125.4 10 < 0.0001 

39 Test 2 79.74 5 < 0.0001 

40 Test 3 16.07 4 0.002922 

41 Test 6a 20.8 3 0.0001156 

42 

43 

44 The p-value for Test 1 is less than .05. There appears to be a 

45 difference between response and/or variances among the dose 

46 levels, it seems appropriate to model the data. 

47 

48 The p-value for Test 2 is less than .1. A non-homogeneous 

49 variance model appears to be appropriate. 

50 

51 The p-value for Test 3 is less than .1. You may want to 

52 consider a different variance model. 

53 

54 The p-value for Test 6a is less than .1. Model 4 may not adequately 

55 describe the data; you may want to consider another model. 

56 

57 

58 Benchmark Dose Computations: 

59 

60 Specified Effect = 1.000000 

61 

62 Risk Type = Estimated standard deviations from control 

63 

64 Confidence Level = 0.950000 

65 

66 BMD = 13706.9 

67 

68 BMDL = 1852.89 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-290 —DO NOT CITE OR QUOTE 

1 E.2.46.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

2 Unrestricted 

 0

 5

 10

 15

 20

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:28 11/20 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.46.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

7 Power Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_hepatic_retinol.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 12:28:10 2009 

15 ==================================================================== 

16 

17 Tbl3, hepatic retinol 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-291 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 5 

17 -------- -------- 

18 lnalpha -1.16065 

19 rho 1.53688 

20 a 15.645 

21 b 4.61687e-005 

22 c 0.0365247 

23 d 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 Variable Model 5 

30 -------- ------- 

31 lnalpha -0.926841 

32 rho 1.77261 

33 a 11.5052 

34 b 5.20223e-005 

35 c 0.0653036 

36 d 1 

37 

38 

39 Table of Stats From Input Data 

40 

41 Dose N Obs Mean Obs Std Dev 

42 ----- --- ---------- ------------- 

43 0 8 14.9 8.768 

44 3969 8 8.4 3.394 

45 6479 8 8.2 2.263 

46 9968 8 5.1 0.8485 

47 4.761e+004 8 2.2 0.8485 

48 1.378e+005 8 0.6 0.5657 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 11.51 5.483 1.751 

56 3969 9.499 4.627 -0.6719 

57 6479 8.428 4.161 -0.1551 

58 9968 7.154 3.599 -1.614 

59 4.761e+004 1.655 0.9832 1.568 

60 1.378e+005 0.7596 0.4931 -0.9156 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-292 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 -87.1567 7 188.3134 

14 A2 -47.28742 12 118.5748 

15 A3 -55.32422 8 126.6484 

16 R -109.967 2 223.934 

17 5 -65.72639 5 141.4528 

18 

19 

20 Additive constant for all log-likelihoods = -44.11. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 

31 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

32 

33 

34 Tests of Interest 

35 

36 Test -2*log(Likelihood Ratio) D. F. p-value 

37 -------- ------------------------ ------ -------------- 

38 Test 1 125.4 10 < 0.0001 

39 Test 2 79.74 5 < 0.0001 

40 Test 3 16.07 4 0.002922 

41 Test 7a 20.8 3 0.0001156 

42 

43 

44 The p-value for Test 1 is less than .05. There appears to be a 

45 difference between response and/or variances among the dose 

46 levels, it seems appropriate to model the data. 

47 

48 The p-value for Test 2 is less than .1. A non-homogeneous 

49 variance model appears to be appropriate. 

50 

51 The p-value for Test 3 is less than .1. You may want to 

52 consider a different variance model. 

53 

54 The p-value for Test 7a is less than .1. Model 5 may not adequately 

55 describe the data; you may want to consider another model. 

56 

57 

58 Benchmark Dose Computations: 

59 

60 Specified Effect = 1.000000 

61 

62 Risk Type = Estimated standard deviations from control 

63 

64 Confidence Level = 0.950000 

65 

66 BMD = 13706.9 

67 

68 BMDL = 1852.89 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-293 —DO NOT CITE OR QUOTE 

1 E.2.46.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 5

 10

 15

 20

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Hill Model

12:28 11/20 2009

BMD

Hill

2 

3 

4 

5 E.2.46.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_hepatic_retinol.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_hepatic_retinol.plt 

13 Fri Nov 20 12:28:12 2009 

14 ==================================================================== 

15 

16 Tbl3, hepatic retinol 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-294 —DO NOT CITE OR QUOTE 

1 lalpha = 2.76506 

2 rho = 0 

3 intercept = 14.9 

4 v = -14.3 

5 n = 3.62162 

6 k = 6985.28 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho intercept v n k 

12 

13 lalpha 1 -0.78 -0.04 0.012 0.036 0.033 

14 

15 rho -0.78 1 -0.099 0.12 -0.046 -0.052 

16 

17 intercept -0.04 -0.099 1 -0.94 -0.25 -0.81 

18 

19 v 0.012 0.12 -0.94 1 0.54 0.75 

20 

21 n 0.036 -0.046 -0.25 0.54 1 0.31 

22 

23 k 0.033 -0.052 -0.81 0.75 0.31 1 

24 

25 

26 

27 Parameter Estimates 

28 

29 95.0% Wald Confidence Interval 

30 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

31 lalpha -1.16164 0.374355 -1.89536 -0.427913 

32 rho 1.69911 0.18585 1.33485 2.06337 

33 intercept 16.6709 2.08161 12.591 20.7508 

34 v -17.0495 2.32002 -21.5967 -12.5023 

35 n 0.763329 0.19632 0.378549 1.14811 

36 k 4251.89 1440.45 1428.66 7075.13 

37 

38 

39 

40 Table of Data and Estimated Values of Interest 

41 

42 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

43 ------ --- -------- -------- ----------- ----------- ---------- 

44 

45 0 8 14.9 16.7 8.77 6.11 -0.82 

46 3969 8 8.4 8.37 3.39 3.4 0.0248 

47 6479 8 8.2 6.79 2.26 2.85 1.4 

48 9968 8 5.1 5.47 0.849 2.37 -0.439 

49 4.761e+004 8 2.2 1.95 0.849 0.987 0.716 

50 1.378e+005 8 0.6 0.741 0.566 0.434 -0.919 

51 

52 

53 

54 Model Descriptions for likelihoods calculated 

55 

56 

57 Model A1: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 

60 Model A2: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma(i)^2 

62 

63 Model A3: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

65 Model A3 uses any fixed variance parameters that 

66 were specified by the user 

67 

68 Model R: Yi = Mu + e(i) 

69 Var{e(i)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-295 —DO NOT CITE OR QUOTE 

1 

2 Likelihoods of Interest 

3 

4 Model Log(likelihood) # Param's AIC 

5 A1 -87.156698 7 188.313395 

6 A2 -47.287416 12 118.574833 

7 A3 -55.324218 8 126.648436 

8 fitted -56.747514 6 125.495027 

9 R -109.967018 2 223.934036 

10 

11 

12 Explanation of Tests 

13 

14 Test 1: Do responses and/or variances differ among Dose levels? 

15 (A2 vs. R) 

16 Test 2: Are Variances Homogeneous? (A1 vs A2) 

17 Test 3: Are variances adequately modeled? (A2 vs. A3) 

18 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

19 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

20 

21 Tests of Interest 

22 

23 Test -2*log(Likelihood Ratio) Test df p-value 

24 

25 Test 1 125.359 10 <.0001 

26 Test 2 79.7386 5 <.0001 

27 Test 3 16.0736 4 0.002922 

28 Test 4 2.84659 2 0.2409 

29 

30 The p-value for Test 1 is less than .05. There appears to be a 

31 difference between response and/or variances among the dose levels 

32 It seems appropriate to model the data 

33 

34 The p-value for Test 2 is less than .1. A non-homogeneous variance 

35 model appears to be appropriate 

36 

37 The p-value for Test 3 is less than .1. You may want to consider a 

38 different variance model 

39 

40 The p-value for Test 4 is greater than .1. The model chosen seems 

41 to adequately describe the data 

42 

43 

44 Benchmark Dose Computation 

45 

46 Specified effect = 1 

47 

48 Risk Type = Estimated standard deviations from the control mean 

49 

50 Confidence level = 0.95 

51 

52 BMD = 1980.88 

53 

54 

55 BMDL computation failed. 

56 

57 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-296 —DO NOT CITE OR QUOTE 

1 E.2.46.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 5

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 15

 20

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:28 11/20 2009

BMDLBMD

 

Power

2 

3 

4 

5 E.2.46.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_hepatic_retinol.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_hepatic_retinol.plt 

13 Fri Nov 20 12:28:14 2009 

14 ==================================================================== 

15 

16 Tbl3, hepatic retinol 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-297 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 2.76506 

3 rho = 0 

4 control = 14.9 

5 slope = -0.92667 

6 power = 0.231239 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 lalpha rho control slope power 

12 

13 lalpha 1 -0.8 -0.042 0.048 0.063 

14 

15 rho -0.8 1 -0.089 -0.038 -0.1 

16 

17 control -0.042 -0.089 1 -0.91 -0.81 

18 

19 slope 0.048 -0.038 -0.91 1 0.98 

20 

21 power 0.063 -0.1 -0.81 0.98 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha -0.986245 0.394723 -1.75989 -0.212602 

30 rho 1.67858 0.202896 1.28091 2.07625 

31 control 16.9266 2.23237 12.5513 21.302 

32 slope -3.10665 1.35883 -5.76991 -0.443384 

33 power 0.139874 0.0269583 0.0870372 0.192712 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 8 14.9 16.9 8.77 6.56 -0.874 

43 3969 8 8.4 7.03 3.39 3.14 1.24 

44 6479 8 8.2 6.32 2.26 2.87 1.85 

45 9968 8 5.1 5.67 0.849 2.62 -0.611 

46 4.761e+004 8 2.2 2.91 0.849 1.5 -1.34 

47 1.378e+005 8 0.6 0.666 0.566 0.434 -0.427 

48 

49 

50 

51 Model Descriptions for likelihoods calculated 

52 

53 

54 Model A1: Yij = Mu(i) + e(ij) 

55 Var{e(ij)} = Sigma^2 

56 

57 Model A2: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma(i)^2 

59 

60 Model A3: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

62 Model A3 uses any fixed variance parameters that 

63 were specified by the user 

64 

65 Model R: Yi = Mu + e(i) 

66 Var{e(i)} = Sigma^2 

67 

68 

69 Likelihoods of Interest 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-298 —DO NOT CITE OR QUOTE 

1 Model Log(likelihood) # Param's AIC 

2 A1 -87.156698 7 188.313395 

3 A2 -47.287416 12 118.574833 

4 A3 -55.324218 8 126.648436 

5 fitted -60.885852 5 131.771704 

6 R -109.967018 2 223.934036 

7 

8 

9 Explanation of Tests 

10 

11 Test 1: Do responses and/or variances differ among Dose levels? 

12 (A2 vs. R) 

13 Test 2: Are Variances Homogeneous? (A1 vs A2) 

14 Test 3: Are variances adequately modeled? (A2 vs. A3) 

15 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

16 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

17 

18 Tests of Interest 

19 

20 Test -2*log(Likelihood Ratio) Test df p-value 

21 

22 Test 1 125.359 10 <.0001 

23 Test 2 79.7386 5 <.0001 

24 Test 3 16.0736 4 0.002922 

25 Test 4 11.1233 3 0.01108 

26 

27 The p-value for Test 1 is less than .05. There appears to be a 

28 difference between response and/or variances among the dose levels 

29 It seems appropriate to model the data 

30 

31 The p-value for Test 2 is less than .1. A non-homogeneous variance 

32 model appears to be appropriate 

33 

34 The p-value for Test 3 is less than .1. You may want to consider a 

35 different variance model 

36 

37 The p-value for Test 4 is less than .1. You may want to try a different 

38 model 

39 

40 

41 Benchmark Dose Computation 

42 

43 Specified effect = 1 

44 

45 Risk Type = Estimated standard deviations from the control mean 

46 

47 Confidence level = 0.95 

48 

49 BMD = 209.498 

50 

51 

52 BMDL = 7.67456 

53 

54 

55 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-299 —DO NOT CITE OR QUOTE 

1 E.2.47. Van Birgelen et al. (1995a): Hepatic Retinol Palmitate 

2 E.2.47.1. Summary Table of BMDS Modeling Results 

Model Degrees of 

Freedom 

Variance 

p-Value a 

χ

 2 Test 

Statistic 

χ 2pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) 4 <0.0001 57.51 <0.0001 460.28 error error nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 57.51 <0.0001 460.28 error error nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 42.23 <0.0001 446.99 7.8E+04 2.0E+04 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 42.23 <0.0001 446.99 7.8E+04 2.0E+04 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 <0.0001 42.23 <0.0001 446.99 7.8E+04 2.0E+04 nonconstant variance, 

power unrestricted 

Hill 3 <.0001 11.47 0.01 416.23 2.0E+03 error nonconstant variance, n 

restricted >1, bound hit 

Hill d 3 <.0001 120.59 <.0001 525.36 5.0E-11 5.0E-11 nonconstant variance, n 

unrestricted 

linear 4 <.0001 83.61 <.0001 486.37 1.9E+05 1.3E+05 nonconstant variance 

polynomial 4 <.0001 128.71 <.0001 531.47 6.2E+04 5.0E+04 nonconstant variance 

power 4 <.0001 83.61 <.0001 486.37 1.9E+05 1.3E+05 nonconstant variance, 

power restricted ≥1, bound 

hit 

power d 3 <.0001 4.22 0.24 408.98 2.9E+01 3.2E-02 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 142.00 <0.0001 649.06 error error constant variance, power 

restricted ≥1 

exponential (M3) 4 <0.0001 142.00 <0.0001 649.06 error error constant variance, power 

restricted ≥1 

exponential (M4) 3 <0.0001 2.84 0.42 511.95 7.9E+02 2.9E+00 constant variance, power 

restricted ≥1 

exponential (M5) 3 <0.0001 2.84 0.42 511.95 7.9E+02 2.0E+00 constant variance, power 

restricted ≥1 

exponential (M5) 3 <0.0001 2.84 0.42 511.95 7.9E+02 2.0E+00 constant variance, power 

unrestricted 

Hill 3 <.0001 0.93 0.82 510.04 3.9E+02 9.5E+01 constant variance, n 

restricted >1, bound hit 

Hill 2 <.0001 0.31 0.86 511.42 2.8E-01 2.8E-01 constant variance, n 

unrestricted 

linear 4 <.0001 43.71 <.0001 550.82 1.1E+05 7.0E+04 constant variance 

polynomial 4 <.0001 43.71 <.0001 550.82 1.1E+05 7.0E+04 constant variance 

power 4 <.0001 43.71 <.0001 550.82 1.1E+05 7.0E+04 constant variance, power 

restricted ≥1, bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-300 —DO NOT CITE OR QUOTE 

Model Degrees of 

Freedom 

Variance 

p-Value a 

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC BMD 

(ng/kg-d) 

BMDL 

(ng/kg-d) Model Notes 

power 3 <.0001 0.33 0.95 509.44 2.0E-04 2.0E-04 constant variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix

d

 Alternate model also presented in this appendix

1 

2 

3 E.2.47.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 100

 200

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 400

 500

 600

 700

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:29 11/20 2009

BMDL BMD

 

Exponential

5 

6 

7 

8 E.2.47.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_hepatic_retinol_palmitate.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 12:29:00 2009 

17 ==================================================================== 

18 

19 Tbl3, hepatic retinol palmitate 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-301 —DO NOT CITE OR QUOTE 

1 The form of the response function by Model: 

2 Model 2: Y[dose] = a * exp{sign * b * dose} 

3 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

4 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

5 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

6 

7 Note: Y[dose] is the median response for exposure = dose; 

8 sign = +1 for increasing trend in data; 

9 sign = -1 for decreasing trend. 

10 

11 Model 2 is nested within Models 3 and 4. 

12 Model 3 is nested within Model 5. 

13 Model 4 is nested within Model 5. 

14 

15 

16 Dependent variable = Mean 

17 Independent variable = Dose 

18 Data are assumed to be distributed: normally 

19 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

20 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 4 

34 -------- -------- 

35 lnalpha 0.284674 

36 rho 1.77158 

37 a 495.6 

38 b 6.13207e-005 

39 c 0.00576502 

40 d 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 Variable Model 4 

47 -------- ------- 

48 lnalpha -0.241584 

49 rho 2.03456 

50 a 223.851 

51 b 5.45885e-005 

52 c 0.012925 

53 d 1 

54 

55 NC = No Convergence 

56 

57 

58 Table of Stats From Input Data 

59 

60 Dose N Obs Mean Obs Std Dev 

61 ----- --- ---------- ------------- 

62 0 8 472 271.5 

63 3969 8 94 67.88 

64 6479 8 107 76.37 

65 9968 8 74 39.6 

66 4.761e+004 8 22 22.63 

67 1.378e+005 8 3 2.828 

68 

69 

70 Estimated Values of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-302 —DO NOT CITE OR QUOTE 

1 

2 Dose Est Mean Est Std Scaled Residual 

3 ------ ---------- --------- ---------------- 

4 0 223.9 217.8 3.222 

5 3969 180.8 175.3 -1.401 

6 6479 158 152.9 -0.9443 

7 9968 131.1 126.4 -1.278 

8 4.761e+004 19.33 18.03 0.4197 

9 1.378e+005 3.013 2.721 -0.01317 

10 

11 

12 

13 Other models for which likelihoods are calculated: 

14 

15 Model A1: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma^2 

17 

18 Model A2: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma(i)^2 

20 

21 Model A3: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

23 

24 Model R: Yij = Mu + e(i) 

25 Var{e(ij)} = Sigma^2 

26 

27 

28 Likelihoods of Interest 

29 

30 Model Log(likelihood) DF AIC 

31 ------- ----------------- ---- ------------ 

32 A1 -250.5548 7 515.1096 

33 A2 -196.7557 12 417.5115 

34 A3 -197.3832 8 410.7663 

35 R -276.7896 2 557.5793 

36 4 -218.4969 5 446.9938 

37 

38 

39 Additive constant for all log-likelihoods = -44.11. This constant added to the 

40 above values gives the log-likelihood including the term that does not 

41 depend on the model parameters. 

42 

43 

44 Explanation of Tests 

45 

46 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

47 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

48 Test 3: Are variances adequately modeled? (A2 vs. A3) 

49 

50 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

51 

52 

53 Tests of Interest 

54 

55 Test -2*log(Likelihood Ratio) D. F. p-value 

56 -------- ------------------------ ------ -------------- 

57 Test 1 160.1 10 < 0.0001 

58 Test 2 107.6 5 < 0.0001 

59 Test 3 1.255 4 0.869 

60 Test 6a 42.23 3 < 0.0001 

61 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose 

65 levels, it seems appropriate to model the data. 

66 

67 The p-value for Test 2 is less than .1. A non-homogeneous 

68 variance model appears to be appropriate. 

69 

70 The p-value for Test 3 is greater than .1. The modeled 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-303 —DO NOT CITE OR QUOTE 

1 variance appears to be appropriate here. 

2 

3 The p-value for Test 6a is less than .1. Model 4 may not adequately 

4 describe the data; you may want to consider another model. 

5 

6 

7 Benchmark Dose Computations: 

8 

9 Specified Effect = 1.000000 

10 

11 Risk Type = Estimated standard deviations from control 

12 

13 Confidence Level = 0.950000 

14 

15 BMD = 77948.7 

16 

17 BMDL = 20092.3 

18 

19 

20 E.2.47.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

21 Unrestricted 

 0

 100

 200

 300

 400

 500

 600

 700

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:29 11/20 2009

BMDL BMD

 

Exponential

22 

23 

24 

25 E.2.47.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

26 Power Unrestricted 

27 

28 

29 ==================================================================== 

30 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

31 Input Data File: 

32 C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_hepatic_retinol_palmitate.(d) 

33 Gnuplot Plotting File: 

34 Fri Nov 20 12:29:18 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-304 —DO NOT CITE OR QUOTE 

1 ==================================================================== 

2 

3 Tbl3, hepatic retinol palmitate 

4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

5 

6 The form of the response function by Model: 

7 Model 2: Y[dose] = a * exp{sign * b * dose} 

8 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

9 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

10 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

11 

12 Note: Y[dose] is the median response for exposure = dose; 

13 sign = +1 for increasing trend in data; 

14 sign = -1 for decreasing trend. 

15 

16 Model 2 is nested within Models 3 and 4. 

17 Model 3 is nested within Model 5. 

18 Model 4 is nested within Model 5. 

19 

20 

21 Dependent variable = Mean 

22 Independent variable = Dose 

23 Data are assumed to be distributed: normally 

24 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

25 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

26 

27 Total number of dose groups = 6 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 MLE solution provided: Exact 

34 

35 

36 Initial Parameter Values 

37 

38 Variable Model 5 

39 -------- -------- 

40 lnalpha 0.284674 

41 rho 1.77158 

42 a 495.6 

43 b 6.13207e-005 

44 c 0.00576502 

45 d 1 

46 

47 

48 

49 Parameter Estimates 

50 

51 Variable Model 5 

52 -------- ------- 

53 lnalpha -0.241584 

54 rho 2.03456 

55 a 223.851 

56 b 5.45885e-005 

57 c 0.012925 

58 d 1 

59 

60 NC = No Convergence 

61 

62 

63 Table of Stats From Input Data 

64 

65 Dose N Obs Mean Obs Std Dev 

66 ----- --- ---------- ------------- 

67 0 8 472 271.5 

68 3969 8 94 67.88 

69 6479 8 107 76.37 

70 9968 8 74 39.6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-305 —DO NOT CITE OR QUOTE 

1 4.761e+004 8 22 22.63 

2 1.378e+005 8 3 2.828 

3 

4 

5 Estimated Values of Interest 

6 

7 Dose Est Mean Est Std Scaled Residual 

8 ------ ---------- --------- ---------------- 

9 0 223.9 217.8 3.222 

10 3969 180.8 175.3 -1.401 

11 6479 158 152.9 -0.9443 

12 9968 131.1 126.4 -1.278 

13 4.761e+004 19.33 18.03 0.4197 

14 1.378e+005 3.013 2.721 -0.01317 

15 

16 

17 

18 Other models for which likelihoods are calculated: 

19 

20 Model A1: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma^2 

22 

23 Model A2: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = Sigma(i)^2 

25 

26 Model A3: Yij = Mu(i) + e(ij) 

27 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

28 

29 Model R: Yij = Mu + e(i) 

30 Var{e(ij)} = Sigma^2 

31 

32 

33 Likelihoods of Interest 

34 

35 Model Log(likelihood) DF AIC 

36 ------- ----------------- ---- ------------ 

37 A1 -250.5548 7 515.1096 

38 A2 -196.7557 12 417.5115 

39 A3 -197.3832 8 410.7663 

40 R -276.7896 2 557.5793 

41 5 -218.4969 5 446.9938 

42 

43 

44 Additive constant for all log-likelihoods = -44.11. This constant added to the 

45 above values gives the log-likelihood including the term that does not 

46 depend on the model parameters. 

47 

48 

49 Explanation of Tests 

50 

51 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

52 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

53 Test 3: Are variances adequately modeled? (A2 vs. A3) 

54 

55 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

56 

57 

58 Tests of Interest 

59 

60 Test -2*log(Likelihood Ratio) D. F. p-value 

61 -------- ------------------------ ------ -------------- 

62 Test 1 160.1 10 < 0.0001 

63 Test 2 107.6 5 < 0.0001 

64 Test 3 1.255 4 0.869 

65 Test 7a 42.23 3 < 0.0001 

66 

67 

68 The p-value for Test 1 is less than .05. There appears to be a 

69 difference between response and/or variances among the dose 

70 levels, it seems appropriate to model the data. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-306 —DO NOT CITE OR QUOTE 

1 

2 The p-value for Test 2 is less than .1. A non-homogeneous 

3 variance model appears to be appropriate. 

4 

5 The p-value for Test 3 is greater than .1. The modeled 

6 variance appears to be appropriate here. 

7 

8 The p-value for Test 7a is less than .1. Model 5 may not adequately 

9 describe the data; you may want to consider another model. 

10 

11 

12 Benchmark Dose Computations: 

13 

14 Specified Effect = 1.000000 

15 

16 Risk Type = Estimated standard deviations from control 

17 

18 Confidence Level = 0.950000 

19 

20 BMD = 77952.3 

21 

22 BMDL = 20092.3 

23 

24 

25 E.2.47.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 100

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 300

 400

 500

 600

 700

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:29 11/20 2009

BMDBMDL

 

Hill

26 

27 

28 

29 E.2.47.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

30 

31 

32 ==================================================================== 

33 Hill Model. (Version: 2.14; Date: 06/26/2008) 

34 Input Data File: 

35 C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_hepatic_retinol_palmitate.(d) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-307 —DO NOT CITE OR QUOTE 

1 Gnuplot Plotting File: 

2 C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_hepatic_retinol_palmitate.plt 

3 Fri Nov 20 12:29:21 2009 

4 ==================================================================== 

5 

6 Tbl3, hepatic retinol palmitate 

7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

8 

9 The form of the response function is: 

10 

11 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

12 

13 

14 Dependent variable = Mean 

15 Independent variable = Dose 

16 Power parameter is not restricted 

17 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

18 

19 Total number of dose groups = 6 

20 Total number of records with missing values = 0 

21 Maximum number of iterations = 250 

22 Relative Function Convergence has been set to: 1e-008 

23 Parameter Convergence has been set to: 1e-008 

24 

25 

26 

27 Default Initial Parameter Values 

28 lalpha = 9.57332 

29 rho = 0 

30 intercept = 472 

31 v = -469 

32 n = 1.6454 

33 k = 2462.18 

34 

35 

36 Asymptotic Correlation Matrix of Parameter Estimates 

37 

38 ( *** The model parameter(s) -k 

39 have been estimated at a boundary point, or have been specified by the user, 

40 and do not appear in the correlation matrix ) 

41 

42 lalpha rho intercept v n 

43 

44 lalpha 1 -0.9 -0.0084 -0.05 0.00043 

45 

46 rho -0.9 1 0.33 -0.25 6.2e-005 

47 

48 intercept -0.0084 0.33 1 -1 0.00089 

49 

50 v -0.05 -0.25 -1 1 -0.00081 

51 

52 n 0.00043 6.2e-005 0.00089 -0.00081 1 

53 

54 

55 

56 Parameter Estimates 

57 

58 95.0% Wald Confidence Interval 

59 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

60 lalpha 9.05753 0.813787 7.46254 10.6525 

61 rho 0.296518 0.132793 0.0362478 0.556789 

62 intercept 733.34 146.204 446.785 1019.89 

63 v -707.607 132.71 -967.713 -447.5 

64 n 0.620012 31.4549 -61.0305 62.2705 

65 k 1.3782e-010 NA 

66 

67 NA - Indicates that this parameter has hit a bound 

68 implied by some inequality constraint and thus 

69 has no standard error. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-308 —DO NOT CITE OR QUOTE 

1 

2 

3 Table of Data and Estimated Values of Interest 

4 

5 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

6 ------ --- -------- -------- ----------- ----------- ---------- 

7 

8 0 8 472 733 272 246 -3 

9 3969 8 94 25.7 67.9 150 1.29 

10 6479 8 107 25.7 76.4 150 1.53 

11 9968 8 74 25.7 39.6 150 0.91 

12 4.761e+004 8 22 25.7 22.6 150 -0.0704 

13 1.378e+005 8 3 25.7 2.83 150 -0.429 

14 

15 

16 

17 Model Descriptions for likelihoods calculated 

18 

19 

20 Model A1: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma^2 

22 

23 Model A2: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = Sigma(i)^2 

25 

26 Model A3: Yij = Mu(i) + e(ij) 

27 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

28 Model A3 uses any fixed variance parameters that 

29 were specified by the user 

30 

31 Model R: Yi = Mu + e(i) 

32 Var{e(i)} = Sigma^2 

33 

34 

35 Likelihoods of Interest 

36 

37 Model Log(likelihood) # Param's AIC 

38 A1 -250.554817 7 515.109634 

39 A2 -196.755746 12 417.511491 

40 A3 -197.383174 8 410.766347 

41 fitted -257.680271 5 525.360542 

42 R -276.789644 2 557.579287 

43 

44 

45 Explanation of Tests 

46 

47 Test 1: Do responses and/or variances differ among Dose levels? 

48 (A2 vs. R) 

49 Test 2: Are Variances Homogeneous? (A1 vs A2) 

50 Test 3: Are variances adequately modeled? (A2 vs. A3) 

51 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

52 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

53 

54 Tests of Interest 

55 

56 Test -2*log(Likelihood Ratio) Test df p-value 

57 

58 Test 1 160.068 10 <.0001 

59 Test 2 107.598 5 <.0001 

60 Test 3 1.25486 4 0.869 

61 Test 4 120.594 3 <.0001 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose levels 

65 It seems appropriate to model the data 

66 

67 The p-value for Test 2 is less than .1. A non-homogeneous variance 

68 model appears to be appropriate 

69 

70 The p-value for Test 3 is greater than .1. The modeled variance appears 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-309 —DO NOT CITE OR QUOTE 

1 to be appropriate here 

2 

3 The p-value for Test 4 is less than .1. You may want to try a different 

4 model 

5 

6 

7 Benchmark Dose Computation 

8 

9 Specified effect = 1 

10 

11 Risk Type = Estimated standard deviations from the control mean 

12 

13 Confidence level = 0.95 

14 

15 BMD = 5.01376e-011 

16 

17 BMDL = 5.01376e-011 

18 

19 

20 

21 E.2.47.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 100

 200

 300

 400

 500

 600

 700

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:29 11/20 2009

BMDBMDL

 

Power

22 

23 

24 

25 E.2.47.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

26 Unrestricted 

27 

28 

29 ==================================================================== 

30 Power Model. (Version: 2.15; Date: 04/07/2008) 

31 Input Data File: 

32 C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_hepatic_retinol_palmitate.(d) 

33 Gnuplot Plotting File: 

34 C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_hepatic_retinol_palmitate.plt 

35 Fri Nov 20 12:29:22 2009 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-310 —DO NOT CITE OR QUOTE 

1 ==================================================================== 

2 

3 Tbl3, hepatic retinol palmitate 

4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

5 

6 The form of the response function is: 

7 

8 Y[dose] = control + slope * dose^power 

9 

10 

11 Dependent variable = Mean 

12 Independent variable = Dose 

13 The power is not restricted 

14 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

15 

16 Total number of dose groups = 6 

17 Total number of records with missing values = 0 

18 Maximum number of iterations = 250 

19 Relative Function Convergence has been set to: 1e-008 

20 Parameter Convergence has been set to: 1e-008 

21 

22 

23 

24 Default Initial Parameter Values 

25 lalpha = 9.57332 

26 rho = 0 

27 control = 472 

28 slope = -204.597 

29 power = 0.0711193 

30 

31 

32 Asymptotic Correlation Matrix of Parameter Estimates 

33 

34 lalpha rho control slope power 

35 

36 lalpha 1 -0.95 0.3 -0.32 -0.3 

37 

38 rho -0.95 1 -0.41 0.37 0.29 

39 

40 control 0.3 -0.41 1 -0.96 -0.82 

41 

42 slope -0.32 0.37 -0.96 1 0.95 

43 

44 power -0.3 0.29 -0.82 0.95 1 

45 

46 

47 

48 Parameter Estimates 

49 

50 95.0% Wald Confidence Interval 

51 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

52 lalpha 0.064014 0.859473 -1.62052 1.74855 

53 rho 1.81132 0.197468 1.42429 2.19835 

54 control 464.289 87.5706 292.654 635.925 

55 slope -216.594 73.4027 -360.461 -72.7275 

56 power 0.0639105 0.0139781 0.0365139 0.0913071 

57 

58 

59 

60 Table of Data and Estimated Values of Interest 

61 

62 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

63 ------ --- -------- -------- ----------- ----------- ---------- 

64 

65 0 8 472 464 272 269 0.0812 

66 3969 8 94 96.5 67.9 64.7 -0.108 

67 6479 8 107 84.8 76.4 57.6 1.09 

68 9968 8 74 74.2 39.6 51 -0.00938 

69 4.761e+004 8 22 33.2 22.6 24.6 -1.28 

70 1.378e+005 8 3 2.86 2.83 2.68 0.145 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-311 —DO NOT CITE OR QUOTE 

1 

2 

3 

4 Model Descriptions for likelihoods calculated 

5 

6 

7 Model A1: Yij = Mu(i) + e(ij) 

8 Var{e(ij)} = Sigma^2 

9 

10 Model A2: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma(i)^2 

12 

13 Model A3: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

15 Model A3 uses any fixed variance parameters that 

16 were specified by the user 

17 

18 Model R: Yi = Mu + e(i) 

19 Var{e(i)} = Sigma^2 

20 

21 

22 Likelihoods of Interest 

23 

24 Model Log(likelihood) # Param's AIC 

25 A1 -250.554817 7 515.109634 

26 A2 -196.755746 12 417.511491 

27 A3 -197.383174 8 410.766347 

28 fitted -199.490894 5 408.981788 

29 R -276.789644 2 557.579287 

30 

31 

32 Explanation of Tests 

33 

34 Test 1: Do responses and/or variances differ among Dose levels? 

35 (A2 vs. R) 

36 Test 2: Are Variances Homogeneous? (A1 vs A2) 

37 Test 3: Are variances adequately modeled? (A2 vs. A3) 

38 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

39 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

40 

41 Tests of Interest 

42 

43 Test -2*log(Likelihood Ratio) Test df p-value 

44 

45 Test 1 160.068 10 <.0001 

46 Test 2 107.598 5 <.0001 

47 Test 3 1.25486 4 0.869 

48 Test 4 4.21544 3 0.2391 

49 

50 The p-value for Test 1 is less than .05. There appears to be a 

51 difference between response and/or variances among the dose levels 

52 It seems appropriate to model the data 

53 

54 The p-value for Test 2 is less than .1. A non-homogeneous variance 

55 model appears to be appropriate 

56 

57 The p-value for Test 3 is greater than .1. The modeled variance appears 

58 to be appropriate here 

59 

60 The p-value for Test 4 is greater than .1. The model chosen seems 

61 to adequately describe the data 

62 

63 

64 Benchmark Dose Computation 

65 

66 Specified effect = 1 

67 

68 Risk Type = Estimated standard deviations from the control mean 

69 

70 Confidence level = 0.95 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-312 —DO NOT CITE OR QUOTE 

1 

2 BMD = 28.9991 

3 

4 

5 BMDL = 0.0324608 

6 

7 

8 

9 E.2.48. Van Birgelen et al. (1995a): Plasma FT4 

10 E.2.48.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) c 4 0.01 2.70 0.61 214.98 4.4E+04 2.8E+04 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.01 2.70 0.61 214.98 4.4E+04 2.8E+04 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.01 1.96 0.58 216.24 3.0E+04 1.2E+04 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.01 1.96 0.58 216.24 3.0E+04 1.2E+04 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 0.01 1.96 0.58 216.24 3.0E+04 1.2E+04 nonconstant variance, 

power unrestricted 

Hill 3 0.01 1.90 0.59 216.19 2.8E+04 8.8E+03 nonconstant variance, n 

restricted >1, bound hit 

Hill d 2 0.01 1.90 0.39 218.19 2.8E+04 7.9E+03 nonconstant variance, n 

unrestricted 

linear 4 0.01 3.98 0.41 216.27 6.0E+04 4.4E+04 nonconstant variance 

polynomial 4 0.01 3.98 0.41 216.27 6.0E+04 4.4E+04 nonconstant variance 

power 4 0.01 3.98 0.41 216.27 6.0E+04 4.4E+04 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 0.01 2.30 0.51 216.59 3.0E+04 7.2E+03 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.01 3.21 0.52 213.50 4.1E+04 2.7E+04 constant variance, 

power restricted ≥1 

exponential (M3) 4 0.01 3.21 0.52 213.50 4.1E+04 2.7E+04 constant variance, 

power restricted ≥1 

exponential (M4) 3 0.01 2.47 0.48 214.76 2.7E+04 1.1E+04 constant variance, 

power restricted ≥1 

exponential (M5) 3 0.01 2.47 0.48 214.76 2.7E+04 1.1E+04 constant variance, 

power restricted ≥1 

exponential (M5) 3 0.01 2.47 0.48 214.76 2.7E+04 1.1E+04 constant variance, 

power unrestricted 

Hill 3 0.01 2.35 0.50 214.64 2.4E+04 8.1E+03 constant variance, n 

restricted >1, bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-313 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

Hill 2 0.01 2.33 0.31 216.62 2.4E+04 7.0E+03 constant variance, n 

unrestricted 

linear 4 0.01 4.50 0.34 214.79 5.7E+04 4.3E+04 constant variance 

polynomial 4 0.01 4.50 0.34 214.79 5.7E+04 4.3E+04 constant variance 

power 4 0.01 4.50 0.34 214.79 5.7E+04 4.3E+04 

constant variance, 

power restricted ≥1, 

bound hit 

power 3 0.01 2.66 0.45 214.95 2.6E+04 6.4E+03 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.2.48.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

4 Restricted ≥1 

 5

 10

 15

 20

 25

 30

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

12:30 11/20 2009

BMDL BMD

 

Exponential

5 

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-314 —DO NOT CITE OR QUOTE 

1 E.2.48.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_plasma_FT4.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 12:30:05 2009 

10 ==================================================================== 

11 

12 Tbl3, plasma FT4 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

35 

36 Total number of dose groups = 6 

37 Total number of records with missing values = 0 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 

40 Parameter Convergence has been set to: 1e-008 

41 

42 MLE solution provided: Exact 

43 

44 

45 Initial Parameter Values 

46 

47 Variable Model 2 

48 -------- -------- 

49 lnalpha 4.29134 

50 rho -0.423761 

51 a 25.725 

52 b 2.47112e-005 

53 c 0.381323 

54 d 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 Variable Model 2 

61 -------- ------- 

62 lnalpha 1.7323 

63 rho 0.534787 

64 a 23.5975 

65 b 1.50877e-005 

66 c 0.358997 

67 d 1 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-315 —DO NOT CITE OR QUOTE 

1 

2 Table of Stats From Input Data 

3 

4 Dose N Obs Mean Obs Std Dev 

5 ----- --- ---------- ------------- 

6 0 8 23.4 3.111 

7 3969 8 24.5 5.657 

8 6479 8 22.4 2.828 

9 9968 8 19.3 9.334 

10 4.761e+004 8 16.3 4.243 

11 1.378e+005 8 10.3 4.808 

12 

13 

14 Estimated Values of Interest 

15 

16 Dose Est Mean Est Std Scaled Residual 

17 ------ ---------- --------- ---------------- 

18 0 23.03 5.531 0.1896 

19 3969 22.47 5.496 1.046 

20 6479 22.12 5.474 0.1445 

21 9968 21.65 5.444 -1.219 

22 4.761e+004 17.13 5.13 -0.4583 

23 1.378e+005 9.779 4.447 0.3314 

24 

25 

26 

27 Other models for which likelihoods are calculated: 

28 

29 Model A1: Yij = Mu(i) + e(ij) 

30 Var{e(ij)} = Sigma^2 

31 

32 Model A2: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma(i)^2 

34 

35 Model A3: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

37 

38 Model R: Yij = Mu + e(i) 

39 Var{e(ij)} = Sigma^2 

40 

41 

42 Likelihoods of Interest 

43 

44 Model Log(likelihood) DF AIC 

45 ------- ----------------- ---- ------------ 

46 A1 -102.145 7 218.2901 

47 A2 -94.04963 12 212.0993 

48 A3 -102.143 8 220.286 

49 R -117.8175 2 239.635 

50 2 -103.491 4 214.9821 

51 

52 

53 Additive constant for all log-likelihoods = -44.11. This constant added to the 

54 above values gives the log-likelihood including the term that does not 

55 depend on the model parameters. 

56 

57 

58 Explanation of Tests 

59 

60 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

61 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

62 Test 3: Are variances adequately modeled? (A2 vs. A3) 

63 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

64 

65 

66 Tests of Interest 

67 

68 Test -2*log(Likelihood Ratio) D. F. p-value 

69 -------- ------------------------ ------ -------------- 

70 Test 1 47.54 10 < 0.0001 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-316 —DO NOT CITE OR QUOTE 

1 Test 2 16.19 5 0.00632 

2 Test 3 16.19 4 0.002778 

3 Test 4 2.696 4 0.6099 

4 

5 

6 The p-value for Test 1 is less than .05. There appears to be a 

7 difference between response and/or variances among the dose 

8 levels, it seems appropriate to model the data. 

9 

10 The p-value for Test 2 is less than .1. A non-homogeneous 

11 variance model appears to be appropriate. 

12 

13 The p-value for Test 3 is less than .1. You may want to 

14 consider a different variance model. 

15 

16 The p-value for Test 4 is greater than .1. Model 2 seems 

17 to adequately describe the data. 

18 

19 

20 Benchmark Dose Computations: 

21 

22 Specified Effect = 1.000000 

23 

24 Risk Type = Estimated standard deviations from control 

25 

26 Confidence Level = 0.950000 

27 

28 BMD = 44193.5 

29 

30 BMDL = 28156.1 

31 

32 

33 E.2.48.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

34 Unrestricted 

 5

 10

 15

 20

 25

 30

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:30 11/20 2009

BMDL BMD

 

Exponential

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-317 —DO NOT CITE OR QUOTE 

1 E.2.48.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

2 Power Unrestricted 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_plasma_FT4.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 12:30:11 2009 

10 ==================================================================== 

11 

12 Tbl3, plasma FT4 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

35 

36 Total number of dose groups = 6 

37 Total number of records with missing values = 0 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 

40 Parameter Convergence has been set to: 1e-008 

41 

42 MLE solution provided: Exact 

43 

44 

45 Initial Parameter Values 

46 

47 Variable Model 5 

48 -------- -------- 

49 lnalpha 4.29134 

50 rho -0.423761 

51 a 25.725 

52 b 2.47112e-005 

53 c 0.381323 

54 d 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 Variable Model 5 

61 -------- ------- 

62 lnalpha 1.7323 

63 rho 0.534787 

64 a 23.5975 

65 b 1.50877e-005 

66 c 0.358997 

67 d 1 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-318 —DO NOT CITE OR QUOTE 

1 

2 Table of Stats From Input Data 

3 

4 Dose N Obs Mean Obs Std Dev 

5 ----- --- ---------- ------------- 

6 0 8 23.4 3.111 

7 3969 8 24.5 5.657 

8 6479 8 22.4 2.828 

9 9968 8 19.3 9.334 

10 4.761e+004 8 16.3 4.243 

11 1.378e+005 8 10.3 4.808 

12 

13 

14 Estimated Values of Interest 

15 

16 Dose Est Mean Est Std Scaled Residual 

17 ------ ---------- --------- ---------------- 

18 0 23.6 5.537 -0.1009 

19 3969 22.72 5.481 0.9194 

20 6479 22.19 5.446 0.1096 

21 9968 21.49 5.4 -1.145 

22 4.761e+004 15.85 4.978 0.2575 

23 1.378e+005 10.36 4.443 -0.03965 

24 

25 

26 

27 Other models for which likelihoods are calculated: 

28 

29 Model A1: Yij = Mu(i) + e(ij) 

30 Var{e(ij)} = Sigma^2 

31 

32 Model A2: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma(i)^2 

34 

35 Model A3: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

37 

38 Model R: Yij = Mu + e(i) 

39 Var{e(ij)} = Sigma^2 

40 

41 

42 Likelihoods of Interest 

43 

44 Model Log(likelihood) DF AIC 

45 ------- ----------------- ---- ------------ 

46 A1 -102.145 7 218.2901 

47 A2 -94.04963 12 212.0993 

48 A3 -102.143 8 220.286 

49 R -117.8175 2 239.635 

50 5 -103.1224 5 216.2449 

51 

52 

53 Additive constant for all log-likelihoods = -44.11. This constant added to the 

54 above values gives the log-likelihood including the term that does not 

55 depend on the model parameters. 

56 

57 

58 Explanation of Tests 

59 

60 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

61 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

62 Test 3: Are variances adequately modeled? (A2 vs. A3) 

63 

64 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

65 

66 

67 Tests of Interest 

68 

69 Test -2*log(Likelihood Ratio) D. F. p-value 

70 -------- ------------------------ ------ -------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-319 —DO NOT CITE OR QUOTE 

1 Test 1 47.54 10 < 0.0001 

2 Test 2 16.19 5 0.00632 

3 Test 3 16.19 4 0.002778 

4 Test 7a 1.959 3 0.581 

5 

6 

7 The p-value for Test 1 is less than .05. There appears to be a 

8 difference between response and/or variances among the dose 

9 levels, it seems appropriate to model the data. 

10 

11 The p-value for Test 2 is less than .1. A non-homogeneous 

12 variance model appears to be appropriate. 

13 

14 The p-value for Test 3 is less than .1. You may want to 

15 consider a different variance model. 

16 

17 The p-value for Test 7a is greater than .1. Model 5 seems 

18 to adequately describe the data. 

19 

20 

21 Benchmark Dose Computations: 

22 

23 Specified Effect = 1.000000 

24 

25 Risk Type = Estimated standard deviations from control 

26 

27 Confidence Level = 0.950000 

28 

29 BMD = 30208.5 

30 

31 BMDL = 12273.2 

32 

33 

34 E.2.48.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 5

 10

 15

 20

 25

 30

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:30 11/20 2009

BMDL BMD

 

Hill

35 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-320 —DO NOT CITE OR QUOTE 

1 E.2.48.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

2 

3 

4 ==================================================================== 

5 Hill Model. (Version: 2.14; Date: 06/26/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_plasma_FT4.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_plasma_FT4.plt 

8 Fri Nov 20 12:30:12 2009 

9 ==================================================================== 

10 

11 Tbl3, plasma FT4 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Power parameter is not restricted 

22 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

23 

24 Total number of dose groups = 6 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 Default Initial Parameter Values 

33 lalpha = 3.38957 

34 rho = 0 

35 intercept = 23.4 

36 v = -13.1 

37 n = 0.996796 

38 k = 40705.6 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 lalpha rho intercept v n k 

44 

45 lalpha 1 -1 0.2 -0.16 -0.19 0.12 

46 

47 rho -1 1 -0.2 0.16 0.19 -0.12 

48 

49 intercept 0.2 -0.2 1 -0.39 -0.59 0.22 

50 

51 v -0.16 0.16 -0.39 1 0.9 -0.98 

52 

53 n -0.19 0.19 -0.59 0.9 1 -0.85 

54 

55 k 0.12 -0.12 0.22 -0.98 -0.85 1 

56 

57 

58 

59 Parameter Estimates 

60 

61 95.0% Wald Confidence Interval 

62 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

63 lalpha 1.81761 2.18889 -2.47254 6.10776 

64 rho 0.505217 0.744572 -0.954117 1.96455 

65 intercept 23.7748 1.72532 20.3933 27.1564 

66 v -21.6283 20.8713 -62.5352 19.2786 

67 n 0.975863 0.6937 -0.383764 2.33549 

68 k 83458.4 171511 -252696 419613 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-321 —DO NOT CITE OR QUOTE 

1 

2 

3 Table of Data and Estimated Values of Interest 

4 

5 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

6 ------ --- -------- -------- ----------- ----------- ---------- 

7 

8 0 8 23.4 23.8 3.11 5.52 -0.192 

9 3969 8 24.5 22.7 5.66 5.46 0.921 

10 6479 8 22.4 22.1 2.83 5.43 0.143 

11 9968 8 19.3 21.4 9.33 5.38 -1.08 

12 4.761e+004 8 16.3 15.9 4.24 4.99 0.255 

13 1.378e+005 8 10.3 10.4 4.81 4.48 -0.0414 

14 

15 

16 

17 Model Descriptions for likelihoods calculated 

18 

19 

20 Model A1: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma^2 

22 

23 Model A2: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = Sigma(i)^2 

25 

26 Model A3: Yij = Mu(i) + e(ij) 

27 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

28 Model A3 uses any fixed variance parameters that 

29 were specified by the user 

30 

31 Model R: Yi = Mu + e(i) 

32 Var{e(i)} = Sigma^2 

33 

34 

35 Likelihoods of Interest 

36 

37 Model Log(likelihood) # Param's AIC 

38 A1 -102.145036 7 218.290071 

39 A2 -94.049629 12 212.099258 

40 A3 -102.143023 8 220.286046 

41 fitted -103.092664 6 218.185329 

42 R -117.817514 2 239.635028 

43 

44 

45 Explanation of Tests 

46 

47 Test 1: Do responses and/or variances differ among Dose levels? 

48 (A2 vs. R) 

49 Test 2: Are Variances Homogeneous? (A1 vs A2) 

50 Test 3: Are variances adequately modeled? (A2 vs. A3) 

51 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

52 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

53 

54 Tests of Interest 

55 

56 Test -2*log(Likelihood Ratio) Test df p-value 

57 

58 Test 1 47.5358 10 <.0001 

59 Test 2 16.1908 5 0.00632 

60 Test 3 16.1868 4 0.002778 

61 Test 4 1.89928 2 0.3869 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose levels 

65 It seems appropriate to model the data 

66 

67 The p-value for Test 2 is less than .1. A non-homogeneous variance 

68 model appears to be appropriate 

69 

70 The p-value for Test 3 is less than .1. You may want to consider a 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-322 —DO NOT CITE OR QUOTE 

1 different variance model 

2 

3 The p-value for Test 4 is greater than .1. The model chosen seems 

4 to adequately describe the data 

5 

6 

7 Benchmark Dose Computation 

8 

9 Specified effect = 1 

10 

11 Risk Type = Estimated standard deviations from the control mean 

12 

13 Confidence level = 0.95 

14 

15 BMD = 27884.5 

16 

17 BMDL = 7907.26 

18 

19 

20 

21 E.2.48.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 5

 10

 15

 20

 25

 30

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:30 11/20 2009

BMDL BMD

 

Power

22 

23 

24 

25 E.2.48.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

26 Unrestricted 

27 

28 

29 ==================================================================== 

30 Power Model. (Version: 2.15; Date: 04/07/2008) 

31 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_plasma_FT4.(d) 

32 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_plasma_FT4.plt 

33 Fri Nov 20 12:30:13 2009 

34 ==================================================================== 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-323 —DO NOT CITE OR QUOTE 

1 Tbl3, plasma FT4 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the response function is: 

5 

6 Y[dose] = control + slope * dose^power 

7 

8 

9 Dependent variable = Mean 

10 Independent variable = Dose 

11 The power is not restricted 

12 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

13 

14 Total number of dose groups = 6 

15 Total number of records with missing values = 0 

16 Maximum number of iterations = 250 

17 Relative Function Convergence has been set to: 1e-008 

18 Parameter Convergence has been set to: 1e-008 

19 

20 

21 

22 Default Initial Parameter Values 

23 lalpha = 3.38957 

24 rho = 0 

25 control = 24.5 

26 slope = -0.0256219 

27 power = 0.537235 

28 

29 

30 Asymptotic Correlation Matrix of Parameter Estimates 

31 

32 lalpha rho control slope power 

33 

34 lalpha 1 -1 0.099 -0.069 -0.06 

35 

36 rho -1 1 -0.1 0.069 0.06 

37 

38 control 0.099 -0.1 1 -0.78 -0.75 

39 

40 slope -0.069 0.069 -0.78 1 1 

41 

42 power -0.06 0.06 -0.75 1 1 

43 

44 

45 

46 Parameter Estimates 

47 

48 95.0% Wald Confidence Interval 

49 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

50 lalpha 1.99957 2.14696 -2.20839 6.20753 

51 rho 0.44594 0.730207 -0.98524 1.87712 

52 control 24.0444 1.65932 20.7922 27.2966 

53 slope -0.0113184 0.0287697 -0.0677059 0.0450692 

54 power 0.601415 0.209424 0.190952 1.01188 

55 

56 

57 

58 Table of Data and Estimated Values of Interest 

59 

60 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

61 ------ --- -------- -------- ----------- ----------- ---------- 

62 

63 0 8 23.4 24 3.11 5.52 -0.33 

64 3969 8 24.5 22.4 5.66 5.44 1.1 

65 6479 8 22.4 21.8 2.83 5.4 0.3 

66 9968 8 19.3 21.2 9.33 5.37 -0.985 

67 4.761e+004 8 16.3 16.7 4.24 5.09 -0.212 

68 1.378e+005 8 10.3 10.1 4.81 4.55 0.129 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-324 —DO NOT CITE OR QUOTE 

1 

2 Model Descriptions for likelihoods calculated 

3 

4 

5 Model A1: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 

8 Model A2: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma(i)^2 

10 

11 Model A3: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

13 Model A3 uses any fixed variance parameters that 

14 were specified by the user 

15 

16 Model R: Yi = Mu + e(i) 

17 Var{e(i)} = Sigma^2 

18 

19 

20 Likelihoods of Interest 

21 

22 Model Log(likelihood) # Param's AIC 

23 A1 -102.145036 7 218.290071 

24 A2 -94.049629 12 212.099258 

25 A3 -102.143023 8 220.286046 

26 fitted -103.295375 5 216.590750 

27 R -117.817514 2 239.635028 

28 

29 

30 Explanation of Tests 

31 

32 Test 1: Do responses and/or variances differ among Dose levels? 

33 (A2 vs. R) 

34 Test 2: Are Variances Homogeneous? (A1 vs A2) 

35 Test 3: Are variances adequately modeled? (A2 vs. A3) 

36 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

37 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

38 

39 Tests of Interest 

40 

41 Test -2*log(Likelihood Ratio) Test df p-value 

42 

43 Test 1 47.5358 10 <.0001 

44 Test 2 16.1908 5 0.00632 

45 Test 3 16.1868 4 0.002778 

46 Test 4 2.3047 3 0.5116 

47 

48 The p-value for Test 1 is less than .05. There appears to be a 

49 difference between response and/or variances among the dose levels 

50 It seems appropriate to model the data 

51 

52 The p-value for Test 2 is less than .1. A non-homogeneous variance 

53 model appears to be appropriate 

54 

55 The p-value for Test 3 is less than .1. You may want to consider a 

56 different variance model 

57 

58 The p-value for Test 4 is greater than .1. The model chosen seems 

59 to adequately describe the data 

60 

61 

62 Benchmark Dose Computation 

63 

64 Specified effect = 1 

65 

66 Risk Type = Estimated standard deviations from the control mean 

67 

68 Confidence level = 0.95 

69 

70 BMD = 29513.9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-325 —DO NOT CITE OR QUOTE 

1 

2 

3 BMDL = 7158.08 

4 

5 

6 

7 E.2.49. Van Birgelen et al. (1995a): Plasma TT4 

8 E.2.49.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 4 0.94 9.91 0.04 241.35 5.6E+04 3.6E+04 nonconstant variance, 

power restricted ≥1 

exponential (M2) 4 0.94 9.91 0.04 241.35 5.6E+04 3.6E+04 nonconstant variance, 

power unrestricted 

exponential (M3) 4 0.94 9.91 0.04 241.35 5.6E+04 3.6E+04 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.94 9.91 0.04 241.35 5.6E+04 3.6E+04 nonconstant variance, 

power unrestricted 

exponential (M4) 3 0.94 9.33 0.03 242.77 3.6E+04 6.8E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.94 9.33 0.03 242.77 3.6E+04 6.8E+03 nonconstant variance, 

power unrestricted 

exponential (M5) 3 0.94 9.33 0.03 242.77 3.6E+04 5.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.94 9.33 0.03 242.77 3.6E+04 5.5E+03 nonconstant variance, 

power unrestricted 

Hill 3 0.94 5.45 0.14 238.89 9.4E+03 error nonconstant variance, n 

restricted >1, bound hit 

Hill 3 0.94 5.45 0.14 238.89 9.4E+03 error nonconstant variance, n 

unrestricted 

linear 4 0.94 10.33 0.04 241.77 6.6E+04 4.5E+04 nonconstant variance 

polynomial 4 0.94 10.33 0.04 241.77 6.6E+04 4.5E+04 nonconstant variance 

power 4 0.94 10.33 0.04 241.77 6.6E+04 4.5E+04 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.94 8.78 0.03 242.22 2.9E+04 5.4E+03 nonconstant variance, 

power unrestricted 

exponential (M2)

c 4 0.94 9.33 0.05 239.35 5.7E+04 3.9E+04 constant variance, 

power restricted ≥1 

exponential (M3) 4 0.94 9.33 0.05 239.35 5.7E+04 3.9E+04 constant variance, 

power restricted ≥1 

exponential (M4) 3 0.94 8.75 0.03 240.78 3.7E+04 9.1E+03 constant variance, 

power restricted ≥1 

exponential (M5) 3 0.94 8.75 0.03 240.78 3.7E+04 9.1E+03 constant variance, 

power restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-326 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M5) d 3 0.94 8.75 0.03 240.78 3.7E+04 9.1E+03 constant variance, 

power unrestricted 

Hill 3 0.94 6.31 0.10 238.33 9.5E+03 error constant variance, n 

restricted >1, bound hit 

Hill d 3 0.94 6.31 0.10 238.33 9.5E+03 error constant variance, n 

unrestricted 

linear 4 0.94 9.75 0.04 239.77 6.6E+04 4.8E+04 constant variance 

polynomial 4 0.94 9.75 0.04 239.77 6.6E+04 4.8E+04 constant variance 

power 4 0.94 9.75 0.04 239.77 6.6E+04 4.8E+04 

constant variance, 

power restricted ≥1, 

bound hit 

power d 3 0.94 8.21 0.04 240.24 3.0E+04 5.8E+03 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-327 —DO NOT CITE OR QUOTE 

1 E.2.49.2. Figure for Selected Model: Exponential (M2), Constant Variance, Power Restricted 

2 ≥1 

 20

 25

 30

 35

 40

 45

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

12:31 11/20 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.49.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_CV_BMR1_plasma_TT4.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 12:31:00 2009 

15 ==================================================================== 

16 

17 Tbl3, plasma TT4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-328 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 rho is set to 0. 

4 A constant variance model is fit. 

5 

6 Total number of dose groups = 6 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 2 

18 -------- -------- 

19 lnalpha 3.66719 

20 rho(S) 0 

21 a 43.47 

22 b 1.98277e-005 

23 c 0.558678 

24 d 1 

25 

26 (S) = Specified 

27 

28 

29 

30 Parameter Estimates 

31 

32 Variable Model 2 

33 -------- ------- 

34 lnalpha 3.84955 

35 rho 0 

36 a 40.4479 

37 b 1.38876e-005 

38 c 0.575097 

39 d 1 

40 

41 

42 Table of Stats From Input Data 

43 

44 Dose N Obs Mean Obs Std Dev 

45 ----- --- ---------- ------------- 

46 0 8 40.9 6.788 

47 3969 8 41.4 5.374 

48 6479 8 41.4 6.505 

49 9968 8 32.3 7.354 

50 4.761e+004 8 33.6 6.223 

51 1.378e+005 8 25.5 7.637 

52 

53 

54 Estimated Values of Interest 

55 

56 Dose Est Mean Est Std Scaled Residual 

57 ------ ---------- --------- ---------------- 

58 0 39.73 6.895 0.4797 

59 3969 39.2 6.895 0.901 

60 6479 38.87 6.895 1.036 

61 9968 38.42 6.895 -2.511 

62 4.761e+004 33.85 6.895 -0.1024 

63 1.378e+005 24.99 6.895 0.2106 

64 

65 

66 

67 Other models for which likelihoods are calculated: 

68 

69 Model A1: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-329 —DO NOT CITE OR QUOTE 

1 

2 Model A2: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma(i)^2 

4 

5 Model A3: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

7 

8 Model R: Yij = Mu + e(i) 

9 Var{e(ij)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) DF AIC 

15 ------- ----------------- ---- ------------ 

16 A1 -112.0125 7 238.025 

17 A2 -111.4015 12 246.8029 

18 A3 -112.0125 7 238.025 

19 R -127.4455 2 258.891 

20 2 -116.6748 3 239.3495 

21 

22 

23 Additive constant for all log-likelihoods = -44.11. This constant added to the 

24 above values gives the log-likelihood including the term that does not 

25 depend on the model parameters. 

26 

27 

28 Explanation of Tests 

29 

30 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

31 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

32 Test 3: Are variances adequately modeled? (A2 vs. A3) 

33 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

34 

35 

36 Tests of Interest 

37 

38 Test -2*log(Likelihood Ratio) D. F. p-value 

39 -------- ------------------------ ------ -------------- 

40 Test 1 32.09 10 0.0003871 

41 Test 2 1.222 5 0.9427 

42 Test 3 1.222 5 0.9427 

43 Test 4 9.325 4 0.05348 

44 

45 

46 The p-value for Test 1 is less than .05. There appears to be a 

47 difference between response and/or variances among the dose 

48 levels, it seems appropriate to model the data. 

49 

50 The p-value for Test 2 is greater than .1. A homogeneous 

51 variance model appears to be appropriate here. 

52 

53 The p-value for Test 3 is greater than .1. The modeled 

54 variance appears to be appropriate here. 

55 

56 The p-value for Test 4 is less than .1. Model 2 may not adequately 

57 describe the data; you may want to consider another model. 

58 

59 

60 Benchmark Dose Computations: 

61 

62 Specified Effect = 1.000000 

63 

64 Risk Type = Estimated standard deviations from control 

65 

66 Confidence Level = 0.950000 

67 

68 BMD = 56637.1 

69 

70 BMDL = 38643.8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-330 —DO NOT CITE OR QUOTE 

1 E.2.49.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

2 Unrestricted 

 20

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 30

 35

 40

 45

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:31 11/20 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.2.49.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

7 Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_CV_Unrest_BMR1_plasma_TT4.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 12:31:08 2009 

15 ==================================================================== 

16 

17 Tbl3, plasma TT4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-331 —DO NOT CITE OR QUOTE 

1 Data are assumed to be distributed: normally 

2 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

3 rho is set to 0. 

4 A constant variance model is fit. 

5 

6 Total number of dose groups = 6 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 5 

18 -------- -------- 

19 lnalpha 3.66719 

20 rho(S) 0 

21 a 43.47 

22 b 1.98277e-005 

23 c 0.558678 

24 d 1 

25 

26 (S) = Specified 

27 

28 

29 

30 Parameter Estimates 

31 

32 Variable Model 5 

33 -------- ------- 

34 lnalpha 3.84955 

35 rho 0 

36 a 40.4479 

37 b 1.38876e-005 

38 c 0.575097 

39 d 1 

40 

41 

42 Table of Stats From Input Data 

43 

44 Dose N Obs Mean Obs Std Dev 

45 ----- --- ---------- ------------- 

46 0 8 40.9 6.788 

47 3969 8 41.4 5.374 

48 6479 8 41.4 6.505 

49 9968 8 32.3 7.354 

50 4.761e+004 8 33.6 6.223 

51 1.378e+005 8 25.5 7.637 

52 

53 

54 Estimated Values of Interest 

55 

56 Dose Est Mean Est Std Scaled Residual 

57 ------ ---------- --------- ---------------- 

58 0 40.45 6.854 0.1866 

59 3969 39.53 6.854 0.7733 

60 6479 38.97 6.854 1.003 

61 9968 38.23 6.854 -2.446 

62 4.761e+004 32.13 6.854 0.6049 

63 1.378e+005 25.8 6.854 -0.1223 

64 

65 

66 

67 Other models for which likelihoods are calculated: 

68 

69 Model A1: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-332 —DO NOT CITE OR QUOTE 

1 

2 Model A2: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma(i)^2 

4 

5 Model A3: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

7 

8 Model R: Yij = Mu + e(i) 

9 Var{e(ij)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) DF AIC 

15 ------- ----------------- ---- ------------ 

16 A1 -112.0125 7 238.025 

17 A2 -111.4015 12 246.8029 

18 A3 -112.0125 7 238.025 

19 R -127.4455 2 258.891 

20 5 -116.3891 4 240.7782 

21 

22 

23 Additive constant for all log-likelihoods = -44.11. This constant added to the 

24 above values gives the log-likelihood including the term that does not 

25 depend on the model parameters. 

26 

27 

28 Explanation of Tests 

29 

30 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

31 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

32 Test 3: Are variances adequately modeled? (A2 vs. A3) 

33 

34 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

35 

36 

37 Tests of Interest 

38 

39 Test -2*log(Likelihood Ratio) D. F. p-value 

40 -------- ------------------------ ------ -------------- 

41 Test 1 32.09 10 0.0003871 

42 Test 2 1.222 5 0.9427 

43 Test 3 1.222 5 0.9427 

44 Test 7a 8.753 3 0.03276 

45 

46 

47 The p-value for Test 1 is less than .05. There appears to be a 

48 difference between response and/or variances among the dose 

49 levels, it seems appropriate to model the data. 

50 

51 The p-value for Test 2 is greater than .1. A homogeneous 

52 variance model appears to be appropriate here. 

53 

54 The p-value for Test 3 is greater than .1. The modeled 

55 variance appears to be appropriate here. 

56 

57 The p-value for Test 7a is less than .1. Model 5 may not adequately 

58 describe the data; you may want to consider another model. 

59 

60 

61 Benchmark Dose Computations: 

62 

63 Specified Effect = 1.000000 

64 

65 Risk Type = Estimated standard deviations from control 

66 

67 Confidence Level = 0.950000 

68 

69 BMD = 36636.4 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-333 —DO NOT CITE OR QUOTE 

1 BMDL = 9124.3 

2 

3 

4 E.2.49.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 20

 25

 30

 35

 40

 45

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Hill Model

12:31 11/20 2009

BMD

Hill

5 

6 

7 

8 E.2.49.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 

9 

10 

11 ==================================================================== 

12 Hill Model. (Version: 2.14; Date: 06/26/2008) 

13 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_CV_Unrest_BMR1_plasma_TT4.(d) 

14 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_CV_Unrest_BMR1_plasma_TT4.plt 

15 Fri Nov 20 12:31:10 2009 

16 ==================================================================== 

17 

18 Tbl3, plasma TT4 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the response function is: 

22 

23 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 rho is set to 0 

29 Power parameter is not restricted 

30 A constant variance model is fit 

31 

32 Total number of dose groups = 6 

33 Total number of records with missing values = 0 

34 Maximum number of iterations = 250 

35 Relative Function Convergence has been set to: 1e-008 

36 Parameter Convergence has been set to: 1e-008 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-334 —DO NOT CITE OR QUOTE 

1 

2 

3 

4 Default Initial Parameter Values 

5 alpha = 44.7333 

6 rho = 0 Specified 

7 intercept = 40.9 

8 v = -15.4 

9 n = 3.33301 

10 k = 9622.52 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -rho -n 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 alpha intercept v k 

20 

21 alpha 1 -6.6e-008 7.9e-008 -1.5e-007 

22 

23 intercept -6.6e-008 1 -0.63 -0.12 

24 

25 v 7.9e-008 -0.63 1 -0.29 

26 

27 k -1.5e-007 -0.12 -0.29 1 

28 

29 

30 

31 Parameter Estimates 

32 

33 95.0% Wald Confidence Interval 

34 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

35 alpha 44.6379 9.11167 26.7793 62.4964 

36 intercept 41.2386 1.36525 38.5627 43.9144 

37 v -11.689 2.1552 -15.9131 -7.46484 

38 n 18 NA 

39 k 9336.14 666.631 8029.56 10642.7 

40 

41 NA - Indicates that this parameter has hit a bound 

42 implied by some inequality constraint and thus 

43 has no standard error. 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 8 40.9 41.2 6.79 6.68 -0.143 

53 3969 8 41.4 41.2 5.37 6.68 0.0683 

54 6479 8 41.4 41.2 6.51 6.68 0.0752 

55 9968 8 32.3 32.3 7.35 6.68 -0.00058 

56 4.761e+004 8 33.6 29.5 6.22 6.68 1.71 

57 1.378e+005 8 25.5 29.5 7.64 6.68 -1.71 

58 

59 

60 

61 Model Descriptions for likelihoods calculated 

62 

63 

64 Model A1: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 

67 Model A2: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma(i)^2 

69 

70 Model A3: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-335 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma^2 

2 Model A3 uses any fixed variance parameters that 

3 were specified by the user 

4 

5 Model R: Yi = Mu + e(i) 

6 Var{e(i)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) # Param's AIC 

12 A1 -112.012501 7 238.025002 

13 A2 -111.401462 12 246.802924 

14 A3 -112.012501 7 238.025002 

15 fitted -115.165987 4 238.331973 

16 R -127.445484 2 258.890968 

17 

18 

19 Explanation of Tests 

20 

21 Test 1: Do responses and/or variances differ among Dose levels? 

22 (A2 vs. R) 

23 Test 2: Are Variances Homogeneous? (A1 vs A2) 

24 Test 3: Are variances adequately modeled? (A2 vs. A3) 

25 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

26 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

27 

28 Tests of Interest 

29 

30 Test -2*log(Likelihood Ratio) Test df p-value 

31 

32 Test 1 32.088 10 0.0003871 

33 Test 2 1.22208 5 0.9427 

34 Test 3 1.22208 5 0.9427 

35 Test 4 6.30697 3 0.09759 

36 

37 The p-value for Test 1 is less than .05. There appears to be a 

38 difference between response and/or variances among the dose levels 

39 It seems appropriate to model the data 

40 

41 The p-value for Test 2 is greater than .1. A homogeneous variance 

42 model appears to be appropriate here 

43 

44 

45 The p-value for Test 3 is greater than .1. The modeled variance appears 

46 to be appropriate here 

47 

48 The p-value for Test 4 is less than .1. You may want to try a different 

49 model 

50 

51 

52 Benchmark Dose Computation 

53 

54 Specified effect = 1 

55 

56 Risk Type = Estimated standard deviations from the control mean 

57 

58 Confidence level = 0.95 

59 

60 BMD = 9486.87 

61 

62 

63 BMDL computation failed. 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-336 —DO NOT CITE OR QUOTE 

1 E.2.49.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 20

 25

 30

 35

 40

 45

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:31 11/20 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.2.49.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

6 

7 

8 ==================================================================== 

9 Power Model. (Version: 2.15; Date: 04/07/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_CV_Unrest_BMR1_plasma_TT4.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_CV_Unrest_BMR1_plasma_TT4.plt 

12 Fri Nov 20 12:31:11 2009 

13 ==================================================================== 

14 

15 Tbl3, plasma TT4 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = control + slope * dose^power 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 The power is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-337 —DO NOT CITE OR QUOTE 

1 alpha = 44.7333 

2 rho = 0 Specified 

3 control = 41.4 

4 slope = -1.4001 

5 power = 0.189211 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha control slope power 

15 

16 alpha 1 -5.9e-009 -5e-011 -3.8e-010 

17 

18 control -5.9e-009 1 -0.78 -0.75 

19 

20 slope -5e-011 -0.78 1 1 

21 

22 power -3.8e-010 -0.75 1 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 46.4461 9.48077 27.8641 65.028 

31 control 41.4607 2.18095 37.1861 45.7352 

32 slope -0.0241896 0.0653588 -0.15229 0.103911 

33 power 0.547925 0.223428 0.110013 0.985836 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 8 40.9 41.5 6.79 6.82 -0.233 

43 3969 8 41.4 39.2 5.37 6.82 0.916 

44 6479 8 41.4 38.5 6.51 6.82 1.21 

45 9968 8 32.3 37.7 7.35 6.82 -2.24 

46 4.761e+004 8 33.6 32.6 6.22 6.82 0.408 

47 1.378e+005 8 25.5 25.6 7.64 6.82 -0.0527 

48 

49 

50 

51 Model Descriptions for likelihoods calculated 

52 

53 

54 Model A1: Yij = Mu(i) + e(ij) 

55 Var{e(ij)} = Sigma^2 

56 

57 Model A2: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma(i)^2 

59 

60 Model A3: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 Model A3 uses any fixed variance parameters that 

63 were specified by the user 

64 

65 Model R: Yi = Mu + e(i) 

66 Var{e(i)} = Sigma^2 

67 

68 

69 Likelihoods of Interest 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-338 —DO NOT CITE OR QUOTE 

1 Model Log(likelihood) # Param's AIC 

2 A1 -112.012501 7 238.025002 

3 A2 -111.401462 12 246.802924 

4 A3 -112.012501 7 238.025002 

5 fitted -116.119011 4 240.238023 

6 R -127.445484 2 258.890968 

7 

8 

9 Explanation of Tests 

10 

11 Test 1: Do responses and/or variances differ among Dose levels? 

12 (A2 vs. R) 

13 Test 2: Are Variances Homogeneous? (A1 vs A2) 

14 Test 3: Are variances adequately modeled? (A2 vs. A3) 

15 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

16 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

17 

18 Tests of Interest 

19 

20 Test -2*log(Likelihood Ratio) Test df p-value 

21 

22 Test 1 32.088 10 0.0003871 

23 Test 2 1.22208 5 0.9427 

24 Test 3 1.22208 5 0.9427 

25 Test 4 8.21302 3 0.04181 

26 

27 The p-value for Test 1 is less than .05. There appears to be a 

28 difference between response and/or variances among the dose levels 

29 It seems appropriate to model the data 

30 

31 The p-value for Test 2 is greater than .1. A homogeneous variance 

32 model appears to be appropriate here 

33 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is less than .1. You may want to try a different 

39 model 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 29589.5 

51 

52 

53 BMDL = 5826.38 

54 

55 

56 E.2.50. White et al. (1986): CH50 

57 E.2.50.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 5 0.09 19.19 0.00 389.66 1.1E+04 6.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 5 0.09 19.19 0.00 389.66 1.1E+04 6.9E+03 nonconstant variance, 

power restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-339 —DO NOT CITE OR QUOTE 

exponential (M4) 4 0.09 18.15 0.00 390.63 7.8E+03 2.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 4 0.09 18.15 0.00 390.63 7.8E+03 2.9E+03 nonconstant variance, 

power restricted ≥1 

Hill c 4 0.09 17.12 0.00 389.60 4.8E+03 8.3E+02 

nonconstant variance, 

n restricted >1, bound 

hit 

Hill d 3 0.09 7.05 0.07 381.53 8.2E+01 7.6E+01 nonconstant variance, n 

unrestricted 

linear 5 0.09 23.97 0.00 394.45 1.9E+04 1.4E+04 nonconstant variance 

polynomial 5 0.09 23.97 0.00 394.45 1.9E+04 1.4E+04 nonconstant variance 

power 5 0.09 23.97 0.00 394.45 1.9E+04 1.4E+04 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 5 0.09 19.89 0.00 388.58 9.6E+03 6.5E+03 constant variance, 

power restricted ≥1 

exponential (M3) 5 0.09 19.89 0.00 388.58 9.6E+03 6.5E+03 constant variance, 

power restricted ≥1 

exponential (M4) 4 0.09 18.80 0.00 389.48 6.5E+03 2.2E+03 constant variance, 

power restricted ≥1 

exponential (M5) 4 0.09 18.80 0.00 389.48 6.5E+03 2.2E+03 constant variance, 

power restricted ≥1 

Hill 4 0.09 17.39 0.00 388.07 3.3E+03 8.4E+02 constant variance, n 

restricted >1, bound hit 

Hill 3 0.09 7.07 0.07 379.75 1.5E+02 6.3E+00 constant variance, n 

unrestricted 

linear 5 0.09 24.48 0.00 393.16 1.8E+04 1.4E+04 constant variance 

polynomial 5 0.09 24.48 0.00 393.16 1.8E+04 1.4E+04 constant variance 

power 5 0.09 24.48 0.00 393.16 1.8E+04 1.4E+04 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-340 —DO NOT CITE OR QUOTE 

1 E.2.50.2. Figure for Selected Model: Hill, Nonconstant Variance, n Restricted >1, Bound Hit 

 0

 20

 40

 60

 80

 100

 0 10000 20000 30000 40000 50000

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:28 11/16 2009

BMDL BMD

 

Hill

2 

3 

4 

5 E.2.50.3. Output File for Selected Model: Hill, Nonconstant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_BMR1_CH50.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_BMR1_CH50.plt 

13 Mon Nov 16 13:28:23 2009 

14 ==================================================================== 

15 

16 [insert study notes] 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter restricted to be greater than 1 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 7 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-341 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 5.60999 

3 rho = 0 

4 intercept = 91 

5 v = -74 

6 n = 0.118036 

7 k = 602.74 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -n 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 lalpha rho intercept v k 

17 

18 lalpha 1 -0.99 0.27 0.23 -0.32 

19 

20 rho -0.99 1 -0.28 -0.24 0.33 

21 

22 intercept 0.27 -0.28 1 0.39 -0.78 

23 

24 v 0.23 -0.24 0.39 1 -0.85 

25 

26 k -0.32 0.33 -0.78 -0.85 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence Interval 

33 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

34 lalpha 4.581 1.66271 1.32215 7.83986 

35 rho 0.312931 0.431612 -0.533012 1.15887 

36 intercept 74.6365 6.33658 62.217 87.056 

37 v -66.2095 14.7868 -95.1911 -37.2278 

38 n 1 NA 

39 k 11475.6 11747.8 -11549.6 34500.8 

40 

41 NA - Indicates that this parameter has hit a bound 

42 implied by some inequality constraint and thus 

43 has no standard error. 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 8 91 74.6 14.1 19.4 2.39 

53 602.7 8 54 71.3 8.49 19.3 -2.54 

54 2250 8 63 63.8 11.3 18.9 -0.117 

55 3934 8 56 57.7 25.5 18.6 -0.263 

56 1.477e+004 8 41 37.4 17 17.4 0.589 

57 2.684e+004 8 32 28.3 17 16.7 0.636 

58 4.99e+004 8 17 20.8 17 15.9 -0.678 

59 

60 

61 

62 Model Descriptions for likelihoods calculated 

63 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-342 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

3 Model A3 uses any fixed variance parameters that 

4 were specified by the user 

5 

6 Model R: Yi = Mu + e(i) 

7 Var{e(i)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) # Param's AIC 

13 A1 -181.340979 8 378.681959 

14 A2 -175.820265 14 379.640529 

15 A3 -181.238690 9 380.477380 

16 fitted -189.800260 5 389.600520 

17 R -212.367055 2 428.734109 

18 

19 

20 Explanation of Tests 

21 

22 Test 1: Do responses and/or variances differ among Dose levels? 

23 (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A1 vs A2) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

27 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

28 

29 Tests of Interest 

30 

31 Test -2*log(Likelihood Ratio) Test df p-value 

32 

33 Test 1 73.0936 12 <.0001 

34 Test 2 11.0414 6 0.0871 

35 Test 3 10.8369 5 0.05471 

36 Test 4 17.1231 4 0.001829 

37 

38 The p-value for Test 1 is less than .05. There appears to be a 

39 difference between response and/or variances among the dose levels 

40 It seems appropriate to model the data 

41 

42 The p-value for Test 2 is less than .1. A non-homogeneous variance 

43 model appears to be appropriate 

44 

45 The p-value for Test 3 is less than .1. You may want to consider a 

46 different variance model 

47 

48 The p-value for Test 4 is less than .1. You may want to try a different 

49 model 

50 

51 

52 Benchmark Dose Computation 

53 

54 Specified effect = 1 

55 

56 Risk Type = Estimated standard deviations from the control mean 

57 

58 Confidence level = 0.95 

59 

60 BMD = 4756.06 

61 

62 BMDL = 825.553 

63 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-343 —DO NOT CITE OR QUOTE 

1 E.2.50.4. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 20

 40

 60

 80

 100

 0 10000 20000 30000 40000 50000

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:28 11/16 2009

BMDBMDL

 

Hill

2 

3 

4 

5 E.2.50.5. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_CH50.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_CH50.plt 

12 Mon Nov 16 13:28:23 2009 

13 ==================================================================== 

14 

15 [insert study notes] 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Power parameter is not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

27 

28 Total number of dose groups = 7 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 5.60999 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-344 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 intercept = 91 

3 v = -74 

4 n = 0.118036 

5 k = 602.74 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho intercept v n k 

11 

12 lalpha 1 -1 0.16 0.19 -0.4 -0.013 

13 

14 rho -1 1 -0.16 -0.19 0.4 0.011 

15 

16 intercept 0.16 -0.16 1 0.15 -0.58 0.015 

17 

18 v 0.19 -0.19 0.15 1 -0.011 -0.93 

19 

20 n -0.4 0.4 -0.58 -0.011 1 -0.36 

21 

22 k -0.013 0.011 0.015 -0.93 -0.36 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha 6.54258 2.08981 2.44663 10.6385 

31 rho -0.246247 0.541898 -1.30835 0.815854 

32 intercept 89.6313 5.59369 78.6679 100.595 

33 v -615.173 706.037 -1998.98 768.633 

34 n 0.246754 0.0587686 0.13157 0.361938 

35 k 2.44083e+008 1.35075e+009 -2.40334e+009 2.89151e+009 

36 

37 

38 

39 Table of Data and Estimated Values of Interest 

40 

41 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

42 ------ --- -------- -------- ----------- ----------- ---------- 

43 

44 0 8 91 89.6 14.1 15.1 0.256 

45 602.7 8 54 65.2 8.49 15.8 -2.01 

46 2250 8 63 56.3 11.3 16 1.17 

47 3934 8 56 51.7 25.5 16.2 0.747 

48 1.477e+004 8 41 38.3 17 16.8 0.453 

49 2.684e+004 8 32 30.9 17 17.3 0.175 

50 4.99e+004 8 17 22.3 17 18 -0.833 

51 

52 

53 

54 Model Descriptions for likelihoods calculated 

55 

56 

57 Model A1: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 

60 Model A2: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma(i)^2 

62 

63 Model A3: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

65 Model A3 uses any fixed variance parameters that 

66 were specified by the user 

67 

68 Model R: Yi = Mu + e(i) 

69 Var{e(i)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-345 —DO NOT CITE OR QUOTE 

1 

2 Likelihoods of Interest 

3 

4 Model Log(likelihood) # Param's AIC 

5 A1 -181.340979 8 378.681959 

6 A2 -175.820265 14 379.640529 

7 A3 -181.238690 9 380.477380 

8 fitted -184.762700 6 381.525401 

9 R -212.367055 2 428.734109 

10 

11 

12 Explanation of Tests 

13 

14 Test 1: Do responses and/or variances differ among Dose levels? 

15 (A2 vs. R) 

16 Test 2: Are Variances Homogeneous? (A1 vs A2) 

17 Test 3: Are variances adequately modeled? (A2 vs. A3) 

18 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

19 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

20 

21 Tests of Interest 

22 

23 Test -2*log(Likelihood Ratio) Test df p-value 

24 

25 Test 1 73.0936 12 <.0001 

26 Test 2 11.0414 6 0.0871 

27 Test 3 10.8369 5 0.05471 

28 Test 4 7.04802 3 0.07038 

29 

30 The p-value for Test 1 is less than .05. There appears to be a 

31 difference between response and/or variances among the dose levels 

32 It seems appropriate to model the data 

33 

34 The p-value for Test 2 is less than .1. A non-homogeneous variance 

35 model appears to be appropriate 

36 

37 The p-value for Test 3 is less than .1. You may want to consider a 

38 different variance model 

39 

40 The p-value for Test 4 is less than .1. You may want to try a different 

41 model 

42 

43 

44 Benchmark Dose Computation 

45 

46 Specified effect = 1 

47 

48 Risk Type = Estimated standard deviations from the control mean 

49 

50 Confidence level = 0.95 

51 

52 BMD = 81.6596 

53 

54 BMDL = 75.5039 

55 

56 

57 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-346 —DO NOT CITE OR QUOTE 

1 E.3. ADMINISTERED DOSE BMDS RESULTS 

2 E.3.1. Amin et al. (2000): Saccharin Consumed, Female (0.25%) 

3 E.3.1.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

linear c 1 0.00 0.84 0.36 179.70 8.8E+01 5.9E+01 nonconstant variance 

polynomial 1 0.00 0.84 0.36 179.70 8.8E+01 5.9E+01 nonconstant variance 

power 1 0.00 0.84 0.36 179.70 8.8E+01 5.9E+01 

nonconstant variance, 

power restricted ≥1, bound 

hit 

linear 1 0.00 0.12 0.73 191.80 6.6E+01 4.3E+01 constant variance 

polynomial 1 0.00 0.12 0.73 191.80 6.6E+01 4.3E+01 constant variance 

power 1 0.00 0.12 0.73 191.80 6.6E+01 4.3E+01 constant variance, power 

restricted ≥1, bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-347 —DO NOT CITE OR QUOTE 

1 E.3.1.2. Figure for Selected Model: Linear, Nonconstant Variance 

 5

 10

 15

 20

 25

 30

 35

 40

 45

 50

 0 20 40 60 80 100

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:41 11/11 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.3.1.3. Output file for Selected Model: Linear, Nonconstant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Linear_BMR1_25_s_c.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Linear_BMR1_25_s_c.plt 

12 Wed Nov 11 13:41:21 2009 

13 ==================================================================== 

14 

15 Rel Male Thymus wt, Tbl 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Signs of the polynomial coefficients are not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 3 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-348 —DO NOT CITE OR QUOTE 

1 lalpha = 5.29482 

2 rho = 0 

3 beta_0 = 30.8266 

4 beta_1 = -0.204134 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 lalpha rho beta_0 beta_1 

10 

11 lalpha 1 -0.99 -0.016 0.03 

12 

13 rho -0.99 1 0.013 -0.026 

14 

15 beta_0 -0.016 0.013 1 -0.94 

16 

17 beta_1 0.03 -0.026 -0.94 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 lalpha -2.55843 1.66185 -5.8156 0.698746 

26 rho 2.42056 0.545617 1.35117 3.48995 

27 beta_0 30.3968 4.03582 22.4868 38.3069 

28 beta_1 -0.196699 0.0443352 -0.283594 -0.109803 

29 

30 

31 

32 Table of Data and Estimated Values of Interest 

33 

34 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

35 ------ --- -------- -------- ----------- ----------- ---------- 

36 

37 0 10 31.7 30.4 20.6 17.3 0.233 

38 25 10 24.6 25.5 12 14 -0.2 

39 100 10 10.7 10.7 5.33 4.92 -0.0204 

40 

41 

42 

43 Model Descriptions for likelihoods calculated 

44 

45 

46 Model A1: Yij = Mu(i) + e(ij) 

47 Var{e(ij)} = Sigma^2 

48 

49 Model A2: Yij = Mu(i) + e(ij) 

50 Var{e(ij)} = Sigma(i)^2 

51 

52 Model A3: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

54 Model A3 uses any fixed variance parameters that 

55 were specified by the user 

56 

57 Model R: Yi = Mu + e(i) 

58 Var{e(i)} = Sigma^2 

59 

60 

61 Likelihoods of Interest 

62 

63 Model Log(likelihood) # Param's AIC 

64 A1 -92.841935 4 193.683870 

65 A2 -85.255316 6 182.510632 

66 A3 -85.429148 5 180.858295 

67 fitted -85.851107 4 179.702213 

68 R -98.136607 2 200.273213 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-349 —DO NOT CITE OR QUOTE 

1 Explanation of Tests 

2 

3 Test 1: Do responses and/or variances differ among Dose levels? 

4 (A2 vs. R) 

5 Test 2: Are Variances Homogeneous? (A1 vs A2) 

6 Test 3: Are variances adequately modeled? (A2 vs. A3) 

7 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

8 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

9 

10 Tests of Interest 

11 

12 Test -2*log(Likelihood Ratio) Test df p-value 

13 

14 Test 1 25.7626 4 <.0001 

15 Test 2 15.1732 2 0.0005072 

16 Test 3 0.347663 1 0.5554 

17 Test 4 0.843918 1 0.3583 

18 

19 The p-value for Test 1 is less than .05. There appears to be a 

20 difference between response and/or variances among the dose levels 

21 It seems appropriate to model the data 

22 

23 The p-value for Test 2 is less than .1. A non-homogeneous variance 

24 model appears to be appropriate 

25 

26 The p-value for Test 3 is greater than .1. The modeled variance appears 

27 to be appropriate here 

28 

29 The p-value for Test 4 is greater than .1. The model chosen seems 

30 to adequately describe the data 

31 

32 

33 Benchmark Dose Computation 

34 

35 Specified effect = 1 

36 

37 Risk Type = Estimated standard deviations from the control mean 

38 

39 Confidence level = 0.95 

40 

41 BMD = 88.1623 

42 

43 

44 BMDL = 58.9029 

45 

46 

47 

48 E.3.2. Amin et al. (2000): Saccharin Consumed, Female (0.50%) 

49 E.3.2.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

linear c 1 <.0001 4.68 0.03 159.74 9.9E+01 6.4E+01 nonconstant 

variance 

polynomial 1 <.0001 4.68 0.03 159.74 9.9E+01 6.4E+01 nonconstant variance 

power 1 <.0001 4.68 0.03 159.74 9.9E+01 6.4E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

linear 1 <.0001 2.57 0.11 175.96 6.5E+01 4.3E+01 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-350 —DO NOT CITE OR QUOTE 

polynomial 1 <.0001 2.57 0.11 175.96 6.5E+01 4.3E+01 constant variance 

power 1 <.0001 2.57 0.11 175.96 6.5E+01 4.3E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

1 

2 

3 E.3.2.2. Figure for Selected Model: Linear, Nonconstant Variance 

 0

 5

 10

 15

 20

 25

 30

 35

 0 20 40 60 80 100

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:41 11/11 2009

BMDL BMD

 

Linear

4 

5 

6 

7 E.3.2.3. Output File for Selected Model: Linear, Nonconstant Variance 

8 

9 

10 ==================================================================== 

11 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

12 Input Data File: C:\USEPA\BMDS21\AD\Linear_BMR1_50_s_c.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Linear_BMR1_50_s_c.plt 

14 Wed Nov 11 13:41:42 2009 

15 ==================================================================== 

16 

17 Rel Male Thymus wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

23 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-351 —DO NOT CITE OR QUOTE 

1 

2 Dependent variable = Mean 

3 Independent variable = Dose 

4 Signs of the polynomial coefficients are not restricted 

5 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

6 

7 Total number of dose groups = 3 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 

14 

15 Default Initial Parameter Values 

16 lalpha = 4.68512 

17 rho = 0 

18 beta_0 = 19.3484 

19 beta_1 = -0.158141 

20 

21 

22 Asymptotic Correlation Matrix of Parameter Estimates 

23 

24 lalpha rho beta_0 beta_1 

25 

26 lalpha 1 -0.97 0.018 -0.0021 

27 

28 rho -0.97 1 -0.027 0.014 

29 

30 beta_0 0.018 -0.027 1 -0.95 

31 

32 beta_1 -0.0021 0.014 -0.95 1 

33 

34 

35 

36 Parameter Estimates 

37 

38 95.0% Wald Confidence Interval 

39 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

40 lalpha -0.997428 0.992786 -2.94325 0.948397 

41 rho 2.13634 0.404989 1.34257 2.9301 

42 beta_0 18.1144 3.10302 12.0326 24.1962 

43 beta_1 -0.135736 0.0331501 -0.200709 -0.0707631 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 10 22.4 18.1 16 13.4 1 

53 25 10 11.4 14.7 7.66 10.7 -0.983 

54 100 10 4.54 4.54 3.33 3.06 -0.00393 

55 

56 

57 

58 Model Descriptions for likelihoods calculated 

59 

60 

61 Model A1: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 

64 Model A2: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma(i)^2 

66 

67 Model A3: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

69 Model A3 uses any fixed variance parameters that 

70 were specified by the user 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-352 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yi = Mu + e(i) 

3 Var{e(i)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) # Param's AIC 

9 A1 -83.696404 4 175.392808 

10 A2 -73.511830 6 159.023660 

11 A3 -73.530233 5 157.060467 

12 fitted -75.868688 4 159.737377 

13 R -90.294746 2 184.589492 

14 

15 

16 Explanation of Tests 

17 

18 Test 1: Do responses and/or variances differ among Dose levels? 

19 (A2 vs. R) 

20 Test 2: Are Variances Homogeneous? (A1 vs A2) 

21 Test 3: Are variances adequately modeled? (A2 vs. A3) 

22 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

23 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

24 

25 Tests of Interest 

26 

27 Test -2*log(Likelihood Ratio) Test df p-value 

28 

29 Test 1 33.5658 4 <.0001 

30 Test 2 20.3691 2 <.0001 

31 Test 3 0.0368066 1 0.8479 

32 Test 4 4.67691 1 0.03057 

33 

34 The p-value for Test 1 is less than .05. There appears to be a 

35 difference between response and/or variances among the dose levels 

36 It seems appropriate to model the data 

37 

38 The p-value for Test 2 is less than .1. A non-homogeneous variance 

39 model appears to be appropriate 

40 

41 The p-value for Test 3 is greater than .1. The modeled variance appears 

42 to be appropriate here 

43 

44 The p-value for Test 4 is less than .1. You may want to try a different 

45 model 

46 

47 

48 Benchmark Dose Computation 

49 

50 Specified effect = 1 

51 

52 Risk Type = Estimated standard deviations from the control mean 

53 

54 Confidence level = 0.95 

55 

56 BMD = 98.7409 

57 

58 

59 BMDL = 64.169 

60 

61 

62 

63 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-353 —DO NOT CITE OR QUOTE 

1 E.3.3. Amin et al. (2000): Saccharin Preference Ratio, Female (0.25%) 

2 E.3.3.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

linear c 1 0.01 9.80 0.00 228.09 1.3E+02 6.1E+01 nonconstant variance 

polynomial 1 0.01 9.80 0.00 228.09 1.3E+02 6.1E+01 nonconstant variance 

power 1 0.01 9.80 0.00 228.09 1.3E+02 6.1E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

linear 1 0.01 3.36 0.07 226.51 1.1E+02 6.1E+01 constant variance 

polynomial 1 0.01 3.36 0.07 226.51 1.1E+02 6.1E+01 constant variance 

power 1 0.01 3.36 0.07 226.51 1.1E+02 6.1E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 

5 E.3.3.2. Figure for Selected Model: Linear, Nonconstant Variance 

 30

 40

 50

 60

 70

 80

 90

 0 20 40 60 80 100 120

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:42 11/11 2009

BMDL BMD

 

Linear

6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-354 —DO NOT CITE OR QUOTE 

1 E.3.3.3. Output File for Selected Model: Linear, Nonconstant Variance 

2 

3 

4 ==================================================================== 

5 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\Linear_BMR1_25_s_p_f.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Linear_BMR1_25_s_p_f.plt 

8 Wed Nov 11 13:42:05 2009 

9 ==================================================================== 

10 

11 Rel Male Thymus wt Tbl 2 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Signs of the polynomial coefficients are not restricted 

22 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

23 

24 Total number of dose groups = 3 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 Default Initial Parameter Values 

33 lalpha = 6.34368 

34 rho = 0 

35 beta_0 = 74.2008 

36 beta_1 = -0.219781 

37 

38 

39 Asymptotic Correlation Matrix of Parameter Estimates 

40 

41 lalpha rho beta_0 beta_1 

42 

43 lalpha 1 -1 0.2 -0.28 

44 

45 rho -1 1 -0.19 0.28 

46 

47 beta_0 0.2 -0.19 1 -0.76 

48 

49 beta_1 -0.28 0.28 -0.76 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 lalpha 0.338774 9.23768 -17.7667 18.4443 

58 rho 1.43998 2.21674 -2.90476 5.78472 

59 beta_0 73.6633 6.6623 60.6054 86.7211 

60 beta_1 -0.207175 0.101074 -0.405276 -0.00907442 

61 

62 

63 

64 Table of Data and Estimated Values of Interest 

65 

66 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

67 ------ --- -------- -------- ----------- ----------- ---------- 

68 

69 0 10 82.1 73.7 13.3 26.2 1.02 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-355 —DO NOT CITE OR QUOTE 

1 25 10 58.1 68.5 33.9 24.8 -1.32 

2 100 10 54.9 52.9 19.5 20.6 0.295 

3 

4 

5 

6 Model Descriptions for likelihoods calculated 

7 

8 

9 Model A1: Yij = Mu(i) + e(ij) 

10 Var{e(ij)} = Sigma^2 

11 

12 Model A2: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma(i)^2 

14 

15 Model A3: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

17 Model A3 uses any fixed variance parameters that 

18 were specified by the user 

19 

20 Model R: Yi = Mu + e(i) 

21 Var{e(i)} = Sigma^2 

22 

23 

24 Likelihoods of Interest 

25 

26 Model Log(likelihood) # Param's AIC 

27 A1 -108.574798 4 225.149597 

28 A2 -104.269377 6 220.538754 

29 A3 -105.147952 5 220.295903 

30 fitted -110.046917 4 228.093834 

31 R -112.382522 2 228.765045 

32 

33 

34 Explanation of Tests 

35 

36 Test 1: Do responses and/or variances differ among Dose levels? 

37 (A2 vs. R) 

38 Test 2: Are Variances Homogeneous? (A1 vs A2) 

39 Test 3: Are variances adequately modeled? (A2 vs. A3) 

40 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

41 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

42 

43 Tests of Interest 

44 

45 Test -2*log(Likelihood Ratio) Test df p-value 

46 

47 Test 1 16.2263 4 0.00273 

48 Test 2 8.61084 2 0.0135 

49 Test 3 1.75715 1 0.185 

50 Test 4 9.79793 1 0.001747 

51 

52 The p-value for Test 1 is less than .05. There appears to be a 

53 difference between response and/or variances among the dose levels 

54 It seems appropriate to model the data 

55 

56 The p-value for Test 2 is less than .1. A non-homogeneous variance 

57 model appears to be appropriate 

58 

59 The p-value for Test 3 is greater than .1. The modeled variance appears 

60 to be appropriate here 

61 

62 The p-value for Test 4 is less than .1. You may want to try a different 

63 model 

64 

65 

66 Benchmark Dose Computation 

67 

68 Specified effect = 1 

69 

70 Risk Type = Estimated standard deviations from the control mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-356 —DO NOT CITE OR QUOTE 

1 

2 Confidence level = 0.95 

3 

4 BMD = 126.365 

5 

6 

7 BMDL = 61.2812 

8 

9 

10 

11 E.3.4. Amin et al. (2000): Saccharin Preference Ratio, Female (0.50%) 

12 E.3.4.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

linear c 1 0.56 2.60 0.11 236.57 9.2E+01 5.2E+01 nonconstant variance 

polynomial 1 0.56 2.60 0.11 236.57 9.2E+01 5.2E+01 nonconstant variance 

power 1 0.56 2.60 0.11 236.57 9.2E+01 5.2E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

linear 1 0.56 2.92 0.09 234.94 8.3E+01 5.1E+01 constant variance 

polynomial 1 0.56 2.92 0.09 234.94 8.3E+01 5.1E+01 constant variance 

power 1 0.56 2.92 0.09 234.94 8.3E+01 5.1E+01 

constant variance, 

power restricted ≥1, 

bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

13 

14 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-357 —DO NOT CITE OR QUOTE 

1 E.3.4.2. Figure for Selected Model: Linear, Nonconstant Variance 

 10

 20

 30

 40

 50

 60

 70

 80

 90

 0 20 40 60 80 100

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:42 11/11 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.3.4.3. Output File for Selected Model: Linear, Nonconstant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Linear_BMR1_50_s_p_f.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Linear_BMR1_50_s_p_f.plt 

12 Wed Nov 11 13:42:27 2009 

13 ==================================================================== 

14 

15 Rel Male Thymus wt, Tbl 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Signs of the polynomial coefficients are not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 3 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-358 —DO NOT CITE OR QUOTE 

1 lalpha = 6.63936 

2 rho = 0 

3 beta_0 = 64.1858 

4 beta_1 = -0.332668 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 lalpha rho beta_0 beta_1 

10 

11 lalpha 1 -1 0.11 -0.18 

12 

13 rho -1 1 -0.11 0.18 

14 

15 beta_0 0.11 -0.11 1 -0.75 

16 

17 beta_1 -0.18 0.18 -0.75 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 lalpha 4.43902 3.53662 -2.49263 11.3707 

26 rho 0.562378 0.909867 -1.22093 2.34569 

27 beta_0 63.7204 7.49597 49.0286 78.4122 

28 beta_1 -0.320869 0.114882 -0.546034 -0.0957048 

29 

30 

31 

32 Table of Data and Estimated Values of Interest 

33 

34 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

35 ------ --- -------- -------- ----------- ----------- ---------- 

36 

37 0 10 72.7 63.7 24.6 29.6 0.962 

38 25 10 44.5 55.7 32.9 28.5 -1.24 

39 100 10 33.8 31.6 24.6 24.3 0.277 

40 

41 

42 

43 Model Descriptions for likelihoods calculated 

44 

45 

46 Model A1: Yij = Mu(i) + e(ij) 

47 Var{e(ij)} = Sigma^2 

48 

49 Model A2: Yij = Mu(i) + e(ij) 

50 Var{e(ij)} = Sigma(i)^2 

51 

52 Model A3: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

54 Model A3 uses any fixed variance parameters that 

55 were specified by the user 

56 

57 Model R: Yi = Mu + e(i) 

58 Var{e(i)} = Sigma^2 

59 

60 

61 Likelihoods of Interest 

62 

63 Model Log(likelihood) # Param's AIC 

64 A1 -113.009921 4 234.019841 

65 A2 -112.428886 6 236.857773 

66 A3 -112.984528 5 235.969055 

67 fitted -114.283840 4 236.567679 

68 R -117.976057 2 239.952114 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-359 —DO NOT CITE OR QUOTE 

1 Explanation of Tests 

2 

3 Test 1: Do responses and/or variances differ among Dose levels? 

4 (A2 vs. R) 

5 Test 2: Are Variances Homogeneous? (A1 vs A2) 

6 Test 3: Are variances adequately modeled? (A2 vs. A3) 

7 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

8 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

9 

10 Tests of Interest 

11 

12 Test -2*log(Likelihood Ratio) Test df p-value 

13 

14 Test 1 11.0943 4 0.02552 

15 Test 2 1.16207 2 0.5593 

16 Test 3 1.11128 1 0.2918 

17 Test 4 2.59862 1 0.107 

18 

19 The p-value for Test 1 is less than .05. There appears to be a 

20 difference between response and/or variances among the dose levels 

21 It seems appropriate to model the data 

22 

23 The p-value for Test 2 is greater than .1. Consider running a 

24 homogeneous model 

25 

26 The p-value for Test 3 is greater than .1. The modeled variance appears 

27 to be appropriate here 

28 

29 The p-value for Test 4 is greater than .1. The model chosen seems 

30 to adequately describe the data 

31 

32 

33 Benchmark Dose Computation 

34 

35 Specified effect = 1 

36 

37 Risk Type = Estimated standard deviations from the control mean 

38 

39 Confidence level = 0.95 

40 

41 BMD = 92.2435 

42 

43 

44 BMDL = 51.5208 

45 

46 

47 

48 E.3.5. Bell et al. (2007): Balano-Preputial Separation in Male Pups (10% Extra Risk) 

49 E.3.5.1. Summary Table of BMDS modeling results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ

 2

 pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 2 1.99 0.37 113.51 7.3E+00 4.7E+00 power restricted ≥1, bound 

hit 

logistic 2 2.88 0.24 114.85 1.5E+01 1.1E+01 

log-logistic b 2 1.57 0.46 112.95 5.2E+00 2.9E+00 slope restricted ≥1, 

bound hit 

log-logistic c 1 0.49 0.48 113.91 2.1E+00 1.4E-01 slope unrestricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-360 —DO NOT CITE OR QUOTE 

log-probit 1 0.60 0.44 114.02 2.2E+00 1.7E-01 slope restricted ≥1 

multistage, 1-

degree 2 1.99 0.37 113.51 7.3E+00 4.7E+00 betas restricted ≥0, bound hit 

probit 2 2.79 0.25 114.72 1.4E+01 1.1E+01 

Weibull 2 1.99 0.37 113.51 7.3E+00 4.7E+00 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

1 

2 

3 E.3.5.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 10 20 30 40

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:43 11/29 2009

BMDL BMD

 

Log-Logistic

4 

5 

6 

7 E.3.5.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

8 

9 

10 ==================================================================== 

11 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

12 Input Data File: C:\USEPA\BMDS21\Nov29\LogLogistic_BMR2_BPS_d49.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogLogistic_BMR2_BPS_d49.plt 

14 Sun Nov 29 11:43:52 2009 

15 ==================================================================== 

16 

17 0 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-361 —DO NOT CITE OR QUOTE 

1 The form of the probability function is: 

2 

3 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

4 

5 

6 Dependent variable = DichEff 

7 Independent variable = Dose 

8 Slope parameter is restricted as slope >= 1 

9 

10 Total number of observations = 4 

11 Total number of records with missing values = 0 

12 Maximum number of iterations = 250 

13 Relative Function Convergence has been set to: 1e-008 

14 Parameter Convergence has been set to: 1e-008 

15 

16 

17 

18 User has chosen the log transformed model 

19 

20 

21 Default Initial Parameter Values 

22 background = 0.0333333 

23 intercept = -3.75371 

24 slope = 1 

25 

26 

27 Asymptotic Correlation Matrix of Parameter Estimates 

28 

29 ( *** The model parameter(s) -slope 

30 have been estimated at a boundary point, or have been specified by the user, 

31 and do not appear in the correlation matrix ) 

32 

33 background intercept 

34 

35 background 1 -0.58 

36 

37 intercept -0.58 1 

38 

39 

40 

41 Parameter Estimates 

42 

43 95.0% Wald Confidence Interval 

44 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

45 background 0.0635251 * * * 

46 intercept -3.84765 * * * 

47 slope 1 * * * 

48 

49 * - Indicates that this value is not calculated. 

50 

51 

52 

53 Analysis of Deviance Table 

54 

55 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

56 Full model -53.7077 4 

57 Fitted model -54.476 2 1.53661 2 0.4638 

58 Reduced model -63.9797 1 20.544 3 0.0001309 

59 

60 AIC: 112.952 

61 

62 

63 Goodness of Fit 

64 Scaled 

65 Dose Est._Prob. Expected Observed Size Residual 

66 ------------------------------------------------------------------------ 

67 0.0000 0.0635 1.906 1.000 30 -0.678 

68 2.4000 0.1091 3.274 5.000 30 1.011 

69 8.0000 0.2000 6.001 6.000 30 -0.000 

70 46.0000 0.5273 15.819 15.000 30 -0.300 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-362 —DO NOT CITE OR QUOTE 

1 

2 Chi^2 = 1.57 d.f. = 2 P-value = 0.4559 

3 

4 

5 Benchmark Dose Computation 

6 

7 Specified effect = 0.1 

8 

9 Risk Type = Extra risk 

10 

11 Confidence level = 0.95 

12 

13 BMD = 5.20918 

14 

15 BMDL = 2.86991 

16 

17 

18 

19 E.3.5.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 10 20 30 40

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:43 11/29 2009

BMDL BMD

 

Log-Logistic

20 

21 

22 

23 E.3.5.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

24 

25 

26 ==================================================================== 

27 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

28 Input Data File: C:\USEPA\BMDS21\Nov29\LogLogistic_Unrest_BMR2_BPS_d49.(d) 

29 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogLogistic_Unrest_BMR2_BPS_d49.plt 

30 Sun Nov 29 11:43:54 2009 

31 ==================================================================== 

32 

33 0 

34 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-363 —DO NOT CITE OR QUOTE 

1 The form of the probability function is: 

2 

3 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

4 

5 

6 Dependent variable = DichEff 

7 Independent variable = Dose 

8 Slope parameter is not restricted 

9 

10 Total number of observations = 4 

11 Total number of records with missing values = 0 

12 Maximum number of iterations = 250 

13 Relative Function Convergence has been set to: 1e-008 

14 Parameter Convergence has been set to: 1e-008 

15 

16 

17 

18 User has chosen the log transformed model 

19 

20 

21 Default Initial Parameter Values 

22 background = 0.0333333 

23 intercept = -2.54947 

24 slope = 0.615936 

25 

26 

27 Asymptotic Correlation Matrix of Parameter Estimates 

28 

29 background intercept slope 

30 

31 background 1 -0.49 0.35 

32 

33 intercept -0.49 1 -0.93 

34 

35 slope 0.35 -0.93 1 

36 

37 

38 

39 Parameter Estimates 

40 

41 95.0% Wald Confidence Interval 

42 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

43 background 0.0354714 * * * 

44 intercept -2.70296 * * * 

45 slope 0.670238 * * * 

46 

47 * - Indicates that this value is not calculated. 

48 

49 

50 

51 Analysis of Deviance Table 

52 

53 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

54 Full model -53.7077 4 

55 Fitted model -53.9541 3 0.492844 1 0.4827 

56 Reduced model -63.9797 1 20.544 3 0.0001309 

57 

58 AIC: 113.908 

59 

60 

61 Goodness of Fit 

62 Scaled 

63 Dose Est._Prob. Expected Observed Size Residual 

64 ------------------------------------------------------------------------ 

65 0.0000 0.0355 1.064 1.000 30 -0.063 

66 2.4000 0.1392 4.176 5.000 30 0.435 

67 8.0000 0.2405 7.216 6.000 30 -0.520 

68 46.0000 0.4848 14.544 15.000 30 0.167 

69 

70 Chi^2 = 0.49 d.f. = 1 P-value = 0.4836 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-364 —DO NOT CITE OR QUOTE 

1 

2 

3 Benchmark Dose Computation 

4 

5 Specified effect = 0.1 

6 

7 Risk Type = Extra risk 

8 

9 Confidence level = 0.95 

10 

11 BMD = 2.12667 

12 

13 BMDL = 0.13633 

14 

15 

16 E.3.6. Bell et al. (2007): Balano-Preputial Separation in Male Pups (5% Extra Risk) 

17 E.3.6.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2 pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 2 1.99 0.37 113.51 3.6E+00 2.3E+00 power restricted ≥1, bound 

hit 

logistic 2 2.88 0.24 114.85 8.4E+00 6.2E+00 

log-logistic b 2 1.57 0.46 112.95 2.5E+00 1.4E+00 slope restricted ≥1, 

bound hit 

log-logistic c 1 0.49 0.48 113.91 7.0E-01 1.1E-02 slope unrestricted 

log-probit 1 0.60 0.44 114.02 8.6E-01 2.1E-02 slope restricted ≥1 

multistage, 1-

degree 2 1.99 0.37 113.51 3.6E+00 2.3E+00 betas restricted ≥0, bound hit 

probit 2 2.79 0.25 114.72 7.7E+00 5.7E+00 

Weibull 2 1.99 0.37 113.51 3.6E+00 2.3E+00 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

18 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-365 —DO NOT CITE OR QUOTE 

1 E.3.6.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 10 20 30 40

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:43 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.3.6.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\LogLogistic_BMR1_BPS_d49.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogLogistic_BMR1_BPS_d49.plt 

12 Sun Nov 29 11:43:49 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is restricted as slope >= 1 

26 

27 Total number of observations = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-366 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0333333 

3 intercept = -3.75371 

4 slope = 1 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -slope 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 background intercept 

14 

15 background 1 -0.58 

16 

17 intercept -0.58 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 background 0.0635251 * * * 

26 intercept -3.84765 * * * 

27 slope 1 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -53.7077 4 

37 Fitted model -54.476 2 1.53661 2 0.4638 

38 Reduced model -63.9797 1 20.544 3 0.0001309 

39 

40 AIC: 112.952 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0635 1.906 1.000 30 -0.678 

48 2.4000 0.1091 3.274 5.000 30 1.011 

49 8.0000 0.2000 6.001 6.000 30 -0.000 

50 46.0000 0.5273 15.819 15.000 30 -0.300 

51 

52 Chi^2 = 1.57 d.f. = 2 P-value = 0.4559 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.05 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 2.46751 

64 

65 BMDL = 1.35943 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-367 —DO NOT CITE OR QUOTE 

1 E.3.6.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 10 20 30 40

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:43 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.3.6.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\LogLogistic_Unrest_BMR1_BPS_d49.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogLogistic_Unrest_BMR1_BPS_d49.plt 

12 Sun Nov 29 11:43:53 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is not restricted 

26 

27 Total number of observations = 4 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-368 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0333333 

3 intercept = -2.54947 

4 slope = 0.615936 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 background intercept slope 

10 

11 background 1 -0.49 0.35 

12 

13 intercept -0.49 1 -0.93 

14 

15 slope 0.35 -0.93 1 

16 

17 

18 

19 Parameter Estimates 

20 

21 95.0% Wald Confidence Interval 

22 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

23 background 0.0354714 * * * 

24 intercept -2.70296 * * * 

25 slope 0.670238 * * * 

26 

27 * - Indicates that this value is not calculated. 

28 

29 

30 

31 Analysis of Deviance Table 

32 

33 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

34 Full model -53.7077 4 

35 Fitted model -53.9541 3 0.492844 1 0.4827 

36 Reduced model -63.9797 1 20.544 3 0.0001309 

37 

38 AIC: 113.908 

39 

40 

41 Goodness of Fit 

42 Scaled 

43 Dose Est._Prob. Expected Observed Size Residual 

44 ------------------------------------------------------------------------ 

45 0.0000 0.0355 1.064 1.000 30 -0.063 

46 2.4000 0.1392 4.176 5.000 30 0.435 

47 8.0000 0.2405 7.216 6.000 30 -0.520 

48 46.0000 0.4848 14.544 15.000 30 0.167 

49 

50 Chi^2 = 0.49 d.f. = 1 P-value = 0.4836 

51 

52 

53 Benchmark Dose Computation 

54 

55 Specified effect = 0.05 

56 

57 Risk Type = Extra risk 

58 

59 Confidence level = 0.95 

60 

61 BMD = 0.697474 

62 

63 BMDL = 0.0111259 

64 

65 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-369 —DO NOT CITE OR QUOTE 

1 E.3.7. Cantoni et al. (1981): Urinary Copro-Porhyrins 

2 E.3.7.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

logistic 2 20.02 0.00 131.96 4.6E+03 3.8E+01 

log-logistic 2 20.02 0.00 131.96 8.0E+07 3.8E+01 slope restricted ≥1, bound 

hit 

log-probit 2 20.02 0.00 131.96 4.6E+03 error slope restricted ≥1 

multistage, 2-

degree 3 20.02 0.00 129.96 error error betas restricted ≥0, bound hit 

probit b 2 20.02 0.00 131.96 4.6E+03 3.8E+01 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.3.7.2. Figure for Selected Model: Probit 

 0.3

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1

 0 1000 2000 3000 4000

Fraction Affected

dose

Probit Model with 0.95 Confidence Level

13:34 11/11 2009

BMDL BMD

 

Probit

6 

7 

8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-370 —DO NOT CITE OR QUOTE 

1 E.3.7.3. Output File for Selected Model: Probit 

2 

3 

4 ==================================================================== 

5 Probit Model. (Version: 3.1; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\Probit_BMR2_BPS_pnd49.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Probit_BMR2_BPS_pnd49.plt 

8 Wed Nov 11 13:34:24 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = CumNorm(Intercept+Slope*Dose), 

17 

18 where CumNorm(.) is the cumulative normal distribution function 

19 

20 

21 Dependent variable = DichEff 

22 Independent variable = Dose 

23 Slope parameter is not restricted 

24 

25 Total number of observations = 4 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 

32 

33 Default Initial (and Specified) Parameter Values 

34 background = 0 Specified 

35 intercept = 1.29116 

36 slope = -0.0292594 

37 

38 

39 Asymptotic Correlation Matrix of Parameter Estimates 

40 

41 ( *** The model parameter(s) -background 

42 have been estimated at a boundary point, or have been specified by the user, 

43 and do not appear in the correlation matrix ) 

44 

45 intercept slope 

46 

47 intercept 1 -0.64 

48 

49 slope -0.64 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 intercept 0.755415 0.164576 0.432851 1.07798 

58 slope 0 0.00651162 -0.0127625 0.0127625 

59 

60 

61 

62 Analysis of Deviance Table 

63 

64 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

65 Full model -53.7077 4 

66 Fitted model -63.9797 2 20.544 2 3.4588333e-005 

67 Reduced model -63.9797 1 20.544 3 0.0001309 

68 

69 AIC: 131.959 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-371 —DO NOT CITE OR QUOTE 

1 

2 

3 Goodness of Fit 

4 Scaled 

5 Dose Est._Prob. Expected Observed Size Residual 

6 ------------------------------------------------------------------------ 

7 0.0000 0.7750 23.250 29.000 30 2.514 

8 2.4000 0.7750 23.250 25.000 30 0.765 

9 8.0000 0.7750 23.250 24.000 30 0.328 

10 46.0000 0.7750 23.250 15.000 30 -3.607 

11 

12 Chi^2 = 20.02 d.f. = 2 P-value = 0.0000 

13 

14 Slope parameter essentially zero. BMD set to 100 * max(Dose). 

15 

16 

17 Benchmark Dose Computation 

18 

19 Specified effect = 0.1 

20 

21 Risk Type = Extra risk 

22 

23 Confidence level = 0.95 

24 

25 BMD = 4600 

26 

27 BMDL = 38.2394 

28 

29 

30 

31 E.3.8. Cantoni et al. (1981): Urinary Porphyrins 

32 E.3.8.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 <0.0001 19.41 <0.0001 58.75 1.2E+01 9.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 <0.0001 19.41 <0.0001 58.75 1.2E+01 9.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 <0.0001 21.80 <0.0001 63.14 2.2E-01 1.1E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 <0.0001 21.80 <0.0001 63.14 2.2E-01 1.1E-01 nonconstant variance, 

power restricted ≥1 

Hill 0 <.0001 19.02 NA 62.36 9.4E+00 4.7E+00 nonconstant variance, 

n restricted >1 

linear c 2 <.0001 23.15 <.0001 62.49 7.7E-01 2.8E-01 nonconstant 

variance 

polynomial 1 <.0001 18.19 <.0001 59.53 6.3E+00 2.0E+00 nonconstant variance 

power 2 <.0001 23.15 <.0001 62.49 7.7E-01 2.8E-01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 <0.0001 0.05 0.98 108.89 7.0E+01 5.0E+01 constant variance, 

power restricted ≥1 

exponential (M3) 2 <0.0001 0.05 0.98 108.89 7.0E+01 5.0E+01 constant variance, 

power restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-372 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M4) 1 <0.0001 0.86 0.35 111.70 1.8E+01 1.0E+01 constant variance, 

power restricted ≥1 

exponential (M5) 0 <0.0001 0.04 N/A 112.88 4.2E+01 1.4E+01 constant variance, 

power restricted ≥1 

Hill 0 <.0001 0.04 NA 112.88 4.2E+01 1.0E+01 constant variance, n 

restricted >1 

linear 2 <.0001 0.85 0.66 109.69 1.8E+01 1.3E+01 constant variance 

polynomial 1 <.0001 0.03 0.86 110.88 4.4E+01 1.1E+01 constant variance 

power 1 <.0001 0.04 0.85 110.88 4.2E+01 1.4E+01 constant variance, 

power restricted ≥1 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

1 

2 

3 E.3.8.2. Figure for Selected Model: Linear, Nonconstant Variance 

 0

 50

 100

 150

 200

 250

 300

 350

 0 20 40 60 80 100 120 140

Mean Response

dose

Linear Model with 0.95 Confidence Level

14:06 10/06 2009

BMDLBMD

 

Linear

4 

5 

6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-373 —DO NOT CITE OR QUOTE 

1 E.3.8.3. Output File for Selected Model: Linear, Nonconstant Variance 

2 

3 

4 ==================================================================== 

5 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

6 Input Data File: C:\USEPA\BMDS21\AniDose\Linear_BMR1_Urinary_porphyrins.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\Linear_BMR1_Urinary_porphyrins.plt 

8 Tue Oct 06 14:06:04 2009 

9 ==================================================================== 

10 

11 Table 1, dose converted to ng per kg per day 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Signs of the polynomial coefficients are not restricted 

22 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

23 

24 Total number of dose groups = 4 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 Default Initial Parameter Values 

33 lalpha = 6.68244 

34 rho = 0 

35 beta_0 = -1.7736 

36 beta_1 = 1.38238 

37 

38 

39 Asymptotic Correlation Matrix of Parameter Estimates 

40 

41 lalpha rho beta_0 beta_1 

42 

43 lalpha 1 -0.89 -0.27 0.2 

44 

45 rho -0.89 1 0.18 -0.082 

46 

47 beta_0 -0.27 0.18 1 -0.31 

48 

49 beta_1 0.2 -0.082 -0.31 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 lalpha -2.51366 0.863504 -4.2061 -0.821228 

58 rho 2.27539 0.314031 1.6599 2.89088 

59 beta_0 2.57041 0.376521 1.83244 3.30838 

60 beta_1 1.07729 0.234062 0.618541 1.53605 

61 

62 

63 

64 Table of Data and Estimated Values of Interest 

65 

66 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

67 ------ --- -------- -------- ----------- ----------- ---------- 

68 

69 0 4 2.27 2.57 0.49 0.833 -0.721 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-374 —DO NOT CITE OR QUOTE 

1 1.43 4 5.55 4.11 0.85 1.42 2.03 

2 14.3 3 7.62 18 1.79 7.61 -2.36 

3 143 3 197 157 63.1 89.4 0.78 

4 

5 

6 

7 Model Descriptions for likelihoods calculated 

8 

9 

10 Model A1: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma^2 

12 

13 Model A2: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma(i)^2 

15 

16 Model A3: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

18 Model A3 uses any fixed variance parameters that 

19 were specified by the user 

20 

21 Model R: Yi = Mu + e(i) 

22 Var{e(i)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) # Param's AIC 

28 A1 -51.421748 5 112.843496 

29 A2 -15.312111 8 46.624223 

30 A3 -15.669627 6 43.339255 

31 fitted -27.243469 4 62.486938 

32 R -68.750584 2 141.501167 

33 

34 

35 Explanation of Tests 

36 

37 Test 1: Do responses and/or variances differ among Dose levels? 

38 (A2 vs. R) 

39 Test 2: Are Variances Homogeneous? (A1 vs A2) 

40 Test 3: Are variances adequately modeled? (A2 vs. A3) 

41 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

42 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

43 

44 Tests of Interest 

45 

46 Test -2*log(Likelihood Ratio) Test df p-value 

47 

48 Test 1 106.877 6 <.0001 

49 Test 2 72.2193 3 <.0001 

50 Test 3 0.715032 2 0.6994 

51 Test 4 23.1477 2 <.0001 

52 

53 The p-value for Test 1 is less than .05. There appears to be a 

54 difference between response and/or variances among the dose levels 

55 It seems appropriate to model the data 

56 

57 The p-value for Test 2 is less than .1. A non-homogeneous variance 

58 model appears to be appropriate 

59 

60 The p-value for Test 3 is greater than .1. The modeled variance appears 

61 to be appropriate here 

62 

63 The p-value for Test 4 is less than .1. You may want to try a different 

64 model 

65 

66 

67 Benchmark Dose Computation 

68 

69 Specified effect = 1 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-375 —DO NOT CITE OR QUOTE 

1 Risk Type = Estimated standard deviations from the control mean 

2 Confidence level = 0.95 

3 BMD = 0.773193 

4 BMDL = 0.281589 

5 

6 

7 

8 E.3.9. Crofton et al. (2005): Serum T4 

9 E.3.9.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 8 0.76 46.09 <0.0001 518.24 2.1E+03 1.2E+03 constant variance, 

power restricted ≥1 

exponential (M3) 8 0.76 46.09 <0.0001 518.24 2.1E+03 1.2E+03 constant variance, 

power restricted ≥1 

exponential (M4)

c 7 0.76 2.05 0.96 476.20 5.6E+01 3.0E+01 constant variance, 

power restricted ≥1 

exponential (M5) 7 0.76 2.05 0.96 476.20 5.6E+01 3.0E+01 constant variance, 

power restricted ≥1 

Hill 6 0.76 1.28 0.97 477.43 5.6E+01 2.6E+01 constant variance, n 

restricted >1 

linear 8 0.76 51.36 <.0001 523.52 4.2E+03 3.1E+03 constant variance 

polynomial 8 0.76 51.36 <.0001 523.52 4.2E+03 3.1E+03 constant variance 

power 8 0.76 51.36 <.0001 523.52 4.2E+03 3.1E+03 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-376 —DO NOT CITE OR QUOTE 

1 E.3.9.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

2 ≥1 

 20

 40

 60

 80

 100

 120

 0 2000 4000 6000 8000 10000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:00 11/11 2009

BMDLBMD

 

Exponential

3 

4 

5 

6 E.3.9.3. Output File for selected Model: Exponential (M4), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\ExpConstVar_BMR1_SerumT4.(d) 

13 Gnuplot Plotting File: 

14 Wed Nov 11 12:00:47 2009 

15 ==================================================================== 

16 

17 0 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-377 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 10 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 4 

19 -------- -------- 

20 lnalpha 5.47437 

21 rho(S) 0 

22 a 104.999 

23 b 0.000371694 

24 c 0.445764 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 4 

34 -------- ------- 

35 lnalpha 5.50283 

36 rho 0 

37 a 99.776 

38 b 0.00728387 

39 c 0.533516 

40 d 1 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 14 100 15.44 

48 0.1 6 96.27 14.98 

49 3 12 98.57 18.11 

50 10 6 99.76 19.04 

51 30 6 93.32 12.11 

52 100 6 70.94 12.74 

53 300 6 62.52 14.75 

54 1000 6 52.68 22.73 

55 3000 6 54.66 19.71 

56 1e+004 4 49.15 11.15 

57 

58 

59 Estimated Values of Interest 

60 

61 Dose Est Mean Est Std Scaled Residual 

62 ------ ---------- --------- ---------------- 

63 0 99.78 15.66 0.05325 

64 0.1 99.74 15.66 -0.5434 

65 3 98.77 15.66 -0.04357 

66 10 96.51 15.66 0.5085 

67 30 90.64 15.66 0.4195 

68 100 75.7 15.66 -0.744 

69 300 58.47 15.66 0.6334 

70 1000 53.26 15.66 -0.09133 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-378 —DO NOT CITE OR QUOTE 

1 3000 53.23 15.66 0.2237 

2 1e+004 53.23 15.66 -0.5218 

3 

4 

5 

6 Other models for which likelihoods are calculated: 

7 

8 Model A1: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma^2 

10 

11 Model A2: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma(i)^2 

13 

14 Model A3: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

16 

17 Model R: Yij = Mu + e(i) 

18 Var{e(ij)} = Sigma^2 

19 

20 

21 Likelihoods of Interest 

22 

23 Model Log(likelihood) DF AIC 

24 ------- ----------------- ---- ------------ 

25 A1 -233.0774 11 488.1549 

26 A2 -230.2028 20 500.4056 

27 A3 -233.0774 11 488.1549 

28 R -268.4038 2 540.8076 

29 4 -234.1019 4 476.2038 

30 

31 

32 Additive constant for all log-likelihoods = -66.16. This constant added to the 

33 above values gives the log-likelihood including the term that does not 

34 depend on the model parameters. 

35 

36 

37 Explanation of Tests 

38 

39 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

40 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

41 Test 3: Are variances adequately modeled? (A2 vs. A3) 

42 

43 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

44 

45 

46 Tests of Interest 

47 

48 Test -2*log(Likelihood Ratio) D. F. p-value 

49 -------- ------------------------ ------ -------------- 

50 Test 1 76.4 18 < 0.0001 

51 Test 2 5.749 9 0.7647 

52 Test 3 5.749 9 0.7647 

53 Test 6a 2.049 7 0.9571 

54 

55 

56 The p-value for Test 1 is less than .05. There appears to be a 

57 difference between response and/or variances among the dose 

58 levels, it seems appropriate to model the data. 

59 

60 The p-value for Test 2 is greater than .1. A homogeneous 

61 variance model appears to be appropriate here. 

62 

63 The p-value for Test 3 is greater than .1. The modeled 

64 variance appears to be appropriate here. 

65 

66 The p-value for Test 6a is greater than .1. Model 4 seems 

67 to adequately describe the data. 

68 

69 

70 Benchmark Dose Computations: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-379 —DO NOT CITE OR QUOTE 

1 

2 Specified Effect = 1.000000 

3 Risk Type = Estimated standard deviations from control 

4 Confidence Level = 0.950000 

5 BMD = 56.3321 

6 BMDL = 30.0635 

7 

8 E.3.10. DeCaprio et al. (1986): Absolute Kidney Weight, Males 

9 E.3.10.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.67 10.85 0.00 -9.87 2.6E+00 1.7E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.67 10.85 0.00 -9.87 2.6E+00 1.7E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.67 0.54 0.46 -18.18 2.7E-01 1.2E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.67 0.54 0.46 -18.18 2.7E-01 1.2E-01 nonconstant variance, 

power restricted ≥1 

Hill 1 0.67 0.08 0.78 -18.64 1.9E-01 7.3E-02 nonconstant variance, n 

restricted >1, bound hit 

linear 2 0.67 11.14 0.00 -9.58 2.8E+00 1.9E+00 nonconstant variance 

polynomial 1 0.67 1.10 0.29 -17.62 3.6E-01 2.3E-01 nonconstant variance 

power 2 0.67 11.14 0.00 -9.58 2.8E+00 1.9E+00 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.67 10.90 0.00 -11.71 2.5E+00 1.7E+00 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.67 10.90 0.00 -11.71 2.5E+00 1.7E+00 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.67 0.52 0.47 -20.10 2.6E-01 1.2E-01 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.67 0.52 0.47 -20.10 2.6E-01 1.2E-01 constant variance, 

power restricted ≥1 

Hill c 1 0.67 0.07 0.79 -20.54 1.9E-01 7.1E-02 

constant variance, n 

restricted >1, bound 

hit 

linear 2 0.67 11.21 0.00 -11.40 2.6E+00 1.9E+00 constant variance 

polynomial 1 0.67 1.08 0.30 -19.53 3.5E-01 2.4E-01 constant variance 

power 2 0.67 11.21 0.00 -11.40 2.6E+00 1.9E+00 

constant variance, 

power restricted ≥1, 

bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-380 —DO NOT CITE OR QUOTE 

1 E.3.10.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 4

 4.5

 5

 5.5

 6

 0 1 2 3 4 5

Mean Response

dose

Hill Model with 0.95 Confidence Level

14:07 10/06 2009

BMDL BMD

 

Hill

2 

3 

4 

5 E.3.10.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_abs_male_kidney_wt.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_abs_male_kidney_wt.plt 

14 Tue Oct 06 14:07:06 2009 

15 ==================================================================== 

16 

17 Abs Male Kidney wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 rho is set to 0 

28 Power parameter restricted to be greater than 1 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-381 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 alpha = 0.202865 

5 rho = 0 Specified 

6 intercept = 5.49 

7 v = -1.19 

8 n = 1.12255 

9 k = 0.399186 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -rho -n 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 alpha intercept v k 

19 

20 alpha 1 -1.7e-009 4.6e-009 -2e-009 

21 

22 intercept -1.7e-009 1 -0.49 -0.54 

23 

24 v 4.6e-009 -0.49 1 -0.27 

25 

26 k -2e-009 -0.54 -0.27 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence Interval 

33 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

34 alpha 0.183391 0.0405044 0.104004 0.262778 

35 intercept 5.47882 0.130251 5.22353 5.7341 

36 v -1.25656 0.197258 -1.64318 -0.869946 

37 n 1 NA 

38 k 0.361009 0.220645 -0.0714485 0.793466 

39 

40 NA - Indicates that this parameter has hit a bound 

41 implied by some inequality constraint and thus 

42 has no standard error. 

43 

44 

45 

46 Table of Data and Estimated Values of Interest 

47 

48 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

49 ------ --- -------- -------- ----------- ----------- ---------- 

50 

51 0 10 5.49 5.48 0.538 0.428 0.0826 

52 0.12 10 5.14 5.17 0.379 0.428 -0.187 

53 0.61 11 4.71 4.69 0.398 0.428 0.159 

54 4.9 10 4.3 4.31 0.474 0.428 -0.0626 

55 

56 

57 

58 Model Descriptions for likelihoods calculated 

59 

60 

61 Model A1: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 

64 Model A2: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma(i)^2 

66 

67 Model A3: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 Model A3 uses any fixed variance parameters that 

70 were specified by the user 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-382 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yi = Mu + e(i) 

3 Var{e(i)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) # Param's AIC 

9 A1 14.306322 5 -18.612644 

10 A2 15.093716 8 -14.187432 

11 A3 14.306322 5 -18.612644 

12 fitted 14.270730 4 -20.541459 

13 R -0.636909 2 5.273819 

14 

15 

16 Explanation of Tests 

17 

18 Test 1: Do responses and/or variances differ among Dose levels? 

19 (A2 vs. R) 

20 Test 2: Are Variances Homogeneous? (A1 vs A2) 

21 Test 3: Are variances adequately modeled? (A2 vs. A3) 

22 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

23 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

24 

25 Tests of Interest 

26 

27 Test -2*log(Likelihood Ratio) Test df p-value 

28 

29 Test 1 31.4613 6 <.0001 

30 Test 2 1.57479 3 0.6651 

31 Test 3 1.57479 3 0.6651 

32 Test 4 0.0711848 1 0.7896 

33 

34 The p-value for Test 1 is less than .05. There appears to be a 

35 difference between response and/or variances among the dose levels 

36 It seems appropriate to model the data 

37 

38 The p-value for Test 2 is greater than .1. A homogeneous variance 

39 model appears to be appropriate here 

40 

41 

42 The p-value for Test 3 is greater than .1. The modeled variance appears 

43 to be appropriate here 

44 

45 The p-value for Test 4 is greater than .1. The model chosen seems 

46 to adequately describe the data 

47 

48 

49 Benchmark Dose Computation 

50 

51 Specified effect = 1 

52 

53 Risk Type = Estimated standard deviations from the control mean 

54 

55 Confidence level = 0.95 

56 

57 BMD = 0.186641 

58 

59 BMDL = 0.0714793 

60 

61 

62 

63 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-383 —DO NOT CITE OR QUOTE 

1 E.3.11. DeCaprio et al. (1986): Absolute Thymus Weight, Males 

2 E.3.11.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 <0.0001 0.74 0.69 -93.74 1.8E+00 4.8E-01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 1 <0.0001 0.70 0.40 -91.78 2.4E+00 4.8E-01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 2 <0.0001 0.74 0.69 -93.74 1.8E+00 4.4E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 <0.0001 0.70 N/A -89.78 2.4E+00 4.8E-01 nonconstant variance, 

power restricted ≥1 

Hill 0 <.0001 0.70 NA -89.78 8.4E-01 error nonconstant variance, n 

restricted >1 

linear 2 <.0001 0.69 0.71 -93.79 2.4E+00 error nonconstant variance 

polynomial 1 <.0001 0.69 0.41 -91.79 2.4E+00 error nonconstant variance 

power c 2 <.0001 0.69 0.71 -93.79 2.4E+00 1.0E+00 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 <0.0001 1.01 0.60 -60.51 1.1E+01 3.7E+00 constant variance, 

power restricted ≥1 

exponential (M3) 2 <0.0001 1.01 0.60 -60.51 1.1E+01 3.7E+00 constant variance, 

power restricted ≥1 

exponential (M4) 1 <0.0001 0.60 0.44 -58.92 error error constant variance, 

power restricted ≥1 

exponential (M5) 1 <0.0001 0.60 0.44 -58.92 error error constant variance, 

power restricted ≥1 

Hill 1 <.0001 0.40 0.53 -59.12 error error constant variance, n 

restricted >1, bound hit 

linear 2 <.0001 1.04 0.59 -60.48 9.0E+00 4.2E+00 constant variance 

polynomial 1 <.0001 0.67 0.41 -58.85 error 5.8E+00 constant variance 

power 2 <.0001 1.04 0.59 -60.48 9.0E+00 4.2E+00 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-384 —DO NOT CITE OR QUOTE 

1 E.3.11.2. Figure for Selected Model: Power, Nonconstant Variance, Power Restricted ≥1, 

2 Bound Hit 

-0.1

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0.8

 0 1 2 3 4 5

Mean Response

dose

Power Model with 0.95 Confidence Level

14:07 10/06 2009

BMDL BMD

 

Power

3 

4 

5 

6 E.3.11.3. Output File for Selected Model: Power, Nonconstant Variance, Power Restricted ≥1, 

7 Bound Hit 

8 

9 

10 ==================================================================== 

11 Power Model. (Version: 2.15; Date: 04/07/2008) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\Pwr_BMR1_abs_thymus_wt.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\Pwr_BMR1_abs_thymus_wt.plt 

14 Tue Oct 06 14:07:51 2009 

15 ==================================================================== 

16 

17 Abs Thymus wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = control + slope * dose^power 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 The power is restricted to be greater than or equal to 1 

28 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

29 

30 Total number of dose groups = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-385 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 lalpha = -2.54423 

5 rho = 0 

6 control = 0.562 

7 slope = -0.216619 

8 power = -0.019526 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -power 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 lalpha rho control slope 

18 

19 lalpha 1 0.99 0.39 -0.97 

20 

21 rho 0.99 1 0.33 -0.98 

22 

23 control 0.39 0.33 1 -0.4 

24 

25 slope -0.97 -0.98 -0.4 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 lalpha -7.29904 2.85129 -12.8875 -1.71062 

34 rho -4.37824 3.97762 -12.1742 3.41775 

35 control 0.500643 0.0242054 0.453202 0.548085 

36 slope -0.0492183 0.0335618 -0.114998 0.0165617 

37 power 1 NA 

38 

39 NA - Indicates that this parameter has hit a bound 

40 implied by some inequality constraint and thus 

41 has no standard error. 

42 

43 

44 

45 Table of Data and Estimated Values of Interest 

46 

47 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

48 ------ --- -------- -------- ----------- ----------- ---------- 

49 

50 0 10 0.562 0.501 0.158 0.118 1.64 

51 0.12 10 0.448 0.495 0.0696 0.121 -1.22 

52 0.61 11 0.445 0.471 0.113 0.135 -0.628 

53 4.9 10 0.352 0.259 0.528 0.498 0.587 

54 

55 

56 

57 Model Descriptions for likelihoods calculated 

58 

59 

60 Model A1: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 

63 Model A2: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma(i)^2 

65 

66 Model A3: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

68 Model A3 uses any fixed variance parameters that 

69 were specified by the user 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-386 —DO NOT CITE OR QUOTE 

1 Model R: Yi = Mu + e(i) 

2 Var{e(i)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) # Param's AIC 

8 A1 33.761192 5 -57.522384 

9 A2 57.094821 8 -98.189643 

10 A3 51.239109 6 -90.478218 

11 fitted 50.896393 4 -93.792785 

12 R 32.253943 2 -60.507885 

13 

14 

15 Explanation of Tests 

16 

17 Test 1: Do responses and/or variances differ among Dose levels? 

18 (A2 vs. R) 

19 Test 2: Are Variances Homogeneous? (A1 vs A2) 

20 Test 3: Are variances adequately modeled? (A2 vs. A3) 

21 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

22 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

23 

24 Tests of Interest 

25 

26 Test -2*log(Likelihood Ratio) Test df p-value 

27 

28 Test 1 49.6818 6 <.0001 

29 Test 2 46.6673 3 <.0001 

30 Test 3 11.7114 2 0.002863 

31 Test 4 0.685433 2 0.7098 

32 

33 The p-value for Test 1 is less than .05. There appears to be a 

34 difference between response and/or variances among the dose levels 

35 It seems appropriate to model the data 

36 

37 The p-value for Test 2 is less than .1. A non-homogeneous variance 

38 model appears to be appropriate 

39 

40 The p-value for Test 3 is less than .1. You may want to consider a 

41 different variance model 

42 

43 The p-value for Test 4 is greater than .1. The model chosen seems 

44 to adequately describe the data 

45 

46 

47 Benchmark Dose Computation 

48 

49 Specified effect = 1 

50 

51 Risk Type = Estimated standard deviations from the control mean 

52 

53 Confidence level = 0.95 

54 

55 BMD = 2.40256 

56 

57 

58 BMDL = 1.00746 

59 

60 

61 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-387 —DO NOT CITE OR QUOTE 

1 E.3.12. DeCaprio et al. (1986): Body Weight, Females 

2 E.3.12.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 0.10 1.49 0.68 380.09 5.5E+00 3.6E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.10 1.49 0.68 380.09 5.5E+00 3.6E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 2 0.10 1.27 0.53 381.87 4.5E+00 2.4E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.10 1.27 0.53 381.87 4.5E+00 2.4E+00 nonconstant variance, 

power restricted ≥1 

Hill 2 0.10 1.26 0.53 381.86 4.5E+00 error nonconstant variance, n 

restricted >1, bound hit 

linear 3 0.10 2.06 0.56 380.66 6.9E+00 4.7E+00 nonconstant variance 

polynomial 2 0.10 1.28 0.53 381.88 4.6E+00 2.6E+00 nonconstant variance 

power 3 0.10 2.06 0.56 380.66 6.9E+00 4.7E+00 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2)

c 3 0.10 1.11 0.78 379.55 6.1E+00 4.5E+00 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.10 1.11 0.78 379.55 6.1E+00 4.5E+00 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.10 0.75 0.69 381.19 4.7E+00 2.6E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.10 0.75 0.69 381.19 4.7E+00 2.6E+00 constant variance, 

power restricted ≥1 

Hill 2 0.10 0.74 0.69 381.18 4.7E+00 2.4E+00 constant variance, n 

restricted >1, bound hit 

linear 3 0.10 1.73 0.63 380.17 7.6E+00 5.9E+00 constant variance 

polynomial 2 0.10 0.76 0.68 381.20 4.7E+00 2.7E+00 constant variance 

power 3 0.10 1.73 0.63 380.17 7.6E+00 5.9E+00 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-388 —DO NOT CITE OR QUOTE 

1 E.3.12.2. Figure for Selected Model: Exponential (M2), Constant Variance, Power Restricted 

2 ≥1 

 200

 300

 400

 500

 600

 0 5 10 15 20 25 30

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

14:08 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.12.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\ExpConstVar_BMR1_fem_BW.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 14:08:53 2009 

15 ==================================================================== 

16 

17 Female BW Tbl 1 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-389 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 5 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 2 

19 -------- -------- 

20 lnalpha 8.08396 

21 rho(S) 0 

22 a 632.1 

23 b 0.0928666 

24 c 0.528849 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 2 

34 -------- ------- 

35 lnalpha 8.10223 

36 rho 0 

37 a 588.488 

38 b 0.0403005 

39 c 0.434663 

40 d 1 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 8 602 33.94 

48 0.12 10 583 69.57 

49 0.68 9 570 66 

50 4.86 10 531 44.27 

51 31 4 351 98 

52 

53 

54 Estimated Values of Interest 

55 

56 Dose Est Mean Est Std Scaled Residual 

57 ------ ---------- --------- ---------------- 

58 0 584.9 57.71 0.839 

59 0.12 583.7 57.71 -0.0379 

60 0.68 578.2 57.71 -0.4248 

61 4.86 538.6 57.71 -0.4161 

62 31 345.7 57.71 0.1845 

63 

64 

65 

66 Other models for which likelihoods are calculated: 

67 

68 Model A1: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-390 —DO NOT CITE OR QUOTE 

1 Model A2: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = Sigma(i)^2 

3 

4 Model A3: Yij = Mu(i) + e(ij) 

5 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

6 

7 Model R: Yij = Mu + e(i) 

8 Var{e(ij)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) DF AIC 

14 ------- ----------------- ---- ------------ 

15 A1 -186.2212 6 384.4424 

16 A2 -182.3775 10 384.755 

17 A3 -186.2212 6 384.4424 

18 R -204.9225 2 413.8449 

19 2 -186.7751 3 379.5501 

20 

21 

22 Additive constant for all log-likelihoods = -37.68. This constant added to the 

23 above values gives the log-likelihood including the term that does not 

24 depend on the model parameters. 

25 

26 

27 Explanation of Tests 

28 

29 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

30 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

31 Test 3: Are variances adequately modeled? (A2 vs. A3) 

32 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

33 

34 

35 Tests of Interest 

36 

37 Test -2*log(Likelihood Ratio) D. F. p-value 

38 -------- ------------------------ ------ -------------- 

39 Test 1 45.09 8 < 0.0001 

40 Test 2 7.687 4 0.1037 

41 Test 3 7.687 4 0.1037 

42 Test 4 1.108 3 0.7752 

43 

44 

45 The p-value for Test 1 is less than .05. There appears to be a 

46 difference between response and/or variances among the dose 

47 levels, it seems appropriate to model the data. 

48 

49 The p-value for Test 2 is greater than .1. A homogeneous 

50 variance model appears to be appropriate here. 

51 

52 The p-value for Test 3 is greater than .1. The modeled 

53 variance appears to be appropriate here. 

54 

55 The p-value for Test 4 is greater than .1. Model 2 seems 

56 to adequately describe the data. 

57 

58 

59 Benchmark Dose Computations: 

60 

61 Specified Effect = 1.000000 

62 

63 Risk Type = Estimated standard deviations from control 

64 

65 Confidence Level = 0.950000 

66 

67 BMD = 6.12391 

68 

69 BMDL = 4.52632 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-391 —DO NOT CITE OR QUOTE 

1 E.3.13. DeCaprio et al. (1986): Body Weight, Males 

2 E.3.13.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 0.79 6.75 0.08 419.55 4.5E+00 2.9E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.79 6.75 0.08 419.55 4.5E+00 2.9E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 2 0.79 4.68 0.10 419.49 2.8E+00 1.5E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.79 4.68 0.10 419.49 2.8E+00 1.5E+00 nonconstant variance, 

power restricted ≥1 

Hill 2 0.79 4.56 0.10 419.36 2.6E+00 error 

nonconstant variance, 

n restricted >1, bound 

hit 

linear 3 0.79 8.23 0.04 421.04 5.8E+00 3.9E+00 nonconstant variance 

polynomial 2 0.79 4.82 0.09 419.63 2.9E+00 1.8E+00 nonconstant variance 

power 3 0.79 8.23 0.04 421.04 5.8E+00 3.9E+00 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 3 0.79 6.14 0.11 417.87 4.8E+00 3.7E+00 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.79 6.14 0.11 417.87 4.8E+00 3.7E+00 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.79 4.08 0.13 417.81 2.9E+00 1.8E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.79 4.08 0.13 417.81 2.9E+00 1.8E+00 constant variance, 

power restricted ≥1 

Hill c 2 0.79 3.98 0.14 417.70 2.8E+00 1.6E+00 

constant variance, n 

restricted >1, bound 

hit 

linear 3 0.79 7.56 0.06 419.29 6.1E+00 4.8E+00 constant variance 

polynomial 2 0.79 4.20 0.12 417.93 3.1E+00 2.0E+00 constant variance 

power 3 0.79 7.56 0.06 419.29 6.1E+00 4.8E+00 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-392 —DO NOT CITE OR QUOTE 

1 E.3.13.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 300

 400

 500

 600

 700

 0 5 10 15 20 25

Mean Response

dose

Hill Model with 0.95 Confidence Level

14:09 10/06 2009

BMDL BMD

 

Hill

2 

3 

4 

5 E.3.13.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_male_BW.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_male_BW.plt 

13 Tue Oct 06 14:09:41 2009 

14 ==================================================================== 

15 

16 Male BW Tbl 1 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter restricted to be greater than 1 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 5 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-393 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 3408.2 

4 rho = 0 Specified 

5 intercept = 713 

6 v = -280 

7 n = 0.5774 

8 k = 8.62353 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -rho -n 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 alpha intercept v k 

18 

19 alpha 1 1.1e-008 5.5e-008 -5.8e-008 

20 

21 intercept 1.1e-008 1 0.27 -0.46 

22 

23 v 5.5e-008 0.27 1 -0.94 

24 

25 k -5.8e-008 -0.46 -0.94 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 alpha 3309.29 697.66 1941.9 4676.68 

34 intercept 688.613 11.4849 666.103 711.123 

35 v -430.869 146.654 -718.305 -143.432 

36 n 1 NA 

37 k 18.1326 12.6279 -6.61762 42.8828 

38 

39 NA - Indicates that this parameter has hit a bound 

40 implied by some inequality constraint and thus 

41 has no standard error. 

42 

43 

44 

45 Table of Data and Estimated Values of Interest 

46 

47 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

48 ------ --- -------- -------- ----------- ----------- ---------- 

49 

50 0 10 713 689 47.4 57.5 1.34 

51 0.12 10 682 686 50.6 57.5 -0.208 

52 0.61 11 651 675 63 57.5 -1.36 

53 4.9 10 603 597 63.2 57.5 0.333 

54 26 4 433 435 76 57.5 -0.0617 

55 

56 

57 

58 Model Descriptions for likelihoods calculated 

59 

60 

61 Model A1: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma^2 

63 

64 Model A2: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma(i)^2 

66 

67 Model A3: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 Model A3 uses any fixed variance parameters that 

70 were specified by the user 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-394 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yi = Mu + e(i) 

3 Var{e(i)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) # Param's AIC 

9 A1 -202.863522 6 417.727044 

10 A2 -202.022697 10 424.045393 

11 A3 -202.863522 6 417.727044 

12 fitted -204.851020 4 417.702041 

13 R -226.717147 2 457.434293 

14 

15 

16 Explanation of Tests 

17 

18 Test 1: Do responses and/or variances differ among Dose levels? 

19 (A2 vs. R) 

20 Test 2: Are Variances Homogeneous? (A1 vs A2) 

21 Test 3: Are variances adequately modeled? (A2 vs. A3) 

22 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

23 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

24 

25 Tests of Interest 

26 

27 Test -2*log(Likelihood Ratio) Test df p-value 

28 

29 Test 1 49.3889 8 <.0001 

30 Test 2 1.68165 4 0.794 

31 Test 3 1.68165 4 0.794 

32 Test 4 3.975 2 0.137 

33 

34 The p-value for Test 1 is less than .05. There appears to be a 

35 difference between response and/or variances among the dose levels 

36 It seems appropriate to model the data 

37 

38 The p-value for Test 2 is greater than .1. A homogeneous variance 

39 model appears to be appropriate here 

40 

41 

42 The p-value for Test 3 is greater than .1. The modeled variance appears 

43 to be appropriate here 

44 

45 The p-value for Test 4 is greater than .1. The model chosen seems 

46 to adequately describe the data 

47 

48 

49 Benchmark Dose Computation 

50 

51 Specified effect = 1 

52 

53 Risk Type = Estimated standard deviations from the control mean 

54 

55 Confidence level = 0.95 

56 

57 BMD = 2.79396 

58 

59 BMDL = 1.55261 

60 

61 

62 

63 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-395 —DO NOT CITE OR QUOTE 

1 E.3.14. DeCaprio et al. (1986): Relative Brain Weight, Males 

2 E.3.14.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.99 5.25 0.07 -194.78 2.9E+00 2.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.99 5.25 0.07 -194.78 2.9E+00 2.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.99 0.02 0.89 -198.01 4.4E-01 1.8E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.99 0.02 0.89 -198.01 4.4E-01 1.8E-01 nonconstant variance, 

power restricted ≥1 

Hill 0 0.99 0.00 NA -196.03 4.1E-01 1.3E-01 nonconstant variance, 

n restricted >1 

linear 2 0.99 5.09 0.08 -194.93 2.8E+00 1.9E+00 nonconstant variance 

polynomial 1 0.99 0.08 0.78 -197.95 4.9E-01 2.7E-01 nonconstant variance 

power 2 0.99 5.09 0.08 -194.93 2.8E+00 1.9E+00 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.99 5.27 0.07 -196.72 2.8E+00 2.1E+00 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.99 5.27 0.07 -196.72 2.8E+00 2.1E+00 constant variance, 

power restricted ≥1 

exponential (M4)

c 1 0.99 0.02 0.89 -199.97 4.6E-01 2.1E-01 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.99 0.02 0.89 -199.97 4.6E-01 2.1E-01 constant variance, 

power restricted ≥1 

Hill 0 0.99 0.00 NA -197.99 4.3E-01 1.5E-01 constant variance, n 

restricted >1 

linear 2 0.99 5.10 0.08 -196.88 2.7E+00 1.9E+00 constant variance 

polynomial 1 0.99 0.08 0.78 -199.91 5.0E-01 3.0E-01 constant variance 

power 2 0.99 5.10 0.08 -196.88 2.7E+00 1.9E+00 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-396 —DO NOT CITE OR QUOTE 

1 E.3.14.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

2 ≥1 

 0.5

 0.55

 0.6

 0.65

 0.7

 0 1 2 3 4 5

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:11 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.14.3. Output File for Selected Model: Exponential (M4), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\ExpConstVar_BMR1_rel_male_brain_wt.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 14:11:05 2009 

15 ==================================================================== 

16 

17 Rel Male Brain wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-397 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 4 

19 -------- -------- 

20 lnalpha -6.07283 

21 rho(S) 0 

22 a 0.5111 

23 b 0.351325 

24 c 1.33125 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 4 

34 -------- ------- 

35 lnalpha -6.07239 

36 rho 0 

37 a 0.53911 

38 b 1.25838 

39 c 1.20224 

40 d 1 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 10 0.538 0.04743 

48 0.12 10 0.556 0.0506 

49 0.61 11 0.597 0.05307 

50 4.9 10 0.648 0.0506 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 0.5391 0.04802 -0.0731 

58 0.12 0.5544 0.04802 0.106 

59 0.61 0.5975 0.04802 -0.03703 

60 4.9 0.6479 0.04802 0.005972 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-398 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 103.9931 5 -197.9862 

14 A2 104.0646 8 -192.1293 

15 A3 103.9931 5 -197.9862 

16 R 92.4089 2 -180.8178 

17 4 103.9841 4 -199.9682 

18 

19 

20 Additive constant for all log-likelihoods = -37.68. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 

31 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

32 

33 

34 Tests of Interest 

35 

36 Test -2*log(Likelihood Ratio) D. F. p-value 

37 -------- ------------------------ ------ -------------- 

38 Test 1 23.31 6 0.0006986 

39 Test 2 0.1431 3 0.9862 

40 Test 3 0.1431 3 0.9862 

41 Test 6a 0.01798 1 0.8933 

42 

43 

44 The p-value for Test 1 is less than .05. There appears to be a 

45 difference between response and/or variances among the dose 

46 levels, it seems appropriate to model the data. 

47 

48 The p-value for Test 2 is greater than .1. A homogeneous 

49 variance model appears to be appropriate here. 

50 

51 The p-value for Test 3 is greater than .1. The modeled 

52 variance appears to be appropriate here. 

53 

54 The p-value for Test 6a is greater than .1. Model 4 seems 

55 to adequately describe the data. 

56 

57 

58 Benchmark Dose Computations: 

59 

60 Specified Effect = 1.000000 

61 

62 Risk Type = Estimated standard deviations from control 

63 

64 Confidence Level = 0.950000 

65 

66 BMD = 0.461347 

67 

68 BMDL = 0.209454 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-399 —DO NOT CITE OR QUOTE 

1 

2 E.3.15. DeCaprio et al. (1986): Relative Liver Weight, Females 

3 E.3.15.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2)

c 2 0.02 5.20 0.07 38.53 3.4E+00 2.1E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 1 0.02 4.15 0.04 39.48 4.7E+00 2.3E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.02 5.33 0.02 40.66 3.3E+00 1.9E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.02 4.15 N/A 41.48 4.6E+00 7.3E-01 nonconstant variance, 

power restricted ≥1 

Hill 0 0.02 4.15 NA 41.48 4.6E+00 7.5E-01 nonconstant variance, n 

restricted >1 

linear 2 0.02 5.33 0.07 38.66 3.3E+00 1.9E+00 nonconstant variance 

polynomial 1 0.02 2.86 0.09 38.20 4.9E+00 2.7E+00 nonconstant variance 

power 1 0.02 4.15 0.04 39.48 4.7E+00 2.2E+00 nonconstant variance, 

power restricted ≥1 

exponential (M2) 2 0.02 0.63 0.73 39.73 3.9E+00 2.7E+00 constant variance, power 

restricted ≥1 

exponential (M3) 1 0.02 0.30 0.58 41.40 4.7E+00 2.7E+00 constant variance, power 

restricted ≥1 

exponential (M4) 1 0.02 0.69 0.41 41.78 3.8E+00 1.2E+00 constant variance, power 

restricted ≥1 

exponential (M5) 0 0.02 0.30 N/A 43.40 4.7E+00 7.2E-01 constant variance, power 

restricted ≥1 

Hill 0 0.02 0.30 NA 43.40 4.7E+00 7.3E-01 constant variance, n 

restricted >1 

linear 2 0.02 0.68 0.71 39.78 3.8E+00 2.5E+00 constant variance 

polynomial 1 0.02 0.24 0.62 41.34 4.6E+00 1.2E+00 constant variance 

power 1 0.02 0.30 0.58 41.40 4.7E+00 2.5E+00 constant variance, power 

restricted ≥1 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

4 

5 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-400 —DO NOT CITE OR QUOTE 

1 E.3.15.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

 3.5

 4

 4.5

 5

 5.5

 6

 6.5

 0 1 2 3 4 5

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

14:10 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.15.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\Exp_BMR1_rel_fem_liver_wt.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 14:10:17 2009 

15 ==================================================================== 

16 

17 Relative Female Liver wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-401 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 4 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 2 

18 -------- -------- 

19 lnalpha -9.34924 

20 rho 5.89997 

21 a 4.0565 

22 b 0.378048 

23 c 1.43399 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 2 

31 -------- ------- 

32 lnalpha -6.47175 

33 rho 4.07772 

34 a 4.36037 

35 b 0.196303 

36 c 1.57543 

37 d 9.64518 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 8 4.3 0.7354 

45 0.12 10 4.49 1.107 

46 0.68 9 4.27 0.48 

47 4.86 10 5.54 1.36 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 4.312 0.7964 -0.04371 

55 0.12 4.338 0.8054 0.5953 

56 0.68 4.462 0.8483 -0.6795 

57 4.86 5.505 1.25 0.08976 

58 

59 

60 

61 Other models for which likelihoods are calculated: 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-402 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yij = Mu + e(i) 

3 Var{e(ij)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) DF AIC 

9 ------- ----------------- ---- ------------ 

10 A1 -16.54794 5 43.09588 

11 A2 -11.40563 8 38.81126 

12 A3 -12.66678 6 37.33356 

13 R -21.58737 2 47.17474 

14 2 -15.2671 4 38.53419 

15 

16 

17 Additive constant for all log-likelihoods = -34. This constant added to the 

18 above values gives the log-likelihood including the term that does not 

19 depend on the model parameters. 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

28 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) D. F. p-value 

33 -------- ------------------------ ------ -------------- 

34 Test 1 20.36 6 0.002385 

35 Test 2 10.28 3 0.0163 

36 Test 3 2.522 2 0.2833 

37 Test 4 5.201 2 0.07425 

38 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose 

42 levels, it seems appropriate to model the data. 

43 

44 The p-value for Test 2 is less than .1. A non-homogeneous 

45 variance model appears to be appropriate. 

46 

47 The p-value for Test 3 is greater than .1. The modeled 

48 variance appears to be appropriate here. 

49 

50 The p-value for Test 4 is less than .1. Model 2 may not adequately 

51 describe the data; you may want to consider another model. 

52 

53 

54 Benchmark Dose Computations: 

55 

56 Specified Effect = 1.000000 

57 

58 Risk Type = Estimated standard deviations from control 

59 

60 Confidence Level = 0.950000 

61 

62 BMD = 3.37444 

63 

64 BMDL = 2.10781 

65 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-403 —DO NOT CITE OR QUOTE 

1 E.3.16. DeCaprio et al. (1986): Relative Liver Weight, Males 

2 E.3.16.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 <0.0001 25.86 <0.0001 65.17 6.2E+00 3.7E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 1 <0.0001 25.30 <0.0001 66.60 5.1E+00 3.9E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 1 <0.0001 16.82 <0.0001 58.12 3.8E-01 1.4E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 <0.0001 7.80 N/A 51.11 3.5E-01 1.3E-01 nonconstant variance, 

power restricted ≥1 

Hill 1 <.0001 7.80 0.01 49.11 2.8E-01 error nonconstant variance, n 

restricted >1, bound hit 

linear 2 <.0001 25.90 <.0001 65.20 6.3E+00 3.4E+00 nonconstant variance 

polynomial 2 <.0001 25.39 <.0001 64.69 5.8E+00 4.4E+00 nonconstant variance 

power 1 <.0001 25.30 <.0001 66.60 5.1E+00 3.7E+00 nonconstant variance, 

power restricted ≥1 

exponential (M2) 2 <0.0001 5.09 0.08 64.15 5.6E+00 3.4E+00 constant variance, 

power restricted ≥1 

exponential (M3) 2 <0.0001 5.09 0.08 64.15 5.6E+00 3.4E+00 constant variance, 

power restricted ≥1 

exponential (M4) 1 <0.0001 2.15 0.14 63.21 1.1E+00 2.7E-01 constant variance, 

power restricted ≥1 

exponential (M5) 0 <0.0001 0.72 N/A 63.78 6.3E-01 1.3E-01 constant variance, 

power restricted ≥1 

Hill 0 <.0001 0.72 NA 63.78 6.5E-01 error constant variance, n 

restricted >1 

linear 2 <.0001 5.00 0.08 64.06 5.5E+00 3.2E+00 constant variance 

polynomial 2 <.0001 5.00 0.08 64.06 5.5E+00 3.2E+00 constant variance 

power 2 <.0001 5.00 0.08 64.06 5.5E+00 3.2E+00 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-404 —DO NOT CITE OR QUOTE 

1 E.3.16.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

 3.5

 4

 4.5

 5

 5.5

 6

 6.5

 7

 0 1 2 3 4 5

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:11 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.16.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\Exp_BMR1_rel_male_liver_wt.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 14:11:44 2009 

15 ==================================================================== 

16 

17 Rel Male Liver wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-405 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 4 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 4 

18 -------- -------- 

19 lnalpha -10.8833 

20 rho 6.71347 

21 a 3.895 

22 b 0.428412 

23 c 1.51772 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 4 

31 -------- ------- 

32 lnalpha -12.146 

33 rho 7.6297 

34 a 4.32 

35 b 2.79927 

36 c 1.2705 

37 d 18 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 10 4.54 0.7273 

45 0.12 10 4.1 0.4427 

46 0.61 11 5.36 2.023 

47 4.9 10 5.63 0.9171 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 4.333 0.6741 0.9699 

55 0.12 4.633 0.8928 -1.889 

56 0.61 5.172 1.417 0.4393 

57 4.9 5.338 1.617 0.5712 

58 

59 

60 

61 Other models for which likelihoods are calculated: 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-406 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yij = Mu + e(i) 

3 Var{e(ij)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) DF AIC 

9 ------- ----------------- ---- ------------ 

10 A1 -26.53142 5 63.06284 

11 A2 -13.9487 8 43.89739 

12 A3 -15.65277 6 43.30554 

13 R -31.57211 2 67.14421 

14 4 -24.06213 5 58.12426 

15 

16 

17 Additive constant for all log-likelihoods = -37.68. This constant added to the 

18 above values gives the log-likelihood including the term that does not 

19 depend on the model parameters. 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 

28 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

29 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) D. F. p-value 

34 -------- ------------------------ ------ -------------- 

35 Test 1 35.25 6 < 0.0001 

36 Test 2 25.17 3 < 0.0001 

37 Test 3 3.408 2 0.1819 

38 Test 6a 16.82 1 < 0.0001 

39 

40 

41 The p-value for Test 1 is less than .05. There appears to be a 

42 difference between response and/or variances among the dose 

43 levels, it seems appropriate to model the data. 

44 

45 The p-value for Test 2 is less than .1. A non-homogeneous 

46 variance model appears to be appropriate. 

47 

48 The p-value for Test 3 is greater than .1. The modeled 

49 variance appears to be appropriate here. 

50 

51 The p-value for Test 6a is less than .1. Model 4 may not adequately 

52 describe the data; you may want to consider another model. 

53 

54 

55 Benchmark Dose Computations: 

56 

57 Specified Effect = 1.000000 

58 

59 Risk Type = Estimated standard deviations from control 

60 

61 Confidence Level = 0.950000 

62 

63 BMD = 0.376095 

64 

65 BMDL = 0.137425 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-407 —DO NOT CITE OR QUOTE 

1 E.3.17. DeCaprio et al. (1986): Relative Thymus Weight, Males 

2 E.3.17.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.07 7.12 0.03 -308.01 6.0E+00 3.4E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.07 7.12 0.03 -308.01 6.0E+00 3.4E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.07 5.77 0.02 -307.36 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.07 5.77 0.02 -307.36 error error nonconstant variance, 

power restricted ≥1 

Hill 1 0.07 4.71 0.03 -308.42 error error 

nonconstant variance, 

n restricted >1, bound 

hit 

linear 2 0.07 7.19 0.03 -307.94 5.9E+00 3.6E+00 nonconstant variance 

polynomial 1 0.07 5.98 0.01 -307.16 2.0E+00 6.8E-01 nonconstant variance 

power 2 0.07 7351250 <0.0001 7350937 error error 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2)

c 2 0.07 4.25 0.12 -306.73 5.1E+00 2.8E+00 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.07 4.25 0.12 -306.73 5.1E+00 2.8E+00 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.07 3.29 0.07 -305.69 1.8E+00 7.6E-03 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.07 3.29 0.07 -305.69 1.8E+00 7.1E-03 constant variance, 

power restricted ≥1 

Hill 1 0.07 2.10 0.15 -306.88 3.2E-01 5.1E-07 

constant variance, n 

restricted >1, bound 

hit 

linear 2 0.07 4.30 0.12 -306.68 5.2E+00 3.1E+00 constant variance 

polynomial 1 0.07 3.48 0.06 -305.50 1.4E+00 5.1E-01 constant variance 

power 2 0.07 4.30 0.12 -306.68 5.2E+00 3.1E+00 

constant variance, 

power restricted ≥1, 

bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-408 —DO NOT CITE OR QUOTE 

1 E.3.17.2. Figure for selected Model: Exponential (M2), Constant Variance, Power Restricted 

2 ≥1 

 0.05

 0.055

 0.06

 0.065

 0.07

 0.075

 0.08

 0.085

 0.09

 0.095

 0 1 2 3 4 5

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

14:12 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.17.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\ExpConstVar_BMR1_rel_male_thymus_wt.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 14:12:33 2009 

15 ==================================================================== 

16 

17 Rel Male Thymus wt, Tbl 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-409 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 2 

19 -------- -------- 

20 lnalpha -8.73123 

21 rho(S) 0 

22 a 0.0819 

23 b 0.468839 

24 c 0.686086 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 2 

34 -------- ------- 

35 lnalpha -8.65107 

36 rho 0 

37 a 0.0739582 

38 b 1.27978 

39 c 0.80201 

40 d 1 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 10 0.078 0.01897 

48 0.12 10 0.066 0.009487 

49 0.61 11 0.068 0.01327 

50 4.9 10 0.059 0.009487 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 0.07145 0.01338 1.548 

58 0.12 0.0711 0.01338 -1.205 

59 0.61 0.0697 0.01338 -0.4219 

60 4.9 0.05857 0.01338 0.1014 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-410 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 158.4903 5 -306.9805 

14 A2 161.9563 8 -307.9126 

15 A3 158.4903 5 -306.9805 

16 R 153.4442 2 -302.8885 

17 2 156.3648 3 -306.7296 

18 

19 

20 Additive constant for all log-likelihoods = -37.68. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

31 

32 

33 Tests of Interest 

34 

35 Test -2*log(Likelihood Ratio) D. F. p-value 

36 -------- ------------------------ ------ -------------- 

37 Test 1 17.02 6 0.009195 

38 Test 2 6.932 3 0.07409 

39 Test 3 6.932 3 0.07409 

40 Test 4 4.251 2 0.1194 

41 

42 

43 The p-value for Test 1 is less than .05. There appears to be a 

44 difference between response and/or variances among the dose 

45 levels, it seems appropriate to model the data. 

46 

47 The p-value for Test 2 is less than .1. Consider running 

48 a non-homogeneous variance model. 

49 

50 The p-value for Test 3 is less than .1. You may want to 

51 consider a different variance model. 

52 

53 The p-value for Test 4 is greater than .1. Model 2 seems 

54 to adequately describe the data. 

55 

56 

57 Benchmark Dose Computations: 

58 

59 Specified Effect = 1.000000 

60 

61 Risk Type = Estimated standard deviations from control 

62 

63 Confidence Level = 0.950000 

64 

65 BMD = 5.11373 

66 

67 BMDL = 2.82487 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-411 —DO NOT CITE OR QUOTE 

1 E.3.18. Hojo et al. (2002): DRL Reinforce per Min 

2 E.3.18.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.43 9.01 0.01 10.48 6.9E+02 1.7E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 1 0.43 8.95 0.00 12.43 3.9E+02 1.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.43 2.92 0.09 6.39 1.0E+01 1.5E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.43 2.31 N/A 7.78 2.0E+01 error nonconstant variance, 

power restricted ≥1 

Hill 1 0.43 1.#QNAN <.0001 7.60 error error nonconstant variance, 

n restricted >1 

linear 2 0.43 9.21 0.01 11.02 error error nonconstant variance 

polynomial 2 0.43 8.79 0.01 10.60 error 4.4E+02 nonconstant variance 

power 2 0.43 8.28 0.02 9.98 error error 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.43 10.12 0.01 9.89 3.0E+02 1.5E+02 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.43 10.12 0.01 9.89 3.0E+02 1.5E+02 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.43 3.47 0.06 5.24 1.7E+01 3.8E-02 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.43 2.70 N/A 6.46 2.1E+01 1.2E-05 constant variance, 

power restricted ≥1 

Hill 0 0.43 2.70 NA 6.46 2.1E+01 1.7E-05 constant variance, n 

restricted >1 

linear c 2 0.43 9.78 0.01 9.55 2.7E+02 1.1E+02 constant variance 

polynomial 2 0.43 9.78 0.01 9.55 2.7E+02 1.1E+02 constant variance 

power 2 0.43 9.78 0.01 9.55 2.7E+02 1.1E+02 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-412 —DO NOT CITE OR QUOTE 

1 E.3.18.2. Figure for Selected Model: Linear, Constant Variance 

-1.5

-1

-0.5

 0

 0.5

 1

 0 50 100 150 200 250

Mean Response

dose

Linear Model with 0.95 Confidence Level

14:33 10/06 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.3.18.3. Output File for Selected Model: Linear, Constant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\AniDose\LinearConstVar_BMR1_DRL_reinforce_per_min.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AniDose\LinearConstVar_BMR1_DRL_reinforce_per_min.plt 

13 Tue Oct 06 14:33:14 2009 

14 ==================================================================== 

15 

16 Table 5 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Signs of the polynomial coefficients are not restricted 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-413 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 0.337763 

4 rho = 0 Specified 

5 beta_0 = -0.404 

6 beta_1 = 0.00249615 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 ( *** The model parameter(s) -rho 

12 have been estimated at a boundary point, or have been specified by the user, 

13 and do not appear in the correlation matrix ) 

14 

15 alpha beta_0 beta_1 

16 

17 alpha 1 -1.4e-008 2.2e-008 

18 

19 beta_0 -1.4e-008 1 -0.69 

20 

21 beta_1 2.2e-008 -0.69 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 alpha 0.435671 0.134451 0.172152 0.69919 

30 beta_0 -0.372098 0.198702 -0.761547 0.017352 

31 beta_1 0.00246548 0.00211361 -0.00167711 0.00660807 

32 

33 

34 

35 Table of Data and Estimated Values of Interest 

36 

37 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

38 ------ --- -------- -------- ----------- ----------- ---------- 

39 

40 0 5 -0.814 -0.372 0.448 0.66 -1.5 

41 20 5 -0.364 -0.323 0.821 0.66 -0.14 

42 60 6 0.374 -0.224 0.54 0.66 2.22 

43 180 5 -0.163 0.0717 0.443 0.66 -0.795 

44 

45 

46 

47 Model Descriptions for likelihoods calculated 

48 

49 

50 Model A1: Yij = Mu(i) + e(ij) 

51 Var{e(ij)} = Sigma^2 

52 

53 Model A2: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma(i)^2 

55 

56 Model A3: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma^2 

58 Model A3 uses any fixed variance parameters that 

59 were specified by the user 

60 

61 Model R: Yi = Mu + e(i) 

62 Var{e(i)} = Sigma^2 

63 

64 

65 Likelihoods of Interest 

66 

67 Model Log(likelihood) # Param's AIC 

68 A1 3.115550 5 3.768900 

69 A2 4.489557 8 7.020886 

70 A3 3.115550 5 3.768900 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-414 —DO NOT CITE OR QUOTE 

1 fitted -1.775882 3 9.551763 

2 R -2.435087 2 8.870174 

3 

4 

5 Explanation of Tests 

6 

7 Test 1: Do responses and/or variances differ among Dose levels? 

8 (A2 vs. R) 

9 Test 2: Are Variances Homogeneous? (A1 vs A2) 

10 Test 3: Are variances adequately modeled? (A2 vs. A3) 

11 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

12 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

13 

14 Tests of Interest 

15 

16 Test -2*log(Likelihood Ratio) Test df p-value 

17 

18 Test 1 13.8493 6 0.03137 

19 Test 2 2.74801 3 0.4321 

20 Test 3 2.74801 3 0.4321 

21 Test 4 9.78286 2 0.007511 

22 

23 The p-value for Test 1 is less than .05. There appears to be a 

24 difference between response and/or variances among the dose levels 

25 It seems appropriate to model the data 

26 

27 The p-value for Test 2 is greater than .1. A homogeneous variance 

28 model appears to be appropriate here 

29 

30 

31 The p-value for Test 3 is greater than .1. The modeled variance appears 

32 to be appropriate here 

33 

34 The p-value for Test 4 is less than .1. You may want to try a different 

35 model 

36 

37 

38 Benchmark Dose Computation 

39 

40 Specified effect = 1 

41 

42 Risk Type = Estimated standard deviations from the control mean 

43 

44 Confidence level = 0.95 

45 

46 BMD = 267.718 

47 

48 

49 BMDL = 110.032 

50 

51 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-415 —DO NOT CITE OR QUOTE 

1 E.3.19. Hojo et al. (2002): DRL Response per Min 

2 E.3.19.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.30 -0.14 N/A 122.33 4.3E+00 error nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.30 25.76 <0.0001 148.23 error error nonconstant variance, 

power restricted ≥1 

exponential (M4) 2 0.30 -0.12 N/A 122.35 4.7E+00 3.2E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.30 0.16 0.69 124.63 6.4E+00 4.1E-01 nonconstant variance, 

power restricted ≥1 

Hill 0 0.30 1.#QNAN NA 127.53 1.3E+01 1.8E-13 nonconstant variance, 

n restricted >1 

linear 2 0.30 11.09 0.00 133.30 2.1E+02 9.9E+01 nonconstant variance 

polynomial 2 0.30 11.09 0.00 133.30 2.1E+02 error nonconstant variance 

power 2 0.30 12.33 0.00 133.30 2.2E+02 9.6E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.30 1.13 0.57 122.98 6.2E+00 error constant variance, 

power restricted ≥1 

exponential (M3) 2 0.30 1.13 0.57 122.98 6.2E+00 error constant variance, 

power restricted ≥1 

exponential (M4)

c 1 0.30 0.50 0.48 124.36 4.8E+00 2.7E-01 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.30 0.50 N/A 126.35 1.1E+01 2.1E-01 constant variance, 

power restricted ≥1 

Hill 0 0.30 0.50 NA 126.35 1.6E+01 1.8E-13 constant variance, n 

restricted >1 

linear 2 0.30 10.97 0.00 132.83 2.1E+02 9.8E+01 constant variance 

polynomial 2 0.30 10.97 0.00 132.83 2.1E+02 9.8E+01 constant variance 

power 2 0.30 10.97 0.00 132.83 2.1E+02 9.8E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-416 —DO NOT CITE OR QUOTE 

1 E.3.19.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

2 ≥1 

-10

 0

 10

 20

 30

 0 20 40 60 80 100 120 140 160 180

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:34 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.19.3. Output File for Selected Model: Exponential (M4), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\ExpConstVar_BMR1_DRL_response_per_min.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 14:34:01 2009 

15 ==================================================================== 

16 

17 Table 5, values adjusted by a constant to allow exponential model 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-417 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 4 

19 -------- -------- 

20 lnalpha 4.51689 

21 rho(S) 0 

22 a 24.6362 

23 b 0.0212679 

24 c 0.0184785 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 4 

34 -------- ------- 

35 lnalpha 4.54064 

36 rho 0 

37 a 23.463 

38 b 0.073228 

39 c 0.100111 

40 d 2.44375 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 5 23.46 7.986 

48 20 5 4.013 10.96 

49 60 6 0.478 7.194 

50 180 5 4.594 15.23 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 23.47 9.683 -0.0004677 

58 20 3.973 9.683 0.009182 

59 60 2.37 9.683 -0.4787 

60 180 2.361 9.683 0.5157 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-418 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 -57.92733 5 125.8547 

14 A2 -56.09669 8 128.1934 

15 A3 -57.92733 5 125.8547 

16 R -64.49611 2 132.9922 

17 4 -58.17787 4 124.3557 

18 

19 

20 Additive constant for all log-likelihoods = -19.3. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 

31 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

32 

33 

34 Tests of Interest 

35 

36 Test -2*log(Likelihood Ratio) D. F. p-value 

37 -------- ------------------------ ------ -------------- 

38 Test 1 16.8 6 0.01005 

39 Test 2 3.661 3 0.3004 

40 Test 3 3.661 3 0.3004 

41 Test 6a 0.5011 1 0.479 

42 

43 

44 The p-value for Test 1 is less than .05. There appears to be a 

45 difference between response and/or variances among the dose 

46 levels, it seems appropriate to model the data. 

47 

48 The p-value for Test 2 is greater than .1. A homogeneous 

49 variance model appears to be appropriate here. 

50 

51 The p-value for Test 3 is greater than .1. The modeled 

52 variance appears to be appropriate here. 

53 

54 The p-value for Test 6a is greater than .1. Model 4 seems 

55 to adequately describe the data. 

56 

57 

58 Benchmark Dose Computations: 

59 

60 Specified Effect = 1.000000 

61 

62 Risk Type = Estimated standard deviations from control 

63 

64 Confidence Level = 0.950000 

65 

66 BMD = 4.77493 

67 

68 BMDL = 0.270447 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-419 —DO NOT CITE OR QUOTE 

E.3.20. Kattainen et al. (2001): 3rd 1 Molar Mesio-Distal Length (Molar Development) 

2 E.3.20.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 <0.0001 38.91 <0.0001 -122.95 4.0E+02 2.4E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 38.91 <0.0001 -122.95 4.0E+02 2.4E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 2 <0.0001 79.12 <0.0001 -80.75 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 <0.0001 79.12 <0.0001 -78.75 error error nonconstant variance, 

power restricted ≥1 

Hill c 2 <.0001 8.72 0.01 -151.15 4.1E+00 2.1E+00 

nonconstant 

variance, n 

restricted >1, bound 

hit 

linear 3 <.0001 39.54 <.0001 -122.33 4.7E+02 3.0E+02 nonconstant variance 

polynomial 2 <.0001 36.57 <.0001 -123.30 1.9E+02 9.0E+01 nonconstant variance 

power 3 <.0001 39.54 <.0001 -122.33 4.7E+02 3.0E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 3 <0.0001 7.81 0.05 -99.70 8.5E+02 5.6E+02 constant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 7.81 0.05 -99.70 8.5E+02 5.6E+02 constant variance, 

power restricted ≥1 

exponential (M4) 2 <0.0001 5.05 0.08 -100.47 2.3E+02 1.0E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 5.05 0.08 -100.47 2.3E+02 8.1E-01 constant variance, 

power restricted ≥1 

Hill 2 <.0001 3.23 0.20 -102.29 8.1E+01 1.1E+01 

constant variance, n 

restricted >1, bound 

hit 

linear 3 <.0001 8.07 0.04 -99.45 8.8E+02 6.2E+02 constant variance 

polynomial 2 <.0001 5.88 0.05 -99.64 3.7E+02 1.8E+02 constant variance 

power 3 <.0001 8.07 0.04 -99.45 8.8E+02 6.2E+02 

constant variance, 

power restricted ≥1, 

bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-420 —DO NOT CITE OR QUOTE 

1 E.3.20.2. Figure for Selected Model: Hill, Nonconstant Variance, n Restricted >1, Bound Hit 

 1.1

 1.2

 1.3

 1.4

 1.5

 1.6

 1.7

 1.8

 1.9

 0 200 400 600 800 1000

Mean Response

dose

Hill Model with 0.95 Confidence Level

14:36 10/06 2009

BMDLBMD

 

Hill

2 

3 

4 

5 E.3.20.3. Output File for Selected Model: Hill, Nonconstant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AniDose\Hill_BMR1_3rd_molar.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\Hill_BMR1_3rd_molar.plt 

13 Tue Oct 06 14:36:22 2009 

14 ==================================================================== 

15 

16 Figure 3 female only 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter restricted to be greater than 1 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-421 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = -2.37155 

3 rho = 0 

4 intercept = 1.85591 

5 v = -0.507874 

6 n = 0.826204 

7 k = 27.3305 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -n 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 lalpha rho intercept v k 

17 

18 lalpha 1 -0.98 -0.16 0.84 -0.37 

19 

20 rho -0.98 1 0.2 -0.79 0.39 

21 

22 intercept -0.16 0.2 1 -0.31 -0.11 

23 

24 v 0.84 -0.79 -0.31 1 -0.48 

25 

26 k -0.37 0.39 -0.11 -0.48 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence Interval 

33 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

34 lalpha 3.34561 1.40443 0.592981 6.09824 

35 rho -14.3325 2.62129 -19.4701 -9.19484 

36 intercept 1.8548 0.0159017 1.82364 1.88597 

37 v -0.441166 0.058852 -0.556513 -0.325818 

38 n 1 NA 

39 k 24.0343 7.84495 8.65852 39.4101 

40 

41 NA - Indicates that this parameter has hit a bound 

42 implied by some inequality constraint and thus 

43 has no standard error. 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 16 1.86 1.85 0.0661 0.0637 0.0692 

53 30 17 1.58 1.61 0.185 0.176 -0.768 

54 100 15 1.6 1.5 0.265 0.293 1.28 

55 300 12 1.5 1.45 0.221 0.378 0.527 

56 1000 19 1.35 1.42 0.515 0.423 -0.783 

57 

58 

59 

60 Model Descriptions for likelihoods calculated 

61 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-422 —DO NOT CITE OR QUOTE 

1 Model A3 uses any fixed variance parameters that 

2 were specified by the user 

3 

4 Model R: Yi = Mu + e(i) 

5 Var{e(i)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) # Param's AIC 

11 A1 56.758717 6 -101.517434 

12 A2 85.856450 10 -151.712901 

13 A3 84.934314 7 -155.868628 

14 fitted 80.575940 5 -151.151880 

15 R 45.373551 2 -86.747101 

16 

17 

18 Explanation of Tests 

19 

20 Test 1: Do responses and/or variances differ among Dose levels? 

21 (A2 vs. R) 

22 Test 2: Are Variances Homogeneous? (A1 vs A2) 

23 Test 3: Are variances adequately modeled? (A2 vs. A3) 

24 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

25 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

26 

27 Tests of Interest 

28 

29 Test -2*log(Likelihood Ratio) Test df p-value 

30 

31 Test 1 80.9658 8 <.0001 

32 Test 2 58.1955 4 <.0001 

33 Test 3 1.84427 3 0.6053 

34 Test 4 8.71675 2 0.0128 

35 

36 The p-value for Test 1 is less than .05. There appears to be a 

37 difference between response and/or variances among the dose levels 

38 It seems appropriate to model the data 

39 

40 The p-value for Test 2 is less than .1. A non-homogeneous variance 

41 model appears to be appropriate 

42 

43 The p-value for Test 3 is greater than .1. The modeled variance appears 

44 to be appropriate here 

45 

46 The p-value for Test 4 is less than .1. You may want to try a different 

47 model 

48 

49 

50 Benchmark Dose Computation 

51 

52 Specified effect = 1 

53 

54 Risk Type = Estimated standard deviations from the control mean 

55 

56 Confidence level = 0.95 

57 

58 BMD = 4.05231 

59 

60 BMDL = 2.14357 

61 

62 

63 

64 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-423 —DO NOT CITE OR QUOTE 

E.3.21. Kattainen et al. (2001): Females 3rd 1 Molar Eruption 

2 E.3.21.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

logistic 3 3.73 0.29 89.06 1.0E+02 7.3E+01 

logistic 3 3.73 0.29 89.06 1.9E+02 1.4E+02 

log-logistic b 3 0.48 0.92 85.53 2.3E+01 1.2E+01 slope restricted ≥1, 

bound hit 

log-logistic 3 0.48 0.92 85.53 4.8E+01 2.5E+01 slope restricted ≥1, bound 

hit 

log-probit 2 0.12 0.94 87.18 1.3E+01 5.2E-01 slope restricted ≥1 

log-probit 2 0.12 0.94 87.18 2.8E+01 2.3E+00 slope restricted ≥1 

multistage, 1-

degree 3 1.68 0.64 86.80 4.2E+01 2.7E+01 betas restricted ≥0 

multistage, 1-

degree 3 1.68 0.64 86.80 8.7E+01 5.5E+01 betas restricted ≥0 

probit 3 3.62 0.31 88.92 9.8E+01 7.1E+01 

probit 3 3.62 0.31 88.92 1.9E+02 1.4E+02 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-424 —DO NOT CITE OR QUOTE 

1 E.3.21.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 0 200 400 600 800 1000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:05 10/15 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.3.21.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: 

11 C:\USEPA\BMDS21\AniDose2\LogLogistic_BMR1_Female_3rd_molar_eruption.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AniDose2\LogLogistic_BMR1_Female_3rd_molar_eruption.plt 

14 Thu Oct 15 11:05:20 2009 

15 ==================================================================== 

16 

17 Figure 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the probability function is: 

21 

22 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

23 

24 

25 Dependent variable = DichEff 

26 Independent variable = Dose 

27 Slope parameter is restricted as slope <= 1 

28 

29 Total number of observations = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-425 —DO NOT CITE OR QUOTE 

1 User has chosen the log transformed model 

2 

3 

4 Default Initial Parameter Values 

5 background = 0.0625 

6 intercept = -6.063 

7 slope = 1 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -slope 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 background intercept 

17 

18 background 1 -0.56 

19 

20 intercept -0.56 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 background 0.0846785 * * * 

29 intercept -6.06063 * * * 

30 slope 1 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -40.5286 5 

40 Fitted model -40.7674 2 0.477533 3 0.9238 

41 Reduced model -50.7341 1 20.411 4 0.0004142 

42 

43 AIC: 85.5347 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0847 1.355 1.000 16 -0.319 

51 30.0000 0.1445 2.457 3.000 17 0.374 

52 100.0000 0.2578 3.867 4.000 15 0.078 

53 300.0000 0.4615 5.538 6.000 12 0.267 

54 1000.0000 0.7254 13.782 13.000 19 -0.402 

55 

56 Chi^2 = 0.48 d.f. = 3 P-value = 0.9231 

57 

58 

59 Benchmark Dose Computation 

60 

61 Specified effect = 0.05 

62 

63 Risk Type = Extra risk 

64 

65 Confidence level = 0.95 

66 

67 BMD = 22.5603 

68 

69 BMDL = 11.7531 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-426 —DO NOT CITE OR QUOTE 

1 E.3.22. Keller et al. (2006): Missing Mandibular Molars in CBA J Mice 

2 E.3.22.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 1 2.63 0.10 52.49 5.2E+01 9.9E+00 power restricted ≥1 

gamma 1 2.63 0.10 52.49 7.3E+01 2.0E+01 power restricted ≥1 

logistic 2 2.28 0.32 50.10 4.6E+01 3.1E+01 

logistic 2 2.28 0.32 50.10 7.2E+01 5.1E+01 

log-logistic 1 2.62 0.11 52.52 8.5E+01 3.6E+01 slope restricted ≥1 

log-logistic 1 2.62 0.11 52.52 9.3E+01 5.3E+01 slope restricted ≥1 

log-probit 1 2.62 0.11 52.52 7.8E+01 3.9E+01 slope restricted ≥1 

log-probit 1 2.62 0.11 52.52 8.9E+01 5.3E+01 slope restricted ≥1 

multistage, 2-

degree 1 2.34 0.13 51.52 2.4E+01 1.1E+01 betas restricted ≥0 

multistage, 1-

degree b 3 3.87 0.28 49.41 1.4E+01 9.2E+00 betas restricted ≥0 

multistage, 2-

degree 1 2.34 0.13 51.52 4.6E+01 2.2E+01 betas restricted ≥0 

multistage, 1-

degree 3 3.87 0.28 49.41 2.8E+01 1.9E+01 betas restricted ≥0 

probit 2 2.25 0.32 50.03 4.3E+01 2.8E+01 

probit 2 2.25 0.32 50.03 6.8E+01 4.8E+01 

Weibull 1 2.58 0.11 52.22 3.7E+01 1.0E+01 power restricted ≥1 

Weibull 1 2.58 0.11 52.22 6.1E+01 2.1E+01 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-427 —DO NOT CITE OR QUOTE 

1 E.3.22.2. Figure for Selected Model: Multistage, 1-Degree, Betas Restricted ≥0 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 200 400 600 800 1000

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:04 10/15 2009

BMDLBMD

 

Multistage

2 

3 

4 

5 E.3.22.3. Output File for Selected Model: Multistage, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AniDose2\Multi1st_BMR1_CBA_J_mandibular.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose2\Multi1st_BMR1_CBA_J_mandibular.plt 

12 Thu Oct 15 11:04:49 2009 

13 ==================================================================== 

14 

15 Table 1 using mandibular molars only 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

36 Maximum number of iterations = 250 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-428 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 Background = 0 

8 Beta(1) = 1.02909e+017 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -Background 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 Beta(1) 

18 

19 Beta(1) 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0 * * * 

28 Beta(1) 0.00379264 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -21.5798 4 

38 Fitted model -23.7044 1 4.24924 3 0.2358 

39 Reduced model -71.326 1 99.4926 3 <.0001 

40 

41 AIC: 49.4088 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0000 0.000 0.000 29 0.000 

49 10.0000 0.0372 0.856 2.000 23 1.260 

50 100.0000 0.3156 9.153 6.000 29 -1.260 

51 1000.0000 0.9775 29.324 30.000 30 0.832 

52 

53 Chi^2 = 3.87 d.f. = 3 P-value = 0.2762 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.05 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 13.5244 

65 

66 BMDL = 9.17426 

67 

68 BMDU = 20.3135 

69 

70 Taken together, (9.17426, 20.3135) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-429 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 

4 

5 E.3.23. Kociba et al. (1978): Urinary Coproporphyrins, Females (Table 2) 

6 E.3.23.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.03 19.68 <0.0001 84.01 7.1E+01 4.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.03 19.68 <0.0001 84.01 7.1E+01 4.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 1 0.03 4.23 0.04 70.56 1.6E+00 7.3E-01 

nonconstant 

variance, power 

restricted ≥1 

exponential (M5) 0 0.03 0.76 N/A 69.09 3.1E+00 1.0E+00 nonconstant variance, 

power restricted ≥1 

linear 2 0.03 19.38 <.0001 83.71 6.2E+01 3.1E+01 nonconstant variance 

polynomial 2 0.03 19.38 <.0001 83.71 6.2E+01 3.1E+01 nonconstant variance 

power 2 0.03 19.38 <.0001 83.71 6.2E+01 3.1E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.03 12.65 0.00 82.04 6.9E+01 4.7E+01 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.03 12.65 0.00 82.04 6.9E+01 4.7E+01 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.03 1.96 0.16 73.36 2.7E+00 1.1E+00 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.03 0.41 N/A 73.80 8.3E+00 1.0E+00 constant variance, 

power restricted ≥1 

Hill 0 0.03 0.41 NA 73.80 7.6E+00 error constant variance, n 

restricted >1 

linear 2 0.03 12.32 0.00 81.72 6.1E+01 3.8E+01 constant variance 

polynomial 2 0.03 12.32 0.00 81.72 6.1E+01 3.8E+01 constant variance 

power 2 0.03 12.32 0.00 81.72 6.1E+01 3.8E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

7 

8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-430 —DO NOT CITE OR QUOTE 

1 E.3.23.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

 6

 8

 10

 12

 14

 16

 18

 20

 22

 24

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:21 11/11 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.23.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Exp_BMR1_urin_copropor_f.(d) 

13 Gnuplot Plotting File: 

14 Wed Nov 11 13:21:02 2009 

15 ==================================================================== 

16 

17 Table2-UrinaryCoproporphyrin 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-431 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 4 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 4 

18 -------- -------- 

19 lnalpha -5.58269 

20 rho 2.98472 

21 a 8.17 

22 b 0.0259469 

23 c 2.23623 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 4 

31 -------- ------- 

32 lnalpha -5.49254 

33 rho 2.91176 

34 a 9.2 

35 b 0.295128 

36 c 1.83696 

37 d 18 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 5 9.8 1.3 

45 1 5 8.6 2 

46 10 5 16.4 4.7 

47 100 5 17.4 4 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 8.93 1.733 1.122 

55 1 10.04 2.038 -1.582 

56 10 15.42 3.683 0.5967 

57 100 17.64 4.436 -0.1211 

58 

59 

60 

61 Other models for which likelihoods are calculated: 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-432 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yij = Mu + e(i) 

3 Var{e(ij)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) DF AIC 

9 ------- ----------------- ---- ------------ 

10 A1 -31.69739 5 73.39478 

11 A2 -27.21541 8 70.43081 

12 A3 -28.16434 6 68.32868 

13 R -41.73188 2 87.46376 

14 4 -30.27804 5 70.55608 

15 

16 

17 Additive constant for all log-likelihoods = -18.38. This constant added to the 

18 above values gives the log-likelihood including the term that does not 

19 depend on the model parameters. 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 

28 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

29 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) D. F. p-value 

34 -------- ------------------------ ------ -------------- 

35 Test 1 29.03 6 < 0.0001 

36 Test 2 8.964 3 0.02977 

37 Test 3 1.898 2 0.3872 

38 Test 6a 4.227 1 0.03978 

39 

40 

41 The p-value for Test 1 is less than .05. There appears to be a 

42 difference between response and/or variances among the dose 

43 levels, it seems appropriate to model the data. 

44 

45 The p-value for Test 2 is less than .1. A non-homogeneous 

46 variance model appears to be appropriate. 

47 

48 The p-value for Test 3 is greater than .1. The modeled 

49 variance appears to be appropriate here. 

50 

51 The p-value for Test 6a is less than .1. Model 4 may not adequately 

52 describe the data; you may want to consider another model. 

53 

54 

55 Benchmark Dose Computations: 

56 

57 Specified Effect = 1.000000 

58 

59 Risk Type = Estimated standard deviations from control 

60 

61 Confidence Level = 0.950000 

62 

63 BMD = 1.62505 

64 

65 BMDL = 0.729987 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-433 —DO NOT CITE OR QUOTE 

1 E.3.24. Kociba et al. (1978): Uroporphyrin per Creatinine, Females 

2 E.3.24.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.49 1.45 0.48 -93.10 3.8E+01 2.6E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.49 1.45 0.48 -93.10 3.8E+01 2.6E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.49 0.73 0.39 -91.82 1.4E+01 4.4E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.49 0.51 N/A -90.03 1.0E+01 4.5E+00 nonconstant variance, 

power restricted ≥1 

Hill 0 0.49 0.51 NA -90.03 1.0E+01 7.7E+00 nonconstant variance, n 

restricted >1 

linear 2 0.49 1.20 0.55 -93.35 2.9E+01 1.8E+01 nonconstant variance 

polynomial 1 0.49 0.72 0.40 -91.83 1.3E+01 4.8E+00 nonconstant variance 

power 2 0.49 1.20 0.55 -93.35 2.9E+01 1.8E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.49 0.83 0.66 -93.56 4.4E+01 3.3E+01 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.49 0.83 0.66 -93.56 4.4E+01 3.3E+01 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.49 0.31 0.58 -92.08 1.7E+01 5.5E+00 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.49 0.20 N/A -90.19 1.1E+01 5.6E+00 constant variance, 

power restricted ≥1 

linear c 2 0.49 0.66 0.72 -93.73 3.5E+01 2.5E+01 constant variance 

polynomial 1 0.49 0.31 0.58 -92.08 1.7E+01 6.1E+00 constant variance 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-434 —DO NOT CITE OR QUOTE 

1 E.3.24.2. Figure for Selected Model: Linear, Constant Variance 

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 20 40 60 80 100

Mean Response

dose

Linear Model with 0.95 Confidence Level

15:00 10/06 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.3.24.3. Output File for Selected Model: Linear, Constant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: 

11 C:\USEPA\BMDS21\AniDose\LinearConstVar_BMR1_Females_uroporphyrin_per_creatinine.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AniDose\LinearConstVar_BMR1_Females_uroporphyrin_per_creatinine.plt 

14 Tue Oct 06 15:00:16 2009 

15 ==================================================================== 

16 

17 Table 2 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 rho is set to 0 

28 Signs of the polynomial coefficients are not restricted 

29 A constant variance model is fit 

30 

31 Total number of dose groups = 4 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-435 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 alpha = 0.0030385 

5 rho = 0 Specified 

6 beta_0 = 0.154759 

7 beta_1 = 0.0014231 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -rho 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 alpha beta_0 beta_1 

17 

18 alpha 1 -2.2e-009 3.5e-009 

19 

20 beta_0 -2.2e-009 1 -0.55 

21 

22 beta_1 3.5e-009 -0.55 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 0.00251184 0.000794315 0.000955015 0.00406867 

31 beta_0 0.154759 0.0134422 0.128413 0.181105 

32 beta_1 0.0014231 0.000267497 0.000898818 0.00194739 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 5 0.157 0.155 0.05 0.0501 0.1 

42 1 5 0.143 0.156 0.037 0.0501 -0.588 

43 10 5 0.181 0.169 0.053 0.0501 0.536 

44 100 5 0.296 0.297 0.074 0.0501 -0.0477 

45 

46 

47 

48 Model Descriptions for likelihoods calculated 

49 

50 

51 Model A1: Yij = Mu(i) + e(ij) 

52 Var{e(ij)} = Sigma^2 

53 

54 Model A2: Yij = Mu(i) + e(ij) 

55 Var{e(ij)} = Sigma(i)^2 

56 

57 Model A3: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 Model A3 uses any fixed variance parameters that 

60 were specified by the user 

61 

62 Model R: Yi = Mu + e(i) 

63 Var{e(i)} = Sigma^2 

64 

65 

66 Likelihoods of Interest 

67 

68 Model Log(likelihood) # Param's AIC 

69 A1 50.195349 5 -90.390697 

70 A2 51.400051 8 -86.800103 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-436 —DO NOT CITE OR QUOTE 

1 A3 50.195349 5 -90.390697 

2 fitted 49.867385 3 -93.734769 

3 R 41.049755 2 -78.099510 

4 

5 

6 Explanation of Tests 

7 

8 Test 1: Do responses and/or variances differ among Dose levels? 

9 (A2 vs. R) 

10 Test 2: Are Variances Homogeneous? (A1 vs A2) 

11 Test 3: Are variances adequately modeled? (A2 vs. A3) 

12 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

13 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

14 

15 Tests of Interest 

16 

17 Test -2*log(Likelihood Ratio) Test df p-value 

18 

19 Test 1 20.7006 6 0.002076 

20 Test 2 2.40941 3 0.4919 

21 Test 3 2.40941 3 0.4919 

22 Test 4 0.655928 2 0.7204 

23 

24 The p-value for Test 1 is less than .05. There appears to be a 

25 difference between response and/or variances among the dose levels 

26 It seems appropriate to model the data 

27 

28 The p-value for Test 2 is greater than .1. A homogeneous variance 

29 model appears to be appropriate here 

30 

31 

32 The p-value for Test 3 is greater than .1. The modeled variance appears 

33 to be appropriate here 

34 

35 The p-value for Test 4 is greater than .1. The model chosen seems 

36 to adequately describe the data 

37 

38 

39 Benchmark Dose Computation 

40 

41 Specified effect = 1 

42 

43 Risk Type = Estimated standard deviations from the control mean 

44 

45 Confidence level = 0.95 

46 

47 BMD = 35.2176 

48 

49 

50 BMDL = 25.0024 

51 

52 

53 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-437 —DO NOT CITE OR QUOTE 

1 E.3.25. Latchoumycandane and Mathur (2002): Daily sperm Production 

2 E.3.25.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.85 20.91 <0.0001 96.01 9.2E+01 4.5E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.85 20.91 <0.0001 96.01 9.2E+01 4.5E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.85 0.16 0.69 77.26 2.4E-01 8.8E-02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.85 0.16 N/A 79.26 2.9E-01 8.8E-02 nonconstant variance, 

power restricted ≥1 

Hill 1 0.85 0.04 0.85 77.14 1.4E-01 1.3E-02 nonconstant variance, n 

restricted >1, bound hit 

linear 2 0.85 21.07 <.0001 96.18 9.5E+01 5.4E+01 nonconstant variance 

polynomial 1 0.85 10.98 0.00 88.08 6.2E+00 3.7E+00 nonconstant variance 

power 2 0.85 21.07 <.0001 96.18 9.5E+01 5.4E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.85 21.99 <0.0001 95.11 7.6E+01 4.0E+01 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.85 21.99 <0.0001 95.11 7.6E+01 4.0E+01 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.85 0.15 0.70 75.26 2.4E-01 1.0E-01 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.85 0.15 N/A 77.26 3.7E-01 1.0E-01 constant variance, 

power restricted ≥1 

Hill c 1 0.85 0.03 0.86 75.14 1.4E-01 1.6E-02 

constant variance, n 

restricted >1, bound 

hit 

linear 2 0.85 22.20 <.0001 95.31 8.3E+01 4.9E+01 constant variance 

polynomial 1 0.85 12.98 0.00 88.09 5.0E+00 3.2E+00 constant variance 

power 2 0.85 22.20 <.0001 95.31 8.3E+01 4.9E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-438 —DO NOT CITE OR QUOTE 

1 E.3.25.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 10

 12

 14

 16

 18

 20

 22

 24

 26

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

15:09 10/06 2009

BMDLBMD

 

Hill

2 

3 

4 

5 E.3.25.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_sperm_prod.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_sperm_prod.plt 

13 Tue Oct 06 15:09:27 2009 

14 ==================================================================== 

15 

16 (x10^6) Table 1 without Vitamin E 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter restricted to be greater than 1 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-439 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 7.23328 

4 rho = 0 Specified 

5 intercept = 22.19 

6 v = -9.09 

7 n = 1.80484 

8 k = 0.697086 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -rho -n 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 alpha intercept v k 

18 

19 alpha 1 6.3e-010 3e-008 8.3e-009 

20 

21 intercept 6.3e-010 1 -0.78 -0.23 

22 

23 v 3e-008 -0.78 1 -0.17 

24 

25 k 8.3e-009 -0.23 -0.17 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 alpha 6.03567 1.74235 2.62073 9.45061 

34 intercept 22.1885 1.00316 20.2223 24.1547 

35 v -9.00869 1.26801 -11.4939 -6.52343 

36 n 1 NA 

37 k 0.386669 0.265663 -0.134021 0.907359 

38 

39 NA - Indicates that this parameter has hit a bound 

40 implied by some inequality constraint and thus 

41 has no standard error. 

42 

43 

44 

45 Table of Data and Estimated Values of Interest 

46 

47 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

48 ------ --- -------- -------- ----------- ----------- ---------- 

49 

50 0 6 22.2 22.2 2.67 2.46 0.00151 

51 1 6 15.7 15.7 2.65 2.46 -0.0218 

52 10 6 13.7 13.5 2.19 2.46 0.134 

53 100 6 13.1 13.2 3.16 2.46 -0.114 

54 

55 

56 

57 Model Descriptions for likelihoods calculated 

58 

59 

60 Model A1: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 

63 Model A2: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma(i)^2 

65 

66 Model A3: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 Model A3 uses any fixed variance parameters that 

69 were specified by the user 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-440 —DO NOT CITE OR QUOTE 

1 Model R: Yi = Mu + e(i) 

2 Var{e(i)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) # Param's AIC 

8 A1 -33.556444 5 77.112888 

9 A2 -33.158811 8 82.317623 

10 A3 -33.556444 5 77.112888 

11 fitted -33.572245 4 75.144490 

12 R -47.392394 2 98.784788 

13 

14 

15 Explanation of Tests 

16 

17 Test 1: Do responses and/or variances differ among Dose levels? 

18 (A2 vs. R) 

19 Test 2: Are Variances Homogeneous? (A1 vs A2) 

20 Test 3: Are variances adequately modeled? (A2 vs. A3) 

21 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

22 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

23 

24 Tests of Interest 

25 

26 Test -2*log(Likelihood Ratio) Test df p-value 

27 

28 Test 1 28.4672 6 <.0001 

29 Test 2 0.795266 3 0.8506 

30 Test 3 0.795266 3 0.8506 

31 Test 4 0.031602 1 0.8589 

32 

33 The p-value for Test 1 is less than .05. There appears to be a 

34 difference between response and/or variances among the dose levels 

35 It seems appropriate to model the data 

36 

37 The p-value for Test 2 is greater than .1. A homogeneous variance 

38 model appears to be appropriate here 

39 

40 

41 The p-value for Test 3 is greater than .1. The modeled variance appears 

42 to be appropriate here 

43 

44 The p-value for Test 4 is greater than .1. The model chosen seems 

45 to adequately describe the data 

46 

47 

48 Benchmark Dose Computation 

49 

50 Specified effect = 1 

51 

52 Risk Type = Estimated standard deviations from the control mean 

53 

54 Confidence level = 0.95 

55 

56 BMD = 0.144988 

57 

58 BMDL = 0.0155926 

59 

60 

61 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-441 —DO NOT CITE OR QUOTE 

1 E.3.26. Li et al. (2006): Hormone Levels (Estradiol) 

2 E.3.26.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.47 4.98 0.08 272.78 3.0E+02 1.0E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.47 4.98 0.08 272.78 3.0E+02 1.0E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.47 0.32 0.57 270.12 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.47 0.32 N/A 272.12 error error nonconstant variance, 

power restricted ≥1 

Hill 1 0.47 0.32 0.57 270.12 error error 

nonconstant variance, 

n restricted >1, bound 

hit 

linear 2 0.47 4.92 0.09 272.72 3.4E+02 9.7E+01 nonconstant variance 

polynomial 2 0.47 4.92 0.09 272.72 3.4E+02 9.7E+01 nonconstant variance 

power 2 0.47 4.92 0.09 272.72 3.4E+02 9.7E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2)

c 2 0.47 3.84 0.15 270.81 3.2E+02 1.1E+02 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.47 3.84 0.15 270.81 3.2E+02 1.1E+02 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.47 0.92 0.34 269.90 error error constant variance, 

power restricted ≥1 

exponential (M5) 0 0.47 0.92 N/A 271.90 error error constant variance, 

power restricted ≥1 

Hill 0 0.47 0.92 NA 271.90 error error constant variance, n 

restricted >1 

linear 2 0.47 3.78 0.15 270.75 3.6E+02 1.1E+02 constant variance 

polynomial 2 0.47 3.78 0.15 270.75 3.6E+02 1.1E+02 constant variance 

power 2 0.47 3.78 0.15 270.75 3.6E+02 1.1E+02 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-442 —DO NOT CITE OR QUOTE 

1 E.3.26.2. Figure for Selected Model: Exponential (M2), Constant Variance, Power Restricted 

2 ≥1 

 0

 5

 10

 15

 20

 25

 30

 35

 0 50 100 150 200 250 300

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

13:21 11/11 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.26.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\ExpConst_BMR1_Li_Estradiol.(d) 

13 Gnuplot Plotting File: 

14 Wed Nov 11 13:21:55 2009 

15 ==================================================================== 

16 

17 Figure 3 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-443 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 2 

19 -------- -------- 

20 lnalpha 5.52431 

21 rho(S) 0 

22 a 9.5 

23 b 0.0162139 

24 c 2.73407 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 2 

34 -------- ------- 

35 lnalpha 5.54738 

36 rho 0 

37 a 10 

38 b 0.842953 

39 c 2.13158 

40 d 1.46715 

41 

42 NC = No Convergence 

43 

44 

45 Table of Stats From Input Data 

46 

47 Dose N Obs Mean Obs Std Dev 

48 ----- --- ---------- ------------- 

49 0 10 10 12.48 

50 2 10 20 19.97 

51 50 10 24.74 14.98 

52 100 10 17.89 18.31 

53 

54 

55 Estimated Values of Interest 

56 

57 Dose Est Mean Est Std Scaled Residual 

58 ------ ---------- --------- ---------------- 

59 0 16.66 16.61 -1.267 

60 2 16.73 16.61 0.6227 

61 50 18.57 16.61 1.173 

62 100 20.71 16.61 -0.5362 

63 

64 

65 

66 Other models for which likelihoods are calculated: 

67 

68 Model A1: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-444 —DO NOT CITE OR QUOTE 

1 Model A2: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = Sigma(i)^2 

3 

4 Model A3: Yij = Mu(i) + e(ij) 

5 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

6 

7 Model R: Yij = Mu + e(i) 

8 Var{e(ij)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) DF AIC 

14 ------- ----------------- ---- ------------ 

15 A1 -130.4861 5 270.9723 

16 A2 -129.2199 8 274.4398 

17 A3 -130.4861 5 270.9723 

18 R -132.6269 2 269.2537 

19 2 -132.404 3 270.8079 

20 

21 

22 Additive constant for all log-likelihoods = -36.76. This constant added to the 

23 above values gives the log-likelihood including the term that does not 

24 depend on the model parameters. 

25 

26 

27 Explanation of Tests 

28 

29 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

30 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

31 Test 3: Are variances adequately modeled? (A2 vs. A3) 

32 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

33 

34 

35 Tests of Interest 

36 

37 Test -2*log(Likelihood Ratio) D. F. p-value 

38 -------- ------------------------ ------ -------------- 

39 Test 1 6.814 6 0.3384 

40 Test 2 2.533 3 0.4694 

41 Test 3 2.533 3 0.4694 

42 Test 4 3.836 2 0.1469 

43 

44 

45 The p-value for Test 1 is greater than .05. There may not be a 

46 diffence between responses and/or variances among the dose levels 

47 Modelling the data with a dose/response curve may not be appropriate. 

48 

49 The p-value for Test 2 is greater than .1. A homogeneous 

50 variance model appears to be appropriate here. 

51 

52 The p-value for Test 3 is greater than .1. The modeled 

53 variance appears to be appropriate here. 

54 

55 The p-value for Test 4 is greater than .1. Model 2 seems 

56 to adequately describe the data. 

57 

58 

59 Benchmark Dose Computations: 

60 

61 Specified Effect = 1.000000 

62 

63 Risk Type = Estimated standard deviations from control 

64 

65 Confidence Level = 0.950000 

66 

67 BMD = 317.497 

68 

69 BMDL = 111.954 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-445 —DO NOT CITE OR QUOTE 

1 E.3.27. Li et al. (2006): Hormone Levels (Progesterone) 

2 E.3.27.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.00 16.99 0.00 330.20 4.9E+01 error nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.00 16.99 0.00 330.20 4.9E+01 error nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 1 0.00 0.82 0.37 316.03 1.6E-01 1.0E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.00 0.82 N/A 318.03 4.9E-01 7.9E-02 nonconstant variance, 

power restricted ≥1 

Hill 1 0.00 0.81 0.37 316.02 2.2E-02 6.4E-05 nonconstant variance, n 

restricted >1, bound hit 

linear 2 0.00 17.93 0.00 331.13 7.5E+01 5.2E+01 nonconstant variance 

polynomial 2 0.00 17.93 0.00 331.13 7.5E+01 5.2E+01 nonconstant variance 

power 2 0.00 17.93 0.00 331.13 7.5E+01 4.5E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.00 3.97 0.14 329.50 6.8E+01 error constant variance, 

power restricted ≥1 

exponential (M3) 2 0.00 3.97 0.14 329.50 6.8E+01 error constant variance, 

power restricted ≥1 

exponential (M4) 1 0.00 0.14 0.71 327.66 2.2E+00 1.3E-01 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.00 0.14 N/A 329.66 2.2E+00 2.8E-01 constant variance, 

power restricted ≥1 

Hill 1 0.00 0.12 0.73 327.64 2.4E+00 3.5E-05 constant variance, n 

restricted >1, bound hit 

linear 2 0.00 4.97 0.08 330.49 9.2E+01 5.7E+01 constant variance 

polynomial 2 0.00 4.97 0.08 330.49 9.2E+01 5.7E+01 constant variance 

power 2 0.00 4.97 0.08 330.49 9.2E+01 5.7E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-446 —DO NOT CITE OR QUOTE 

1 E.3.27.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

-20

 0

 20

 40

 60

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:22 11/11 2009

BMDLBMD

 

Exponential

3 

4 

5 

6 E.3.27.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Exp_BMR1_Li_Progesterone.(d) 

13 Gnuplot Plotting File: 

14 Wed Nov 11 13:22:19 2009 

15 ==================================================================== 

16 

17 Figure 4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-447 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 4 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 4 

18 -------- -------- 

19 lnalpha 11.2757 

20 rho -1.43319 

21 a 65.0395 

22 b 0.0460242 

23 c 0.162232 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 4 

31 -------- ------- 

32 lnalpha 14.0852 

33 rho -2.26856 

34 a 61.9568 

35 b 1.02041 

36 c 0.315961 

37 d 1.78188 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 10 61.94 11.15 

45 2 10 30.72 39.81 

46 50 10 16.62 33.44 

47 100 10 11.08 44.59 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 61.96 10.61 -0.0043 

55 2 20.78 36.65 0.858 

56 50 19.58 39.21 -0.2385 

57 100 19.58 39.21 -0.6853 

58 

59 

60 

61 Other models for which likelihoods are calculated: 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-448 —DO NOT CITE OR QUOTE 

1 

2 Model R: Yij = Mu + e(i) 

3 Var{e(ij)} = Sigma^2 

4 

5 

6 Likelihoods of Interest 

7 

8 Model Log(likelihood) DF AIC 

9 ------- ----------------- ---- ------------ 

10 A1 -159.7613 5 329.5225 

11 A2 -151.9206 8 319.8412 

12 A3 -152.6038 6 317.2077 

13 R -165.9023 2 335.8046 

14 4 -153.0132 5 316.0265 

15 

16 

17 Additive constant for all log-likelihoods = -36.76. This constant added to the 

18 above values gives the log-likelihood including the term that does not 

19 depend on the model parameters. 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 

28 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

29 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) D. F. p-value 

34 -------- ------------------------ ------ -------------- 

35 Test 1 27.96 6 < 0.0001 

36 Test 2 15.68 3 0.001318 

37 Test 3 1.366 2 0.505 

38 Test 6a 0.8188 1 0.3655 

39 

40 

41 The p-value for Test 1 is less than .05. There appears to be a 

42 difference between response and/or variances among the dose 

43 levels, it seems appropriate to model the data. 

44 

45 The p-value for Test 2 is less than .1. A non-homogeneous 

46 variance model appears to be appropriate. 

47 

48 The p-value for Test 3 is greater than .1. The modeled 

49 variance appears to be appropriate here. 

50 

51 The p-value for Test 6a is greater than .1. Model 4 seems 

52 to adequately describe the data. 

53 

54 

55 Benchmark Dose Computations: 

56 

57 Specified Effect = 1.000000 

58 

59 Risk Type = Estimated standard deviations from control 

60 

61 Confidence Level = 0.950000 

62 

63 BMD = 0.161712 

64 

65 BMDL = 0.100383 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-449 —DO NOT CITE OR QUOTE 

1 E.3.28. Markowski et al. (2001): FR10 Run Opp 

2 E.3.28.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.17 6.17 0.05 119.08 2.3E+02 5.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 1 0.17 10.00 0.00 124.91 1.6E+05 1.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.17 2.09 0.15 117.00 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.17 1.52 N/A 118.43 error error nonconstant variance, 

power restricted ≥1 

Hill 0 0.17 1.51 NA 118.43 error error nonconstant variance, n 

restricted >1 

linear 2 0.17 6.66 0.04 119.57 2.5E+02 1.1E+02 nonconstant variance 

polynomial 1 0.17 0.00 1.00 114.91 6.2E+01 2.7E+01 nonconstant variance 

power 2 0.17 6.66 0.04 119.57 2.5E+02 1.1E+02 

nonconstant variance, 

power restricted ≥1, bound 

hit 

exponential (M2)

c 2 0.17 2.79 0.25 117.56 1.7E+02 5.0E+01 constant variance, power 

restricted ≥1 

exponential (M3) 2 0.17 2.79 0.25 117.56 1.7E+02 5.0E+01 constant variance, power 

restricted ≥1 

exponential (M4) 1 0.17 0.67 0.41 117.44 4.7E+01 1.7E-01 constant variance, power 

restricted ≥1 

exponential (M5) 0 0.17 0.15 N/A 118.92 3.2E+01 4.0E-05 constant variance, power 

restricted ≥1 

Hill 0 0.17 0.15 NA 118.92 2.3E+01 6.7E-06 constant variance, n 

restricted >1 

linear 2 0.17 3.32 0.19 118.09 2.1E+02 1.1E+02 constant variance 

polynomial 2 0.17 3.32 0.19 118.09 2.1E+02 1.1E+02 constant variance 

power 2 0.17 3.32 0.19 118.09 2.1E+02 1.1E+02 constant variance, power 

restricted ≥1, bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-450 —DO NOT CITE OR QUOTE 

1 E.3.28.2. Figure for Selected Model: Exponential (M2), Constant Variance, Power Restricted 

2 ≥1 

 0

 5

 10

 15

 20

 0 20 40 60 80 100 120 140 160 180

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

15:18 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.28.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\ExpConstVar_BMR1_FR10_run_opp.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 15:18:28 2009 

15 ==================================================================== 

16 

17 Table 3 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-451 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 2 

19 -------- -------- 

20 lnalpha 3.5321 

21 rho(S) 0 

22 a 13.9545 

23 b 0.0143568 

24 c 0.392432 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 2 

34 -------- ------- 

35 lnalpha 3.53824 

36 rho 0 

37 a 13.29 

38 b 0.0376253 

39 c 0.483301 

40 d 3.66691 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 7 13.29 8.65 

48 20 4 11.25 5.56 

49 60 6 5.75 3.53 

50 180 7 7 6.01 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 11.94 6.197 0.5745 

58 20 10.93 6.197 0.1025 

59 60 9.158 6.197 -1.347 

60 180 5.385 6.197 0.6897 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-452 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 -54.38526 5 118.7705 

14 A2 -51.88568 8 119.7714 

15 A3 -54.38526 5 118.7705 

16 R -57.45429 2 118.9086 

17 2 -55.77871 3 117.5574 

18 

19 

20 Additive constant for all log-likelihoods = -22.05. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

31 

32 

33 Tests of Interest 

34 

35 Test -2*log(Likelihood Ratio) D. F. p-value 

36 -------- ------------------------ ------ -------------- 

37 Test 1 11.14 6 0.08423 

38 Test 2 4.999 3 0.1719 

39 Test 3 4.999 3 0.1719 

40 Test 4 2.787 2 0.2482 

41 

42 

43 The p-value for Test 1 is greater than .05. There may not be a 

44 diffence between responses and/or variances among the dose levels 

45 Modelling the data with a dose/response curve may not be appropriate. 

46 

47 The p-value for Test 2 is greater than .1. A homogeneous 

48 variance model appears to be appropriate here. 

49 

50 The p-value for Test 3 is greater than .1. The modeled 

51 variance appears to be appropriate here. 

52 

53 The p-value for Test 4 is greater than .1. Model 2 seems 

54 to adequately describe the data. 

55 

56 

57 Benchmark Dose Computations: 

58 

59 Specified Effect = 1.000000 

60 

61 Risk Type = Estimated standard deviations from control 

62 

63 Confidence Level = 0.950000 

64 

65 BMD = 165.284 

66 

67 BMDL = 50.2488 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-453 —DO NOT CITE OR QUOTE 

1 E.3.29. Markowski et al. (2001): FR2 Revolutions 

2 E.3.29.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.11 5.71 0.06 216.09 3.6E+02 1.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.11 5.71 0.06 216.09 3.6E+02 1.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.11 1.94 0.16 214.33 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.11 0.45 N/A 214.83 error error nonconstant variance, 

power restricted ≥1 

Hill 1 0.11 0.45 0.50 212.83 error error nonconstant variance, n 

restricted >1, bound hit 

linear 2 0.11 6.08 0.05 216.46 3.3E+02 1.4E+02 nonconstant variance 

polynomial 2 0.11 6.08 0.05 216.46 3.3E+02 1.4E+02 nonconstant variance 

power 2 0.11 6.08 0.05 216.46 3.3E+02 1.4E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2)

c 2 0.11 3.31 0.19 217.64 1.6E+02 5.8E+01 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.11 3.31 0.19 217.64 1.6E+02 5.8E+01 constant variance, power 

restricted ≥1 

exponential (M4) 1 0.11 1.08 0.30 217.41 4.7E+01 2.0E-01 constant variance, power 

restricted ≥1 

exponential (M5) 0 0.11 0.20 N/A 218.53 3.3E+01 1.2E+01 constant variance, power 

restricted ≥1 

Hill 0 0.11 0.20 NA 218.53 2.4E+01 7.3E+00 constant variance, n 

restricted >1, bound hit 

linear 2 0.11 3.80 0.15 218.13 2.0E+02 1.0E+02 constant variance 

polynomial 2 0.11 3.80 0.15 218.13 2.0E+02 1.0E+02 constant variance 

power 2 0.11 3.80 0.15 218.13 2.0E+02 1.0E+02 constant variance, power 

restricted ≥1, bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-454 —DO NOT CITE OR QUOTE 

1 E.3.29.2. Figure for Selected Model: Exponential (M2), Constant Variance, Power Restricted 

2 ≥1 

 0

 50

 100

 150

 200

 0 20 40 60 80 100 120 140 160 180

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

15:18 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.29.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\ExpConstVar_BMR1_FR2_revolutions.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 15:18:54 2009 

15 ==================================================================== 

16 

17 Table 3 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-455 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 4 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 2 

19 -------- -------- 

20 lnalpha 7.68046 

21 rho(S) 0 

22 a 125.255 

23 b 0.0134965 

24 c 0.429602 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 2 

34 -------- ------- 

35 lnalpha 7.68885 

36 rho 0 

37 a 119.29 

38 b 0.0345516 

39 c 0.526177 

40 d 4.19941 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 7 119.3 69.9 

48 20 4 108.5 61 

49 60 6 56.5 31.21 

50 180 7 68.14 33.23 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 108.9 49.85 0.5497 

58 20 101 49.85 0.2994 

59 60 86.93 49.85 -1.495 

60 180 55.35 49.85 0.6786 

61 

62 

63 

64 Other models for which likelihoods are calculated: 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-456 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

4 

5 Model R: Yij = Mu + e(i) 

6 Var{e(ij)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) DF AIC 

12 ------- ----------------- ---- ------------ 

13 A1 -104.1655 5 218.331 

14 A2 -101.1402 8 218.2803 

15 A3 -104.1655 5 218.331 

16 R -107.5993 2 219.1985 

17 2 -105.8179 3 217.6357 

18 

19 

20 Additive constant for all log-likelihoods = -22.05. This constant added to the 

21 above values gives the log-likelihood including the term that does not 

22 depend on the model parameters. 

23 

24 

25 Explanation of Tests 

26 

27 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

31 

32 

33 Tests of Interest 

34 

35 Test -2*log(Likelihood Ratio) D. F. p-value 

36 -------- ------------------------ ------ -------------- 

37 Test 1 12.92 6 0.04435 

38 Test 2 6.051 3 0.1092 

39 Test 3 6.051 3 0.1092 

40 Test 4 3.305 2 0.1916 

41 

42 

43 The p-value for Test 1 is less than .05. There appears to be a 

44 difference between response and/or variances among the dose 

45 levels, it seems appropriate to model the data. 

46 

47 The p-value for Test 2 is greater than .1. A homogeneous 

48 variance model appears to be appropriate here. 

49 

50 The p-value for Test 3 is greater than .1. The modeled 

51 variance appears to be appropriate here. 

52 

53 The p-value for Test 4 is greater than .1. Model 2 seems 

54 to adequately describe the data. 

55 

56 

57 Benchmark Dose Computations: 

58 

59 Specified Effect = 1.000000 

60 

61 Risk Type = Estimated standard deviations from control 

62 

63 Confidence Level = 0.950000 

64 

65 BMD = 162.682 

66 

67 BMDL = 58.0677 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-457 —DO NOT CITE OR QUOTE 

1 E.3.30. Markowski et al. (2001): FR5 Run Opp 

2 E.3.30.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 2 0.23 5.55 0.06 134.53 1.4E+02 5.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 0.23 5.55 0.06 134.53 1.4E+02 5.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 1 0.23 1.05 0.31 132.03 3.6E+01 1.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 0 0.23 0.08 N/A 133.06 2.8E+01 1.4E+01 nonconstant variance, 

power restricted ≥1 

Hill 0 0.23 0.08 NA 133.06 2.2E+01 error nonconstant variance, 

n restricted >1 

linear 2 0.23 6.35 0.04 135.33 1.8E+02 9.3E+01 nonconstant variance 

polynomial 1 0.23 0.06 0.81 131.04 4.0E+01 2.2E+01 nonconstant variance 

power 2 0.23 6.35 0.04 135.33 1.8E+02 9.3E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 2 0.23 3.80 0.15 133.83 9.5E+01 4.3E+01 constant variance, 

power restricted ≥1 

exponential (M3) 2 0.23 3.80 0.15 133.83 9.5E+01 4.3E+01 constant variance, 

power restricted ≥1 

exponential (M4) 1 0.23 1.06 0.30 133.09 3.0E+01 9.4E+00 constant variance, 

power restricted ≥1 

exponential (M5) 0 0.23 0.01 N/A 134.03 2.9E+01 1.2E+01 constant variance, 

power restricted ≥1 

Hill c 1 0.23 0.01 0.94 132.03 2.2E+01 1.1E+01 

constant variance, n 

restricted >1, bound 

hit 

linear 2 0.23 4.80 0.09 134.82 1.3E+02 8.1E+01 constant variance 

polynomial 1 0.23 0.36 0.55 132.39 3.1E+01 1.8E+01 constant variance 

power 2 0.23 4.80 0.09 134.82 1.3E+02 8.1E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-458 —DO NOT CITE OR QUOTE 

1 E.3.30.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 5

 10

 15

 20

 25

 30

 35

 40

 0 20 40 60 80 100 120 140 160 180

Mean Response

dose

Hill Model with 0.95 Confidence Level

15:22 10/06 2009

BMDL BMD

 

Hill

2 

3 

4 

5 E.3.30.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_FR5_run_opp.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_FR5_run_opp.plt 

13 Tue Oct 06 15:22:42 2009 

14 ==================================================================== 

15 

16 Table 3 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter restricted to be greater than 1 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-459 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 77.4849 

4 rho = 0 Specified 

5 intercept = 26.14 

6 v = -13.34 

7 n = 2.36002 

8 k = 35.0654 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -rho -n 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 alpha intercept v k 

18 

19 alpha 1 -3.6e-009 9.8e-009 3.6e-008 

20 

21 intercept -3.6e-009 1 -0.81 -0.51 

22 

23 v 9.8e-009 -0.81 1 0.36 

24 

25 k 3.6e-008 -0.51 0.36 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 alpha 64.5863 18.6445 28.0438 101.129 

34 intercept 26.14 3.03753 20.1865 32.0935 

35 v -13.1569 3.7676 -20.5413 -5.77257 

36 n 18 NA 

37 k 21.5963 2.68136 16.3409 26.8517 

38 

39 NA - Indicates that this parameter has hit a bound 

40 implied by some inequality constraint and thus 

41 has no standard error. 

42 

43 

44 

45 Table of Data and Estimated Values of Interest 

46 

47 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

48 ------ --- -------- -------- ----------- ----------- ---------- 

49 

50 0 7 26.1 26.1 12.3 8.04 1.02e-008 

51 20 4 23.5 23.5 7.04 8.04 -1.39e-007 

52 60 6 12.8 13 6.17 8.04 -0.0558 

53 180 7 13.1 13 7.14 8.04 0.0517 

54 

55 

56 

57 Model Descriptions for likelihoods calculated 

58 

59 

60 Model A1: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 

63 Model A2: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma(i)^2 

65 

66 Model A3: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 Model A3 uses any fixed variance parameters that 

69 were specified by the user 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-460 —DO NOT CITE OR QUOTE 

1 Model R: Yi = Mu + e(i) 

2 Var{e(i)} = Sigma^2 

3 

4 

5 Likelihoods of Interest 

6 

7 Model Log(likelihood) # Param's AIC 

8 A1 -62.013133 5 134.026266 

9 A2 -59.839035 8 135.678070 

10 A3 -62.013133 5 134.026266 

11 fitted -62.016024 4 132.032049 

12 R -67.530040 2 139.060081 

13 

14 

15 Explanation of Tests 

16 

17 Test 1: Do responses and/or variances differ among Dose levels? 

18 (A2 vs. R) 

19 Test 2: Are Variances Homogeneous? (A1 vs A2) 

20 Test 3: Are variances adequately modeled? (A2 vs. A3) 

21 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

22 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

23 

24 Tests of Interest 

25 

26 Test -2*log(Likelihood Ratio) Test df p-value 

27 

28 Test 1 15.382 6 0.01748 

29 Test 2 4.3482 3 0.2262 

30 Test 3 4.3482 3 0.2262 

31 Test 4 0.0057833 1 0.9394 

32 

33 The p-value for Test 1 is less than .05. There appears to be a 

34 difference between response and/or variances among the dose levels 

35 It seems appropriate to model the data 

36 

37 The p-value for Test 2 is greater than .1. A homogeneous variance 

38 model appears to be appropriate here 

39 

40 

41 The p-value for Test 3 is greater than .1. The modeled variance appears 

42 to be appropriate here 

43 

44 The p-value for Test 4 is greater than .1. The model chosen seems 

45 to adequately describe the data 

46 

47 

48 Benchmark Dose Computation 

49 

50 Specified effect = 1 

51 

52 Risk Type = Estimated standard deviations from the control mean 

53 

54 Confidence level = 0.95 

55 

56 BMD = 22.144 

57 

58 BMDL = 11.165 

59 

60 

61 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-461 —DO NOT CITE OR QUOTE 

1 E.3.31. Mietinnin et al. (2006): Caries 

2 E.3.31.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 3 3.32 0.34 162.70 3.7E+01 2.0E+01 power restricted ≥1, bound 

hit 

gamma 3 3.32 0.34 162.70 7.5E+01 4.1E+01 power restricted ≥1, bound 

hit 

logistic 3 3.54 0.32 162.91 4.4E+01 2.6E+01 

logistic 3 3.54 0.32 162.91 9.0E+01 5.2E+01 

log-logistic b 3 2.33 0.51 161.77 1.5E+01 5.0E+00 slope restricted ≥1, 

bound hit 

log-logistic 3 2.33 0.51 161.77 3.1E+01 1.1E+01 slope restricted ≥1, bound 

hit 

log-probit 2 0.64 0.73 161.99 1.2E-01 error slope restricted ≥1 

log-probit 2 0.64 0.73 161.99 5.1E-01 error slope restricted ≥1 

multistage, 2-

degree 3 3.32 0.34 162.70 3.7E+01 2.0E+01 betas restricted ≥0, bound hit 

multistage, 2-

degree 3 3.32 0.34 162.70 7.5E+01 4.1E+01 betas restricted ≥0, bound hit 

probit 3 3.67 0.30 163.03 4.9E+01 3.1E+01 

probit 3 3.67 0.30 163.03 9.9E+01 6.2E+01 

Weibull 3 3.32 0.34 162.70 3.7E+01 2.0E+01 power restricted ≥1, bound 

hit 

Weibull 3 3.32 0.34 162.70 7.5E+01 4.1E+01 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-462 —DO NOT CITE OR QUOTE 

1 E.3.31.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1

 0 200 400 600 800 1000

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

15:23 10/06 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.3.31.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AniDose\LogLogistic_BMR1_Caries.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\LogLogistic_BMR1_Caries.plt 

12 Tue Oct 06 15:23:23 2009 

13 ==================================================================== 

14 

15 Table 2 converting the percentage into the number of animals, and control is Control II from the 

16 study. Dose is in ng per kg and is from Table 1 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

22 

23 

24 Dependent variable = DichEff 

25 Independent variable = Dose 

26 Slope parameter is restricted as slope <= 1 

27 

28 Total number of observations = 5 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 User has chosen the log transformed model 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-463 —DO NOT CITE OR QUOTE 

1 

2 

3 Default Initial Parameter Values 

4 background = 0.595238 

5 intercept = -5.52519 

6 slope = 1 

7 

8 

9 Asymptotic Correlation Matrix of Parameter Estimates 

10 

11 ( *** The model parameter(s) -slope 

12 have been estimated at a boundary point, or have been specified by the user, 

13 and do not appear in the correlation matrix ) 

14 

15 background intercept 

16 

17 background 1 -0.64 

18 

19 intercept -0.64 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 background 0.658158 * * * 

28 intercept -5.64068 * * * 

29 slope 1 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -77.6769 5 

39 Fitted model -78.8837 2 2.41374 3 0.4911 

40 Reduced model -83.2067 1 11.0597 4 0.0259 

41 

42 AIC: 161.767 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.6582 27.643 25.000 42 -0.860 

50 30.0000 0.6911 20.041 23.000 29 1.189 

51 100.0000 0.7477 18.693 19.000 25 0.141 

52 300.0000 0.8345 20.027 20.000 24 -0.015 

53 1000.0000 0.9249 29.596 29.000 32 -0.400 

54 

55 Chi^2 = 2.33 d.f. = 3 P-value = 0.5062 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.05 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 14.824 

67 

68 BMDL = 4.99044 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-464 —DO NOT CITE OR QUOTE 

1 

2 E.3.32. National Toxicology Program (1982): Male Mice, Toxic Hepatitis 

3 E.3.32.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 1 4.93 0.03 113.10 1.6E+01 5.2E+00 power restricted ≥1 

logistic b 2 4.76 0.09 110.71 1.8E+01 1.4E+01 

log-logistic 1 4.93 0.03 113.09 1.5E+01 6.6E+00 slope restricted ≥1 

log-probit 1 4.89 0.03 113.11 1.4E+01 7.2E+00 slope restricted ≥1 

multistage, 2-

degree 1 5.18 0.02 112.86 1.2E+01 4.6E+00 betas restricted ≥0 

probit 2 4.86 0.09 110.70 1.6E+01 1.3E+01 

Weibull 1 4.99 0.03 113.06 1.6E+01 4.9E+00 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

4 

5 

6 E.3.32.2. Figure for Selected Model: Logistic 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Logistic Model with 0.95 Confidence Level

12:25 11/04 2009

BMDL BMD

 

Logistic

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-465 —DO NOT CITE OR QUOTE 

1 E.3.32.3. Output file for Selected Model: Logistic 

2 

3 

4 ==================================================================== 

5 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\AniDose\Logistic_BMR2_Toxic_hepatitis.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\Logistic_BMR2_Toxic_hepatitis.plt 

8 Wed Nov 04 12:25:18 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = 1/[1+EXP(-intercept-slope*dose)] 

17 

18 

19 Dependent variable = DichEff 

20 Independent variable = Dose 

21 Slope parameter is not restricted 

22 

23 Total number of observations = 4 

24 Total number of records with missing values = 0 

25 Maximum number of iterations = 250 

26 Relative Function Convergence has been set to: 1e-008 

27 Parameter Convergence has been set to: 1e-008 

28 

29 

30 

31 Default Initial Parameter Values 

32 background = 0 Specified 

33 intercept = -3.05581 

34 slope = 0.0703319 

35 

36 

37 Asymptotic Correlation Matrix of Parameter Estimates 

38 

39 ( *** The model parameter(s) -background 

40 have been estimated at a boundary point, or have been specified by the user, 

41 and do not appear in the correlation matrix ) 

42 

43 intercept slope 

44 

45 intercept 1 -0.66 

46 

47 slope -0.66 1 

48 

49 

50 

51 Parameter Estimates 

52 

53 95.0% Wald Confidence Interval 

54 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

55 intercept -3.08708 0.358526 -3.78978 -2.38438 

56 slope 0.07156 0.00813416 0.0556174 0.0875027 

57 

58 

59 

60 Analysis of Deviance Table 

61 

62 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

63 Full model -51.0633 4 

64 Fitted model -53.3562 2 4.58581 2 0.101 

65 Reduced model -121.743 1 141.358 3 <.0001 

66 

67 AIC: 110.712 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-466 —DO NOT CITE OR QUOTE 

1 Goodness of Fit 

2 Scaled 

3 Dose Est._Prob. Expected Observed Size Residual 

4 ------------------------------------------------------------------------ 

5 0.0000 0.0436 3.186 1.000 73 -1.252 

6 1.4000 0.0480 2.353 5.000 49 1.769 

7 7.1000 0.0705 3.455 3.000 49 -0.254 

8 71.0000 0.8801 44.007 44.000 50 -0.003 

9 

10 Chi^2 = 4.76 d.f. = 2 P-value = 0.0925 

11 

12 

13 Benchmark Dose Computation 

14 

15 Specified effect = 0.1 

16 

17 Risk Type = Extra risk 

18 

19 Confidence level = 0.95 

20 

21 BMD = 17.6885 

22 

23 BMDL = 13.8272 

24 

25 

26 

27 E.3.33. National Toxicology Program (2006): Alveolar Metaplasia 

28 E.3.33.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 34.09 0.00 340.13 2.2E+00 1.8E+00 power restricted ≥1, bound 

hit 

logistic 4 45.56 0.00 358.35 5.0E+00 4.1E+00 

log-logistic 4 3.98 0.41 312.97 6.6E-01 5.0E-01 slope restricted ≥1, bound 

hit 

log-probit b 3 1.31 0.73 312.54 3.3E-01 9.0E-02 slope restricted ≥1 

multistage, 2-

degree 4 34.09 0.00 340.13 2.2E+00 1.8E+00 betas restricted ≥0, bound hit 

probit 4 46.73 0.00 362.18 5.7E+00 4.8E+00 

Weibull 4 34.09 0.00 340.13 2.2E+00 1.8E+00 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

29 

30 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-467 —DO NOT CITE OR QUOTE 

1 E.3.33.2. Figure for Selected Model: Log-Probit, Slope Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

12:26 11/04 2009

BMDLBMD

 

LogProbit

2 

3 

4 

5 E.3.33.3. Output File for Selected Model: Log-Probit, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Probit Model. (Version: 3.1; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AniDose\LogProbit_BMR2_Alveolar_metaplasia.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\LogProbit_BMR2_Alveolar_metaplasia.plt 

12 Wed Nov 04 12:26:52 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = Background 

21 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

22 

23 where CumNorm(.) is the cumulative normal distribution function 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 Slope parameter is not restricted 

29 

30 Total number of observations = 6 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-468 —DO NOT CITE OR QUOTE 

1 

2 User has chosen the log transformed model 

3 

4 

5 Default Initial (and Specified) Parameter Values 

6 background = 0.0377358 

7 intercept = -0.759264 

8 slope = 0.469642 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 background intercept slope 

14 

15 background 1 -0.24 0.12 

16 

17 intercept -0.24 1 -0.9 

18 

19 slope 0.12 -0.9 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 background 0.0374101 0.0259232 -0.0133985 0.0882186 

28 intercept -0.761678 0.210613 -1.17447 -0.348885 

29 slope 0.471021 0.0755121 0.32302 0.619022 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -152.615 6 

37 Fitted model -153.271 3 1.31226 3 0.7262 

38 Reduced model -216.802 1 128.374 5 <.0001 

39 

40 AIC: 312.543 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0374 1.983 2.000 53 0.012 

48 2.1400 0.3679 19.868 19.000 54 -0.245 

49 7.1400 0.5815 30.819 33.000 53 0.607 

50 15.7000 0.7149 37.174 35.000 52 -0.668 

51 32.9000 0.8187 43.389 45.000 53 0.574 

52 71.4000 0.8981 46.701 46.000 52 -0.321 

53 

54 Chi^2 = 1.31 d.f. = 3 P-value = 0.7272 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.1 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 0.331636 

66 

67 BMDL = 0.0896842 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-469 —DO NOT CITE OR QUOTE 

1 E.3.34. National Toxicology Program (2006): Gingival Hyperplasia Squamous, 2 Years 

2 E.3.34.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2 pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 12.82 0.01 318.87 2.3E+01 1.4E+01 power restricted ≥1, bound 

hit 

logistic 4 13.78 0.01 320.91 3.6E+01 2.6E+01 

log-logistic b 4 12.38 0.01 317.97 1.8E+01 1.0E+01 slope restricted ≥1, 

bound hit 

log-logistic c 3 1.53 0.68 307.42 3.7E-01 1.5E-07 slope unrestricted 

log-probit 3 1.47 0.69 307.35 4.7E-01 8.9E-07 slope restricted ≥1 

multistage, 1-

degree 4 12.82 0.01 318.87 2.3E+01 1.4E+01 betas restricted ≥0, bound hit 

probit 4 13.67 0.01 320.69 3.4E+01 2.4E+01 

Weibull 4 12.82 0.01 318.87 2.3E+01 1.4E+01 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-470 —DO NOT CITE OR QUOTE 

1 E.3.34.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.1

 0.2

 0.3

 0.4

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:44 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.3.34.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\LogLogistic_BMR2_Ging_Hyp_2yr.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogLogistic_BMR2_Ging_Hyp_2yr.plt 

12 Sun Nov 29 11:44:28 2009 

13 ==================================================================== 

14 

15 [insert study notes] 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is restricted as slope >= 1 

26 

27 Total number of observations = 6 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-471 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0188679 

3 intercept = -4.5509 

4 slope = 1 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -slope 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 background intercept 

14 

15 background 1 -0.71 

16 

17 intercept -0.71 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 background 0.117717 * * * 

26 intercept -5.10866 * * * 

27 slope 1 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -149.95 6 

37 Fitted model -156.985 2 14.0696 4 0.007076 

38 Reduced model -162.631 1 25.3627 5 0.0001186 

39 

40 AIC: 317.969 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.1177 6.239 1.000 53 -2.233 

48 2.1400 0.1290 6.965 7.000 54 0.014 

49 7.1400 0.1542 8.174 14.000 53 2.216 

50 15.7000 0.1942 10.292 13.000 53 0.940 

51 32.9000 0.2641 13.995 15.000 53 0.313 

52 71.4000 0.3837 20.335 16.000 53 -1.225 

53 

54 Chi^2 = 12.38 d.f. = 4 P-value = 0.0147 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.1 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 18.3832 

66 

67 BMDL = 10.4359 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-472 —DO NOT CITE OR QUOTE 

1 E.3.34.4. Figure for Unrestricted Model: Log-Logistic, Slope Unrestricted 

 0

 0.1

 0.2

 0.3

 0.4

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:44 11/29 2009

BMDL BMD

 

Log-Logistic

2 

3 

4 

5 E.3.34.5. Output File for Unrestricted Model: Log-Logistic, Slope Unrestricted 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov29\LogLogistic_Unrest_BMR2_Ging_Hyp_2yr.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogLogistic_Unrest_BMR2_Ging_Hyp_2yr.plt 

12 Sun Nov 29 11:44:31 2009 

13 ==================================================================== 

14 

15 [insert study notes] 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

21 

22 

23 Dependent variable = DichEff 

24 Independent variable = Dose 

25 Slope parameter is not restricted 

26 

27 Total number of observations = 6 

28 Total number of records with missing values = 0 

29 Maximum number of iterations = 250 

30 Relative Function Convergence has been set to: 1e-008 

31 Parameter Convergence has been set to: 1e-008 

32 

33 

34 

35 User has chosen the log transformed model 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-473 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 background = 0.0188679 

3 intercept = -2.04571 

4 slope = 0.299277 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 background intercept slope 

10 

11 background 1 -0.3 0.12 

12 

13 intercept -0.3 1 -0.91 

14 

15 slope 0.12 -0.91 1 

16 

17 

18 

19 Parameter Estimates 

20 

21 95.0% Wald Confidence Interval 

22 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

23 background 0.0185126 * * * 

24 intercept -1.93464 * * * 

25 slope 0.264795 * * * 

26 

27 * - Indicates that this value is not calculated. 

28 

29 

30 

31 Analysis of Deviance Table 

32 

33 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

34 Full model -149.95 6 

35 Fitted model -150.708 3 1.5163 3 0.6785 

36 Reduced model -162.631 1 25.3627 5 0.0001186 

37 

38 AIC: 307.416 

39 

40 

41 Goodness of Fit 

42 Scaled 

43 Dose Est._Prob. Expected Observed Size Residual 

44 ------------------------------------------------------------------------ 

45 0.0000 0.0185 0.981 1.000 53 0.019 

46 2.1400 0.1659 8.959 7.000 54 -0.717 

47 7.1400 0.2105 11.155 14.000 53 0.959 

48 15.7000 0.2447 12.972 13.000 53 0.009 

49 32.9000 0.2806 14.873 15.000 53 0.039 

50 71.4000 0.3219 17.059 16.000 53 -0.311 

51 

52 Chi^2 = 1.53 d.f. = 3 P-value = 0.6750 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.1 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 0.370958 

64 

65 BMDL = 1.50494e-007 

66 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-474 —DO NOT CITE OR QUOTE 

1 E.3.35. National Toxicology Program (2006): Heart, Cardiomyopathy 

2 E.3.35.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 6.23 0.18 398.01 6.5E+00 4.8E+00 power restricted ≥1, bound 

hit 

logistic 4 10.70 0.03 402.78 1.1E+01 9.2E+00 

log-logistic b 4 2.42 0.66 394.22 3.7E+00 2.5E+00 slope restricted ≥1, 

bound hit 

log-probit 3 0.93 0.82 394.80 2.1E+00 5.1E-01 slope restricted ≥1 

multistage, 2-

degree 4 6.23 0.18 398.01 6.5E+00 4.8E+00 betas restricted ≥0, bound hit 

probit 4 10.72 0.03 402.80 1.1E+01 9.3E+00 

Weibull 4 6.23 0.18 398.01 6.5E+00 4.8E+00 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.3.35.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0.8

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

11:58 11/11 2009

BMDL BMD

 

Log-Logistic

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-475 —DO NOT CITE OR QUOTE 

1 E.3.35.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

2 

3 

4 ==================================================================== 

5 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\LogLogistic_BMR2_Cardiomyopathy.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\LogLogistic_BMR2_Cardiomyopathy.plt 

8 Wed Nov 11 11:58:41 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

17 

18 

19 Dependent variable = DichEff 

20 Independent variable = Dose 

21 Slope parameter is restricted as slope <= 1 

22 

23 Total number of observations = 6 

24 Total number of records with missing values = 0 

25 Maximum number of iterations = 250 

26 Relative Function Convergence has been set to: 1e-008 

27 Parameter Convergence has been set to: 1e-008 

28 

29 

30 

31 User has chosen the log transformed model 

32 

33 

34 Default Initial Parameter Values 

35 background = 0.188679 

36 intercept = -3.47661 

37 slope = 1 

38 

39 

40 Asymptotic Correlation Matrix of Parameter Estimates 

41 

42 ( *** The model parameter(s) -slope 

43 have been estimated at a boundary point, or have been specified by the user, 

44 and do not appear in the correlation matrix ) 

45 

46 background intercept 

47 

48 background 1 -0.65 

49 

50 intercept -0.65 1 

51 

52 

53 

54 Parameter Estimates 

55 

56 95.0% Wald Confidence Interval 

57 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

58 background 0.20346 * * * 

59 intercept -3.50681 * * * 

60 slope 1 * * * 

61 

62 * - Indicates that this value is not calculated. 

63 

64 

65 

66 Analysis of Deviance Table 

67 

68 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

69 Full model -193.93 6 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-476 —DO NOT CITE OR QUOTE 

1 Fitted model -195.111 2 2.36161 4 0.6696 

2 Reduced model -216.802 1 45.7449 5 <.0001 

3 

4 AIC: 394.221 

5 

6 

7 Goodness of Fit 

8 Scaled 

9 Dose Est._Prob. Expected Observed Size Residual 

10 ------------------------------------------------------------------------ 

11 0.0000 0.2035 10.783 10.000 53 -0.267 

12 2.1400 0.2515 13.581 12.000 54 -0.496 

13 7.1400 0.3440 18.229 22.000 53 1.090 

14 15.7000 0.4585 23.840 25.000 52 0.323 

15 32.9000 0.5991 31.751 32.000 53 0.070 

16 71.4000 0.7464 38.815 36.000 52 -0.897 

17 

18 Chi^2 = 2.42 d.f. = 4 P-value = 0.6589 

19 

20 

21 Benchmark Dose Computation 

22 

23 Specified effect = 0.1 

24 

25 Risk Type = Extra risk 

26 

27 Confidence level = 0.95 

28 

29 BMD = 3.70462 

30 

31 BMDL = 2.50223 

32 

33 

34 

35 E.3.36. National Toxicology Program (2006): Hepatocyte Hypertrophy, 2 Years 

36 E.3.36.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 4 26.48 0.00 290.37 1.6E+00 1.3E+00 power restricted ≥1, bound 

hit 

logistic 4 35.54 0.00 310.49 4.3E+00 3.6E+00 

log-logistic b 5 15.18 0.01 278.08 7.0E-01 5.5E-01 slope restricted ≥1, 

bound hit 

log-probit 4 14.46 0.01 279.20 7.2E-01 3.3E-01 slope restricted ≥1 

multistage, 2-

degree 4 26.48 0.00 290.37 1.6E+00 1.3E+00 betas restricted ≥0, bound hit 

probit 4 41.23 0.00 313.84 4.6E+00 3.9E+00 

Weibull 4 26.48 0.00 290.37 1.6E+00 1.3E+00 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

37 

38 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-477 —DO NOT CITE OR QUOTE 

1 E.3.36.2. Figure for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Log-Logistic Model with 0.95 Confidence Level

18:49 10/06 2009

BMDLBMD

 

Log-Logistic

2 

3 

4 

5 E.3.36.3. Output File for Selected Model: Log-Logistic, Slope Restricted ≥1, Bound Hit 

6 

7 

8 ==================================================================== 

9 Logistic Model. (Version: 2.12; Date: 05/16/2008) 

10 Input Data File: 

11 C:\USEPA\BMDS21\AniDose\LogLogistic_BMR2_Hepatocyte_hypertrophy_2years.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\AniDose\LogLogistic_BMR2_Hepatocyte_hypertrophy_2years.plt 

14 Tue Oct 06 18:49:36 2009 

15 ==================================================================== 

16 

17 [insert study notes] 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the probability function is: 

21 

22 P[response] = background+(1-background)/[1+EXP(-intercept-slope*Log(dose))] 

23 

24 

25 Dependent variable = DichEff 

26 Independent variable = Dose 

27 Slope parameter is restricted as slope <= 1 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-478 —DO NOT CITE OR QUOTE 

1 User has chosen the log transformed model 

2 

3 

4 Default Initial Parameter Values 

5 background = 0 

6 intercept = -2.2119 

7 slope = 1.23746 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -background -slope 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 intercept 

17 

18 intercept 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 background 0 * * * 

27 intercept -1.83737 * * * 

28 slope 1 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -129.986 6 

38 Fitted model -138.041 1 16.1104 5 0.006536 

39 Reduced model -219.97 1 179.968 5 <.0001 

40 

41 AIC: 278.082 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0000 0.000 0.000 53 0.000 

49 2.1400 0.2542 13.724 19.000 54 1.649 

50 7.1400 0.5320 28.198 19.000 53 -2.532 

51 15.7000 0.7143 37.857 42.000 53 1.260 

52 32.9000 0.8397 44.505 41.000 53 -1.312 

53 71.4000 0.9192 48.715 52.000 53 1.655 

54 

55 Chi^2 = 15.18 d.f. = 5 P-value = 0.0096 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.1 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 0.697776 

67 

68 BMDL = 0.545416 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-479 —DO NOT CITE OR QUOTE 

1 

2 E.3.37. National Toxicology Program (2006): Liver, Eosinophilic Focus, Multiple 

3 E.3.37.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 4.30 0.37 330.46 5.7E+00 4.5E+00 power restricted ≥1, bound 

hit 

logistic 4 6.46 0.17 333.34 1.3E+01 1.1E+01 

log-logistic 3 5.90 0.12 334.15 4.7E+00 2.9E+00 slope restricted ≥1 

log-probit 3 6.58 0.09 334.85 4.8E+00 1.8E+00 slope restricted ≥1 

multistage, 2-

degree 3 4.18 0.24 332.36 6.2E+00 4.5E+00 betas restricted ≥0 

probit 4 6.16 0.19 332.96 1.2E+01 1.0E+01 

Weibull b 4 4.30 0.37 330.46 5.7E+00 4.5E+00 power restricted ≥1, 

bound hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

4 

5 

6 E.3.37.2. Figure for Selected Model: Weibull, Power Restricted ≥1, Bound Hit 

 0

 0.2

 0.4

 0.6

 0.8

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Weibull Model with 0.95 Confidence Level

11:44 11/11 2009

BMDL BMD

 

Weibull

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-480 —DO NOT CITE OR QUOTE 

1 E.3.37.3. Output File for Selected Model: Weibull, Power Restricted ≥1, Bound Hit 

2 

3 

4 ==================================================================== 

5 Weibull Model using Weibull Model (Version: 2.12; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\Weibull_BMR2_liver_eosin_focus.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Weibull_BMR2_liver_eosin_focus.plt 

8 Wed Nov 11 11:44:27 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background + (1-background)*[1-EXP(-slope*dose^power)] 

17 

18 

19 Dependent variable = DichEff 

20 Independent variable = Dose 

21 Power parameter is restricted as power >=1 

22 

23 Total number of observations = 6 

24 Total number of records with missing values = 0 

25 Maximum number of iterations = 250 

26 Relative Function Convergence has been set to: 1e-008 

27 Parameter Convergence has been set to: 1e-008 

28 

29 

30 

31 Default Initial (and Specified) Parameter Values 

32 Background = 0.0648148 

33 Slope = 0.00246576 

34 Power = 1.49873 

35 

36 

37 Asymptotic Correlation Matrix of Parameter Estimates 

38 

39 ( *** The model parameter(s) -Power 

40 have been estimated at a boundary point, or have been specified by the user, 

41 and do not appear in the correlation matrix ) 

42 

43 Background Slope 

44 

45 Background 1 -0.49 

46 

47 Slope -0.49 1 

48 

49 

50 

51 Parameter Estimates 

52 

53 95.0% Wald Confidence Interval 

54 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

55 Background 0.0893152 0.0297295 0.0310464 0.147584 

56 Slope 0.0185641 0.00270697 0.0132586 0.0238697 

57 Power 1 NA 

58 

59 NA - Indicates that this parameter has hit a bound 

60 implied by some inequality constraint and thus 

61 has no standard error. 

62 

63 

64 

65 Analysis of Deviance Table 

66 

67 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

68 Full model -161.07 6 

69 Fitted model -163.229 2 4.31726 4 0.3648 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-481 —DO NOT CITE OR QUOTE 

1 Reduced model -202.816 1 83.4925 5 <.0001 

2 

3 AIC: 330.457 

4 

5 

6 Goodness of Fit 

7 Scaled 

8 Dose Est._Prob. Expected Observed Size Residual 

9 ------------------------------------------------------------------------ 

10 0.0000 0.0893 4.734 3.000 53 -0.835 

11 2.1400 0.1248 6.738 8.000 54 0.520 

12 7.1400 0.2024 10.725 14.000 53 1.120 

13 15.7000 0.3196 16.937 17.000 53 0.019 

14 32.9000 0.5056 26.794 22.000 53 -1.317 

15 71.4000 0.7581 40.177 42.000 53 0.585 

16 

17 Chi^2 = 4.30 d.f. = 4 P-value = 0.3672 

18 

19 

20 Benchmark Dose Computation 

21 

22 Specified effect = 0.1 

23 

24 Risk Type = Extra risk 

25 

26 Confidence level = 0.95 

27 

28 BMD = 5.67549 

29 

30 BMDL = 4.5323 

31 

32 

33 

34 E.3.38. National Toxicology Program (2006): Liver, Fatty Change, Diffuse 

35 E.3.38.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 4 2.37 0.67 252.29 4.2E+00 3.2E+00 power restricted ≥1 

logistic 4 15.06 0.00 269.83 1.1E+01 9.3E+00 

log-logistic 4 4.96 0.29 255.08 4.7E+00 3.2E+00 slope restricted ≥1 

log-probit 4 5.05 0.28 255.26 4.6E+00 3.2E+00 slope restricted ≥1 

multistage, 2-

degree b 4 2.03 0.73 251.93 4.2E+00 3.2E+00 betas restricted ≥0 

probit 4 14.92 0.00 269.43 1.1E+01 9.1E+00 

Weibull 4 2.31 0.68 252.22 4.3E+00 3.2E+00 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-482 —DO NOT CITE OR QUOTE 

1 E.3.39. Figure for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:44 11/11 2009

BMDL BMD

 

Multistage

2 

3 

4 

5 E.3.40. Output File for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Multistage_BMR2_liver_fatty_change_diff.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Multistage_BMR2_liver_fatty_change_diff.plt 

12 Wed Nov 11 11:44:50 2009 

13 ==================================================================== 

14 

15 NTP_liver_fatty_change_diffuse 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 3 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 2 

34 

35 

36 Maximum number of iterations = 250 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-483 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 Background = 0.02888 

8 Beta(1) = 0.0193083 

9 Beta(2) = 0.000185869 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) Beta(2) 

19 

20 Beta(1) 1 -0.89 

21 

22 Beta(2) -0.89 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 Background 0 * * * 

31 Beta(1) 0.0248561 * * * 

32 Beta(2) 9.42857e-005 * * * 

33 

34 * - Indicates that this value is not calculated. 

35 

36 

37 

38 Analysis of Deviance Table 

39 

40 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

41 Full model -122.992 6 

42 Fitted model -123.966 2 1.94705 4 0.7455 

43 Reduced model -204.846 1 163.708 5 <.0001 

44 

45 AIC: 251.932 

46 

47 

48 Goodness of Fit 

49 Scaled 

50 Dose Est._Prob. Expected Observed Size Residual 

51 ------------------------------------------------------------------------ 

52 0.0000 0.0000 0.000 0.000 53 0.000 

53 2.1400 0.0522 2.819 2.000 54 -0.501 

54 7.1400 0.1666 8.831 12.000 53 1.168 

55 15.7000 0.3387 17.949 17.000 53 -0.275 

56 32.9000 0.6014 31.875 30.000 53 -0.526 

57 71.4000 0.8952 47.444 48.000 53 0.249 

58 

59 Chi^2 = 2.03 d.f. = 4 P-value = 0.7302 

60 

61 

62 Benchmark Dose Computation 

63 

64 Specified effect = 0.1 

65 

66 Risk Type = Extra risk 

67 

68 Confidence level = 0.95 

69 

70 BMD = 4.17277 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-484 —DO NOT CITE OR QUOTE 

1 

2 BMDL = 3.20452 

3 

4 BMDU = 5.73352 

5 

6 Taken together, (3.20452, 5.73352) is a 90 % two-sided confidence 

7 interval for the BMD 

8 

9 

10 E.3.41. National Toxicology Program (2006): Liver Necrosis 

11 E.3.41.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

 pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 4 1.85 0.76 235.58 2.0E+01 1.4E+01 power restricted ≥1, bound 

hit 

logistic 4 4.07 0.40 238.31 3.5E+01 2.8E+01 

log-logistic 4 1.60 0.81 235.27 1.8E+01 1.2E+01 slope restricted ≥1, bound 

hit 

log-probit b 3 1.14 0.77 236.74 1.1E+01 3.5E+00 slope restricted ≥1 

multistage, 2-

degree 4 1.85 0.76 235.58 2.0E+01 1.4E+01 betas restricted ≥0, bound hit 

probit 4 3.72 0.45 237.89 3.3E+01 2.6E+01 

Weibull 4 1.85 0.76 235.58 2.0E+01 1.4E+01 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-485 —DO NOT CITE OR QUOTE 

1 E.3.41.2. Figure for Selected Model: LogProbit 

2 

3 

4 

5 E.3.41.3. Output File for Selected Model: Log-Probit 

6 

7 ==================================================================== 

8 Probit Model. (Version: 3.1; Date: 05/16/2008) 

9 Input Data File: C:\USEPA\BMDS21\Nov29\LogProbit_BMR2_liver_necrosis.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov29\LogProbit_BMR2_liver_necrosis.plt 

11 Sun Nov 29 12:24:51 2009 

12 ==================================================================== 

13 

14 NTP_liver_necrosis 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the probability function is: 

18 

19 P[response] = Background 

20 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

21 

22 where CumNorm(.) is the cumulative normal distribution function 

23 

24 

25 Dependent variable = DichEff 

26 Independent variable = Dose 

27 Slope parameter is not restricted 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 User has chosen the log transformed model 

38 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-486 —DO NOT CITE OR QUOTE 

1 

2 Default Initial (and Specified) Parameter Values 

3 background = 0.0188679 

4 intercept = -1.98094 

5 slope = 0.316942 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 background intercept slope 

11 

12 background 1 -0.69 0.59 

13 

14 intercept -0.69 1 -0.97 

15 

16 slope 0.59 -0.97 1 

17 

18 

19 

20 Parameter Estimates 

21 

22 95.0% Wald Confidence Interval 

23 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

24 background 0.0228339 0.0230818 -0.0224057 0.0680734 

25 intercept -2.14844 0.527256 -3.18184 -1.11503 

26 slope 0.367034 0.139055 0.0944904 0.639577 

27 

28 

29 

30 Analysis of Deviance Table 

31 

32 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

33 Full model -114.813 6 

34 Fitted model -115.371 3 1.1157 3 0.7733 

35 Reduced model -127.98 1 26.3331 5 <.0001 

36 

37 AIC: 236.742 

38 

39 

40 Goodness of Fit 

41 Scaled 

42 Dose Est._Prob. Expected Observed Size Residual 

43 ------------------------------------------------------------------------ 

44 0.0000 0.0228 1.210 1.000 53 -0.193 

45 2.1400 0.0529 2.858 4.000 54 0.694 

46 7.1400 0.0979 5.187 4.000 53 -0.549 

47 15.7000 0.1475 7.819 8.000 53 0.070 

48 32.9000 0.2116 11.215 10.000 53 -0.409 

49 71.4000 0.2968 15.729 17.000 53 0.382 

50 

51 Chi^2 = 1.14 d.f. = 3 P-value = 0.7678 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 0.1 

57 

58 Risk Type = Extra risk 

59 

60 Confidence level = 0.95 

61 

62 BMD = 10.6107 

63 

64 BMDL = 3.49791 

65 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-487 —DO NOT CITE OR QUOTE 

1 E.3.42. National Toxicology Program (2006): Liver, Pigmentation 

2 E.3.42.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 3 3.05 0.38 197.66 1.5E+00 8.1E-01 power restricted ≥1 

logistic 4 29.12 0.00 203.52 2.3E+00 1.9E+00 

log-logistic 3 0.19 0.98 195.60 2.2E+00 1.5E+00 slope restricted ≥1 

log-probit b 3 0.18 0.98 195.45 2.1E+00 1.4E+00 slope restricted ≥1 

multistage, 2-

degree 3 4.53 0.21 199.85 9.4E-01 7.1E-01 betas restricted ≥0 

probit 4 131.22 0.00 210.31 2.3E+00 1.9E+00 

Weibull 3 3.75 0.29 198.49 1.3E+00 7.5E-01 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.3.42.2. Figure for Selected Model: Log-Probit, Slope Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

11:59 11/11 2009

BMDL BMD

 

LogProbit

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-488 —DO NOT CITE OR QUOTE 

1 E.3.42.3. Output File for Selected Model: Log-Probit, Slope Restricted ≥1 

2 

3 

4 ==================================================================== 

5 Probit Model. (Version: 3.1; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\LogProbit_BMR2_Pigmentation.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\LogProbit_BMR2_Pigmentation.plt 

8 Wed Nov 11 11:59:31 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = Background 

17 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

18 

19 where CumNorm(.) is the cumulative normal distribution function 

20 

21 

22 Dependent variable = DichEff 

23 Independent variable = Dose 

24 Slope parameter is not restricted 

25 

26 Total number of observations = 6 

27 Total number of records with missing values = 0 

28 Maximum number of iterations = 250 

29 Relative Function Convergence has been set to: 1e-008 

30 Parameter Convergence has been set to: 1e-008 

31 

32 

33 

34 User has chosen the log transformed model 

35 

36 

37 Default Initial (and Specified) Parameter Values 

38 background = 0.0754717 

39 intercept = -1.91144 

40 slope = 1.07385 

41 

42 

43 Asymptotic Correlation Matrix of Parameter Estimates 

44 

45 background intercept slope 

46 

47 background 1 -0.45 0.35 

48 

49 intercept -0.45 1 -0.94 

50 

51 slope 0.35 -0.94 1 

52 

53 

54 

55 Parameter Estimates 

56 

57 95.0% Wald Confidence Interval 

58 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

59 background 0.0735956 0.0343284 0.00631316 0.140878 

60 intercept -2.19294 0.400053 -2.97703 -1.40885 

61 slope 1.25068 0.169731 0.918012 1.58335 

62 

63 

64 

65 Analysis of Deviance Table 

66 

67 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

68 Full model -94.6177 6 

69 Fitted model -94.7248 3 0.214232 3 0.9753 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-489 —DO NOT CITE OR QUOTE 

1 Reduced model -210.717 1 232.198 5 <.0001 

2 

3 AIC: 195.45 

4 

5 

6 Goodness of Fit 

7 Scaled 

8 Dose Est._Prob. Expected Observed Size Residual 

9 ------------------------------------------------------------------------ 

10 0.0000 0.0736 3.901 4.000 53 0.052 

11 2.1400 0.1729 9.338 9.000 54 -0.122 

12 7.1400 0.6338 33.591 34.000 53 0.117 

13 15.7000 0.9023 47.822 48.000 53 0.082 

14 32.9000 0.9863 52.275 52.000 53 -0.325 

15 71.4000 0.9992 52.959 53.000 53 0.202 

16 

17 Chi^2 = 0.18 d.f. = 3 P-value = 0.9801 

18 

19 

20 Benchmark Dose Computation 

21 

22 Specified effect = 0.1 

23 

24 Risk Type = Extra risk 

25 

26 Confidence level = 0.95 

27 

28 BMD = 2.07241 

29 

30 BMDL = 1.39932 

31 

32 

33 

34 E.3.43. National Toxicology Program (2006): Lung, Alveolar to Bronchiolar Epithelial 

35 Metaplasia (Alveolar Epithelium, Metaplasia, Bronchiolar) 

36 E.3.43.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 4 34.09 0.00 340.13 2.2E+00 1.8E+00 power restricted ≥1, bound 

hit 

logistic 4 45.56 0.00 358.35 5.0E+00 4.1E+00 

log-logistic 4 3.98 0.41 312.97 6.6E-01 5.0E-01 slope restricted ≥1, bound 

hit 

log-probit b 3 1.31 0.73 312.54 3.3E-01 9.0E-02 slope restricted ≥1 

multistage, 2-

degree 4 34.09 0.00 340.13 2.2E+00 1.8E+00 betas restricted ≥0, bound hit 

probit 4 46.73 0.00 362.18 5.7E+00 4.8E+00 

Weibull 4 34.09 0.00 340.13 2.2E+00 1.8E+00 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-490 —DO NOT CITE OR QUOTE 

1 E.3.43.2. Figure for Selected Model: Log-Probit, Slope Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

12:00 11/11 2009

BMDLBMD

 

LogProbit

2 

3 

4 

5 E.3.43.3. Output File for Selected Model: Log-Probit, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Probit Model. (Version: 3.1; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\LogProbit_BMR2_Alv_bronch_epith_metapl.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\LogProbit_BMR2_Alv_bronch_epith_metapl.plt 

12 Wed Nov 11 12:00:22 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = Background 

21 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

22 

23 where CumNorm(.) is the cumulative normal distribution function 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 Slope parameter is not restricted 

29 

30 Total number of observations = 6 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-491 —DO NOT CITE OR QUOTE 

1 

2 User has chosen the log transformed model 

3 

4 

5 Default Initial (and Specified) Parameter Values 

6 background = 0.0377358 

7 intercept = -0.759264 

8 slope = 0.469642 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 background intercept slope 

14 

15 background 1 -0.24 0.12 

16 

17 intercept -0.24 1 -0.9 

18 

19 slope 0.12 -0.9 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 background 0.0374101 0.0259232 -0.0133985 0.0882186 

28 intercept -0.761678 0.210613 -1.17447 -0.348885 

29 slope 0.471021 0.0755121 0.32302 0.619022 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -152.615 6 

37 Fitted model -153.271 3 1.31226 3 0.7262 

38 Reduced model -216.802 1 128.374 5 <.0001 

39 

40 AIC: 312.543 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0374 1.983 2.000 53 0.012 

48 2.1400 0.3679 19.868 19.000 54 -0.245 

49 7.1400 0.5815 30.819 33.000 53 0.607 

50 15.7000 0.7149 37.174 35.000 52 -0.668 

51 32.9000 0.8187 43.389 45.000 53 0.574 

52 71.4000 0.8981 46.701 46.000 52 -0.321 

53 

54 Chi^2 = 1.31 d.f. = 3 P-value = 0.7272 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.1 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 0.331636 

66 

67 BMDL = 0.0896842 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-492 —DO NOT CITE OR QUOTE 

1 E.3.44. National Toxicology Program (2006): Oval Cell Hyperplasia, 2 Years 

2 E.3.44.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

gamma 3 7.00 0.07 199.45 9.0E+00 5.5E+00 power restricted ≥1 

logistic 4 8.72 0.07 199.88 9.8E+00 8.2E+00 

log-logistic 3 8.38 0.04 202.01 9.7E+00 7.2E+00 slope restricted ≥1 

log-probit 3 7.12 0.07 200.42 1.0E+01 7.8E+00 slope restricted ≥1 

multistage, 2-

degree b 4 6.33 0.18 195.33 5.8E+00 4.0E+00 betas restricted ≥0 

probit 4 7.50 0.11 198.17 9.1E+00 7.7E+00 

Weibull 3 6.92 0.07 198.69 7.7E+00 4.7E+00 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.3.44.2. Figure for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

11:59 11/11 2009

BMDL BMD

 

Multistage

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-493 —DO NOT CITE OR QUOTE 

1 E.3.44.3. Output File for Selected Model: Multistage, 2-Degree, Betas Restricted ≥0 

2 

3 

4 ==================================================================== 

5 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\AD\Multistage_BMR2_Oval_cell_hyperplasia.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Multistage_BMR2_Oval_cell_hyperplasia.plt 

8 Wed Nov 11 11:59:06 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background + (1-background)*[1-EXP( 

17 -beta1*dose^1-beta2*dose^2)] 

18 

19 The parameter betas are restricted to be positive 

20 

21 

22 Dependent variable = DichEff 

23 Independent variable = Dose 

24 

25 Total number of observations = 6 

26 Total number of records with missing values = 0 

27 Total number of parameters in model = 3 

28 Total number of specified parameters = 0 

29 Degree of polynomial = 2 

30 

31 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 Background = 0 

40 Beta(1) = 0 

41 Beta(2) = 1.98687e+016 

42 

43 

44 Asymptotic Correlation Matrix of Parameter Estimates 

45 

46 ( *** The model parameter(s) -Background 

47 have been estimated at a boundary point, or have been specified by the user, 

48 and do not appear in the correlation matrix ) 

49 

50 Beta(1) Beta(2) 

51 

52 Beta(1) 1 -0.89 

53 

54 Beta(2) -0.89 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 95.0% Wald Confidence Interval 

61 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

62 Background 0 * * * 

63 Beta(1) 0.0133632 * * * 

64 Beta(2) 0.00083535 * * * 

65 

66 * - Indicates that this value is not calculated. 

67 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-494 —DO NOT CITE OR QUOTE 

1 Analysis of Deviance Table 

2 

3 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

4 Full model -92.4898 6 

5 Fitted model -95.6669 2 6.35417 4 0.1742 

6 Reduced model -210.191 1 235.402 5 <.0001 

7 

8 AIC: 195.334 

9 

10 

11 Goodness of Fit 

12 Scaled 

13 Dose Est._Prob. Expected Observed Size Residual 

14 ------------------------------------------------------------------------ 

15 0.0000 0.0000 0.000 0.000 53 0.000 

16 2.1400 0.0319 1.723 4.000 54 1.763 

17 7.1400 0.1289 6.832 3.000 53 -1.571 

18 15.7000 0.3401 18.027 20.000 53 0.572 

19 32.9000 0.7392 39.175 38.000 53 -0.368 

20 71.4000 0.9946 52.711 53.000 53 0.539 

21 

22 Chi^2 = 6.33 d.f. = 4 P-value = 0.1759 

23 

24 

25 Benchmark Dose Computation 

26 

27 Specified effect = 0.1 

28 

29 Risk Type = Extra risk 

30 

31 Confidence level = 0.95 

32 

33 BMD = 5.78926 

34 

35 BMDL = 4.04553 

36 

37 BMDU = 9.63861 

38 

39 Taken together, (4.04553, 9.63861) is a 90 % two-sided confidence 

40 interval for the BMD 

41 

42 

43 E.3.45. National Toxicology Program (2006): Toxic Hepatopathy 

44 E.3.45.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma b 4 1.80 0.77 185.63 4.7E+00 3.3E+00 power restricted ≥1 

logistic 4 12.79 0.01 198.45 7.1E+00 5.9E+00 

log-logistic 3 3.20 0.36 190.06 5.7E+00 4.0E+00 slope restricted ≥1 

log-probit 3 3.09 0.38 189.86 6.1E+00 4.1E+00 slope restricted ≥1 

multistage, 2-

degree 4 2.89 0.58 186.52 4.2E+00 2.7E+00 betas restricted ≥0 

multistage, 2-

degree 4 2.89 0.58 186.52 4.2E+00 2.7E+00 betas unrestricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-495 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

multistage, 1-

degree 5 10.28 0.07 194.94 2.1E+00 1.8E+00 betas unrestricted 

probit 4 11.78 0.02 197.16 6.8E+00 5.7E+00 

Weibull c 4 1.95 0.75 185.66 4.5E+00 3.2E+00 power restricted ≥1 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

c

 Alternate model also presented in this appendix 

1 

2 

3 E.3.45.2. Figure for Selected Model: Gamma, Power Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Gamma Multi-Hit Model with 0.95 Confidence Level

16:49 11/20 2009

BMDL BMD

 

Gamma Multi-Hit

4 

5 

6 

7 E.3.45.3. Output file for Selected Model: Gamma, Power Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Gamma Model. (Version: 2.13; Date: 05/16/2008) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Gamma_BMR2_Toxic_hepatopathy.(d) 

13 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Gamma_BMR2_Toxic_hepatopathy.plt 

14 Fri Nov 20 16:49:26 2009 

15 ==================================================================== 

16 

17 0 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-496 —DO NOT CITE OR QUOTE 

1 

2 The form of the probability function is: 

3 

4 P[response]= background+(1-background)*CumGamma[slope*dose,power], 

5 where CumGamma(.) is the cummulative Gamma distribution function 

6 

7 

8 Dependent variable = DichEff 

9 Independent variable = Dose 

10 Power parameter is restricted as power >=1 

11 

12 Total number of observations = 6 

13 Total number of records with missing values = 0 

14 Maximum number of iterations = 250 

15 Relative Function Convergence has been set to: 1e-008 

16 Parameter Convergence has been set to: 1e-008 

17 

18 

19 

20 Default Initial (and Specified) Parameter Values 

21 Background = 0.00925926 

22 Slope = 0.0683125 

23 Power = 1.3 

24 

25 

26 Asymptotic Correlation Matrix of Parameter Estimates 

27 

28 ( *** The model parameter(s) -Background 

29 have been estimated at a boundary point, or have been specified by the user, 

30 and do not appear in the correlation matrix ) 

31 

32 Slope Power 

33 

34 Slope 1 0.94 

35 

36 Power 0.94 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 95.0% Wald Confidence Interval 

43 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

44 Background 0 NA 

45 Slope 0.105412 0.0237428 0.0588765 0.151947 

46 Power 1.92239 0.361359 1.21414 2.63064 

47 

48 NA - Indicates that this parameter has hit a bound 

49 implied by some inequality constraint and thus 

50 has no standard error. 

51 

52 

53 

54 Analysis of Deviance Table 

55 

56 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

57 Full model -89.8076 6 

58 Fitted model -90.8168 2 2.01832 4 0.7324 

59 Reduced model -218.207 1 256.799 5 <.0001 

60 

61 AIC: 185.634 

62 

63 

64 Goodness of Fit 

65 Scaled 

66 Dose Est._Prob. Expected Observed Size Residual 

67 ------------------------------------------------------------------------ 

68 0.0000 0.0000 0.000 0.000 53 0.000 

69 2.1400 0.0265 1.429 2.000 54 0.484 

70 7.1400 0.1926 10.205 8.000 53 -0.768 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-497 —DO NOT CITE OR QUOTE 

1 15.7000 0.5170 27.403 30.000 53 0.714 

2 32.9000 0.8723 46.232 45.000 53 -0.507 

3 71.4000 0.9960 52.788 53.000 53 0.462 

4 

5 Chi^2 = 1.80 d.f. = 4 P-value = 0.7716 

6 

7 

8 Benchmark Dose Computation 

9 

10 Specified effect = 0.1 

11 

12 Risk Type = Extra risk 

13 

14 Confidence level = 0.95 

15 

16 BMD = 4.66805 

17 

18 BMDL = 3.31743 

19 

20 

21 

22 E.3.45.4. Figure for Unrestricted Model: Weibull, Power Restricted ≥1 

 0

 0.2

 0.4

 0.6

 0.8

 1

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Weibull Model with 0.95 Confidence Level

16:49 11/20 2009

BMDL BMD

 

Weibull

23 

24 

25 

26 E.3.45.5. Output File for Unrestricted Model: Weibull, Power Restricted ≥1 

27 

28 

29 ==================================================================== 

30 Weibull Model using Weibull Model (Version: 2.12; Date: 05/16/2008) 

31 Input Data File: C:\USEPA\BMDS21\Nov20\Weibull_BMR2_Toxic_hepatopathy.(d) 

32 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Weibull_BMR2_Toxic_hepatopathy.plt 

33 Fri Nov 20 16:49:32 2009 

34 ==================================================================== 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-498 —DO NOT CITE OR QUOTE 

1 0 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the probability function is: 

5 

6 P[response] = background + (1-background)*[1-EXP(-slope*dose^power)] 

7 

8 

9 Dependent variable = DichEff 

10 Independent variable = Dose 

11 Power parameter is restricted as power >=1 

12 

13 Total number of observations = 6 

14 Total number of records with missing values = 0 

15 Maximum number of iterations = 250 

16 Relative Function Convergence has been set to: 1e-008 

17 Parameter Convergence has been set to: 1e-008 

18 

19 

20 

21 Default Initial (and Specified) Parameter Values 

22 Background = 0.00925926 

23 Slope = 0.0286401 

24 Power = 1.19362 

25 

26 

27 Asymptotic Correlation Matrix of Parameter Estimates 

28 

29 ( *** The model parameter(s) -Background 

30 have been estimated at a boundary point, or have been specified by the user, 

31 and do not appear in the correlation matrix ) 

32 

33 Slope Power 

34 

35 Slope 1 -0.97 

36 

37 Power -0.97 1 

38 

39 

40 

41 Parameter Estimates 

42 

43 95.0% Wald Confidence Interval 

44 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

45 Background 0 NA 

46 Slope 0.0113696 0.00592954 -0.000252127 0.0229912 

47 Power 1.4905 0.169532 1.15823 1.82278 

48 

49 NA - Indicates that this parameter has hit a bound 

50 implied by some inequality constraint and thus 

51 has no standard error. 

52 

53 

54 

55 Analysis of Deviance Table 

56 

57 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

58 Full model -89.8076 6 

59 Fitted model -90.8285 2 2.04181 4 0.7281 

60 Reduced model -218.207 1 256.799 5 <.0001 

61 

62 AIC: 185.657 

63 

64 

65 Goodness of Fit 

66 Scaled 

67 Dose Est._Prob. Expected Observed Size Residual 

68 ------------------------------------------------------------------------ 

69 0.0000 0.0000 0.000 0.000 53 0.000 

70 2.1400 0.0347 1.875 2.000 54 0.093 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-499 —DO NOT CITE OR QUOTE 

1 7.1400 0.1918 10.164 8.000 53 -0.755 

2 15.7000 0.4979 26.391 30.000 53 0.992 

3 32.9000 0.8745 46.349 45.000 53 -0.559 

4 71.4000 0.9986 52.927 53.000 53 0.270 

5 

6 Chi^2 = 1.95 d.f. = 4 P-value = 0.7454 

7 

8 

9 Benchmark Dose Computation 

10 

11 Specified effect = 0.1 

12 

13 Risk Type = Extra risk 

14 

15 Confidence level = 0.95 

16 

17 BMD = 4.4538 

18 

19 BMDL = 3.15886 

20 

21 

22 

23 E.3.46. Ohsako et al. (2001): Anogenital PND120 

24 E.3.46.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 0.46 5.02 0.17 185.44 7.5E+02 4.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.46 5.02 0.17 185.44 7.5E+02 4.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 2 0.46 4.29 0.12 186.72 4.8E+02 1.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.46 4.29 0.12 186.72 4.8E+02 1.1E+01 nonconstant variance, 

power restricted ≥1 

Hill 2 0.46 3.11 0.21 185.54 7.1E+01 1.3E+01 nonconstant variance, n 

restricted >1, bound hit 

linear 3 0.46 5.09 0.17 185.52 7.6E+02 5.1E+02 nonconstant variance 

polynomial 2 0.46 4.45 0.11 186.88 4.8E+02 1.5E+02 nonconstant variance 

power 3 0.46 5.09 0.17 185.52 7.6E+02 5.1E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 3 0.46 7.00 0.07 185.90 6.5E+02 4.2E+02 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.46 7.00 0.07 185.90 6.5E+02 4.2E+02 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.46 3.17 0.20 184.07 4.1E+01 1.2E+01 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.46 2.84 0.09 185.74 3.8E+01 1.3E+01 constant variance, 

power restricted ≥1 

Hill c 2 0.46 2.74 0.25 183.64 6.0E+01 1.2E+01 constant variance, n 

restricted >1, bound 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-500 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

hit 

linear 3 0.46 7.12 0.07 186.02 6.6E+02 4.4E+02 constant variance 

polynomial 2 0.46 5.55 0.06 186.45 2.7E+02 1.3E+02 constant variance 

power 3 0.46 7.12 0.07 186.02 6.6E+02 4.4E+02 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

1 

2 

3 E.3.46.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 22

 24

 26

 28

 30

 32

 0 100 200 300 400 500 600 700 800

Mean Response

dose

Hill Model with 0.95 Confidence Level

18:59 10/06 2009

BMDL BMD

 

Hill

4 

5 

6 

7 E.3.46.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

8 Hit 

9 

10 

11 ==================================================================== 

12 Hill Model. (Version: 2.14; Date: 06/26/2008) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-501 —DO NOT CITE OR QUOTE 

1 Input Data File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_Anogenital_PND120.(d) 

2 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_Anogenital_PND120.plt 

3 Tue Oct 06 18:59:02 2009 

4 ==================================================================== 

5 

6 Figure 7 

7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

8 

9 The form of the response function is: 

10 

11 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

12 

13 

14 Dependent variable = Mean 

15 Independent variable = Dose 

16 rho is set to 0 

17 Power parameter restricted to be greater than 1 

18 A constant variance model is fit 

19 

20 Total number of dose groups = 5 

21 Total number of records with missing values = 0 

22 Maximum number of iterations = 250 

23 Relative Function Convergence has been set to: 1e-008 

24 Parameter Convergence has been set to: 1e-008 

25 

26 

27 

28 Default Initial Parameter Values 

29 alpha = 9.96434 

30 rho = 0 Specified 

31 intercept = 28.9146 

32 v = -5.04512 

33 n = 1.44913 

34 k = 35.3408 

35 

36 

37 Asymptotic Correlation Matrix of Parameter Estimates 

38 

39 ( *** The model parameter(s) -rho -n 

40 have been estimated at a boundary point, or have been specified by the user, 

41 and do not appear in the correlation matrix ) 

42 

43 alpha intercept v k 

44 

45 alpha 1 -4.2e-009 -3.6e-008 2.3e-008 

46 

47 intercept -4.2e-009 1 -0.63 -0.52 

48 

49 v -3.6e-008 -0.63 1 -0.13 

50 

51 k 2.3e-008 -0.52 -0.13 1 

52 

53 

54 

55 Parameter Estimates 

56 

57 95.0% Wald Confidence Interval 

58 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

59 alpha 9.51224 1.83063 5.92427 13.1002 

60 intercept 28.9963 0.861586 27.3077 30.685 

61 v -4.77893 1.14548 -7.02403 -2.53384 

62 n 1 NA 

63 k 33.2115 32.41 -30.3109 96.7338 

64 

65 NA - Indicates that this parameter has hit a bound 

66 implied by some inequality constraint and thus 

67 has no standard error. 

68 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-502 —DO NOT CITE OR QUOTE 

1 Table of Data and Estimated Values of Interest 

2 

3 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

4 ------ --- -------- -------- ----------- ----------- ---------- 

5 

6 0 12 28.9 29 3.54 3.08 -0.0918 

7 12.5 10 28.1 27.7 2.52 3.08 0.399 

8 50 10 25.3 26.1 3.59 3.08 -0.836 

9 200 10 26.1 24.9 3.59 3.08 1.2 

10 800 12 23.9 24.4 2.36 3.08 -0.605 

11 

12 

13 

14 Model Descriptions for likelihoods calculated 

15 

16 

17 Model A1: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma^2 

19 

20 Model A2: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma(i)^2 

22 

23 Model A3: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = Sigma^2 

25 Model A3 uses any fixed variance parameters that 

26 were specified by the user 

27 

28 Model R: Yi = Mu + e(i) 

29 Var{e(i)} = Sigma^2 

30 

31 

32 Likelihoods of Interest 

33 

34 Model Log(likelihood) # Param's AIC 

35 A1 -86.449919 6 184.899838 

36 A2 -84.654549 10 189.309098 

37 A3 -86.449919 6 184.899838 

38 fitted -87.819648 4 183.639297 

39 R -95.473923 2 194.947846 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Do responses and/or variances differ among Dose levels? 

45 (A2 vs. R) 

46 Test 2: Are Variances Homogeneous? (A1 vs A2) 

47 Test 3: Are variances adequately modeled? (A2 vs. A3) 

48 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

49 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) Test df p-value 

54 

55 Test 1 21.6387 8 0.005631 

56 Test 2 3.59074 4 0.4642 

57 Test 3 3.59074 4 0.4642 

58 Test 4 2.73946 2 0.2542 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose levels 

62 It seems appropriate to model the data 

63 

64 The p-value for Test 2 is greater than .1. A homogeneous variance 

65 model appears to be appropriate here 

66 

67 

68 The p-value for Test 3 is greater than .1. The modeled variance appears 

69 to be appropriate here 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-503 —DO NOT CITE OR QUOTE 

1 The p-value for Test 4 is greater than .1. The model chosen seems 

2 to adequately describe the data 

3 

4 

5 Benchmark Dose Computation 

6 

7 Specified effect = 1 

8 Risk Type = Estimated standard deviations from the control mean 

9 Confidence level = 0.95 

10 BMD = 60.4402 

11 BMDL = 12.1546 

12 

13 

14 

15 E.3.47. Schantz et al. (1996): Maze Errors Per Block, Female 

16 E.3.47.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

linear 1 0.71 3.25 0.07 20.63 6.7E+01 3.8E+01 nonconstant variance 

polynomial 1 0.71 3.25 0.07 20.63 6.7E+01 3.8E+01 nonconstant variance 

power 1 0.71 3.25 0.07 20.63 6.7E+01 3.8E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

linear c 1 0.71 2.77 0.10 18.72 7.1E+01 4.6E+01 constant variance 

polynomial 1 0.71 2.77 0.10 18.72 7.1E+01 4.6E+01 constant variance 

power 1 0.71 2.77 0.10 18.72 7.1E+01 4.6E+01 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

17 

18 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-504 —DO NOT CITE OR QUOTE 

1 E.3.47.2. Figure for Selected Model: Linear, Constant Variance 

 2

 2.5

 3

 3.5

 4

 0 20 40 60 80 100

Mean Response

dose

Linear Model with 0.95 Confidence Level

13:40 11/11 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.3.47.3. Output File for Selected Model: Linear, Constant Variance 

6 

7 ==================================================================== 

8 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

9 Input Data File: C:\USEPA\BMDS21\AD\LinearConstVar_BMR4_maze_errors.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\LinearConstVar_BMR4_maze_errors.plt 

11 Wed Nov 11 13:40:58 2009 

12 ==================================================================== 

13 

14 Rel Male Thymus wt, Tbl 2 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the response function is: 

18 

19 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 rho is set to 0 

25 Signs of the polynomial coefficients are not restricted 

26 A constant variance model is fit 

27 

28 Total number of dose groups = 3 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-505 —DO NOT CITE OR QUOTE 

1 alpha = 0.569565 

2 rho = 0 Specified 

3 beta_0 = 3.32773 

4 beta_1 = -0.0105912 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -rho 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 alpha beta_0 beta_1 

14 

15 alpha 1 1.3e-010 3.9e-011 

16 

17 beta_0 1.3e-010 1 -0.7 

18 

19 beta_1 3.9e-011 -0.7 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 alpha 0.562168 0.145151 0.277677 0.846659 

28 beta_0 3.32773 0.191722 2.95196 3.7035 

29 beta_1 -0.0105912 0.00322157 -0.0169054 -0.00427705 

30 

31 

32 

33 Table of Data and Estimated Values of Interest 

34 

35 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

36 ------ --- -------- -------- ----------- ----------- ---------- 

37 

38 0 10 3.55 3.33 0.639 0.75 0.957 

39 25 10 2.76 3.06 0.806 0.75 -1.28 

40 100 10 2.34 2.27 0.806 0.75 0.319 

41 

42 

43 

44 Model Descriptions for likelihoods calculated 

45 

46 

47 Model A1: Yij = Mu(i) + e(ij) 

48 Var{e(ij)} = Sigma^2 

49 

50 Model A2: Yij = Mu(i) + e(ij) 

51 Var{e(ij)} = Sigma(i)^2 

52 

53 Model A3: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 Model A3 uses any fixed variance parameters that 

56 were specified by the user 

57 

58 Model R: Yi = Mu + e(i) 

59 Var{e(i)} = Sigma^2 

60 

61 

62 Likelihoods of Interest 

63 

64 Model Log(likelihood) # Param's AIC 

65 A1 -4.976366 4 17.952732 

66 A2 -4.638353 6 21.276707 

67 A3 -4.976366 4 17.952732 

68 fitted -6.360686 3 18.721371 

69 R -10.975997 2 25.951993 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-506 —DO NOT CITE OR QUOTE 

1 

2 Explanation of Tests 

3 

4 Test 1: Do responses and/or variances differ among Dose levels? 

5 (A2 vs. R) 

6 Test 2: Are Variances Homogeneous? (A1 vs A2) 

7 Test 3: Are variances adequately modeled? (A2 vs. A3) 

8 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

9 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

10 

11 Tests of Interest 

12 

13 Test -2*log(Likelihood Ratio) Test df p-value 

14 

15 Test 1 12.6753 4 0.01298 

16 Test 2 0.676025 2 0.7132 

17 Test 3 0.676025 2 0.7132 

18 Test 4 2.76864 1 0.09613 

19 

20 The p-value for Test 1 is less than .05. There appears to be a 

21 difference between response and/or variances among the dose levels 

22 It seems appropriate to model the data 

23 

24 The p-value for Test 2 is greater than .1. A homogeneous variance 

25 model appears to be appropriate here 

26 

27 

28 The p-value for Test 3 is greater than .1. The modeled variance appears 

29 to be appropriate here 

30 

31 The p-value for Test 4 is less than .1. You may want to try a different 

32 model 

33 

34 

35 Benchmark Dose Computation 

36 

37 Specified effect = 1 

38 

39 Risk Type = Estimated standard deviations from the control mean 

40 

41 Confidence level = 0.95 

42 

43 BMD = 70.7926 

44 

45 

46 BMDL = 45.8305 

47 

48 

49 

50 E.3.48. Shi et al. (2007): Estradiol 

51 E.3.48.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 3 0.05 15.48 0.00 395.70 1.7E+01 9.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.05 15.48 0.00 395.70 1.7E+01 9.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M4)

c 2 0.05 1.41 0.49 383.64 5.6E-01 2.2E-01 nonconstant variance, 

power restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-507 —DO NOT CITE OR QUOTE 

exponential (M5) 2 0.05 1.41 0.49 383.64 5.6E-01 2.2E-01 nonconstant variance, 

power restricted ≥1 

Hill 2 0.05 0.52 0.77 382.74 4.4E-01 error nonconstant variance, n 

restricted >1, bound hit 

linear 3 0.05 17.26 0.00 397.48 2.2E+01 1.5E+01 nonconstant variance 

polynomial 2 0.05 7.34 0.03 389.57 5.4E+00 3.6E+00 nonconstant variance 

power 3 0.05 17.26 0.00 397.48 2.2E+01 1.5E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 3 0.05 13.33 0.00 396.06 1.2E+01 6.6E+00 constant variance, power 

restricted ≥1 

exponential (M3) 3 0.05 13.33 0.00 396.06 1.2E+01 6.6E+00 constant variance, power 

restricted ≥1 

exponential (M4) 2 0.05 0.87 0.65 385.59 3.9E-01 1.5E-01 constant variance, power 

restricted ≥1 

exponential (M5) 2 0.05 0.87 0.65 385.59 3.9E-01 1.5E-01 constant variance, power 

restricted ≥1 

Hill 2 0.05 0.37 0.83 385.09 3.1E-01 1.0E-01 constant variance, n 

restricted >1, bound hit 

linear 3 0.05 15.40 0.00 398.12 1.9E+01 1.3E+01 constant variance 

polynomial 2 0.05 8.10 0.02 392.82 4.5E+00 2.9E+00 constant variance 

power 3 0.05 15.40 0.00 398.12 1.9E+01 1.3E+01 constant variance, power 

restricted ≥1, bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix

1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-508 —DO NOT CITE OR QUOTE 

1 E.3.48.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

 20

 40

 60

 80

 100

 120

 140

 0 5 10 15 20 25 30

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

19:13 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.48.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\Exp_BMR1_Shi_estradiol_17B_conc_PE9.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 19:13:28 2009 

15 ==================================================================== 

16 

17 Figure 4 PE9 only 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-509 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 5 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 4 

18 -------- -------- 

19 lnalpha 2.65881 

20 rho 0.913414 

21 a 108 

22 b 0.136287 

23 c 0.340136 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 4 

31 -------- ------- 

32 lnalpha 1.81331 

33 rho 1.12126 

34 a 100.526 

35 b 1.53823 

36 c 0.431796 

37 d 1 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 10 102.9 41.41 

45 0.143 10 86.19 19.58 

46 0.714 10 63.33 29.36 

47 7.14 10 48.1 18.82 

48 28.6 10 38.57 22.59 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 100.5 32.83 0.2245 

56 0.143 89.25 30.71 -0.3147 

57 0.714 62.45 25.14 0.1108 

58 7.14 43.41 20.5 0.723 

59 28.6 43.41 20.5 -0.7458 

60 

61 

62 

63 Other models for which likelihoods are calculated: 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-510 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

3 

4 Model R: Yij = Mu + e(i) 

5 Var{e(ij)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) DF AIC 

11 ------- ----------------- ---- ------------ 

12 A1 -188.3615 6 388.7231 

13 A2 -183.667 10 387.3339 

14 A3 -186.1132 7 386.2263 

15 R -203.3606 2 410.7211 

16 4 -186.8176 5 383.6352 

17 

18 

19 Additive constant for all log-likelihoods = -45.95. This constant added to the 

20 above values gives the log-likelihood including the term that does not 

21 depend on the model parameters. 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

27 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

28 Test 3: Are variances adequately modeled? (A2 vs. A3) 

29 

30 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

31 

32 

33 Tests of Interest 

34 

35 Test -2*log(Likelihood Ratio) D. F. p-value 

36 -------- ------------------------ ------ -------------- 

37 Test 1 39.39 8 < 0.0001 

38 Test 2 9.389 4 0.05208 

39 Test 3 4.892 3 0.1798 

40 Test 6a 1.409 2 0.4944 

41 

42 

43 The p-value for Test 1 is less than .05. There appears to be a 

44 difference between response and/or variances among the dose 

45 levels, it seems appropriate to model the data. 

46 

47 The p-value for Test 2 is less than .1. A non-homogeneous 

48 variance model appears to be appropriate. 

49 

50 The p-value for Test 3 is greater than .1. The modeled 

51 variance appears to be appropriate here. 

52 

53 The p-value for Test 6a is greater than .1. Model 4 seems 

54 to adequately describe the data. 

55 

56 

57 Benchmark Dose Computations: 

58 

59 Specified Effect = 1.000000 

60 

61 Risk Type = Estimated standard deviations from control 

62 

63 Confidence Level = 0.950000 

64 

65 BMD = 0.555948 

66 

67 BMDL = 0.223612 

68 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-511 —DO NOT CITE OR QUOTE 

1 E.3.49. Smialowicz et al. (2008): PFC per 10^6 Cells 

2 E.3.49.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) c 3 <0.0001 11.58 0.01 890.56 1.1E+02 7.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 2 <0.0001 10.85 0.00 891.83 1.3E+02 7.6E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 11.58 0.01 890.56 1.1E+02 7.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 10.85 0.00 891.83 1.3E+02 7.6E+01 nonconstant variance, 

power restricted ≥1 

Hill 2 <.0001 10.26 0.01 891.23 1.3E+02 error nonconstant variance, n 

restricted >1, bound hit 

linear 3 <.0001 11.79 0.01 890.77 1.8E+02 1.5E+02 nonconstant variance 

polynomial 2 <.0001 10.36 0.01 891.34 1.3E+02 8.4E+01 nonconstant variance 

power 3 <.0001 11.79 0.01 890.77 1.8E+02 1.5E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 3 <0.0001 7.92 0.05 903.59 8.2E+01 4.8E+01 constant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 7.92 0.05 903.59 8.2E+01 4.8E+01 constant variance, 

power restricted ≥1 

exponential (M4) 2 <0.0001 7.91 0.02 905.58 8.0E+01 6.2E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 7.91 0.02 905.58 8.0E+01 6.2E+00 constant variance, 

power restricted ≥1 

Hill 2 <.0001 7.31 0.03 904.98 1.6E+01 2.2E+00 constant variance, n 

restricted >1, bound hit 

linear 3 <.0001 10.33 0.02 905.99 1.5E+02 1.1E+02 constant variance 

polynomial 2 <.0001 8.14 0.02 905.80 8.8E+01 5.5E+01 constant variance 

power 3 <.0001 10.33 0.02 905.99 1.5E+02 1.1E+02 

constant variance, 

power restricted ≥1, 

bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-512 —DO NOT CITE OR QUOTE 

1 E.3.49.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 500

 1000

 1500

 2000

 0 50 100 150 200 250 300

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

19:14 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.49.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\Exp_BMR1_PFC_per_cells.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 19:14:43 2009 

15 ==================================================================== 

16 

17 Anti Response to SRBCs, PFC per 10^6 cells, Table 4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-513 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 5 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 2 

18 -------- -------- 

19 lnalpha 3.29848 

20 rho 1.2578 

21 a 1565.55 

22 b 0.00725727 

23 c 0.00205679 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 2 

31 -------- ------- 

32 lnalpha 1.84544 

33 rho 1.53651 

34 a 1195.73 

35 b 0.00560912 

36 c 0 

37 d 1.22053 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 15 1491 716 

45 1.07 14 1129 171 

46 10.7 15 945 516 

47 107 15 677 465 

48 321 8 161 117 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 1232 593.6 1.688 

56 1.07 1224 590.7 -0.6027 

57 10.7 1153 565 -1.428 

58 107 635.7 362 0.442 

59 321 169.2 134.6 -0.1716 

60 

61 

62 

63 Other models for which likelihoods are calculated: 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-514 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

3 

4 Model R: Yij = Mu + e(i) 

5 Var{e(ij)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) DF AIC 

11 ------- ----------------- ---- ------------ 

12 A1 -444.8329 6 901.6657 

13 A2 -425.4028 10 870.8057 

14 A3 -435.4894 7 884.9787 

15 R -463.7537 2 931.5074 

16 2 -441.2778 4 890.5555 

17 

18 

19 Additive constant for all log-likelihoods = -61.57. This constant added to the 

20 above values gives the log-likelihood including the term that does not 

21 depend on the model parameters. 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

27 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

28 Test 3: Are variances adequately modeled? (A2 vs. A3) 

29 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

30 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) D. F. p-value 

35 -------- ------------------------ ------ -------------- 

36 Test 1 76.7 8 < 0.0001 

37 Test 2 38.86 4 < 0.0001 

38 Test 3 20.17 3 0.0001563 

39 Test 4 11.58 3 0.008983 

40 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose 

44 levels, it seems appropriate to model the data. 

45 

46 The p-value for Test 2 is less than .1. A non-homogeneous 

47 variance model appears to be appropriate. 

48 

49 The p-value for Test 3 is less than .1. You may want to 

50 consider a different variance model. 

51 

52 The p-value for Test 4 is less than .1. Model 2 may not adequately 

53 describe the data; you may want to consider another model. 

54 

55 

56 Benchmark Dose Computations: 

57 

58 Specified Effect = 1.000000 

59 

60 Risk Type = Estimated standard deviations from control 

61 

62 Confidence Level = 0.950000 

63 

64 BMD = 106.252 

65 

66 BMDL = 71.9153 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-515 —DO NOT CITE OR QUOTE 

1 E.3.50. Smialowicz et al. (2008): PFC per Spleen 

2 E.3.50.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) c 3 0.00 5.60 0.13 377.40 1.3E+02 8.4E+01 

nonconstant 

variance, power 

restricted ≥1 

exponential (M3) 3 0.00 5.60 0.13 377.40 1.3E+02 8.4E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.00 5.60 0.13 377.40 1.3E+02 8.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 5.60 0.06 379.40 1.3E+02 8.2E+01 nonconstant variance, 

power restricted ≥1 

Hill 2 0.00 5.35 0.07 379.15 1.4E+02 error 

nonconstant variance, 

n restricted >1, bound 

hit 

linear 3 0.00 8.09 0.04 379.89 2.2E+02 1.7E+02 nonconstant variance 

polynomial 2 0.00 5.58 0.06 379.38 1.4E+02 8.9E+01 nonconstant variance 

power 3 0.00 8.09 0.04 379.89 2.2E+02 1.7E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 3 0.00 5.58 0.13 392.71 1.0E+02 5.5E+01 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.00 5.58 0.13 392.71 1.0E+02 5.5E+01 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.00 5.58 0.06 394.71 1.0E+02 6.5E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 5.58 0.06 394.71 1.0E+02 6.5E+00 constant variance, 

power restricted ≥1 

Hill 2 0.00 5.36 0.07 394.49 8.4E+01 1.7E+00 

constant variance, n 

restricted >1, bound 

hit 

linear 3 0.00 7.31 0.06 394.44 1.7E+02 1.3E+02 constant variance 

polynomial 2 0.00 5.74 0.06 394.87 1.1E+02 6.3E+01 constant variance 

power 3 0.00 7.31 0.06 394.44 1.7E+02 1.3E+02 

constant variance, 

power restricted ≥1, 

bound hit a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-516 —DO NOT CITE OR QUOTE 

1 E.3.50.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 5

 10

 15

 20

 25

 30

 35

 0 50 100 150 200 250 300

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

19:15 10/06 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.50.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AniDose\Exp_BMR1_PFC_per_spleen.(d) 

13 Gnuplot Plotting File: 

14 Tue Oct 06 19:15:26 2009 

15 ==================================================================== 

16 

17 Anti Response to SRBCs - PFC x 10 to the 4 per spleen, Table 4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-517 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 5 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 MLE solution provided: Exact 

13 

14 

15 Initial Parameter Values 

16 

17 Variable Model 2 

18 -------- -------- 

19 lnalpha 0.786146 

20 rho 1.36372 

21 a 29.19 

22 b 0.00907371 

23 c 0.0513875 

24 d 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 Variable Model 2 

31 -------- ------- 

32 lnalpha 0.525138 

33 rho 1.45988 

34 a 22.9464 

35 b 0.00618274 

36 c 0 

37 d 1 

38 

39 

40 Table of Stats From Input Data 

41 

42 Dose N Obs Mean Obs Std Dev 

43 ----- --- ---------- ------------- 

44 0 15 27.8 13.4 

45 1.07 14 21 13.6 

46 10.7 15 17.6 9.4 

47 107 15 12.6 8.7 

48 321 8 3 3.1 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 22.95 12.8 1.468 

56 1.07 22.8 12.74 -0.5272 

57 10.7 21.48 12.2 -1.231 

58 107 11.84 7.899 0.3719 

59 321 3.153 3.007 -0.1444 

60 

61 

62 

63 Other models for which likelihoods are calculated: 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-518 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

3 

4 Model R: Yij = Mu + e(i) 

5 Var{e(ij)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) DF AIC 

11 ------- ----------------- ---- ------------ 

12 A1 -190.565 6 393.13 

13 A2 -181.4763 10 382.9526 

14 A3 -181.9 7 377.8001 

15 R -204.6365 2 413.273 

16 2 -184.6977 4 377.3954 

17 

18 

19 Additive constant for all log-likelihoods = -61.57. This constant added to the 

20 above values gives the log-likelihood including the term that does not 

21 depend on the model parameters. 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

27 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

28 Test 3: Are variances adequately modeled? (A2 vs. A3) 

29 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

30 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) D. F. p-value 

35 -------- ------------------------ ------ -------------- 

36 Test 1 46.32 8 < 0.0001 

37 Test 2 18.18 4 0.001139 

38 Test 3 0.8475 3 0.8381 

39 Test 4 5.595 3 0.133 

40 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose 

44 levels, it seems appropriate to model the data. 

45 

46 The p-value for Test 2 is less than .1. A non-homogeneous 

47 variance model appears to be appropriate. 

48 

49 The p-value for Test 3 is greater than .1. The modeled 

50 variance appears to be appropriate here. 

51 

52 The p-value for Test 4 is greater than .1. Model 2 seems 

53 to adequately describe the data. 

54 

55 

56 Benchmark Dose Computations: 

57 

58 Specified Effect = 1.000000 

59 

60 Risk Type = Estimated standard deviations from control 

61 

62 Confidence Level = 0.950000 

63 

64 BMD = 132.016 

65 

66 BMDL = 84.3108 

67 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-519 —DO NOT CITE OR QUOTE 

1 E.3.51. Toth et al. (1978): Amyloidosis 

2 E.3.51.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

multistage, 1-

degree b 1 0.00 1.00 33.16 8.7E-01 4.5E-01 betas restricted ≥0 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

3 

4 

5 E.3.51.2. Figure for Selected Model: Multistage, 1-Degree, Betas Restricted ≥0 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 0.2 0.4 0.6 0.8 1

Fraction Affected

dose

Multistage Model with 0.95 Confidence Level

19:21 10/06 2009

BMDL BMD

 

Multistage

6 

7 

8 

9 E.3.51.3. Output File for Selected Model: Multistage, 1-Degree, Betas Restricted ≥0 

10 

11 

12 ==================================================================== 

13 Multistage Model. (Version: 3.0; Date: 05/16/2008) 

14 Input Data File: C:\USEPA\BMDS21\AniDose\mult2_0.1_amyloidosis_1yr.(d) 

15 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\mult2_0.1_amyloidosis_1yr.plt 

16 Tue Oct 06 19:21:03 2009 

17 ==================================================================== 

18 

19 Table 2 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the probability function is: 

23 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-520 —DO NOT CITE OR QUOTE 

1 P[response] = background + (1-background)*[1-EXP( 

2 -beta1*dose^1)] 

3 

4 The parameter betas are restricted to be positive 

5 

6 

7 Dependent variable = DichEff 

8 Independent variable = Dose 

9 

10 Total number of observations = 2 

11 Total number of records with missing values = 0 

12 Total number of parameters in model = 2 

13 Total number of specified parameters = 0 

14 Degree of polynomial = 1 

15 

16 

17 Maximum number of iterations = 250 

18 Relative Function Convergence has been set to: 1e-008 

19 Parameter Convergence has been set to: 1e-008 

20 

21 

22 

23 Default Initial Parameter Values 

24 Background = 0 

25 Beta(1) = 0.120628 

26 

27 

28 Asymptotic Correlation Matrix of Parameter Estimates 

29 

30 ( *** The model parameter(s) -Background 

31 have been estimated at a boundary point, or have been specified by the user, 

32 and do not appear in the correlation matrix ) 

33 

34 Beta(1) 

35 

36 Beta(1) 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 95.0% Wald Confidence Interval 

43 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

44 Background 0 * * * 

45 Beta(1) 0.120628 * * * 

46 

47 * - Indicates that this value is not calculated. 

48 

49 

50 

51 Analysis of Deviance Table 

52 

53 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

54 Full model -15.5783 2 

55 Fitted model -15.5783 1 1.42109e-014 1 1 

56 Reduced model -18.8308 1 6.50504 1 0.01076 

57 

58 AIC: 33.1565 

59 

60 

61 Goodness of Fit 

62 Scaled 

63 Dose Est._Prob. Expected Observed Size Residual 

64 ------------------------------------------------------------------------ 

65 0.0000 0.0000 0.000 0.000 38 0.000 

66 1.0000 0.1136 5.000 5.000 44 -0.000 

67 

68 Chi^2 = 0.00 d.f. = 1 P-value = 1.0000 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-521 —DO NOT CITE OR QUOTE 

1 Benchmark Dose Computation 

2 

3 Specified effect = 0.1 

4 

5 Risk Type = Extra risk 

6 

7 Confidence level = 0.95 

8 

9 BMD = 0.873433 

10 

11 BMDL = 0.453242 

12 

13 BMDU = 2.10749 

14 

15 Taken together, (0.453242, 2.10749) is a 90 % two-sided confidence 

16 interval for the BMD 

17 

18 

19 

20 E.3.52. Toth et al. (1978): Skin Lesions 

21 E.3.52.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

χ

 2 Test 

Statistic 

χ

 2

pValue a AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

gamma 2 9.35 0.01 159.22 1.2E+02 8.3E+01 power restricted ≥1, bound 

hit 

logistic 2 12.19 0.00 162.97 2.7E+02 2.1E+02 

log-logistic 2 7.10 0.03 156.57 6.7E+01 4.1E+01 slope restricted ≥1, bound 

hit 

log-probit b 2 1.17 0.56 148.22 1.1E+00 6.8E-02 slope restricted ≥1 

multistage, 2-

degree 2 9.35 0.01 159.22 1.2E+02 8.3E+01 betas restricted ≥0, bound hit 

probit 2 11.98 0.00 162.68 2.5E+02 2.0E+02 

Weibull 2 9.35 0.01 159.22 1.2E+02 8.3E+01 power restricted ≥1, bound 

hit 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

22 

23 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-522 —DO NOT CITE OR QUOTE 

1 E.3.52.2. Figure for Selected Model: Log-Probit, Slope Restricted ≥1 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 200 400 600 800 1000

Fraction Affected

dose

LogProbit Model with 0.95 Confidence Level

19:21 10/06 2009

BMDLBMD

 

LogProbit

2 

3 

4 

5 E.3.52.3. Output File for Selected Model: Log-Probit, Slope Restricted ≥1 

6 

7 

8 ==================================================================== 

9 Probit Model. (Version: 3.1; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\AniDose\LogProbit_BMR2_Skin_lesion_1yr.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\LogProbit_BMR2_Skin_lesion_1yr.plt 

12 Tue Oct 06 19:21:47 2009 

13 ==================================================================== 

14 

15 Table 2 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = Background 

21 + (1-Background) * CumNorm(Intercept+Slope*Log(Dose)), 

22 

23 where CumNorm(.) is the cumulative normal distribution function 

24 

25 

26 Dependent variable = DichEff 

27 Independent variable = Dose 

28 Slope parameter is not restricted 

29 

30 Total number of observations = 4 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-523 —DO NOT CITE OR QUOTE 

1 

2 User has chosen the log transformed model 

3 

4 

5 Default Initial (and Specified) Parameter Values 

6 background = 0 

7 intercept = -1.26532 

8 slope = 0.195762 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -background 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 intercept slope 

18 

19 intercept 1 -0.87 

20 

21 slope -0.87 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 background 0 NA 

30 intercept -1.30013 0.240943 -1.77237 -0.827887 

31 slope 0.202414 0.0463497 0.111571 0.293258 

32 

33 NA - Indicates that this parameter has hit a bound 

34 implied by some inequality constraint and thus 

35 has no standard error. 

36 

37 

38 

39 Analysis of Deviance Table 

40 

41 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

42 Full model -71.5177 4 

43 Fitted model -72.1089 2 1.18249 2 0.5536 

44 Reduced model -95.8498 1 48.6642 3 <.0001 

45 

46 AIC: 148.218 

47 

48 

49 Goodness of Fit 

50 Scaled 

51 Dose Est._Prob. Expected Observed Size Residual 

52 ------------------------------------------------------------------------ 

53 0.0000 0.0000 0.000 0.000 38 0.000 

54 1.0000 0.0968 4.258 5.000 44 0.378 

55 100.0000 0.3564 15.684 13.000 44 -0.845 

56 1000.0000 0.5391 23.180 25.000 43 0.557 

57 

58 Chi^2 = 1.17 d.f. = 2 P-value = 0.5581 

59 

60 

61 Benchmark Dose Computation 

62 

63 Specified effect = 0.1 

64 

65 Risk Type = Extra risk 

66 

67 Confidence level = 0.95 

68 

69 BMD = 1.09611 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-524 —DO NOT CITE OR QUOTE 

1 BMDL = 0.0684731 

2 

3 

4 E.3.53. Van Birgelen et al. (1995a): Hepatic Retinol 

5 E.3.53.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 4 <0.0001 45.69 <0.0001 164.34 2.9E+02 error nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 45.69 <0.0001 164.34 2.9E+02 error nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 27.40 <0.0001 148.05 1.2E+02 7.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 27.40 <0.0001 148.05 1.2E+02 7.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 <0.0001 27.40 <0.0001 148.05 1.2E+02 7.1E+01 nonconstant variance, 

power unrestricted 

Hill 3 <.0001 8.11 0.04 128.76 1.3E+01 error nonconstant variance, n 

restricted >1, bound hit 

Hill d 2 <.0001 2.62 0.27 125.27 5.6E+00 error nonconstant variance, n 

unrestricted 

linear 4 <.0001 60.09 <.0001 178.73 7.8E+02 6.0E+02 nonconstant variance 

polynomial 4 <.0001 60.09 <.0001 178.73 7.8E+02 6.0E+02 nonconstant variance 

power 4 <.0001 60.09 <.0001 178.73 7.8E+02 6.0E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 9.34 0.03 129.99 4.2E-01 8.5E-03 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 141.80 <0.0001 322.09 error error constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 141.80 <0.0001 322.09 error error constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 2.71 0.44 185.03 1.2E+01 7.0E+00 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 2.71 0.44 185.03 1.2E+01 7.0E+00 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 2.71 0.44 185.03 1.2E+01 7.0E+00 constant variance, 

power unrestricted 

Hill 3 <.0001 1.37 0.71 183.68 8.3E+00 4.2E+00 constant variance, n 

restricted >1, bound hit 

Hill 2 <.0001 0.89 0.64 185.20 4.5E+00 5.8E-02 constant variance, n 

unrestricted 

linear 4 <.0001 27.00 <.0001 207.31 5.3E+02 3.9E+02 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-525 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

polynomial 4 <.0001 27.00 <.0001 207.31 5.3E+02 3.9E+02 constant variance 

power 4 <.0001 27.00 <.0001 207.31 5.3E+02 3.9E+02 

constant variance, 

power restricted ≥1, 

bound hit 

power 3 <.0001 1.92 0.59 184.23 4.4E-01 6.6E-03 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.3.53.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 5

 10

 15

 20

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:29 11/20 2009

BMDL BMD

 

Exponential

5 

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-526 —DO NOT CITE OR QUOTE 

1 E.3.53.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

2 Restricted ≥1 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_hepatic_retinol.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 14:29:52 2009 

10 ==================================================================== 

11 

12 Tbl3, hepatic retinol 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

35 

36 Total number of dose groups = 6 

37 Total number of records with missing values = 0 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 

40 Parameter Convergence has been set to: 1e-008 

41 

42 MLE solution provided: Exact 

43 

44 

45 Initial Parameter Values 

46 

47 Variable Model 4 

48 -------- -------- 

49 lnalpha -1.16065 

50 rho 1.53688 

51 a 15.645 

52 b 0.00625117 

53 c 0.0365247 

54 d 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 Variable Model 4 

61 -------- ------- 

62 lnalpha -0.882224 

63 rho 1.82707 

64 a 10.5294 

65 b 0.00720346 

66 c 0.068866 

67 d 1 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-527 —DO NOT CITE OR QUOTE 

1 

2 Table of Stats From Input Data 

3 

4 Dose N Obs Mean Obs Std Dev 

5 ----- --- ---------- ------------- 

6 0 8 14.9 8.768 

7 14 8 8.4 3.394 

8 26 8 8.2 2.263 

9 47 8 5.1 0.8485 

10 320 8 2.2 0.8485 

11 1024 8 0.6 0.5657 

12 

13 

14 Estimated Values of Interest 

15 

16 Dose Est Mean Est Std Scaled Residual 

17 ------ ---------- --------- ---------------- 

18 0 10.53 5.526 2.237 

19 14 9.589 5.073 -0.6628 

20 26 8.855 4.717 -0.3926 

21 47 7.714 4.159 -1.778 

22 320 1.703 1.046 1.343 

23 1024 0.7313 0.4833 -0.7681 

24 

25 

26 

27 Other models for which likelihoods are calculated: 

28 

29 Model A1: Yij = Mu(i) + e(ij) 

30 Var{e(ij)} = Sigma^2 

31 

32 Model A2: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma(i)^2 

34 

35 Model A3: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

37 

38 Model R: Yij = Mu + e(i) 

39 Var{e(ij)} = Sigma^2 

40 

41 

42 Likelihoods of Interest 

43 

44 Model Log(likelihood) DF AIC 

45 ------- ----------------- ---- ------------ 

46 A1 -87.1567 7 188.3134 

47 A2 -47.28742 12 118.5748 

48 A3 -55.32422 8 126.6484 

49 R -109.967 2 223.934 

50 4 -69.02619 5 148.0524 

51 

52 

53 Additive constant for all log-likelihoods = -44.11. This constant added to the 

54 above values gives the log-likelihood including the term that does not 

55 depend on the model parameters. 

56 

57 

58 Explanation of Tests 

59 

60 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

61 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

62 Test 3: Are variances adequately modeled? (A2 vs. A3) 

63 

64 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

65 

66 

67 Tests of Interest 

68 

69 Test -2*log(Likelihood Ratio) D. F. p-value 

70 -------- ------------------------ ------ -------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-528 —DO NOT CITE OR QUOTE 

1 Test 1 125.4 10 < 0.0001 

2 Test 2 79.74 5 < 0.0001 

3 Test 3 16.07 4 0.002922 

4 Test 6a 27.4 3 < 0.0001 

5 

6 

7 The p-value for Test 1 is less than .05. There appears to be a 

8 difference between response and/or variances among the dose 

9 levels, it seems appropriate to model the data. 

10 

11 The p-value for Test 2 is less than .1. A non-homogeneous 

12 variance model appears to be appropriate. 

13 

14 The p-value for Test 3 is less than .1. You may want to 

15 consider a different variance model. 

16 

17 The p-value for Test 6a is less than .1. Model 4 may not adequately 

18 describe the data; you may want to consider another model. 

19 

20 

21 Benchmark Dose Computations: 

22 

23 Specified Effect = 1.000000 

24 

25 Risk Type = Estimated standard deviations from control 

26 

27 Confidence Level = 0.950000 

28 

29 BMD = 115.128 

30 

31 BMDL = 70.981 

32 

33 

34 E.3.53.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

35 Unrestricted 

 0

 5

 10

 15

 20

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:30 11/20 2009

BMDL BMD

 

Exponential

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-529 —DO NOT CITE OR QUOTE 

1 E.3.53.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

2 Power Unrestricted 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_hepatic_retinol.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 14:30:05 2009 

10 ==================================================================== 

11 

12 Tbl3, hepatic retinol 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

35 

36 Total number of dose groups = 6 

37 Total number of records with missing values = 0 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 

40 Parameter Convergence has been set to: 1e-008 

41 

42 MLE solution provided: Exact 

43 

44 

45 Initial Parameter Values 

46 

47 Variable Model 5 

48 -------- -------- 

49 lnalpha -1.16065 

50 rho 1.53688 

51 a 15.645 

52 b 0.00625117 

53 c 0.0365247 

54 d 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 Variable Model 5 

61 -------- ------- 

62 lnalpha -0.882224 

63 rho 1.82707 

64 a 10.5294 

65 b 0.00720346 

66 c 0.068866 

67 d 1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-530 —DO NOT CITE OR QUOTE 

1 

2 

3 Table of Stats From Input Data 

4 

5 Dose N Obs Mean Obs Std Dev 

6 ----- --- ---------- ------------- 

7 0 8 14.9 8.768 

8 14 8 8.4 3.394 

9 26 8 8.2 2.263 

10 47 8 5.1 0.8485 

11 320 8 2.2 0.8485 

12 1024 8 0.6 0.5657 

13 

14 

15 Estimated Values of Interest 

16 

17 Dose Est Mean Est Std Scaled Residual 

18 ------ ---------- --------- ---------------- 

19 0 10.53 5.526 2.237 

20 14 9.589 5.073 -0.6628 

21 26 8.855 4.717 -0.3926 

22 47 7.714 4.159 -1.778 

23 320 1.703 1.046 1.343 

24 1024 0.7313 0.4833 -0.7681 

25 

26 

27 

28 Other models for which likelihoods are calculated: 

29 

30 Model A1: Yij = Mu(i) + e(ij) 

31 Var{e(ij)} = Sigma^2 

32 

33 Model A2: Yij = Mu(i) + e(ij) 

34 Var{e(ij)} = Sigma(i)^2 

35 

36 Model A3: Yij = Mu(i) + e(ij) 

37 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

38 

39 Model R: Yij = Mu + e(i) 

40 Var{e(ij)} = Sigma^2 

41 

42 

43 Likelihoods of Interest 

44 

45 Model Log(likelihood) DF AIC 

46 ------- ----------------- ---- ------------ 

47 A1 -87.1567 7 188.3134 

48 A2 -47.28742 12 118.5748 

49 A3 -55.32422 8 126.6484 

50 R -109.967 2 223.934 

51 5 -69.02619 5 148.0524 

52 

53 

54 Additive constant for all log-likelihoods = -44.11. This constant added to the 

55 above values gives the log-likelihood including the term that does not 

56 depend on the model parameters. 

57 

58 

59 Explanation of Tests 

60 

61 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

62 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

63 Test 3: Are variances adequately modeled? (A2 vs. A3) 

64 

65 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

66 

67 

68 Tests of Interest 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-531 —DO NOT CITE OR QUOTE 

1 Test -2*log(Likelihood Ratio) D. F. p-value 

2 -------- ------------------------ ------ -------------- 

3 Test 1 125.4 10 < 0.0001 

4 Test 2 79.74 5 < 0.0001 

5 Test 3 16.07 4 0.002922 

6 Test 7a 27.4 3 < 0.0001 

7 

8 

9 The p-value for Test 1 is less than .05. There appears to be a 

10 difference between response and/or variances among the dose 

11 levels, it seems appropriate to model the data. 

12 

13 The p-value for Test 2 is less than .1. A non-homogeneous 

14 variance model appears to be appropriate. 

15 

16 The p-value for Test 3 is less than .1. You may want to 

17 consider a different variance model. 

18 

19 The p-value for Test 7a is less than .1. Model 5 may not adequately 

20 describe the data; you may want to consider another model. 

21 

22 

23 Benchmark Dose Computations: 

24 

25 Specified Effect = 1.000000 

26 

27 Risk Type = Estimated standard deviations from control 

28 

29 Confidence Level = 0.950000 

30 

31 BMD = 115.128 

32 

33 BMDL = 70.981 

34 

35 

36 E.3.53.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 5

 10

 15

 20

 0 200 400 600 800 1000

Mean Response

dose

Hill Model

14:30 11/20 2009

BMD

Hill

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-532 —DO NOT CITE OR QUOTE 

1 E.3.53.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

2 

3 

4 ==================================================================== 

5 Hill Model. (Version: 2.14; Date: 06/26/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_hepatic_retinol.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_hepatic_retinol.plt 

8 Fri Nov 20 14:30:12 2009 

9 ==================================================================== 

10 

11 Tbl3, hepatic retinol 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Power parameter is not restricted 

22 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

23 

24 Total number of dose groups = 6 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 Default Initial Parameter Values 

33 lalpha = 2.76506 

34 rho = 0 

35 intercept = 14.9 

36 v = -14.3 

37 n = 2.92354 

38 k = 29.0484 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 lalpha rho intercept v n k 

44 

45 lalpha 1 -0.78 -0.041 0.015 0.037 0.029 

46 

47 rho -0.78 1 -0.098 0.11 -0.047 -0.046 

48 

49 intercept -0.041 -0.098 1 -0.9 -0.25 -0.8 

50 

51 v 0.015 0.11 -0.9 1 0.63 0.63 

52 

53 n 0.037 -0.047 -0.25 0.63 1 0.15 

54 

55 k 0.029 -0.046 -0.8 0.63 0.15 1 

56 

57 

58 

59 Parameter Estimates 

60 

61 95.0% Wald Confidence Interval 

62 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

63 lalpha -1.16547 0.373814 -1.89813 -0.432809 

64 rho 1.69882 0.185479 1.33529 2.06235 

65 intercept 16.6759 2.07841 12.6023 20.7495 

66 v -17.4464 2.46627 -22.2801 -12.6126 

67 n 0.570647 0.161383 0.254343 0.886951 

68 k 16.5364 7.36467 2.10191 30.9709 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-533 —DO NOT CITE OR QUOTE 

1 

2 

3 

4 Table of Data and Estimated Values of Interest 

5 

6 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

7 ------ --- -------- -------- ----------- ----------- ---------- 

8 

9 0 8 14.9 16.7 8.77 6.1 -0.824 

10 14 8 8.4 8.37 3.39 3.39 0.0276 

11 26 8 8.2 6.83 2.26 2.86 1.35 

12 47 8 5.1 5.43 0.849 2.35 -0.394 

13 320 8 2.2 1.95 0.849 0.983 0.732 

14 1024 8 0.6 0.742 0.566 0.434 -0.929 

15 

16 

17 

18 Model Descriptions for likelihoods calculated 

19 

20 

21 Model A1: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = Sigma^2 

23 

24 Model A2: Yij = Mu(i) + e(ij) 

25 Var{e(ij)} = Sigma(i)^2 

26 

27 Model A3: Yij = Mu(i) + e(ij) 

28 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

29 Model A3 uses any fixed variance parameters that 

30 were specified by the user 

31 

32 Model R: Yi = Mu + e(i) 

33 Var{e(i)} = Sigma^2 

34 

35 

36 Likelihoods of Interest 

37 

38 Model Log(likelihood) # Param's AIC 

39 A1 -87.156698 7 188.313395 

40 A2 -47.287416 12 118.574833 

41 A3 -55.324218 8 126.648436 

42 fitted -56.636555 6 125.273110 

43 R -109.967018 2 223.934036 

44 

45 

46 Explanation of Tests 

47 

48 Test 1: Do responses and/or variances differ among Dose levels? 

49 (A2 vs. R) 

50 Test 2: Are Variances Homogeneous? (A1 vs A2) 

51 Test 3: Are variances adequately modeled? (A2 vs. A3) 

52 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

53 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

54 

55 Tests of Interest 

56 

57 Test -2*log(Likelihood Ratio) Test df p-value 

58 

59 Test 1 125.359 10 <.0001 

60 Test 2 79.7386 5 <.0001 

61 Test 3 16.0736 4 0.002922 

62 Test 4 2.62467 2 0.2692 

63 

64 The p-value for Test 1 is less than .05. There appears to be a 

65 difference between response and/or variances among the dose levels 

66 It seems appropriate to model the data 

67 

68 The p-value for Test 2 is less than .1. A non-homogeneous variance 

69 model appears to be appropriate 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-534 —DO NOT CITE OR QUOTE 

1 

2 The p-value for Test 3 is less than .1. You may want to consider a 

3 different variance model 

4 

5 The p-value for Test 4 is greater than .1. The model chosen seems 

6 to adequately describe the data 

7 

8 

9 Benchmark Dose Computation 

10 

11 Specified effect = 1 

12 

13 Risk Type = Estimated standard deviations from the control mean 

14 

15 Confidence level = 0.95 

16 

17 BMD = 5.56122 

18 

19 

20 BMDL computation failed. 

21 

22 

23 E.3.53.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 5

 10

 15

 20

 0 200 400 600 800 1000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:30 11/20 2009

BMDLBMD

 

Power

24 

25 

26 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-535 —DO NOT CITE OR QUOTE 

1 E.3.53.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

2 Unrestricted 

3 

4 

5 ==================================================================== 

6 Power Model. (Version: 2.15; Date: 04/07/2008) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_hepatic_retinol.(d) 

8 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_hepatic_retinol.plt 

9 Fri Nov 20 14:30:13 2009 

10 ==================================================================== 

11 

12 Tbl3, hepatic retinol 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function is: 

16 

17 Y[dose] = control + slope * dose^power 

18 

19 

20 Dependent variable = Mean 

21 Independent variable = Dose 

22 The power is not restricted 

23 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

24 

25 Total number of dose groups = 6 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 

32 

33 Default Initial Parameter Values 

34 lalpha = 2.76506 

35 rho = 0 

36 control = 14.9 

37 slope = -3.78637 

38 power = 0.191713 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 lalpha rho control slope power 

44 

45 lalpha 1 -0.8 -0.047 0.042 0.065 

46 

47 rho -0.8 1 -0.085 -0.0029 -0.11 

48 

49 control -0.047 -0.085 1 -0.95 -0.81 

50 

51 slope 0.042 -0.0029 -0.95 1 0.96 

52 

53 power 0.065 -0.11 -0.81 0.96 1 

54 

55 

56 

57 Parameter Estimates 

58 

59 95.0% Wald Confidence Interval 

60 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

61 lalpha -1.02622 0.389164 -1.78897 -0.263475 

62 rho 1.68421 0.199212 1.29376 2.07466 

63 control 16.9577 2.21133 12.6235 21.2918 

64 slope -7.19097 1.99708 -11.1052 -3.27676 

65 power 0.117935 0.0225396 0.0737578 0.162111 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-536 —DO NOT CITE OR QUOTE 

1 

2 Table of Data and Estimated Values of Interest 

3 

4 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

5 ------ --- -------- -------- ----------- ----------- ---------- 

6 

7 0 8 14.9 17 8.77 6.49 -0.896 

8 14 8 8.4 7.14 3.39 3.13 1.14 

9 26 8 8.2 6.4 2.26 2.86 1.78 

10 47 8 5.1 5.63 0.849 2.57 -0.588 

11 320 8 2.2 2.76 0.849 1.41 -1.12 

12 1024 8 0.6 0.672 0.566 0.428 -0.475 

13 

14 

15 

16 Model Descriptions for likelihoods calculated 

17 

18 

19 Model A1: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = Sigma^2 

21 

22 Model A2: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma(i)^2 

24 

25 Model A3: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

27 Model A3 uses any fixed variance parameters that 

28 were specified by the user 

29 

30 Model R: Yi = Mu + e(i) 

31 Var{e(i)} = Sigma^2 

32 

33 

34 Likelihoods of Interest 

35 

36 Model Log(likelihood) # Param's AIC 

37 A1 -87.156698 7 188.313395 

38 A2 -47.287416 12 118.574833 

39 A3 -55.324218 8 126.648436 

40 fitted -59.994980 5 129.989960 

41 R -109.967018 2 223.934036 

42 

43 

44 Explanation of Tests 

45 

46 Test 1: Do responses and/or variances differ among Dose levels? 

47 (A2 vs. R) 

48 Test 2: Are Variances Homogeneous? (A1 vs A2) 

49 Test 3: Are variances adequately modeled? (A2 vs. A3) 

50 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

51 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

52 

53 Tests of Interest 

54 

55 Test -2*log(Likelihood Ratio) Test df p-value 

56 

57 Test 1 125.359 10 <.0001 

58 Test 2 79.7386 5 <.0001 

59 Test 3 16.0736 4 0.002922 

60 Test 4 9.34152 3 0.02508 

61 

62 The p-value for Test 1 is less than .05. There appears to be a 

63 difference between response and/or variances among the dose levels 

64 It seems appropriate to model the data 

65 

66 The p-value for Test 2 is less than .1. A non-homogeneous variance 

67 model appears to be appropriate 

68 

69 The p-value for Test 3 is less than .1. You may want to consider a 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-537 —DO NOT CITE OR QUOTE 

1 different variance model 

2 

3 The p-value for Test 4 is less than .1. You may want to try a different 

4 model 

5 

6 

7 Benchmark Dose Computation 

8 

9 Specified effect = 1 

10 

11 Risk Type = Estimated standard deviations from the control mean 

12 

13 Confidence level = 0.95 

14 

15 BMD = 0.420475 

16 

17 

18 BMDL = 0.00850422 

19 

20 

21 

22 E.3.54. Van Birgelen et al. (1995a): Hepatic Retinol Palmitate 

23 E.3.54.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a 

χ 2 Test 

Statistic 

χ 2pValue b AIC BMD 

(ng/kg-d)

BMDL 

(ng/kg-d) Model Notes 

exponential (M2) 4 <0.0001 64.68 <0.0001 467.45 error error nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 64.68 <0.0001 467.45 error error nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 49.32 <0.0001 454.09 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 49.32 <0.0001 454.09 error error nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 49.32 <0.0001 454.09 error error nonconstant variance, 

power unrestricted 

Hill 3 <.0001 158.81 <.0001 563.58 error error nonconstant variance, n 

restricted >1 

Hill d 3 <.0001 117.56 <.0001 522.32 2.4E-12 2.4E-12 nonconstant variance, n 

unrestricted 

linear c 4 <.0001 85.68 <.0001 488.45 1.4E+03 9.9E+02 nonconstant variance 

polynomial 4 <.0001 85.68 <.0001 488.45 1.4E+03 9.9E+02 nonconstant variance 

power 4 <.0001 85.68 <.0001 488.45 1.4E+03 9.9E+02 nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 3.30 0.35 408.06 3.8E-02 1.2E-05 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 140.00 <0.0001 647.15 error error constant variance, power 

restricted ≥1 

exponential (M3) 4 <0.0001 140.00 <0.0001 647.15 error error constant variance, power 

restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-538 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a 

χ

 2 Test 

Statistic 

χ 2pValue b AIC BMD 

(ng/kg-d)

BMDL 

(ng/kg-d) Model Notes 

exponential (M4) 3 <0.0001 3.50 0.32 512.61 2.5E+00 9.0E-03 constant variance, power 

restricted ≥1 

exponential (M5) 3 <0.0001 3.50 0.32 512.61 2.5E+00 9.0E-03 constant variance, power 

restricted ≥1 

exponential (M5) d 3 <0.0001 3.50 0.32 512.61 2.5E+00 9.0E-03 constant variance, power 

unrestricted 

Hill 3 <.0001 1.33 0.72 510.44 1.3E+00 2.5E-01 constant variance, n 

restricted >1, bound hit 

Hill 2 <.0001 0.29 0.86 511.40 7.9E-06 7.9E-06 constant variance, n 

unrestricted 

linear 4 <.0001 44.59 <.0001 551.70 8.7E+02 5.5E+02 constant variance 

polynomial 4 <.0001 44.59 <.0001 551.70 8.7E+02 5.5E+02 constant variance 

power 4 <.0001 44.59 <.0001 551.70 8.7E+02 5.5E+02 constant variance, power 

restricted ≥1, bound hit 

power 3 <.0001 0.29 0.96 509.40 2.2E-08 2.2E-08 constant variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix

d

 Alternate model also presented in this appendix 

1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-539 —DO NOT CITE OR QUOTE 

1 E.3.54.2. Figure for Selected Model: Hill, Nonconstant Variance, n Unrestricted

 0

 100

 200

 300

 400

 500

 600

 700

 0 200 400 600 800 1000

Mean Response

dose

Hill Model with 0.95 Confidence Level

14:31 11/20 2009

BMDBMDL

 

Hill

2 

3 

4 

5 E.3.54.3. Output File for Selected Model: Hill, Nonconstant Variance, n Unrestricted 

6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_hepatic_retinol_palmitate.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_hepatic_retinol_palmitate.plt 

13 Fri Nov 20 14:31:05 2009 

14 ==================================================================== 

15 

16 Tbl3, hepatic retinol palmitate 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-540 —DO NOT CITE OR QUOTE 

1 Default Initial Parameter Values 

2 lalpha = 9.57332 

3 rho = 0 

4 intercept = 472 

5 v = -469 

6 n = 1.50651 

7 k = 8.68519 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -k 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 lalpha rho intercept v n 

17 

18 lalpha 1 -1 -0.43 0.39 -0.014 

19 

20 rho -1 1 0.44 -0.41 0.015 

21 

22 intercept -0.43 0.44 1 -1 0.027 

23 

24 v 0.39 -0.41 -1 1 -0.026 

25 

26 n -0.014 0.015 0.027 -0.026 1 

27 

28 

29 

30 Parameter Estimates 

31 

32 95.0% Wald Confidence Interval 

33 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

34 lalpha 2.09439 1.99191 -1.80969 5.99847 

35 rho 1.43616 0.388229 0.675242 2.19707 

36 intercept 640.986 167.573 312.548 969.423 

37 v -495.665 166.074 -821.163 -170.167 

38 n 0.451934 0.597514 -0.719171 1.62304 

39 k 1.024e-012 NA 

40 

41 NA - Indicates that this parameter has hit a bound 

42 implied by some inequality constraint and thus 

43 has no standard error. 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 8 472 641 272 295 -1.62 

53 14 8 94 145 67.9 102 -1.43 

54 26 8 107 145 76.4 102 -1.07 

55 47 8 74 145 39.6 102 -1.98 

56 320 8 22 145 22.6 102 -3.43 

57 1024 8 3 145 2.83 102 -3.96 

58 

59 

60 

61 Model Descriptions for likelihoods calculated 

62 

63 

64 Model A1: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 

67 Model A2: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma(i)^2 

69 

70 Model A3: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-541 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

2 Model A3 uses any fixed variance parameters that 

3 were specified by the user 

4 

5 Model R: Yi = Mu + e(i) 

6 Var{e(i)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) # Param's AIC 

12 A1 -250.554817 7 515.109634 

13 A2 -196.755746 12 417.511491 

14 A3 -197.383174 8 410.766347 

15 fitted -256.161039 5 522.322077 

16 R -276.789644 2 557.579287 

17 

18 

19 Explanation of Tests 

20 

21 Test 1: Do responses and/or variances differ among Dose levels? 

22 (A2 vs. R) 

23 Test 2: Are Variances Homogeneous? (A1 vs A2) 

24 Test 3: Are variances adequately modeled? (A2 vs. A3) 

25 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

26 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

27 

28 Tests of Interest 

29 

30 Test -2*log(Likelihood Ratio) Test df p-value 

31 

32 Test 1 160.068 10 <.0001 

33 Test 2 107.598 5 <.0001 

34 Test 3 1.25486 4 0.869 

35 Test 4 117.556 3 <.0001 

36 

37 The p-value for Test 1 is less than .05. There appears to be a 

38 difference between response and/or variances among the dose levels 

39 It seems appropriate to model the data 

40 

41 The p-value for Test 2 is less than .1. A non-homogeneous variance 

42 model appears to be appropriate 

43 

44 The p-value for Test 3 is greater than .1. The modeled variance appears 

45 to be appropriate here 

46 

47 The p-value for Test 4 is less than .1. You may want to try a different 

48 model 

49 

50 

51 Benchmark Dose Computation 

52 

53 Specified effect = 1 

54 

55 Risk Type = Estimated standard deviations from the control mean 

56 

57 Confidence level = 0.95 

58 

59 BMD = 2.41754e-012 

60 

61 BMDL = 2.41754e-012 

62 

63 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-542 —DO NOT CITE OR QUOTE 

1 E.3.54.4. Figure for Unrestricted Model: Linear, Nonconstant Variance 

-100

 0

 100

 200

 300

 400

 500

 600

 700

 0 200 400 600 800 1000 1200 1400

Mean Response

dose

Linear Model with 0.95 Confidence Level

14:30 11/20 2009

BMDL BMD

 

Linear

2 

3 

4 

5 E.3.54.5. Output File for Unrestricted Model: Linear, Nonconstant Variance 

6 

7 

8 ==================================================================== 

9 Polynomial Model. (Version: 2.13; Date: 04/08/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov20\Linear_BMR1_hepatic_retinol_palmitate.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Linear_BMR1_hepatic_retinol_palmitate.plt 

12 Fri Nov 20 14:30:57 2009 

13 ==================================================================== 

14 

15 Tbl3, hepatic retinol palmitate 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Signs of the polynomial coefficients are not restricted 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-543 —DO NOT CITE OR QUOTE 

1 lalpha = 9.57332 

2 rho = 0 

3 beta_0 = 177.506 

4 beta_1 = -0.204775 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 lalpha rho beta_0 beta_1 

10 

11 lalpha 1 -0.95 -0.017 0.022 

12 

13 rho -0.95 1 0.00019 -0.0048 

14 

15 beta_0 -0.017 0.00019 1 -1 

16 

17 beta_1 0.022 -0.0048 -1 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 lalpha -0.723216 0.638291 -1.97424 0.527811 

26 rho 2.26615 0.140196 1.99137 2.54093 

27 beta_0 150.535 31.5457 88.7064 212.363 

28 beta_1 -0.143931 0.0308317 -0.20436 -0.0835018 

29 

30 

31 

32 Table of Data and Estimated Values of Interest 

33 

34 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

35 ------ --- -------- -------- ----------- ----------- ---------- 

36 

37 0 8 472 151 272 204 4.45 

38 14 8 94 149 67.9 201 -0.766 

39 26 8 107 147 76.4 199 -0.567 

40 47 8 74 144 39.6 194 -1.02 

41 320 8 22 104 22.6 135 -1.73 

42 1024 8 3 3.15 2.83 2.56 -0.166 

43 

44 

45 

46 Model Descriptions for likelihoods calculated 

47 

48 

49 Model A1: Yij = Mu(i) + e(ij) 

50 Var{e(ij)} = Sigma^2 

51 

52 Model A2: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = Sigma(i)^2 

54 

55 Model A3: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

57 Model A3 uses any fixed variance parameters that 

58 were specified by the user 

59 

60 Model R: Yi = Mu + e(i) 

61 Var{e(i)} = Sigma^2 

62 

63 

64 Likelihoods of Interest 

65 

66 Model Log(likelihood) # Param's AIC 

67 A1 -250.554817 7 515.109634 

68 A2 -196.755746 12 417.511491 

69 A3 -197.383174 8 410.766347 

70 fitted -240.223107 4 488.446215 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-544 —DO NOT CITE OR QUOTE 

1 R -276.789644 2 557.579287 

2 

3 

4 Explanation of Tests 

5 

6 Test 1: Do responses and/or variances differ among Dose levels? 

7 (A2 vs. R) 

8 Test 2: Are Variances Homogeneous? (A1 vs A2) 

9 Test 3: Are variances adequately modeled? (A2 vs. A3) 

10 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

11 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

12 

13 Tests of Interest 

14 

15 Test -2*log(Likelihood Ratio) Test df p-value 

16 

17 Test 1 160.068 10 <.0001 

18 Test 2 107.598 5 <.0001 

19 Test 3 1.25486 4 0.869 

20 Test 4 85.6799 4 <.0001 

21 

22 The p-value for Test 1 is less than .05. There appears to be a 

23 difference between response and/or variances among the dose levels 

24 It seems appropriate to model the data 

25 

26 The p-value for Test 2 is less than .1. A non-homogeneous variance 

27 model appears to be appropriate 

28 

29 The p-value for Test 3 is greater than .1. The modeled variance appears 

30 to be appropriate here 

31 

32 The p-value for Test 4 is less than .1. You may want to try a different 

33 model 

34 

35 

36 Benchmark Dose Computation 

37 

38 Specified effect = 1 

39 

40 Risk Type = Estimated standard deviations from the control mean 

41 

42 Confidence level = 0.95 

43 

44 BMD = 1419.81 

45 

46 

47 BMDL = 988.945 

48 

49 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-545 —DO NOT CITE OR QUOTE 

1 E.3.54.6. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

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 300

 400

 500

 600

 700

 0 200 400 600 800 1000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:31 11/20 2009

BMDBMDL

 

Power

2 

3 

4 

5 E.3.54.7. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted 

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_hepatic_retinol_palmitate.(d) 

12 Gnuplot Plotting File: 

13 C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_hepatic_retinol_palmitate.plt 

14 Fri Nov 20 14:31:06 2009 

15 ==================================================================== 

16 

17 Tbl3, hepatic retinol palmitate 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function is: 

21 

22 Y[dose] = control + slope * dose^power 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 The power is not restricted 

28 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

29 

30 Total number of dose groups = 6 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-546 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 lalpha = 9.57332 

4 rho = 0 

5 control = 472 

6 slope = -315.054 

7 power = 0.0586881 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 lalpha rho control slope power 

13 

14 lalpha 1 -0.95 0.29 -0.31 -0.3 

15 

16 rho -0.95 1 -0.4 0.39 0.29 

17 

18 control 0.29 -0.4 1 -0.98 -0.82 

19 

20 slope -0.31 0.39 -0.98 1 0.91 

21 

22 power -0.3 0.29 -0.82 0.91 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha 0.0734958 0.849559 -1.59161 1.7386 

31 rho 1.80632 0.194602 1.42491 2.18774 

32 control 465.497 86.914 295.149 635.845 

33 slope -318.06 82.4127 -479.586 -156.534 

34 power 0.0540573 0.0117709 0.0309869 0.0771278 

35 

36 

37 

38 Table of Data and Estimated Values of Interest 

39 

40 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

41 ------ --- -------- -------- ----------- ----------- ---------- 

42 

43 0 8 472 465 272 266 0.069 

44 14 8 94 98.7 67.9 65.6 -0.201 

45 26 8 107 86.2 76.4 58.1 1.01 

46 47 8 74 73.8 39.6 50.5 0.0086 

47 320 8 22 31.1 22.6 23.1 -1.11 

48 1024 8 3 2.86 2.83 2.68 0.145 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-547 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 -250.554817 7 515.109634 

4 A2 -196.755746 12 417.511491 

5 A3 -197.383174 8 410.766347 

6 fitted -199.031154 5 408.062307 

7 R -276.789644 2 557.579287 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 160.068 10 <.0001 

24 Test 2 107.598 5 <.0001 

25 Test 3 1.25486 4 0.869 

26 Test 4 3.29596 3 0.3482 

27 

28 The p-value for Test 1 is less than .05. There appears to be a 

29 difference between response and/or variances among the dose levels 

30 It seems appropriate to model the data 

31 

32 The p-value for Test 2 is less than .1. A non-homogeneous variance 

33 model appears to be appropriate 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is greater than .1. The model chosen seems 

39 to adequately describe the data 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 0.0376489 

51 

52 

53 BMDL = 1.20769e-005 

54 

55 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-548 —DO NOT CITE OR QUOTE 

1 E.3.54.8. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

2 Unrestricted 

 0

 100

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 300

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 600

 700

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:31 11/20 2009

BMDLBMD

 

Exponential

3 

4 

5 

6 E.3.54.9. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

7 Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_CV_Unrest_BMR1_hepatic_retinol_palmitate.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 14:31:06 2009 

15 ==================================================================== 

16 

17 Tbl3, hepatic retinol palmitate 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-549 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 6 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 5 

19 -------- -------- 

20 lnalpha 9.43978 

21 rho(S) 0 

22 a 495.6 

23 b 0.00826283 

24 c 0.00576502 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 5 

34 -------- ------- 

35 lnalpha 9.51279 

36 rho 0 

37 a 470.237 

38 b 0.126105 

39 c 0.0898547 

40 d 1 

41 

42 NC = No Convergence 

43 

44 

45 Table of Stats From Input Data 

46 

47 Dose N Obs Mean Obs Std Dev 

48 ----- --- ---------- ------------- 

49 0 8 472 271.5 

50 14 8 94 67.88 

51 26 8 107 76.37 

52 47 8 74 39.6 

53 320 8 22 22.63 

54 1024 8 3 2.828 

55 

56 

57 Estimated Values of Interest 

58 

59 Dose Est Mean Est Std Scaled Residual 

60 ------ ---------- --------- ---------------- 

61 0 470.2 116.3 0.04286 

62 14 115.5 116.3 -0.5224 

63 26 58.38 116.3 1.182 

64 47 43.39 116.3 0.7442 

65 320 42.25 116.3 -0.4924 

66 1024 42.25 116.3 -0.9544 

67 

68 

69 

70 Other models for which likelihoods are calculated: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-550 —DO NOT CITE OR QUOTE 

1 

2 Model A1: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma^2 

4 

5 Model A2: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma(i)^2 

7 

8 Model A3: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

10 

11 Model R: Yij = Mu + e(i) 

12 Var{e(ij)} = Sigma^2 

13 

14 

15 Likelihoods of Interest 

16 

17 Model Log(likelihood) DF AIC 

18 ------- ----------------- ---- ------------ 

19 A1 -250.5548 7 515.1096 

20 A2 -196.7557 12 417.5115 

21 A3 -250.5548 7 515.1096 

22 R -276.7896 2 557.5793 

23 5 -252.3071 4 512.6141 

24 

25 

26 Additive constant for all log-likelihoods = -44.11. This constant added to the 

27 above values gives the log-likelihood including the term that does not 

28 depend on the model parameters. 

29 

30 

31 Explanation of Tests 

32 

33 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

34 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

35 Test 3: Are variances adequately modeled? (A2 vs. A3) 

36 

37 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

38 

39 

40 Tests of Interest 

41 

42 Test -2*log(Likelihood Ratio) D. F. p-value 

43 -------- ------------------------ ------ -------------- 

44 Test 1 160.1 10 < 0.0001 

45 Test 2 107.6 5 < 0.0001 

46 Test 3 107.6 5 < 0.0001 

47 Test 7a 3.504 3 0.3202 

48 

49 

50 The p-value for Test 1 is less than .05. There appears to be a 

51 difference between response and/or variances among the dose 

52 levels, it seems appropriate to model the data. 

53 

54 The p-value for Test 2 is less than .1. Consider running 

55 a non-homogeneous variance model. 

56 

57 The p-value for Test 3 is less than .1. You may want to 

58 consider a different variance model. 

59 

60 The p-value for Test 7a is greater than .1. Model 5 seems 

61 to adequately describe the data. 

62 

63 

64 Benchmark Dose Computations: 

65 

66 Specified Effect = 1.000000 

67 

68 Risk Type = Estimated standard deviations from control 

69 

70 Confidence Level = 0.950000 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-551 —DO NOT CITE OR QUOTE 

1 

2 BMD = 2.5152 

3 

4 BMDL = 0.00902578 

5 

6 

7 E.3.55. Van Birgelen et al. (1995a): Plasma FT4 

8 E.3.55.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ

 2 Test 

Statistic 

χ

 2

 pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) Model Notes 

exponential (M2) c 4 0.01 3.18 0.53 215.46 3.4E+02 2.2E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.01 3.18 0.53 215.46 3.4E+02 2.2E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.01 2.13 0.55 216.42 2.2E+02 8.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.01 2.13 0.55 216.42 2.2E+02 8.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 0.01 2.13 0.55 216.42 2.2E+02 8.3E+01 nonconstant variance, 

power unrestricted 

Hill 3 0.01 2.02 0.57 216.30 1.9E+02 4.2E+01 nonconstant variance, n 

restricted >1, bound hit 

Hill d 2 0.01 1.87 0.39 218.16 1.7E+02 3.5E+01 nonconstant variance, n 

unrestricted 

linear 4 0.01 4.52 0.34 216.81 4.6E+02 3.3E+02 nonconstant variance 

polynomial 4 0.01 4.52 0.34 216.81 4.6E+02 3.3E+02 nonconstant variance 

power 4 0.01 4.52 0.34 216.81 4.6E+02 3.3E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 0.01 2.09 0.55 216.38 1.8E+02 3.2E+01 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.01 3.77 0.44 214.06 3.1E+02 2.1E+02 constant variance, power 

restricted ≥1 

exponential (M3) 4 0.01 3.77 0.44 214.06 3.1E+02 2.1E+02 constant variance, power 

restricted ≥1 

exponential (M4) 3 0.01 2.79 0.43 215.08 1.9E+02 6.7E+01 constant variance, power 

restricted ≥1 

exponential (M5) 3 0.01 2.79 0.43 215.08 1.9E+02 6.7E+01 constant variance, power 

restricted ≥1 

exponential (M5) 3 0.01 2.79 0.43 215.08 1.9E+02 6.7E+01 constant variance, power 

unrestricted 

Hill 3 0.01 2.58 0.46 214.87 1.6E+02 3.7E+01 constant variance, n 

restricted >1, bound hit 

Hill 2 0.01 2.29 0.32 216.58 1.4E+02 3.0E+01 constant variance, n 

unrestricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-552 —DO NOT CITE OR QUOTE 

linear 4 0.01 5.11 0.28 215.40 4.3E+02 3.3E+02 constant variance 

polynomial 4 0.01 5.11 0.28 215.40 4.3E+02 3.3E+02 constant variance 

power 4 0.01 5.11 0.28 215.40 4.3E+02 3.3E+02 constant variance, power 

restricted ≥1, bound hit 

power 3 0.01 2.46 0.48 214.75 1.5E+02 2.8E+01 constant variance, power 

unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.3.55.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

4 Restricted ≥1 

 5

 10

 15

 20

 25

 30

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

14:31 11/20 2009

BMDL BMD

 

Exponential

5 

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-553 —DO NOT CITE OR QUOTE 

1 E.3.55.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_plasma_FT4.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 14:31:57 2009 

10 ==================================================================== 

11 

12 Tbl3, plasma FT4 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

35 

36 Total number of dose groups = 6 

37 Total number of records with missing values = 0 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 

40 Parameter Convergence has been set to: 1e-008 

41 

42 MLE solution provided: Exact 

43 

44 

45 Initial Parameter Values 

46 

47 Variable Model 2 

48 -------- -------- 

49 lnalpha 4.29134 

50 rho -0.423761 

51 a 25.725 

52 b 0.00336354 

53 c 0.381323 

54 d 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 Variable Model 2 

61 -------- ------- 

62 lnalpha 1.55298 

63 rho 0.59724 

64 a 23.1888 

65 b 0.00232277 

66 c 0.391713 

67 d 1 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-554 —DO NOT CITE OR QUOTE 

1 

2 Table of Stats From Input Data 

3 

4 Dose N Obs Mean Obs Std Dev 

5 ----- --- ---------- ------------- 

6 0 8 23.4 3.111 

7 14 8 24.5 5.657 

8 26 8 22.4 2.828 

9 47 8 19.3 9.334 

10 320 8 16.3 4.243 

11 1024 8 10.3 4.808 

12 

13 

14 Estimated Values of Interest 

15 

16 Dose Est Mean Est Std Scaled Residual 

17 ------ ---------- --------- ---------------- 

18 0 22.66 5.554 0.3768 

19 14 22.4 5.536 1.073 

20 26 22.18 5.521 0.1131 

21 47 21.8 5.495 -1.286 

22 320 17.4 5.17 -0.6029 

23 1024 9.735 4.417 0.3618 

24 

25 

26 

27 Other models for which likelihoods are calculated: 

28 

29 Model A1: Yij = Mu(i) + e(ij) 

30 Var{e(ij)} = Sigma^2 

31 

32 Model A2: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma(i)^2 

34 

35 Model A3: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

37 

38 Model R: Yij = Mu + e(i) 

39 Var{e(ij)} = Sigma^2 

40 

41 

42 Likelihoods of Interest 

43 

44 Model Log(likelihood) DF AIC 

45 ------- ----------------- ---- ------------ 

46 A1 -102.145 7 218.2901 

47 A2 -94.04963 12 212.0993 

48 A3 -102.143 8 220.286 

49 R -117.8175 2 239.635 

50 2 -103.7322 4 215.4645 

51 

52 

53 Additive constant for all log-likelihoods = -44.11. This constant added to the 

54 above values gives the log-likelihood including the term that does not 

55 depend on the model parameters. 

56 

57 

58 Explanation of Tests 

59 

60 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

61 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

62 Test 3: Are variances adequately modeled? (A2 vs. A3) 

63 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

64 

65 

66 Tests of Interest 

67 

68 Test -2*log(Likelihood Ratio) D. F. p-value 

69 -------- ------------------------ ------ -------------- 

70 Test 1 47.54 10 < 0.0001 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-555 —DO NOT CITE OR QUOTE 

1 Test 2 16.19 5 0.00632 

2 Test 3 16.19 4 0.002778 

3 Test 4 3.178 4 0.5284 

4 

5 

6 The p-value for Test 1 is less than .05. There appears to be a 

7 difference between response and/or variances among the dose 

8 levels, it seems appropriate to model the data. 

9 

10 The p-value for Test 2 is less than .1. A non-homogeneous 

11 variance model appears to be appropriate. 

12 

13 The p-value for Test 3 is less than .1. You may want to 

14 consider a different variance model. 

15 

16 The p-value for Test 4 is greater than .1. Model 2 seems 

17 to adequately describe the data. 

18 

19 

20 Benchmark Dose Computations: 

21 

22 Specified Effect = 1.000000 

23 

24 Risk Type = Estimated standard deviations from control 

25 

26 Confidence Level = 0.950000 

27 

28 BMD = 340.749 

29 

30 BMDL = 217.397 

31 

32 

33 E.3.55.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

34 Unrestricted 

 5

 10

 15

 20

 25

 30

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:32 11/20 2009

BMDL BMD

 

Exponential

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-556 —DO NOT CITE OR QUOTE 

1 E.3.55.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

2 Power Unrestricted 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_plasma_FT4.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 14:32:02 2009 

10 ==================================================================== 

11 

12 Tbl3, plasma FT4 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

35 

36 Total number of dose groups = 6 

37 Total number of records with missing values = 0 

38 Maximum number of iterations = 250 

39 Relative Function Convergence has been set to: 1e-008 

40 Parameter Convergence has been set to: 1e-008 

41 

42 MLE solution provided: Exact 

43 

44 

45 Initial Parameter Values 

46 

47 Variable Model 5 

48 -------- -------- 

49 lnalpha 4.29134 

50 rho -0.423761 

51 a 25.725 

52 b 0.00336354 

53 c 0.381323 

54 d 1 

55 

56 

57 

58 Parameter Estimates 

59 

60 Variable Model 5 

61 -------- ------- 

62 lnalpha 1.55298 

63 rho 0.59724 

64 a 23.1888 

65 b 0.00232277 

66 c 0.391713 

67 d 1 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-557 —DO NOT CITE OR QUOTE 

1 

2 Table of Stats From Input Data 

3 

4 Dose N Obs Mean Obs Std Dev 

5 ----- --- ---------- ------------- 

6 0 8 23.4 3.111 

7 14 8 24.5 5.657 

8 26 8 22.4 2.828 

9 47 8 19.3 9.334 

10 320 8 16.3 4.243 

11 1024 8 10.3 4.808 

12 

13 

14 Estimated Values of Interest 

15 

16 Dose Est Mean Est Std Scaled Residual 

17 ------ ---------- --------- ---------------- 

18 0 23.19 5.558 0.1075 

19 14 22.74 5.526 0.9022 

20 26 22.36 5.498 0.01946 

21 47 21.73 5.451 -1.261 

22 320 15.79 4.956 0.2904 

23 1024 10.39 4.373 -0.0587 

24 

25 

26 

27 Other models for which likelihoods are calculated: 

28 

29 Model A1: Yij = Mu(i) + e(ij) 

30 Var{e(ij)} = Sigma^2 

31 

32 Model A2: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma(i)^2 

34 

35 Model A3: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

37 

38 Model R: Yij = Mu + e(i) 

39 Var{e(ij)} = Sigma^2 

40 

41 

42 Likelihoods of Interest 

43 

44 Model Log(likelihood) DF AIC 

45 ------- ----------------- ---- ------------ 

46 A1 -102.145 7 218.2901 

47 A2 -94.04963 12 212.0993 

48 A3 -102.143 8 220.286 

49 R -117.8175 2 239.635 

50 5 -103.2077 5 216.4154 

51 

52 

53 Additive constant for all log-likelihoods = -44.11. This constant added to the 

54 above values gives the log-likelihood including the term that does not 

55 depend on the model parameters. 

56 

57 

58 Explanation of Tests 

59 

60 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

61 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

62 Test 3: Are variances adequately modeled? (A2 vs. A3) 

63 

64 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

65 

66 

67 Tests of Interest 

68 

69 Test -2*log(Likelihood Ratio) D. F. p-value 

70 -------- ------------------------ ------ -------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-558 —DO NOT CITE OR QUOTE 

1 Test 1 47.54 10 < 0.0001 

2 Test 2 16.19 5 0.00632 

3 Test 3 16.19 4 0.002778 

4 Test 7a 2.129 3 0.546 

5 

6 

7 The p-value for Test 1 is less than .05. There appears to be a 

8 difference between response and/or variances among the dose 

9 levels, it seems appropriate to model the data. 

10 

11 The p-value for Test 2 is less than .1. A non-homogeneous 

12 variance model appears to be appropriate. 

13 

14 The p-value for Test 3 is less than .1. You may want to 

15 consider a different variance model. 

16 

17 The p-value for Test 7a is greater than .1. Model 5 seems 

18 to adequately describe the data. 

19 

20 

21 Benchmark Dose Computations: 

22 

23 Specified Effect = 1.000000 

24 

25 Risk Type = Estimated standard deviations from control 

26 

27 Confidence Level = 0.950000 

28 

29 BMD = 215.664 

30 

31 BMDL = 83.4225 

32 

33 

34 E.3.55.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 5

 10

 15

 20

 25

 30

 0 200 400 600 800 1000

Mean Response

dose

Hill Model with 0.95 Confidence Level

14:32 11/20 2009

BMDL BMD

 

Hill

35 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-559 —DO NOT CITE OR QUOTE 

1 E.3.55.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

2 

3 

4 ==================================================================== 

5 Hill Model. (Version: 2.14; Date: 06/26/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_plasma_FT4.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_plasma_FT4.plt 

8 Fri Nov 20 14:32:03 2009 

9 ==================================================================== 

10 

11 Tbl3, plasma FT4 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Power parameter is not restricted 

22 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

23 

24 Total number of dose groups = 6 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 Default Initial Parameter Values 

33 lalpha = 3.38957 

34 rho = 0 

35 intercept = 23.4 

36 v = -13.1 

37 n = 0.834965 

38 k = 269.95 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 lalpha rho intercept v n k 

44 

45 lalpha 1 -1 0.2 -0.14 -0.19 0.12 

46 

47 rho -1 1 -0.2 0.14 0.19 -0.12 

48 

49 intercept 0.2 -0.2 1 -0.35 -0.58 0.27 

50 

51 v -0.14 0.14 -0.35 1 0.9 -0.99 

52 

53 n -0.19 0.19 -0.58 0.9 1 -0.89 

54 

55 k 0.12 -0.12 0.27 -0.99 -0.89 1 

56 

57 

58 

59 Parameter Estimates 

60 

61 95.0% Wald Confidence Interval 

62 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

63 lalpha 1.83708 2.19197 -2.4591 6.13327 

64 rho 0.498362 0.745649 -0.963083 1.95981 

65 intercept 23.7686 1.71713 20.403 27.1341 

66 v -26.4457 39.0446 -102.972 50.0802 

67 n 0.751729 0.57261 -0.370565 1.87402 

68 k 988.089 3688.99 -6242.2 8218.37 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-560 —DO NOT CITE OR QUOTE 

1 

2 

3 Table of Data and Estimated Values of Interest 

4 

5 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

6 ------ --- -------- -------- ----------- ----------- ---------- 

7 

8 0 8 23.4 23.8 3.11 5.52 -0.189 

9 14 8 24.5 22.7 5.66 5.46 0.916 

10 26 8 22.4 22.2 2.83 5.42 0.127 

11 47 8 19.3 21.3 9.33 5.37 -1.07 

12 320 8 16.3 15.8 4.24 4.99 0.263 

13 1024 8 10.3 10.4 4.81 4.49 -0.043 

14 

15 

16 

17 Model Descriptions for likelihoods calculated 

18 

19 

20 Model A1: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma^2 

22 

23 Model A2: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = Sigma(i)^2 

25 

26 Model A3: Yij = Mu(i) + e(ij) 

27 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

28 Model A3 uses any fixed variance parameters that 

29 were specified by the user 

30 

31 Model R: Yi = Mu + e(i) 

32 Var{e(i)} = Sigma^2 

33 

34 

35 Likelihoods of Interest 

36 

37 Model Log(likelihood) # Param's AIC 

38 A1 -102.145036 7 218.290071 

39 A2 -94.049629 12 212.099258 

40 A3 -102.143023 8 220.286046 

41 fitted -103.078418 6 218.156836 

42 R -117.817514 2 239.635028 

43 

44 

45 Explanation of Tests 

46 

47 Test 1: Do responses and/or variances differ among Dose levels? 

48 (A2 vs. R) 

49 Test 2: Are Variances Homogeneous? (A1 vs A2) 

50 Test 3: Are variances adequately modeled? (A2 vs. A3) 

51 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

52 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

53 

54 Tests of Interest 

55 

56 Test -2*log(Likelihood Ratio) Test df p-value 

57 

58 Test 1 47.5358 10 <.0001 

59 Test 2 16.1908 5 0.00632 

60 Test 3 16.1868 4 0.002778 

61 Test 4 1.87079 2 0.3924 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose levels 

65 It seems appropriate to model the data 

66 

67 The p-value for Test 2 is less than .1. A non-homogeneous variance 

68 model appears to be appropriate 

69 

70 The p-value for Test 3 is less than .1. You may want to consider a 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-561 —DO NOT CITE OR QUOTE 

1 different variance model 

2 

3 The p-value for Test 4 is greater than .1. The model chosen seems 

4 to adequately describe the data 

5 

6 

7 Benchmark Dose Computation 

8 

9 Specified effect = 1 

10 

11 Risk Type = Estimated standard deviations from the control mean 

12 

13 Confidence level = 0.95 

14 

15 BMD = 167.752 

16 

17 BMDL = 34.6031 

18 

19 

20 

21 E.3.55.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 5

 10

 15

 20

 25

 30

 0 200 400 600 800 1000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:32 11/20 2009

BMDL BMD

 

Power

22 

23 

24 

25 E.3.55.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

26 Unrestricted 

27 

28 

29 ==================================================================== 

30 Power Model. (Version: 2.15; Date: 04/07/2008) 

31 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_plasma_FT4.(d) 

32 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_plasma_FT4.plt 

33 Fri Nov 20 14:32:04 2009 

34 ==================================================================== 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-562 —DO NOT CITE OR QUOTE 

1 Tbl3, plasma FT4 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the response function is: 

5 

6 Y[dose] = control + slope * dose^power 

7 

8 

9 Dependent variable = Mean 

10 Independent variable = Dose 

11 The power is not restricted 

12 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

13 

14 Total number of dose groups = 6 

15 Total number of records with missing values = 0 

16 Maximum number of iterations = 250 

17 Relative Function Convergence has been set to: 1e-008 

18 Parameter Convergence has been set to: 1e-008 

19 

20 

21 

22 Default Initial Parameter Values 

23 lalpha = 3.38957 

24 rho = 0 

25 control = 24.5 

26 slope = -0.64474 

27 power = 0.449494 

28 

29 

30 Asymptotic Correlation Matrix of Parameter Estimates 

31 

32 lalpha rho control slope power 

33 

34 lalpha 1 -1 0.11 -0.098 -0.083 

35 

36 rho -1 1 -0.12 0.099 0.083 

37 

38 control 0.11 -0.12 1 -0.8 -0.75 

39 

40 slope -0.098 0.099 -0.8 1 0.99 

41 

42 power -0.083 0.083 -0.75 0.99 1 

43 

44 

45 

46 Parameter Estimates 

47 

48 95.0% Wald Confidence Interval 

49 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

50 lalpha 1.96489 2.14806 -2.24522 6.175 

51 rho 0.456282 0.730608 -0.975684 1.88825 

52 control 23.9768 1.64641 20.7499 27.2037 

53 slope -0.373722 0.513355 -1.37988 0.632435 

54 power 0.52088 0.188688 0.151059 0.890701 

55 

56 

57 

58 Table of Data and Estimated Values of Interest 

59 

60 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

61 ------ --- -------- -------- ----------- ----------- ---------- 

62 

63 0 8 23.4 24 3.11 5.51 -0.296 

64 14 8 24.5 22.5 5.66 5.43 1.04 

65 26 8 22.4 21.9 2.83 5.4 0.242 

66 47 8 19.3 21.2 9.33 5.36 -1 

67 320 8 16.3 16.4 4.24 5.06 -0.0759 

68 1024 8 10.3 10.2 4.81 4.53 0.0903 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-563 —DO NOT CITE OR QUOTE 

1 

2 Model Descriptions for likelihoods calculated 

3 

4 

5 Model A1: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 

8 Model A2: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma(i)^2 

10 

11 Model A3: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

13 Model A3 uses any fixed variance parameters that 

14 were specified by the user 

15 

16 Model R: Yi = Mu + e(i) 

17 Var{e(i)} = Sigma^2 

18 

19 

20 Likelihoods of Interest 

21 

22 Model Log(likelihood) # Param's AIC 

23 A1 -102.145036 7 218.290071 

24 A2 -94.049629 12 212.099258 

25 A3 -102.143023 8 220.286046 

26 fitted -103.188719 5 216.377438 

27 R -117.817514 2 239.635028 

28 

29 

30 Explanation of Tests 

31 

32 Test 1: Do responses and/or variances differ among Dose levels? 

33 (A2 vs. R) 

34 Test 2: Are Variances Homogeneous? (A1 vs A2) 

35 Test 3: Are variances adequately modeled? (A2 vs. A3) 

36 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

37 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

38 

39 Tests of Interest 

40 

41 Test -2*log(Likelihood Ratio) Test df p-value 

42 

43 Test 1 47.5358 10 <.0001 

44 Test 2 16.1908 5 0.00632 

45 Test 3 16.1868 4 0.002778 

46 Test 4 2.09139 3 0.5537 

47 

48 The p-value for Test 1 is less than .05. There appears to be a 

49 difference between response and/or variances among the dose levels 

50 It seems appropriate to model the data 

51 

52 The p-value for Test 2 is less than .1. A non-homogeneous variance 

53 model appears to be appropriate 

54 

55 The p-value for Test 3 is less than .1. You may want to consider a 

56 different variance model 

57 

58 The p-value for Test 4 is greater than .1. The model chosen seems 

59 to adequately describe the data 

60 

61 

62 Benchmark Dose Computation 

63 

64 Specified effect = 1 

65 

66 Risk Type = Estimated standard deviations from the control mean 

67 

68 Confidence level = 0.95 

69 

70 BMD = 175.43 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-564 —DO NOT CITE OR QUOTE 

1 

2 

3 BMDL = 32.1986 

4 

5 

6 E.3.56. Van Birgelen et al. (1995a): Plasma TT4 

7 E.3.56.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 4 0.94 10.42 0.03 241.86 4.4E+02 2.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.94 10.42 0.03 241.86 4.4E+02 2.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.94 9.83 0.02 243.27 2.8E+02 2.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.94 9.83 0.02 243.27 2.8E+02 2.0E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.94 9.83 0.02 243.27 2.8E+02 2.0E+01 nonconstant variance, 

power unrestricted 

Hill 3 0.94 5.45 0.14 238.89 4.4E+01 error nonconstant variance, n 

restricted >1, bound hit 

Hill 3 0.94 5.45 0.14 238.89 4.4E+01 error nonconstant variance, n 

unrestricted 

linear 4 0.94 10.82 0.03 242.26 5.0E+02 3.5E+02 nonconstant variance 

polynomial 4 0.94 10.82 0.03 242.26 5.0E+02 3.5E+02 nonconstant variance 

power 4 0.94 10.82 0.03 242.26 5.0E+02 3.5E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.94 8.70 0.03 242.14 1.6E+02 2.2E+01 nonconstant variance, 

power unrestricted 

exponential 

(M2) c 4 0.94 9.83 0.04 239.86 4.4E+02 3.0E+02 constant variance, power restricted ≥1 

exponential (M3) 4 0.94 9.83 0.04 239.86 4.4E+02 3.0E+02 constant variance, 

power restricted ≥1 

exponential (M4) 3 0.94 9.24 0.03 241.27 2.8E+02 2.6E+01 constant variance, 

power restricted ≥1 

exponential (M5) 3 0.94 9.24 0.03 241.27 2.8E+02 2.3E+01 constant variance, 

power restricted ≥1 

exponential (M5)

d 3 0.94 9.24 0.03 241.27 2.8E+02 2.3E+01 constant variance, 

power unrestricted 

Hill 3 0.94 6.31 0.10 238.33 4.5E+01 error constant variance, n 

restricted >1, bound hit 

Hill d 3 0.94 6.31 0.10 238.33 4.5E+01 error constant variance, n 

unrestricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-565 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ 2 Test 

Statistic 

χ 2pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

linear 4 0.94 10.23 0.04 240.26 5.0E+02 3.7E+02 constant variance 

polynomial 4 0.94 10.23 0.04 240.26 5.0E+02 3.7E+02 constant variance 

power 4 0.94 10.23 0.04 240.26 5.0E+02 3.7E+02 

constant variance, 

power restricted ≥1, 

bound hit 

power d 3 0.94 8.14 0.04 240.16 1.7E+02 2.4E+01 constant variance, 

power unrestricted 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

 Alternate model also presented in this appendix 

1 

2 

3 E.3.56.2. Figure for Selected Model: Exponential (M2), Constant Variance, Power Restricted 

4 ≥1 

 20

 25

 30

 35

 40

 45

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

14:32 11/20 2009

BMDL BMD

 

Exponential

5 

6 

7 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-566 —DO NOT CITE OR QUOTE 

1 E.3.56.3. Output File for Selected Model: Exponential (M2), Constant Variance, Power 

2 Restricted ≥1 

3 

4 

5 ==================================================================== 

6 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_CV_BMR1_plasma_TT4.(d) 

8 Gnuplot Plotting File: 

9 Fri Nov 20 14:32:54 2009 

10 ==================================================================== 

11 

12 Tbl3, plasma TT4 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function by Model: 

16 Model 2: Y[dose] = a * exp{sign * b * dose} 

17 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

18 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

19 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

20 

21 Note: Y[dose] is the median response for exposure = dose; 

22 sign = +1 for increasing trend in data; 

23 sign = -1 for decreasing trend. 

24 

25 Model 2 is nested within Models 3 and 4. 

26 Model 3 is nested within Model 5. 

27 Model 4 is nested within Model 5. 

28 

29 

30 Dependent variable = Mean 

31 Independent variable = Dose 

32 Data are assumed to be distributed: normally 

33 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

34 rho is set to 0. 

35 A constant variance model is fit. 

36 

37 Total number of dose groups = 6 

38 Total number of records with missing values = 0 

39 Maximum number of iterations = 250 

40 Relative Function Convergence has been set to: 1e-008 

41 Parameter Convergence has been set to: 1e-008 

42 

43 MLE solution provided: Exact 

44 

45 

46 Initial Parameter Values 

47 

48 Variable Model 2 

49 -------- -------- 

50 lnalpha 3.66719 

51 rho(S) 0 

52 a 43.47 

53 b 0.00268876 

54 c 0.558678 

55 d 1 

56 

57 (S) = Specified 

58 

59 

60 

61 Parameter Estimates 

62 

63 Variable Model 2 

64 -------- ------- 

65 lnalpha 3.85975 

66 rho 0 

67 a 39.9223 

68 b 0.00192618 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-567 —DO NOT CITE OR QUOTE 

1 c 0.587293 

2 d 1 

3 

4 

5 Table of Stats From Input Data 

6 

7 Dose N Obs Mean Obs Std Dev 

8 ----- --- ---------- ------------- 

9 0 8 40.9 6.788 

10 14 8 41.4 5.374 

11 26 8 41.4 6.505 

12 47 8 32.3 7.354 

13 320 8 33.6 6.223 

14 1024 8 25.5 7.637 

15 

16 

17 Estimated Values of Interest 

18 

19 Dose Est Mean Est Std Scaled Residual 

20 ------ ---------- --------- ---------------- 

21 0 39.36 6.931 0.6265 

22 14 39.12 6.931 0.9302 

23 26 38.91 6.931 1.015 

24 47 38.55 6.931 -2.551 

25 320 34.15 6.931 -0.2227 

26 1024 24.97 6.931 0.2158 

27 

28 

29 

30 Other models for which likelihoods are calculated: 

31 

32 Model A1: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma^2 

34 

35 Model A2: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = Sigma(i)^2 

37 

38 Model A3: Yij = Mu(i) + e(ij) 

39 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

40 

41 Model R: Yij = Mu + e(i) 

42 Var{e(ij)} = Sigma^2 

43 

44 

45 Likelihoods of Interest 

46 

47 Model Log(likelihood) DF AIC 

48 ------- ----------------- ---- ------------ 

49 A1 -112.0125 7 238.025 

50 A2 -111.4015 12 246.8029 

51 A3 -112.0125 7 238.025 

52 R -127.4455 2 258.891 

53 2 -116.929 3 239.858 

54 

55 

56 Additive constant for all log-likelihoods = -44.11. This constant added to the 

57 above values gives the log-likelihood including the term that does not 

58 depend on the model parameters. 

59 

60 

61 Explanation of Tests 

62 

63 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

64 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

65 Test 3: Are variances adequately modeled? (A2 vs. A3) 

66 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

67 

68 

69 Tests of Interest 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-568 —DO NOT CITE OR QUOTE 

1 Test -2*log(Likelihood Ratio) D. F. p-value 

2 -------- ------------------------ ------ -------------- 

3 Test 1 32.09 10 0.0003871 

4 Test 2 1.222 5 0.9427 

5 Test 3 1.222 5 0.9427 

6 Test 4 9.833 4 0.04334 

7 

8 

9 The p-value for Test 1 is less than .05. There appears to be a 

10 difference between response and/or variances among the dose 

11 levels, it seems appropriate to model the data. 

12 

13 The p-value for Test 2 is greater than .1. A homogeneous 

14 variance model appears to be appropriate here. 

15 

16 The p-value for Test 3 is greater than .1. The modeled 

17 variance appears to be appropriate here. 

18 

19 The p-value for Test 4 is less than .1. Model 2 may not adequately 

20 describe the data; you may want to consider another model. 

21 

22 

23 Benchmark Dose Computations: 

24 

25 Specified Effect = 1.000000 

26 

27 Risk Type = Estimated standard deviations from control 

28 

29 Confidence Level = 0.950000 

30 

31 BMD = 435.731 

32 

33 BMDL = 296.489 

34 

35 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-569 —DO NOT CITE OR QUOTE 

1 E.3.56.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

2 Unrestricted 

 20

 25

 30

 35

 40

 45

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:33 11/20 2009

BMDL BMD

 

Exponential

3 

4 

5 

6 E.3.56.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

7 Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_CV_Unrest_BMR1_plasma_TT4.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 14:33:03 2009 

15 ==================================================================== 

16 

17 Tbl3, plasma TT4 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-570 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 Data are assumed to be distributed: normally 

3 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

4 rho is set to 0. 

5 A constant variance model is fit. 

6 

7 Total number of dose groups = 6 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 MLE solution provided: Exact 

14 

15 

16 Initial Parameter Values 

17 

18 Variable Model 5 

19 -------- -------- 

20 lnalpha 3.66719 

21 rho(S) 0 

22 a 43.47 

23 b 0.00268876 

24 c 0.558678 

25 d 1 

26 

27 (S) = Specified 

28 

29 

30 

31 Parameter Estimates 

32 

33 Variable Model 5 

34 -------- ------- 

35 lnalpha 3.85975 

36 rho 0 

37 a 39.9223 

38 b 0.00192618 

39 c 0.587293 

40 d 1 

41 

42 

43 Table of Stats From Input Data 

44 

45 Dose N Obs Mean Obs Std Dev 

46 ----- --- ---------- ------------- 

47 0 8 40.9 6.788 

48 14 8 41.4 5.374 

49 26 8 41.4 6.505 

50 47 8 32.3 7.354 

51 320 8 33.6 6.223 

52 1024 8 25.5 7.637 

53 

54 

55 Estimated Values of Interest 

56 

57 Dose Est Mean Est Std Scaled Residual 

58 ------ ---------- --------- ---------------- 

59 0 39.92 6.889 0.4014 

60 14 39.48 6.889 0.7867 

61 26 39.12 6.889 0.9372 

62 47 38.5 6.889 -2.544 

63 320 32.34 6.889 0.5167 

64 1024 25.74 6.889 -0.09785 

65 

66 

67 

68 Other models for which likelihoods are calculated: 

69 

70 Model A1: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-571 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma^2 

2 

3 Model A2: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = Sigma(i)^2 

5 

6 Model A3: Yij = Mu(i) + e(ij) 

7 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

8 

9 Model R: Yij = Mu + e(i) 

10 Var{e(ij)} = Sigma^2 

11 

12 

13 Likelihoods of Interest 

14 

15 Model Log(likelihood) DF AIC 

16 ------- ----------------- ---- ------------ 

17 A1 -112.0125 7 238.025 

18 A2 -111.4015 12 246.8029 

19 A3 -112.0125 7 238.025 

20 R -127.4455 2 258.891 

21 5 -116.634 4 241.268 

22 

23 

24 Additive constant for all log-likelihoods = -44.11. This constant added to the 

25 above values gives the log-likelihood including the term that does not 

26 depend on the model parameters. 

27 

28 

29 Explanation of Tests 

30 

31 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

32 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

33 Test 3: Are variances adequately modeled? (A2 vs. A3) 

34 

35 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

36 

37 

38 Tests of Interest 

39 

40 Test -2*log(Likelihood Ratio) D. F. p-value 

41 -------- ------------------------ ------ -------------- 

42 Test 1 32.09 10 0.0003871 

43 Test 2 1.222 5 0.9427 

44 Test 3 1.222 5 0.9427 

45 Test 7a 9.243 3 0.02623 

46 

47 

48 The p-value for Test 1 is less than .05. There appears to be a 

49 difference between response and/or variances among the dose 

50 levels, it seems appropriate to model the data. 

51 

52 The p-value for Test 2 is greater than .1. A homogeneous 

53 variance model appears to be appropriate here. 

54 

55 The p-value for Test 3 is greater than .1. The modeled 

56 variance appears to be appropriate here. 

57 

58 The p-value for Test 7a is less than .1. Model 5 may not adequately 

59 describe the data; you may want to consider another model. 

60 

61 

62 Benchmark Dose Computations: 

63 

64 Specified Effect = 1.000000 

65 

66 Risk Type = Estimated standard deviations from control 

67 

68 Confidence Level = 0.950000 

69 

70 BMD = 281.101 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-572 —DO NOT CITE OR QUOTE 

1 

2 BMDL = 23.4709 

3 

4 

5 E.3.56.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 20

 25

 30

 35

 40

 45

 0 200 400 600 800 1000

Mean Response

dose

Hill Model

14:33 11/20 2009

BMD

Hill

6 

7 

8 

9 E.3.56.7. Output File for Unrestricted Model: Hill, constant Variance, n Unrestricted 

10 

11 

12 ==================================================================== 

13 Hill Model. (Version: 2.14; Date: 06/26/2008) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_CV_Unrest_BMR1_plasma_TT4.(d) 

15 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_CV_Unrest_BMR1_plasma_TT4.plt 

16 Fri Nov 20 14:33:05 2009 

17 ==================================================================== 

18 

19 Tbl3, plasma TT4 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function is: 

23 

24 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

25 

26 

27 Dependent variable = Mean 

28 Independent variable = Dose 

29 rho is set to 0 

30 Power parameter is not restricted 

31 A constant variance model is fit 

32 

33 Total number of dose groups = 6 

34 Total number of records with missing values = 0 

35 Maximum number of iterations = 250 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-573 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 alpha = 44.7333 

8 rho = 0 Specified 

9 intercept = 40.9 

10 v = -15.4 

11 n = 2.59801 

12 k = 44.9231 

13 

14 

15 Asymptotic Correlation Matrix of Parameter Estimates 

16 

17 ( *** The model parameter(s) -rho -n 

18 have been estimated at a boundary point, or have been specified by the user, 

19 and do not appear in the correlation matrix ) 

20 

21 alpha intercept v k 

22 

23 alpha 1 1.6e-009 -1e-009 8.3e-008 

24 

25 intercept 1.6e-009 1 -0.63 -0.12 

26 

27 v -1e-009 -0.63 1 -0.29 

28 

29 k 8.3e-008 -0.12 -0.29 1 

30 

31 

32 

33 Parameter Estimates 

34 

35 95.0% Wald Confidence Interval 

36 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

37 alpha 44.637 9.11149 26.7788 62.4952 

38 intercept 41.2336 1.36385 38.5605 43.9067 

39 v -11.6836 2.15625 -15.9098 -7.45747 

40 n 18 NA 

41 k 44.0222 3.14538 37.8573 50.187 

42 

43 NA - Indicates that this parameter has hit a bound 

44 implied by some inequality constraint and thus 

45 has no standard error. 

46 

47 

48 

49 Table of Data and Estimated Values of Interest 

50 

51 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

52 ------ --- -------- -------- ----------- ----------- ---------- 

53 

54 0 8 40.9 41.2 6.79 6.68 -0.141 

55 14 8 41.4 41.2 5.37 6.68 0.0704 

56 26 8 41.4 41.2 6.51 6.68 0.0708 

57 47 8 32.3 32.3 7.35 6.68 -3.05e-005 

58 320 8 33.6 29.5 6.22 6.68 1.71 

59 1024 8 25.5 29.5 7.64 6.68 -1.71 

60 

61 

62 

63 Model Descriptions for likelihoods calculated 

64 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-574 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma^2 

4 Model A3 uses any fixed variance parameters that 

5 were specified by the user 

6 

7 Model R: Yi = Mu + e(i) 

8 Var{e(i)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) # Param's AIC 

14 A1 -112.012501 7 238.025002 

15 A2 -111.401462 12 246.802924 

16 A3 -112.012501 7 238.025002 

17 fitted -115.165512 4 238.331023 

18 R -127.445484 2 258.890968 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Do responses and/or variances differ among Dose levels? 

24 (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A1 vs A2) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

28 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) Test df p-value 

33 

34 Test 1 32.088 10 0.0003871 

35 Test 2 1.22208 5 0.9427 

36 Test 3 1.22208 5 0.9427 

37 Test 4 6.30602 3 0.09763 

38 

39 The p-value for Test 1 is less than .05. There appears to be a 

40 difference between response and/or variances among the dose levels 

41 It seems appropriate to model the data 

42 

43 The p-value for Test 2 is greater than .1. A homogeneous variance 

44 model appears to be appropriate here 

45 

46 

47 The p-value for Test 3 is greater than .1. The modeled variance appears 

48 to be appropriate here 

49 

50 The p-value for Test 4 is less than .1. You may want to try a different 

51 model 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 1 

57 

58 Risk Type = Estimated standard deviations from the control mean 

59 

60 Confidence level = 0.95 

61 

62 BMD = 44.7355 

63 

64 

65 BMDL computation failed. 

66 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-575 —DO NOT CITE OR QUOTE 

1 E.3.56.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 20

 25

 30

 35

 40

 45

 0 200 400 600 800 1000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:33 11/20 2009

BMDL BMD

 

Power

2 

3 

4 

5 E.3.56.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

6 

7 ==================================================================== 

8 Power Model. (Version: 2.15; Date: 04/07/2008) 

9 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_CV_Unrest_BMR1_plasma_TT4.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_CV_Unrest_BMR1_plasma_TT4.plt 

11 Fri Nov 20 14:33:06 2009 

12 ==================================================================== 

13 

14 Tbl3, plasma TT4 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the response function is: 

18 

19 Y[dose] = control + slope * dose^power 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 rho is set to 0 

25 The power is not restricted 

26 A constant variance model is fit 

27 

28 Total number of dose groups = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-576 —DO NOT CITE OR QUOTE 

1 alpha = 44.7333 

2 rho = 0 Specified 

3 control = 41.4 

4 slope = -4.42652 

5 power = 0.155038 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha control slope power 

15 

16 alpha 1 5.3e-011 3.5e-010 5.9e-010 

17 

18 control 5.3e-011 1 -0.81 -0.76 

19 

20 slope 3.5e-010 -0.81 1 0.99 

21 

22 power 5.9e-010 -0.76 0.99 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 alpha 46.3718 9.4656 27.8195 64.924 

31 control 41.441 2.1824 37.1636 45.7184 

32 slope -0.626626 0.890104 -2.3712 1.11795 

33 power 0.464532 0.195802 0.0807676 0.848296 

34 

35 

36 

37 Table of Data and Estimated Values of Interest 

38 

39 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

40 ------ --- -------- -------- ----------- ----------- ---------- 

41 

42 0 8 40.9 41.4 6.79 6.81 -0.225 

43 14 8 41.4 39.3 5.37 6.81 0.87 

44 26 8 41.4 38.6 6.51 6.81 1.17 

45 47 8 32.3 37.7 7.35 6.81 -2.24 

46 320 8 33.6 32.3 6.22 6.81 0.538 

47 1024 8 25.5 25.8 7.64 6.81 -0.108 

48 

49 

50 

51 Model Descriptions for likelihoods calculated 

52 

53 

54 Model A1: Yij = Mu(i) + e(ij) 

55 Var{e(ij)} = Sigma^2 

56 

57 Model A2: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma(i)^2 

59 

60 Model A3: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma^2 

62 Model A3 uses any fixed variance parameters that 

63 were specified by the user 

64 

65 Model R: Yi = Mu + e(i) 

66 Var{e(i)} = Sigma^2 

67 

68 

69 Likelihoods of Interest 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-577 —DO NOT CITE OR QUOTE 

1 Model Log(likelihood) # Param's AIC 

2 A1 -112.012501 7 238.025002 

3 A2 -111.401462 12 246.802924 

4 A3 -112.012501 7 238.025002 

5 fitted -116.080583 4 240.161165 

6 R -127.445484 2 258.890968 

7 

8 

9 Explanation of Tests 

10 

11 Test 1: Do responses and/or variances differ among Dose levels? 

12 (A2 vs. R) 

13 Test 2: Are Variances Homogeneous? (A1 vs A2) 

14 Test 3: Are variances adequately modeled? (A2 vs. A3) 

15 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

16 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

17 

18 Tests of Interest 

19 

20 Test -2*log(Likelihood Ratio) Test df p-value 

21 

22 Test 1 32.088 10 0.0003871 

23 Test 2 1.22208 5 0.9427 

24 Test 3 1.22208 5 0.9427 

25 Test 4 8.13616 3 0.04328 

26 

27 The p-value for Test 1 is less than .05. There appears to be a 

28 difference between response and/or variances among the dose levels 

29 It seems appropriate to model the data 

30 

31 The p-value for Test 2 is greater than .1. A homogeneous variance 

32 model appears to be appropriate here 

33 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is less than .1. You may want to try a different 

39 model 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 170.004 

51 

52 

53 BMDL = 24.0807 

54 

55 

56 

57 

58 

59 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-578 —DO NOT CITE OR QUOTE 

1 E.3.57. White et al. (1986): CH50 

2 E.3.57.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a

χ

 2 Test 

Statistic 

χ

 2

pValue b AIC 

BMD 

(ng/kgd) 

BMDL 

(ng/kgd) 

Model Notes 

exponential (M2) 5 0.09 20.99 0.00 391.47 4.5E+02 2.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 5 0.09 20.99 0.00 391.47 4.5E+02 2.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) 4 0.09 19.65 0.00 392.13 3.1E+02 1.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 4 0.09 19.65 0.00 392.13 3.1E+02 1.1E+02 nonconstant variance, 

power restricted ≥1 

Hill 4 0.09 18.75 0.00 391.22 2.0E+02 3.6E+01 nonconstant variance, n 

restricted >1, bound hit 

linear 5 0.09 25.95 <.0001 396.43 8.1E+02 5.9E+02 nonconstant variance 

polynomial 5 0.09 25.95 <.0001 396.43 8.1E+02 5.9E+02 nonconstant variance 

power 5 0.09 25.95 <.0001 396.43 8.1E+02 5.9E+02 

nonconstant variance, 

power restricted ≥1, bound 

hit 

exponential (M2) 5 0.09 21.77 0.00 390.45 4.0E+02 2.6E+02 constant variance, power 

restricted ≥1 

exponential (M3) 5 0.09 21.77 0.00 390.45 4.0E+02 2.6E+02 constant variance, power 

restricted ≥1 

exponential (M4) 4 0.09 20.51 0.00 391.19 2.7E+02 7.2E+01 constant variance, power 

restricted ≥1 

exponential (M5) 4 0.09 20.51 0.00 391.19 2.7E+02 7.2E+01 constant variance, power 

restricted ≥1 

Hill c 4 0.09 19.30 0.00 389.98 1.3E+02 2.9E+01 constant variance, n 

restricted >1, bound hit 

linear 5 0.09 26.50 <.0001 395.18 7.3E+02 5.7E+02 constant variance 

polynomial 5 0.09 26.50 <.0001 395.18 7.3E+02 5.7E+02 constant variance 

power 5 0.09 26.50 <.0001 395.18 7.3E+02 5.7E+02 constant variance, power 

restricted ≥1, bound hit 

a

 Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected b

 Values <0.1 fail to meet BMDS goodness-of-fit criteria c

 Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-579 —DO NOT CITE OR QUOTE 

1 E.3.57.2. Figure for Selected Model: Hill, Constant Variance, n Restricted >1, Bound Hit 

 0

 20

 40

 60

 80

 100

 0 500 1000 1500 2000

Mean Response

dose

Hill Model with 0.95 Confidence Level

19:52 10/06 2009

BMDL BMD

 

Hill

2 

3 

4 

5 E.3.57.3. Output File for Selected Model: Hill, Constant Variance, n Restricted >1, Bound 

6 Hit 

7 

8 

9 ==================================================================== 

10 Hill Model. (Version: 2.14; Date: 06/26/2008) 

11 Input Data File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_CH50.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\AniDose\HillConstVar_BMR1_CH50.plt 

13 Tue Oct 06 19:52:50 2009 

14 ==================================================================== 

15 

16 [insert study notes] 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 rho is set to 0 

27 Power parameter restricted to be greater than 1 

28 A constant variance model is fit 

29 

30 Total number of dose groups = 7 

31 Total number of records with missing values = 0 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-580 —DO NOT CITE OR QUOTE 

1 

2 Default Initial Parameter Values 

3 alpha = 273.143 

4 rho = 0 Specified 

5 intercept = 91 

6 v = -74 

7 n = 0.0969998 

8 k = 10 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 ( *** The model parameter(s) -rho -n 

14 have been estimated at a boundary point, or have been specified by the user, 

15 and do not appear in the correlation matrix ) 

16 

17 alpha intercept v k 

18 

19 alpha 1 -1.4e-008 -3.3e-008 6.7e-009 

20 

21 intercept -1.4e-008 1 0.38 -0.8 

22 

23 v -3.3e-008 0.38 1 -0.81 

24 

25 k 6.7e-009 -0.8 -0.81 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 alpha 337.326 63.7486 212.381 462.271 

34 intercept 73.1945 6.21329 61.0167 85.3723 

35 v -58.2543 12.308 -82.3776 -34.131 

36 n 1 NA 

37 k 289.939 354.891 -405.635 985.512 

38 

39 NA - Indicates that this parameter has hit a bound 

40 implied by some inequality constraint and thus 

41 has no standard error. 

42 

43 

44 

45 Table of Data and Estimated Values of Interest 

46 

47 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

48 ------ --- -------- -------- ----------- ----------- ---------- 

49 

50 0 8 91 73.2 14.1 18.4 2.74 

51 10 8 54 71.3 8.49 18.4 -2.66 

52 50 8 63 64.6 11.3 18.4 -0.25 

53 100 8 56 58.3 25.5 18.4 -0.347 

54 500 8 41 36.3 17 18.4 0.72 

55 1000 8 32 28 17 18.4 0.611 

56 2000 8 17 22.3 17 18.4 -0.819 

57 

58 

59 

60 Model Descriptions for likelihoods calculated 

61 

62 

63 Model A1: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 

66 Model A2: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma(i)^2 

68 

69 Model A3: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-581 —DO NOT CITE OR QUOTE 

1 Model A3 uses any fixed variance parameters that 

2 were specified by the user 

3 

4 Model R: Yi = Mu + e(i) 

5 Var{e(i)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) # Param's AIC 

11 A1 -181.340979 8 378.681959 

12 A2 -175.820265 14 379.640529 

13 A3 -181.340979 8 378.681959 

14 fitted -190.989397 4 389.978794 

15 R -212.367055 2 428.734109 

16 

17 

18 Explanation of Tests 

19 

20 Test 1: Do responses and/or variances differ among Dose levels? 

21 (A2 vs. R) 

22 Test 2: Are Variances Homogeneous? (A1 vs A2) 

23 Test 3: Are variances adequately modeled? (A2 vs. A3) 

24 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

25 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

26 

27 Tests of Interest 

28 

29 Test -2*log(Likelihood Ratio) Test df p-value 

30 

31 Test 1 73.0936 12 <.0001 

32 Test 2 11.0414 6 0.0871 

33 Test 3 11.0414 6 0.0871 

34 Test 4 19.2968 4 0.0006871 

35 

36 The p-value for Test 1 is less than .05. There appears to be a 

37 difference between response and/or variances among the dose levels 

38 It seems appropriate to model the data 

39 

40 The p-value for Test 2 is less than .1. Consider running a 

41 non-homogeneous variance model 

42 

43 The p-value for Test 3 is less than .1. You may want to consider a 

44 different variance model 

45 

46 The p-value for Test 4 is less than .1. You may want to try a different 

47 model 

48 

49 

50 Benchmark Dose Computation 

51 

52 Specified effect = 1 

53 

54 Risk Type = Estimated standard deviations from the control mean 

55 

56 Confidence level = 0.95 

57 

58 BMD = 133.503 

59 

60 BMDL = 28.903 

61 

62 

63 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-582 —DO NOT CITE OR QUOTE 

1 E.4. REFERENCES 

2 Amin, S; Moore, RW; Peterson, RE; et al. (2000) Gestational and lactational exposure to TCDD 

3 or coplanar PCBs alters adult expression of saccharin preference behavior in female rats. 

4 Neurotoxicol Teratol 22(5):675–682. 

5 Bell, DR; Clode, S; Fan, MQ; et al. (2007a) Toxicity of 2,3,7,8-tetrachlorodibenzo-p-dioxin in 

6 the developing male Wistar(Han) rat. II: Chronic dosing causes developmental delay. Toxicol 

7 Sci 99(1):224−233. 

8 Bell, DR; Clode, S; Fan, MQ; et al. (2007b) Relationships between tissue levels of 2,3,7,8-

9 tetrachlorodibenzo-p-dioxin (TCDD), mRNAs, and toxicity in the developing male Wistar (Han) 

10 rat. Toxicol Sci 99(2):591-604. 

11 Cantoni, L; Salmona, M; Rizzardini, M. (1981) Porphyrogenic effect of chronic treatment with 

12 2,3,7,8-tetrachlorodibenzo-p-dioxin in female rates. Dose-effect relationship following urinary 

13 excretion of porphyrins. Toxicol Appl Pharmacol 57:156−157. 

14 Crofton, KM; Craft, ES; Hedge, JM; et al. (2005) Thyroid-hormone-disrupting chemicals: 

15 evidence for dose-dependent additivity or synergism. Environ Health Perspect 113(11):1549–

16 1554. 

17 DeCaprio, AP; McMartin, DN; O’Keefe, PE; et al. (1986) Subchronic oral toxicity of 2,3,7,8-

18 tetrachlorodibenzo-p-dioxin in the guinea pig: comparisons with a PCB-containing transformer 

19 fluid pyrolysate. Fund Appl Toxicol 6:454–463. 

20 Hojo, R; Stern, S; Zareba, G; et al. (2002) Sexually dimorphic behavioral responses to prenatal 

21 dioxin exposure. Environ Health Perspect 110(3):247−254. 

22 Kattainen, H; Tuukanan, J; Simanainen, U; et al. (2001) In utero/lactational 2,3,7,8-

23 tetrachlorodibenzo-p-dioxin exposure impairs molar tooth development in rats. Toxicol Appl 

24 Pharmacol 17:216−224. 

25 Keller, JM; Huet-Hudson, YM; Leamy, LJ. (2007) Qualitative effects of dioxin on molars vary 

26 among inbred mouse strains. Arch Oral Biol 52:450−454. 

27 Keller, JM; Zelditch, ML; Huet, YM; et al. (2008a) Genetic differences in sensitivity to 

28 alterations of mandible structure caused by the teratogen 2,3,7,8-tetrachlorodibenzo-p-dioxin. 

29 Toxicol Pathol 36:1006–1013. 

30 Keller, JM; Huet-Hudson, Y; Leamy, LJ. (2008b) Effects of 2,3,7,8-tetrachlorodibenzo-p-dioxin 

31 on molar development among non-resistant inbred strains of mice: a geometric morphometric 

32 analysis. Growth Devel Aging 71:3−16. 

33 Kociba, RJ; Keyes, DG; Beyer, JE; et al. (1978) Results of a two-year chronic toxicity and 

34 oncogenicity study of 2,3,7,8-tetrachlorodibenzo-p-dioxin in rats. Toxicol Appl Pharmacol 

35 46(2):279−303. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-583 —DO NOT CITE OR QUOTE 

1 Latchoumycandane, C; Mathur, PP. (2002) Effects of vitamin E on reactive oxygen species2 mediated 2,3,7,8-tetrachlorodi-benzo-p-dioxin toxicity in rat testis. J Appl Toxicol 22(5):345–

3 351. 

4 Li, B; Liu, H-Y; Dai, L-J; et al. (2006) The early embryo loss caused by 2,3,7,8-

5 tetrachlorodibenzo-p-dioxin may be related to the accumulation of this compound in the uterus. 

6 Reprod Toxicol 21:301−306. 

7 Markowski, VP; Zareba, G; Stern, S; et al. (2001) Altered operant responding for motor 

8 reinforcement and the determination of benchmark doses following perinatal exposure to low9 level 2,3,7,8-tetrachlorodibenzo-p-dioxin. Environ Health Perspect 109(6):621−627. 

10 Miettinen, HM; Sorvari, R; Alaluusua, S; et al. (2006) The Effect of perinatal TCDD exposure 

11 on caries susceptibility in rats. Toxicol Sci 91(2):568−575. 

12 NTP (National Toxicology Program). (1982) NTP Technical Report on carcinogenesis bioassay 

13 of 2,3,7,8-tetrachlorodibenzo-p-dioxin in Osborne-Mendel rats and B6C3F1 mice (gavage 

14 study). Public Health Service, U.S. Department of Health and Human Services; NTP TR 209. 

15 Available from the National Institute of Environmental Health Sciences, Research Triangle Park, 

16 NC. 

17 NTP (National Toxicology Program). (2006) Toxicology and carcinogenesis studies of a mixture 

18 of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) (CAS No. 1746-01-6), 2,3,4,7,8-

19 pentachlorodibenzofuran (PeCDF) (CAS No. 57117-31-4), and 3,3',4,4',5-pentachlorobiphenyl 

20 (PCB 126) (CAS No. 57465-28-8) in female Harlan Sprague-Dawley Rats (gavage studies). 

21 Public Health Service, U.S. Department of Health and Human Services; NTP TR 526. Available 

22 from the National Institute of Environmental Health Sciences, Research Triangle Park, NC. 

23 Available at: http://ntp.niehs.nih.gov/index.cfm?objectid=070B7300-0E62-BF12-

24 F4C3E3B5B645A92B 

25 Ohsako, S; Miyabara, Y; Nishimura, N; et al. (2001) Maternal exposure to a low dose of 2,3,7,8-

26 tetrachlorodibenzo-p-dioxin (TCDD) suppressed the development of reproductive organs of male 

27 rats: dose-dependent increase of mRNA levels of 5α-reductase type 2 in contrast to decrease of 

28 androgren receptor in the pubertal ventral prostate. Toxicol Sci 60:132–143. 

29 Schantz, SL; Seo, BW; Moshtaghian, J; et al. (1996) Effects of gestational and lactational 

30 exposure to TCDD or coplanar PCBs on spatial learning. Neurotoxicol Teratol 18(3):305–313. 

31 Shi, Z; Valdez, KE; Ying, AY; et al. (2007) Ovarian endocrine disruption underlies premature 

32 reproduction senescence following environmentally relevant chronic exposure to aryl 

33 hydrocarbon receptor agonist 2,3,7,8-tetrachlorodibenzo-p-dioxin. Biol Reprod 30(4):293−342. 

34 Smialowicz, RJ; DeVito, MJ; Williams, WC; et al. (2008) Relative potency based on hepatic 

35 enzyme induction predicts immunosuppressive effects of a mixture of PCDDS/PCDFS and 

36 PCBS. Toxicol Appl Pharmacol 227:477–484. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT E-584 —DO NOT CITE OR QUOTE 

1 Toth, KJ; Sugar, S; Somfai-Relle, S; et al. (1978) Carcinogenic bioassay of the herbicide 2,4,5-

2 trichlorphenoxy ethanol (TCPE) with Swiss mice. Prog Biochem Pharmacol 14:82−93. 

3 Toth, L; Somfai-Relle, S; Sugár, J; et al. (1979) Carcinogenicity testing of herbicide 2,4,5-

4 trichlorophenoxyethanol containing dioxin and of pure dioxin in Swiss mice. Nature 

5 278:548−549. 

6 Van Birgelen, AP; Van der Kolk, J; Fase, KM; et al. (1995) Subchronic dose-response study of 

7 2,3,7,8-tetrachlorodibenzo-p-dioxin in female Sprague-Dawley rats. Toxicol Appl Pharmacol 

8 132:1-13. 

9 White, KL, Jr; Lysy, HH; McCay, JA; et al. (1986) Modulation of serum complement levels 

10 following exposure to polychlorinated dibenzo-p-dioxins. Toxicol Appl Pharmacol 84:209–219. 
DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX F 

Cancer Benchmark Dose Modeling 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-ii —DO NOT CITE OR QUOTE 

CONTENTS—APPENDIX F: Cancer Benchmark Dose Modeling 

APPENDIX F. CANCER BENCHMARK DOSE MODELING ...............................................F-1 

F.1. BLOOD SERUM BMDS RESULTS ...........................................................................F-1 

F.1.1. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma 

of Hard Palate or Nasal Turbinates...................................................................F-1 

F.1.1.1. Summary Table of BMDS Modeling Results ..................................F-1 

F.1.1.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0...........................................................................F-2 

F.1.1.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0..........................................................F-2 

F.1.2. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma 

of Tongue ..........................................................................................................F-4 

F.1.2.1. Summary Table of BMDS Modeling Results ..................................F-4 

F.1.2.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0...........................................................................F-4 

F.1.2.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0..........................................................F-5 

F.1.3. Kociba et al. (1978): Female, Adenoma of Adrenal Cortex............................F-6 

F.1.3.1. Summary Table of BMDS Modeling Results ..................................F-6 

F.1.3.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0...........................................................................F-7 

F.1.3.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0..........................................................F-7 

F.1.4. Kociba et al. (1978): Female, Hepatocellular Adenoma(s) or 

Carcinoma(s).....................................................................................................F-9 

F.1.4.1. Summary Table of BMDS Modeling Results ..................................F-9 

F.1.4.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0...........................................................................F-9 

F.1.4.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-10 

F.1.5. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma 

of Hard Palate or Nasal Turbinates.................................................................F-11 

F.1.5.1. Summary Table of BMDS Modeling Results ................................F-11 

F.1.5.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-12 

F.1.5.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-12 

F.1.6. Kociba et al. (1978): Female, Keratinizing Squamous Cell 

Carcinoma of Lung .........................................................................................F-14 

F.1.6.1. Summary Table of BMDS Modeling Results ................................F-14 

F.1.6.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-15 

F.1.6.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-15 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-iii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.1.7. National Toxicology Program (1982): Female Rat, Subcutaneous 

Tissue. Fibrosarcoma ......................................................................................F-17 

F.1.7.1. Summary Table of BMDS Modeling Results ................................F-17 

F.1.7.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-17 

F.1.7.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-18 

F.1.8. National Toxicology Program (1982): Female Rat, Liver, Neoplastic 

Nodule or Hepatocellular Carcinoma .............................................................F-19 

F.1.8.1. Summary Table of BMDS Modeling Results ................................F-19 

F.1.8.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-20 

F.1.8.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-20 

F.1.9. National Toxicology Program (1982): Female Rat, Adrenal, Cortical 

Adenoma, or Carcinoma or Adenoma, NOS ..................................................F-22 

F.1.9.1. Summary Table of BMDS Modeling Results ................................F-22 

F.1.9.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-22 

F.1.9.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-23 

F.1.10. National Toxicology Program (1982): Female Rat, Thyroid, 

Follicular-Cell Adenoma ................................................................................F-24 

F.1.10.1. Summary Table of BMDS Modeling Results ................................F-24 

F.1.10.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-25 

F.1.10.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-25 

F.1.11. National Toxicology Program (1982): Male Rat, Liver, Neoplastic 

Nodule or Hepatocellular Carcinoma .............................................................F-27 

F.1.11.1. Summary Table of BMDS Modeling Results ................................F-27 

F.1.11.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-28 

F.1.11.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-28 

F.1.12. National Toxicology Program (1982): Male Ra, Thyroid, 

Follicular-Cell Adenoma or Carcinoma..........................................................F-30 

F.1.12.1. Summary Table of BMDS Modeling Results ................................F-30 

F.1.12.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-31 

F.1.12.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-31 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-iv —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.1.13. National Toxicology Program (1982): Male Rat, Adrenal Cortex, 

Adenoma.........................................................................................................F-33 

F.1.13.1. Summary Table of BMDS Modeling Results ................................F-33 

F.1.13.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-34 

F.1.13.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-34 

F.1.14. National Toxicology Program (1982): Female Mice, Subcutaneous 

Tissue, Fibrosarcoma ......................................................................................F-36 

F.1.14.1. Summary Table of BMDS Modeling Results ................................F-36 

F.1.14.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-37 

F.1.14.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-37 

F.1.15. National Toxicology Program (1982): Female Mice, Hematopoietic 

System, Lymphoma ........................................................................................F-39 

F.1.15.1. Summary Table of BMDS Modeling Results ................................F-39 

F.1.15.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-40 

F.1.15.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-40 

F.1.16. National Toxicology Program (1982): Female Mice, Liver, 

Hepatocellular Adenoma or Carcinoma..........................................................F-42 

F.1.16.1. Summary Table of BMDS Modeling Results ................................F-42 

F.1.16.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-43 

F.1.16.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-43 

F.1.17. National Toxicology Program (1982): Female Mice, Thyroid, 

Follicular-Cell Adenoma ................................................................................F-45 

F.1.17.1. Summary Table of BMDS Modeling Results ................................F-45 

F.1.17.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-46 

F.1.17.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-46 

F.1.18. National Toxicology Program (1982): Male Mice, Lung, 

Alveolar/Bronchiolar Adenoma or Carcinoma...............................................F-48 

F.1.18.1. Summary Table of BMDS Modeling Results ................................F-48 

F.1.18.2. Figure for Selected Model: Multistage Cancer, 2-Degree, 

Betas Restricted ≥0.........................................................................F-49 

F.1.18.3. Output File for Selected Model: Multistage Cancer, 

2-Degree, Betas Restricted ≥0........................................................F-49 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-v —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.1.19. National Toxicology Program (1982): Male Mice, Liver, 

Hepatocellular Adenoma or Carcinoma..........................................................F-51 

F.1.19.1. Summary Table of BMDS Modeling Results ................................F-51 

F.1.19.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-52 

F.1.19.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-52 

F.1.20. National Toxicology Program (2006): Liver, Cholangiocarcinoma..............F-54 

F.1.20.1. Summary Table of BMDS Modeling Results ................................F-54 

F.1.20.2. Figure for Selected Model: Multistage Cancer, 3-Degree, 

Betas Restricted ≥0.........................................................................F-55 

F.1.20.3. Output File for Selected Model: Multistage Cancer, 

3-Degree, Betas Restricted ≥0........................................................F-55 

F.1.21. National Toxicology Program (2006): Liver, Hepatocellular 

Adenoma.........................................................................................................F-57 

F.1.21.1. Summary Table of BMDS Modeling Results ................................F-57 

F.1.21.2. Figure for Selected Model: Multistage Cancer, 3-Degree, 

Betas Restricted ≥0.........................................................................F-58 

F.1.21.3. Output File for Selected Model: Multistage Cancer, 

3-Degree, Betas Restricted ≥0........................................................F-58 

F.1.22. National Toxicology Program (2006): Oral mucosa, Squamous Cell 

Carcinoma.......................................................................................................F-60 

F.1.22.1. Summary Table of BMDS Modeling Results ................................F-60 

F.1.22.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0, Bound Hit......................................................F-61 

F.1.22.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0, Bound Hit .....................................F-61 

F.1.23. National Toxicology Program (2006): Pancreas, Adenoma or 

Carcinoma.......................................................................................................F-63 

F.1.23.1. Summary Table of BMDS Modeling Results ................................F-63 

F.1.23.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-64 

F.1.23.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-64 

F.1.24. National Toxicology Program (2006): Lung, Cystic Keratinizing 

Epithelioma.....................................................................................................F-66 

F.1.24.1. Summary Table of BMDS Modeling Results ................................F-66 

F.1.24.2. Figure for Selected Model: Multistage Cancer, 2-Degree, 

Betas Restricted ≥0.........................................................................F-67 

F.1.24.3. Output File for Selected Model: Multistage Cancer, 

2-Degree, Betas Restricted ≥0........................................................F-67 

F.1.25. Toth et al. (1978): 1YR, Liver, Tumors.........................................................F-69 

F.1.25.1. Summary Table of BMDS Modeling Results ................................F-69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-vi —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.1.25.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-70 

F.1.25.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-70 

F.2. ADMINISTERED DOSE BMDS RESULTS ............................................................F-72 

F.2.1. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma 

of Hard Palate or Nasal Turbinates.................................................................F-72 

F.2.1.1. Summary Table of BMDS Modeling Results ................................F-72 

F.2.1.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-73 

F.2.1.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-73 

F.2.2. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma 

of Tongue ........................................................................................................F-75 

F.2.2.1. Summary Table of BMDS Modeling Results ................................F-75 

F.2.2.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-76 

F.2.2.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-76 

F.2.3. Kociba et al. (1978): Female. Adenoma of Adrenal Cortex..........................F-78 

F.2.3.1. Summary Table of BMDS Modeling Results ................................F-78 

F.2.3.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-79 

F.2.3.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-79 

F.2.4. Kociba et al. (1978): Female, Hepatocellular Adenoma(S) or 

Carcinoma(s)...................................................................................................F-81 

F.2.4.1. Summary Table of BMDS Modeling Results ................................F-81 

F.2.4.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-82 

F.2.4.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-82 

F.2.5. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma 

of Hard Palate or Nasal Turbinates.................................................................F-84 

F.2.5.1. Summary Table of BMDS Modeling Results ................................F-84 

F.2.5.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-85 

F.2.5.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-85 

F.2.6. Kociba et al. (1978): Female, Keratinizing Squamous Cell 

Carcinoma of Lung .........................................................................................F-87 

F.2.6.1. Summary Table of BMDS Modeling Results ................................F-87 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-vii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.2.6.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-88 

F.2.6.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-88 

F.2.7. National Toxicology Program (1982): Female Rats, Subcutaneous 

Tissue, Fibrosarcoma ......................................................................................F-90 

F.2.7.1. Summary Table of BMDS Modeling Results ................................F-90 

F.2.7.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-91 

F.2.7.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-91 

F.2.8. National Toxicology Program (1982): Female Rats, Liver, 

Neoplastic Nodule or Hepatocellular Carcinoma ...........................................F-93 

F.2.8.1. Summary Table of BMDS Modeling Results ................................F-93 

F.2.8.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-94 

F.2.8.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-94 

F.2.9. National Toxicology Program (1982): Female Rats, Adrenal, 

Cortical Adenoma, or Carcinoma or Adenoma, NOS ....................................F-96 

F.2.9.1. Summary Table of BMDS Modeling Results ................................F-96 

F.2.9.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.........................................................................F-97 

F.2.9.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0........................................................F-97 

F.2.10. National Toxicology Program (1982): Female Rats, Thyroid, 

Follicular-Cell Adenoma ................................................................................F-99 

F.2.10.1. Summary Table of BMDS Modeling Results ................................F-99 

F.2.10.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-100 

F.2.10.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-100 

F.2.11. National Toxicology Program (1982): Male Rats, Liver, Neoplastic 

Nodule or Hepatocellular Carcinoma ...........................................................F-102 

F.2.11.1. Summary Table of BMDS Modeling Results ..............................F-102 

F.2.11.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-103 

F.2.11.3. Output File for selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-103 

F.2.12. National Toxicology Program (1982): Male Rats, Thyroid, 

Follicular-Cell Adenoma or Carcinoma........................................................F-105 

F.2.12.1. Summary Table of BMDS Modeling Results ..............................F-105 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-viii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.2.12.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-106 

F.2.12.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-106 

F.2.13. National Toxicology Program (1982): Male Rats, Adrenal cortex, 

Adenoma.......................................................................................................F-108 

F.2.13.1. Summary Table of BMDS Modeling Results ..............................F-108 

F.2.13.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-109 

F.2.13.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-109 

F.2.14. National Toxicology Program (1982): Female Mice, Subcutaneous 

Tissue, Fibrosarcoma ....................................................................................F-111 

F.2.14.1. Summary Table of BMDS Modeling Results ..............................F-111 

F.2.14.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-112 

F.2.14.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-112 

F.2.15. National Toxicology Program (1982): Female Mice, Hematopoietic 

System, Lymphoma ......................................................................................F-114 

F.2.15.1. Summary Table of BMDS Modeling Results ..............................F-114 

F.2.15.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-115 

F.2.15.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-115 

F.2.16. National Toxicology Program (1982): Female Mice, Liver, 

Hepatocellular Adenoma or Carcinoma........................................................F-117 

F.2.16.1. Summary Table of BMDS Modeling Results ..............................F-117 

F.2.16.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-118 

F.2.16.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-118 

F.2.17. National Toxicology Program (1982): Female Mice, Thyroid 

Follicular Cell Adenoma...............................................................................F-120 

F.2.17.1. Summary Table of BMDS Modeling Results ..............................F-120 

F.2.17.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-121 

F.2.17.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-121 

F.2.18. National Toxicology Program (1982): Male Mice, Lung, 

Alveolar/Bronchiolar Adenoma or Carcinoma.............................................F-123 

F.2.18.1. Summary Table of BMDS Modeling Results ..............................F-123 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-ix —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.2.18.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-124 

F.2.18.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-124 

F.2.19. National Toxicology Program (1982): Male Mice, Liver, 

Hepatocellular Adenoma or Carcinoma........................................................F-126 

F.2.19.1. Summary Table of BMDS Modeling Results ..............................F-126 

F.2.19.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-127 

F.2.19.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-127 

F.2.20. National Toxicology Program (2006): Liver, Cholangiocarcinoma............F-129 

F.2.20.1. Summary Table of BMDS Modeling Results ..............................F-129 

F.2.20.2. Figure for Selected Model: Multistage Cancer, 3-Degree, 

Betas Restricted ≥0.......................................................................F-130 

F.2.20.3. Output File for Selected Model: Multistage Cancer, 

3-Degree, Betas Restricted ≥0......................................................F-130 

F.2.21. National Toxicology Program (2006): Liver, Hepatocellular 

Adenoma.......................................................................................................F-132 

F.2.21.1. Summary Table of BMDS Modeling Results ..............................F-132 

F.2.21.2. Figure for Selected Model: Multistage Cancer, 3-Degree, 

Betas Restricted ≥0.......................................................................F-133 

F.2.21.3. Output File for Selected Model: Multistage Cancer, 

3-Degree, Betas Restricted ≥0......................................................F-133 

F.2.22. National Toxicology Program (2006): Oral Mucosa, Squamous Cell 

Carcinoma.....................................................................................................F-135 

F.2.22.1. Summary Table of BMDS Modeling Results ..............................F-135 

F.2.22.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0, Bound Hit....................................................F-136 

F.2.22.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0, Bound Hit ...................................F-136 

F.2.23. National Toxicology Program (2006): Pancreas, Adenoma or 

Carcinoma.....................................................................................................F-138 

F.2.23.1. Summary Table of BMDS Modeling Results ..............................F-138 

F.2.23.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-139 

F.2.23.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-139 

F.2.24. National Toxicology Program (2006): Lung, Cystic Keratinizing 

Epithelioma...................................................................................................F-141 

F.2.24.1. Summary Table of BMDS Modeling Results ..............................F-141 

F.2.24.2. Figure for Selected Model: Multistage Cancer, 2-Degree, 

Betas Restricted ≥0.......................................................................F-142 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-x —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

F.2.24.3. Output File for Selected Model: Multistage Cancer, 

2-Degree, Betas Restricted ≥0......................................................F-142 

F.2.25. Toth et al. (1978): 1YR, Liver, Tumors.......................................................F-144 

F.2.25.1. Summary Table of BMDS Modeling Results ..............................F-144 

F.2.25.2. Figure for Selected Model: Multistage Cancer, 1-Degree, 

Betas Restricted ≥0.......................................................................F-145 

F.2.25.3. Output File for Selected Model: Multistage Cancer, 

1-Degree, Betas Restricted ≥0......................................................F-145 

F.3. HUMAN EQUIVALENT DOSES FOR 1, 5, AND 10% EXTRA RISK................F-148 

F.4. REFERENCES .........................................................................................................F-149 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-1 —DO NOT CITE OR QUOTE 

1 APPENDIX F. CANCER BENCHMARK DOSE MODELING 

2 

3 

4 F.1. BLOOD SERUM BMDS RESULTS 

5 F.1.1. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma of Hard Palate 

6 or Nasal Turbinates 

7 F.1.1.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.94 0.82 31.56 3.2E+03 1.5E+03 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.15 0.99 30.17 7.5E+03 1.9E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.03 1.00 29.93 1.1E+04 2.0E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-2 —DO NOT CITE OR QUOTE 

1 F.1.1.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 F.1.1.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

5 

6 

7 ==================================================================== 

8 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

9 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_palate_nasal.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_palate_nasal.plt 

11 Mon Nov 23 15:42:08 2009 

12 ==================================================================== 

13 

14 Source - Table 4 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the probability function is: 

18 

19 P[response] = background + (1-background)*[1-EXP( 

20 -beta1*dose^1)] 

21 

22 The parameter betas are restricted to be positive 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 

28 Total number of observations = 5 

29 Total number of records with missing values = 1 

30 Total number of parameters in model = 2 

31 Total number of specified parameters = 0 

32 Degree of polynomial = 1 

33 

34 

35 Maximum number of iterations = 250 

36 Relative Function Convergence has been set to: 1e-008 

 0

 0.05

 0.1

 0.15

 0.2

 0 5000 10000 15000 20000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:42 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-3 —DO NOT CITE OR QUOTE 

1 Parameter Convergence has been set to: 1e-008 

2 

3 

4 

5 Default Initial Parameter Values 

6 Background = 0 

7 Beta(1) = 4.1047e-006 

8 

9 

10 Asymptotic Correlation Matrix of Parameter Estimates 

11 

12 ( *** The model parameter(s) -Background 

13 have been estimated at a boundary point, or have been specified by the user, 

14 and do not appear in the correlation matrix ) 

15 

16 Beta(1) 

17 

18 Beta(1) 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0 * * * 

27 Beta(1) 3.16499e-006 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -13.9385 4 

37 Fitted model -14.782 1 1.68697 3 0.6398 

38 Reduced model -20.2589 1 12.6409 3 0.005481 

39 

40 AIC: 31.5639 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0000 0.000 0.000 85 0.000 

48 860.4590 0.0027 0.136 0.000 50 -0.369 

49 3944.9299 0.0124 0.620 0.000 50 -0.793 

50 21334.0000 0.0653 3.265 4.000 50 0.421 

51 

52 Chi^2 = 0.94 d.f. = 3 P-value = 0.8153 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 3175.47 

64 

65 BMDL = 1539.87 

66 

67 BMDU = 8231.22 

68 

69 Taken together, (1539.87, 8231.22) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-4 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 6.49406e-006 

3 

4 

5 F.1.2. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma of Tongue 

6 F.1.2.1. Summary Table of BMDS Modeling Results 

7 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 1.50 0.47 47.93 3.4E+03 1.4E+03 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 1.50 0.47 47.93 3.4E+03 1.4E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 1.50 0.47 47.93 3.4E+03 1.4E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

8 

9 

10 F.1.2.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

11 

 0

 0.05

 0.1

 0.15

 0 5000 10000 15000 20000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:42 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-5 —DO NOT CITE OR QUOTE 

1 F.1.2.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 ==================================================================== 

5 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_tongue.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_tongue.plt 

8 Mon Nov 23 15:42:27 2009 

9 ==================================================================== 

10 

11 Source - Table 4 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background + (1-background)*[1-EXP( 

17 -beta1*dose^1)] 

18 

19 The parameter betas are restricted to be positive 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 

25 Total number of observations = 5 

26 Total number of records with missing values = 1 

27 Total number of parameters in model = 2 

28 Total number of specified parameters = 0 

29 Degree of polynomial = 1 

30 

31 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 Background = 0.00925136 

40 Beta(1) = 2.49061e-006 

41 

42 

43 Asymptotic Correlation Matrix of Parameter Estimates 

44 

45 Background Beta(1) 

46 

47 Background 1 -0.58 

48 

49 Beta(1) -0.58 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 Background 0.00510493 * * * 

58 Beta(1) 2.99496e-006 * * * 

59 

60 * - Indicates that this value is not calculated. 

61 

62 

63 

64 Analysis of Deviance Table 

65 

66 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

67 Full model -21.1523 4 

68 Fitted model -21.9667 2 1.6288 2 0.4429 

69 Reduced model -24.1972 1 6.08976 3 0.1073 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-6 —DO NOT CITE OR QUOTE 

1 

2 AIC: 47.9334 

3 

4 

5 Goodness of Fit 

6 Scaled 

7 Dose Est._Prob. Expected Observed Size Residual 

8 ------------------------------------------------------------------------ 

9 0.0000 0.0051 0.434 0.000 85 -0.660 

10 860.4590 0.0077 0.383 1.000 50 1.000 

11 3944.9299 0.0168 0.840 1.000 50 0.177 

12 21334.0000 0.0667 3.334 3.000 50 -0.189 

13 

14 Chi^2 = 1.50 d.f. = 2 P-value = 0.4716 

15 

16 

17 Benchmark Dose Computation 

18 

19 Specified effect = 0.01 

20 

21 Risk Type = Extra risk 

22 

23 Confidence level = 0.95 

24 

25 BMD = 3355.75 

26 

27 BMDL = 1432.78 

28 

29 BMDU = 19112.8 

30 

31 Taken together, (1432.78, 19112.8) is a 90 % two-sided confidence 

32 interval for the BMD 

33 

34 Multistage Cancer Slope Factor = 6.97946e-006 

35 

36 

37 F.1.3. Kociba et al. (1978): Female, Adenoma of Adrenal Cortex 

38 F.1.3.1. Summary Table of BMDS Modeling Results 

39 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 1.09 0.78 52.49 1.8E+03 1.0E+03 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 1.09 0.78 52.49 1.8E+03 1.0E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 1.09 0.78 52.49 1.8E+03 1.0E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

40 

41 

42 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-7 —DO NOT CITE OR QUOTE 

1 F.1.3.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.3.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adre_adenoma.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adre_adenoma.plt 

12 Mon Nov 23 15:42:49 2009 

13 ==================================================================== 

14 

15 Source - Table 5 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 5 

30 Total number of records with missing values = 1 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0 5000 10000 15000 20000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:42 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-8 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.00493749 

9 Beta(1) = 4.83499e-006 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 5.60622e-006 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -24.6514 4 

39 Fitted model -25.2438 1 1.18487 3 0.7566 

40 Reduced model -31.4904 1 13.6781 3 0.003378 

41 

42 AIC: 52.4876 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 85 0.000 

50 860.4590 0.0048 0.241 0.000 50 -0.492 

51 3944.9299 0.0219 1.094 2.000 50 0.876 

52 21334.0000 0.1127 5.636 5.000 50 -0.285 

53 

54 Chi^2 = 1.09 d.f. = 3 P-value = 0.7793 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 1792.71 

66 

67 BMDL = 1020.18 

68 

69 BMDU = 3628.63 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-9 —DO NOT CITE OR QUOTE 

1 Taken together, (1020.18, 3628.63) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 9.8022e-006 

5 

6 

7 F.1.4. Kociba et al. (1978): Female, Hepatocellular Adenoma(s) or Carcinoma(s) 

8 F.1.4.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 2.81 0.24 143.26 3.9E+02 2.8E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 2.81 0.24 143.26 3.9E+02 2.8E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 2.81 0.24 143.26 3.9E+02 2.8E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 

12 F.1.4.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

13 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 5000 10000 15000 20000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:43 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-10 —DO NOT CITE OR QUOTE 

1 F.1.4.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 ==================================================================== 

5 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_liver_ad_carc.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_liver_ad_carc.plt 

8 Mon Nov 23 15:43:10 2009 

9 ==================================================================== 

10 

11 Source - Table 1 in Goodman and Sauer 1992 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background + (1-background)*[1-EXP( 

17 -beta1*dose^1)] 

18 

19 The parameter betas are restricted to be positive 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 

25 Total number of observations = 4 

26 Total number of records with missing values = 0 

27 Total number of parameters in model = 2 

28 Total number of specified parameters = 0 

29 Degree of polynomial = 1 

30 

31 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 Background = 0.0400267 

40 Beta(1) = 2.26421e-005 

41 

42 

43 Asymptotic Correlation Matrix of Parameter Estimates 

44 

45 Background Beta(1) 

46 

47 Background 1 -0.51 

48 

49 Beta(1) -0.51 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 Background 0.022147 * * * 

58 Beta(1) 2.60216e-005 * * * 

59 

60 * - Indicates that this value is not calculated. 

61 

62 

63 

64 Analysis of Deviance Table 

65 

66 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

67 Full model -68.2561 4 

68 Fitted model -69.6304 2 2.74863 2 0.253 

69 Reduced model -89.1983 1 41.8843 3 <.0001 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-11 —DO NOT CITE OR QUOTE 

1 

2 AIC: 143.261 

3 

4 

5 Goodness of Fit 

6 Scaled 

7 Dose Est._Prob. Expected Observed Size Residual 

8 ------------------------------------------------------------------------ 

9 0.0000 0.0221 1.905 2.000 86 0.070 

10 852.5169 0.0436 2.180 1.000 50 -0.817 

11 3941.9464 0.1175 5.874 9.000 50 1.373 

12 21246.0000 0.4374 19.685 18.000 45 -0.506 

13 

14 Chi^2 = 2.81 d.f. = 2 P-value = 0.2449 

15 

16 

17 Benchmark Dose Computation 

18 

19 Specified effect = 0.01 

20 

21 Risk Type = Extra risk 

22 

23 Confidence level = 0.95 

24 

25 BMD = 386.23 

26 

27 BMDL = 276.228 

28 

29 BMDU = 577.635 

30 

31 Taken together, (276.228, 577.635) is a 90 % two-sided confidence 

32 interval for the BMD 

33 

34 Multistage Cancer Slope Factor = 3.6202e-005 

35 

36 

37 F.1.5. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma of Hard Palate 

38 or Nasal Turbinates 

39 F.1.5.1. Summary Table of BMDS Modeling Results 

40 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.94 0.82 31.56 3.2E+03 1.5E+03 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.15 0.99 30.17 7.5E+03 1.9E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.03 1.00 29.93 1.1E+04 2.0E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

41 

42 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-12 —DO NOT CITE OR QUOTE 

1 F.1.5.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.5.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_nasal.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_nasal.plt 

12 Mon Nov 23 15:43:31 2009 

13 ==================================================================== 

14 

15 Source - Table 5 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0 5000 10000 15000 20000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:43 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-13 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 7.11589e-005 

10 Beta(1) = 4.0351e-006 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(1) 

20 

21 Beta(1) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 4.0463e-006 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -18.7562 4 

40 Fitted model -18.9547 1 0.397016 3 0.9409 

41 Reduced model -24.1972 1 10.882 3 0.01238 

42 

43 AIC: 39.9093 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0000 0.000 0.000 86 0.000 

51 852.5169 0.0034 0.172 0.000 50 -0.416 

52 3941.9464 0.0158 0.791 1.000 50 0.237 

53 21246.0000 0.0824 4.036 4.000 49 -0.019 

54 

55 Chi^2 = 0.23 d.f. = 3 P-value = 0.9728 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.01 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 2483.84 

67 

68 BMDL = 1289.34 

69 

70 BMDU = 5762.51 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-14 —DO NOT CITE OR QUOTE 

1 

2 Taken together, (1289.34, 5762.51) is a 90 % two-sided confidence 

3 interval for the BMD 

4 

5 Multistage Cancer Slope Factor = 7.7559e-006 

6 

7 

8 F.1.6. Kociba et al. (1978): Female, Keratinizing Squamous Cell Carcinoma of Lung 

9 F.1.6.1. Summary Table of BMDS Modeling Results 

10 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 1.75 0.63 45.30 1.7E+03 9.8E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.28 0.96 42.74 5.5E+03 1.5E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.05 1.00 42.29 8.6E+03 1.7E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

11 

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-15 —DO NOT CITE OR QUOTE 

1 F.1.6.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.6.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_kera_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_kera_carc.plt 

12 Mon Nov 23 15:43:52 2009 

13 ==================================================================== 

14 

15 Source - Table 5 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0 5000 10000 15000 20000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:43 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-16 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 7.61927e-006 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 5.80969e-006 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -20.0957 4 

39 Fitted model -21.6489 1 3.10635 3 0.3755 

40 Reduced model -31.4904 1 22.7894 3 <.0001 

41 

42 AIC: 45.2978 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 86 0.000 

50 852.5169 0.0049 0.247 0.000 50 -0.498 

51 3941.9464 0.0226 1.132 0.000 50 -1.076 

52 21246.0000 0.1161 5.690 7.000 49 0.584 

53 

54 Chi^2 = 1.75 d.f. = 3 P-value = 0.6263 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 1729.93 

66 

67 BMDL = 984.302 

68 

69 BMDU = 3461.69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-17 —DO NOT CITE OR QUOTE 

1 Taken together, (984.302, 3461.69) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 1.01595e-005 

5 

6 

7 F.1.7. National Toxicology Program (1982): Female Rat, Subcutaneous Tissue. 

8 Fibrosarcoma 

9 F.1.7.1. Summary Table of BMDS Modeling Results 

10 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

11 

12 

13 F.1.7.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

14 

 0

 0.05

 0.1

 0.15

 0.2

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:44 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-18 —DO NOT CITE OR QUOTE 

1 F.1.7.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 ==================================================================== 

5 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_sub_fibro.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_sub_fibro.plt 

8 Mon Nov 23 15:44:12 2009 

9 ==================================================================== 

10 

11 Source - Table 10 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background + (1-background)*[1-EXP( 

17 -beta1*dose^1)] 

18 

19 The parameter betas are restricted to be positive 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 

25 Total number of observations = 4 

26 Total number of records with missing values = 0 

27 Total number of parameters in model = 2 

28 Total number of specified parameters = 0 

29 Degree of polynomial = 1 

30 

31 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 Background = 0.026791 

40 Beta(1) = 3.88561e-006 

41 

42 

43 Asymptotic Correlation Matrix of Parameter Estimates 

44 

45 Background Beta(1) 

46 

47 Background 1 -0.63 

48 

49 Beta(1) -0.63 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 Background 0.0149169 * * * 

58 Beta(1) 5.91146e-006 * * * 

59 

60 * - Indicates that this value is not calculated. 

61 

62 

63 

64 Analysis of Deviance Table 

65 

66 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

67 Full model -33.5998 4 

68 Fitted model -35.6885 2 4.17734 2 0.1239 

69 Reduced model -37.7465 1 8.29346 3 0.04032 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-19 —DO NOT CITE OR QUOTE 

1 

2 AIC: 75.3769 

3 

4 

5 Goodness of Fit 

6 Scaled 

7 Dose Est._Prob. Expected Observed Size Residual 

8 ------------------------------------------------------------------------ 

9 0.0000 0.0149 1.119 0.000 75 -1.066 

10 1072.2652 0.0211 1.057 2.000 50 0.927 

11 3111.2349 0.0329 1.643 3.000 50 1.076 

12 16207.0000 0.1049 5.141 4.000 49 -0.532 

13 

14 Chi^2 = 3.44 d.f. = 2 P-value = 0.1795 

15 

16 

17 Benchmark Dose Computation 

18 

19 Specified effect = 0.01 

20 

21 Risk Type = Extra risk 

22 

23 Confidence level = 0.95 

24 

25 BMD = 1700.14 

26 

27 BMDL = 751.001 

28 

29 BMDU = 1.77581e+009 

30 

31 Taken together, (751.001, 1.77581e+009) is a 90 % two-sided confidence 

32 interval for the BMD 

33 

34 Multistage Cancer Slope Factor = 1.33156e-005 

35 

36 

37 F.1.8. National Toxicology Program (1982): Female Rat, Liver, Neoplastic Nodule or 

38 Hepatocellular Carcinoma 

39 F.1.8.1. Summary Table of BMDS Modeling Results 

40 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.80 0.22 135.20 6.4E+02 4.0E+02 betas restricted 

≥0 

Multistage 

cancer, 

2-degree 

3 0.13 0.49 133.45 3.0E+03 4.8E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.02 0.24 135.44 3.9E+03 4.8E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

41 

42 

43 

44 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-20 —DO NOT CITE OR QUOTE 

1 F.1.8.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.8.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_liver_nod.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_liver_nod.plt 

12 Mon Nov 23 15:45:38 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:45 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-21 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0 

10 Beta(1) = 4.03747e-006 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(1) 

20 

21 Beta(1) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 3.00492e-006 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -11.3484 4 

40 Fitted model -12.0545 1 1.41226 3 0.7027 

41 Reduced model -15.9189 1 9.14109 3 0.02747 

42 

43 AIC: 26.109 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0000 0.000 0.000 74 0.000 

51 1071.8576 0.0032 0.161 0.000 50 -0.402 

52 3115.7313 0.0093 0.466 0.000 50 -0.686 

53 16272.0000 0.0477 2.386 3.000 50 0.407 

54 

55 Chi^2 = 0.80 d.f. = 3 P-value = 0.8501 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.01 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 3344.63 

67 

68 BMDL = 1472.42 

69 

70 BMDU = 10322.4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-22 —DO NOT CITE OR QUOTE 

1 

2 Taken together, (1472.42, 10322.4) is a 90 % two-sided confidence 

3 interval for the BMD 

4 

5 Multistage Cancer Slope Factor = 6.79156e-006 

6 

7 

8 F.1.9. National Toxicology Program (1982): Female Rat, Adrenal, Cortical Adenoma, or 

9 Carcinoma or Adenoma, NOS 

10 F.1.9.1. Summary Table of BMDS Modeling Results 

11 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 2.18 0.34 203.83 8.8E+02 4.4E+02 betas restricted 

≥0 

Multistage 

cancer, 

2-degree 

2 1.51 0.47 203.03 3.6E+03 4.9E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 1.37 0.51 202.87 5.9E+03 5.0E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

12 

13 

14 F.1.9.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

15 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:44 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-23 —DO NOT CITE OR QUOTE 

1 F.1.9.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 ==================================================================== 

5 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adre_cort_ad_carc.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adre_cort_ad_carc.plt 

8 Mon Nov 23 15:44:55 2009 

9 ==================================================================== 

10 

11 Source - Table 10 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the probability function is: 

15 

16 P[response] = background + (1-background)*[1-EXP( 

17 -beta1*dose^1)] 

18 

19 The parameter betas are restricted to be positive 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 

25 Total number of observations = 4 

26 Total number of records with missing values = 0 

27 Total number of parameters in model = 2 

28 Total number of specified parameters = 0 

29 Degree of polynomial = 1 

30 

31 

32 Maximum number of iterations = 250 

33 Relative Function Convergence has been set to: 1e-008 

34 Parameter Convergence has been set to: 1e-008 

35 

36 

37 

38 Default Initial Parameter Values 

39 Background = 0.134119 

40 Beta(1) = 1.27888e-005 

41 

42 

43 Asymptotic Correlation Matrix of Parameter Estimates 

44 

45 Background Beta(1) 

46 

47 Background 1 -0.54 

48 

49 Beta(1) -0.54 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 Background 0.139831 * * * 

58 Beta(1) 1.14475e-005 * * * 

59 

60 * - Indicates that this value is not calculated. 

61 

62 

63 

64 Analysis of Deviance Table 

65 

66 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

67 Full model -98.7282 4 

68 Fitted model -99.9133 2 2.37035 2 0.3057 

69 Reduced model -102.201 1 6.94636 3 0.07363 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-24 —DO NOT CITE OR QUOTE 

1 

2 AIC: 203.827 

3 

4 

5 Goodness of Fit 

6 Scaled 

7 Dose Est._Prob. Expected Observed Size Residual 

8 ------------------------------------------------------------------------ 

9 0.0000 0.1398 10.208 11.000 73 0.267 

10 1072.2652 0.1503 7.366 9.000 49 0.653 

11 3111.2349 0.1699 8.326 5.000 49 -1.265 

12 16207.0000 0.2855 13.132 14.000 46 0.283 

13 

14 Chi^2 = 2.18 d.f. = 2 P-value = 0.3363 

15 

16 

17 Benchmark Dose Computation 

18 

19 Specified effect = 0.01 

20 

21 Risk Type = Extra risk 

22 

23 Confidence level = 0.95 

24 

25 BMD = 877.947 

26 

27 BMDL = 443.554 

28 

29 BMDU = 6.93624e+008 

30 

31 Taken together, (443.554, 6.93624e+008) is a 90 % two-sided confidence 

32 interval for the BMD 

33 

34 Multistage Cancer Slope Factor = 2.25452e-005 

35 

36 

37 F.1.10. National Toxicology Program (1982): Female Rat, Thyroid, Follicular-Cell 

38 Adenoma 

39 F.1.10.1. Summary Table of BMDS Modeling Results 

40 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 1.13 0.57 92.41 1.8E+03 8.5E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 0.62 0.74 91.75 5.2E+03 9.2E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 0.52 0.77 91.63 7.5E+03 9.4E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

41 

42 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-25 —DO NOT CITE OR QUOTE 

1 F.1.10.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.10.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_thy_ad.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_thy_ad.plt 

12 Mon Nov 23 15:45:17 2009 

13 ==================================================================== 

14 

15 Source - Table 10 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:45 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-26 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.0282954 

10 Beta(1) = 6.36609e-006 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.54 

18 

19 Beta(1) -0.54 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.0332349 * * * 

28 Beta(1) 5.46313e-006 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -43.5264 4 

38 Fitted model -44.2066 2 1.36031 2 0.5065 

39 Reduced model -46.2299 1 5.40699 3 0.1443 

40 

41 AIC: 92.4132 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0332 2.426 3.000 73 0.375 

49 1072.2652 0.0389 1.750 2.000 45 0.193 

50 3111.2349 0.0495 2.427 1.000 49 -0.939 

51 16207.0000 0.1152 5.412 6.000 47 0.269 

52 

53 Chi^2 = 1.13 d.f. = 2 P-value = 0.5677 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 1839.67 

65 

66 BMDL = 846.279 

67 

68 BMDU = 11586.6 

69 

70 Taken together, (846.279, 11586.6) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-27 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 1.18164e-005 

4 

5 

6 F.1.11. National Toxicology Program (1982): Male Rat, Liver, Neoplastic Nodule or 

7 Hepatocellular Carcinoma 

8 F.1.11.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.80 0.22 135.20 6.4E+02 4.0E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.13 0.49 133.45 3.0E+03 4.8E+02 betas restricted ≥0 

<ultistage 

cancer, 

3-degree 

3 0.02 0.24 135.44 3.9E+03 4.8E+02 betas restricted ≥0 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-28 —DO NOT CITE OR QUOTE 

1 F.1.11.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.11.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_liver_nod.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_liver_nod.plt 

12 Mon Nov 23 15:45:38 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:45 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-29 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0 

10 Beta(1) = 4.03747e-006 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(1) 

20 

21 Beta(1) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 3.00492e-006 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -11.3484 4 

40 Fitted model -12.0545 1 1.41226 3 0.7027 

41 Reduced model -15.9189 1 9.14109 3 0.02747 

42 

43 AIC: 26.109 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0000 0.000 0.000 74 0.000 

51 1071.8576 0.0032 0.161 0.000 50 -0.402 

52 3115.7313 0.0093 0.466 0.000 50 -0.686 

53 16272.0000 0.0477 2.386 3.000 50 0.407 

54 

55 Chi^2 = 0.80 d.f. = 3 P-value = 0.8501 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.01 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 3344.63 

67 

68 BMDL = 1472.42 

69 

70 BMDU = 10322.4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-30 —DO NOT CITE OR QUOTE 

1 

2 Taken together, (1472.42, 10322.4) is a 90 % two-sided confidence 

3 interval for the BMD 

4 

5 Multistage Cancer Slope Factor = 6.79156e-006 

6 

7 

8 F.1.12. National Toxicology Program (1982): Male Ra, Thyroid, Follicular-Cell Adenoma 

9 or Carcinoma 

10 F.1.12.1. Summary Table of BMDS Modeling Results 

11 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 5.73 0.06 149.25 6.6E+02 3.8E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 5.73 0.06 149.25 6.6E+02 3.8E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 5.73 0.06 149.25 6.6E+02 3.8E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-31 —DO NOT CITE OR QUOTE 

1 F.1.12.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.12.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_thyroid.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_thyroid.plt 

12 Mon Nov 23 15:45:59 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:45 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-32 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.0767848 

10 Beta(1) = 1.11362e-005 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.62 

18 

19 Beta(1) -0.62 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.0527729 * * * 

28 Beta(1) 1.52871e-005 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -69.5946 4 

38 Fitted model -72.6245 2 6.05993 2 0.04832 

39 Reduced model -77.5267 1 15.8643 3 0.001209 

40 

41 AIC: 149.249 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0528 3.641 1.000 69 -1.422 

49 1071.8576 0.0682 3.272 5.000 48 0.990 

50 3115.7313 0.0968 4.842 8.000 50 1.510 

51 16272.0000 0.2614 13.069 11.000 50 -0.666 

52 

53 Chi^2 = 5.73 d.f. = 2 P-value = 0.0571 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 657.439 

65 

66 BMDL = 380.166 

67 

68 BMDU = 1571.51 

69 

70 Taken together, (380.166, 1571.51) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-33 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 2.63043e-005 

4 

5 

6 F.1.13. National Toxicology Program (1982): Male Rat, Adrenal Cortex, Adenoma 

7 F.1.13.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 5.55 0.06 199.31 2.2E+03 6.7E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 5.55 0.06 199.31 2.2E+03 6.7E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 5.55 0.06 199.31 2.2E+03 6.7E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-34 —DO NOT CITE OR QUOTE 

1 F.1.13.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.13.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adre_cort.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adre_cort.plt 

12 Mon Nov 23 15:46:20 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:46 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-35 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.16365 

9 Beta(1) = 2.66257e-006 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.61 

17 

18 Beta(1) -0.61 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.146024 * * * 

27 Beta(1) 4.6499e-006 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -94.8672 4 

37 Fitted model -97.6531 2 5.57181 2 0.06167 

38 Reduced model -98.0432 1 6.35197 3 0.09569 

39 

40 AIC: 199.306 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.1460 10.514 6.000 72 -1.506 

48 1071.8576 0.1503 7.513 9.000 50 0.588 

49 3115.7313 0.1583 7.757 12.000 49 1.661 

50 16272.0000 0.2083 10.204 9.000 49 -0.424 

51 

52 Chi^2 = 5.55 d.f. = 2 P-value = 0.0623 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 2161.41 

64 

65 BMDL = 665.411 

66 

67 

68 BMDU did not converge for BMR = 0.010000 

69 BMDU calculation failed 

70 BMDU = Inf 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-36 —DO NOT CITE OR QUOTE 

1 

2 

3 F.1.14. National Toxicology Program (1982): Female Mice, Subcutaneous Tissue, 

4 Fibrosarcoma 

5 F.1.14.1. Summary Table of BMDS Modeling Results 

6 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistag

e cancer, 

1-degreeb

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

7 

8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-37 —DO NOT CITE OR QUOTE 

1 F.1.14.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.14.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_subcu_fibro.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_subcu_fibro.plt 

12 Mon Nov 23 15:46:40 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:46 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-38 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.0104441 

10 Beta(1) = 5.78849e-006 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.55 

18 

19 Beta(1) -0.55 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.0124215 * * * 

28 Beta(1) 5.43453e-006 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -30.9876 4 

38 Fitted model -31.0699 2 0.16463 2 0.921 

39 Reduced model -34.3291 1 6.68308 3 0.08272 

40 

41 AIC: 66.1398 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0124 0.919 1.000 74 0.085 

49 1063.6377 0.0181 0.906 1.000 50 0.100 

50 3184.3353 0.0294 1.410 1.000 48 -0.350 

51 17406.0000 0.1016 4.773 5.000 47 0.110 

52 

53 Chi^2 = 0.15 d.f. = 2 P-value = 0.9269 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 1849.35 

65 

66 BMDL = 916.028 

67 

68 BMDU = 6164.32 

69 

70 Taken together, (916.028, 6164.32) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-39 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 1.09167e-005 

4 

5 

6 F.1.15. National Toxicology Program (1982): Female Mice, Hematopoietic System, 

7 Lymphoma 

8 F.1.15.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistag

e cancer, 

1-degreeb

2 0.05 0.98 261.45 6.2E+02 3.3E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

1 0.03 0.87 263.43 9.3E+02 3.3E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

1 0.03 0.87 263.43 9.3E+02 3.3E+02 betas restricted ≥0 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-40 —DO NOT CITE OR QUOTE 

1 F.1.15.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.15.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_f_lymphoma.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_f_lymphoma.plt 

12 Mon Nov 23 15:47:00 2009 

13 ==================================================================== 

14 

15 Table 15 page 64 Hematopoietic System Lymphoma or Leukemia 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:47 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-41 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.234156 

10 Beta(1) = 1.645e-005 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.54 

18 

19 Beta(1) -0.54 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.236108 * * * 

28 Beta(1) 1.61681e-005 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -128.699 4 

38 Fitted model -128.723 2 0.0471776 2 0.9767 

39 Reduced model -131.412 1 5.42487 3 0.1432 

40 

41 AIC: 261.446 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.2361 17.472 18.000 74 0.145 

49 1063.6377 0.2491 12.457 12.000 50 -0.149 

50 3184.3353 0.2744 13.173 13.000 48 -0.056 

51 17406.0000 0.4235 19.904 20.000 47 0.028 

52 

53 Chi^2 = 0.05 d.f. = 2 P-value = 0.9767 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 621.617 

65 

66 BMDL = 330.742 

67 

68 BMDU = 2332.7 

69 

70 Taken together, (330.742, 2332.7 ) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-42 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 3.0235e-005 

4 

5 

6 F.1.16. National Toxicology Program (1982): Female Mice, Liver, Hepatocellular 

7 Adenoma or Carcinoma 

8 F.1.16.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 2.15 0.34 155.21 8.1E+02 4.5E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 2.15 0.34 155.21 8.1E+02 4.5E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 2.15 0.34 155.21 8.1E+02 4.5E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-43 —DO NOT CITE OR QUOTE 

1 F.1.16.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 F.1.16.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

5 

6 

7 ==================================================================== 

8 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

9 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_f_liv_aden_carc.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_f_liv_aden_carc.plt 

11 Mon Nov 23 15:47:20 2009 

12 ==================================================================== 

13 

14 0 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the probability function is: 

18 

19 P[response] = background + (1-background)*[1-EXP( 

20 -beta1*dose^1)] 

21 

22 The parameter betas are restricted to be positive 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 

28 Total number of observations = 4 

29 Total number of records with missing values = 0 

30 Total number of parameters in model = 2 

31 Total number of specified parameters = 0 

32 Degree of polynomial = 1 

33 

34 

35 Maximum number of iterations = 250 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:47 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-44 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 Background = 0.0808715 

8 Beta(1) = 1.07435e-005 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 Background Beta(1) 

14 

15 Background 1 -0.57 

16 

17 Beta(1) -0.57 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 Background 0.0691337 * * * 

26 Beta(1) 1.24516e-005 * * * 

27 

28 * - Indicates that this value is not calculated. 

29 

30 

31 

32 Analysis of Deviance Table 

33 

34 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

35 Full model -74.5177 4 

36 Fitted model -75.603 2 2.17074 2 0.3378 

37 Reduced model -79.6703 1 10.3053 3 0.01614 

38 

39 AIC: 155.206 

40 

41 

42 Goodness of Fit 

43 Scaled 

44 Dose Est._Prob. Expected Observed Size Residual 

45 ------------------------------------------------------------------------ 

46 0.0000 0.0691 5.047 3.000 73 -0.944 

47 1063.6377 0.0814 4.069 6.000 50 0.999 

48 3184.3353 0.1053 5.055 6.000 48 0.444 

49 17406.0000 0.2505 11.774 11.000 47 -0.261 

50 

51 Chi^2 = 2.15 d.f. = 2 P-value = 0.3405 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 0.01 

57 

58 Risk Type = Extra risk 

59 

60 Confidence level = 0.95 

61 

62 BMD = 807.155 

63 

64 BMDL = 448.599 

65 

66 BMDU = 2161.58 

67 

68 Taken together, (448.599, 2161.58) is a 90 % two-sided confidence 

69 interval for the BMD 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-45 —DO NOT CITE OR QUOTE 

1 Multistage Cancer Slope Factor = 2.22916e-005 

2 

3 

4 F.1.17. National Toxicology Program (1982): Female Mice, Thyroid, Follicular-Cell 

5 Adenoma 

6 F.1.17.1. Summary Table of BMDS Modeling Results 

7 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.44 0.18 75.38 1.7E+03 7.5E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

8 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-46 —DO NOT CITE OR QUOTE 

1 F.1.17.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.17.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_f_thyroid_aden.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_f_thyroid_aden.plt 

12 Mon Nov 23 15:47:40 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:47 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-47 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.0202008 

10 Beta(1) = 5.39488e-006 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.58 

18 

19 Beta(1) -0.58 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.0152512 * * * 

28 Beta(1) 6.07986e-006 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -32.0017 4 

38 Fitted model -34.3878 2 4.77223 2 0.09199 

39 Reduced model -37.2405 1 10.4776 3 0.01491 

40 

41 AIC: 72.7756 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0153 1.052 0.000 69 -1.034 

49 1063.6377 0.0216 1.080 3.000 50 1.868 

50 3184.3353 0.0341 1.604 1.000 47 -0.485 

51 17406.0000 0.1141 5.250 5.000 46 -0.116 

52 

53 Chi^2 = 4.81 d.f. = 2 P-value = 0.0904 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 1653.05 

65 

66 BMDL = 778.784 

67 

68 BMDU = 6460.82 

69 

70 Taken together, (778.784, 6460.82) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-48 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 1.28405e-005 

4 

5 

6 F.1.18. National Toxicology Program (1982): Male Mice, Lung, Alveolar/Bronchiolar 

7 Adenoma or Carcinoma 

8 F.1.18.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degree 

2 4.87 0.09 168.35 3.5E+02 1.9E+02 betas restricted ≥0 

Multistag

e cancer, 

2-degreeb

2 3.58 0.17 166.95 1.4E+03 2.3E+02 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.41 0.18 166.80 2.3E+03 2.3E+02 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-49 —DO NOT CITE OR QUOTE 

1 F.1.18.2. Figure for Selected Model: Multistage Cancer, 2-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.18.3. Output File for Selected Model: Multistage Cancer, 2-Degree, Betas Restricted ≥0

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc2_ngkgd_lung_aden_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc2_ngkgd_lung_aden_carc.plt 

12 Mon Nov 23 15:48:02 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 3 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 2 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 1000 2000 3000 4000 5000 6000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:48 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-50 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.086839 

10 Beta(1) = 0 

11 Beta(2) = 5.59843e-009 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 ( *** The model parameter(s) -Beta(1) 

17 have been estimated at a boundary point, or have been specified by the user, 

18 and do not appear in the correlation matrix ) 

19 

20 Background Beta(2) 

21 

22 Background 1 -0.46 

23 

24 Beta(2) -0.46 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 95.0% Wald Confidence Interval 

31 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

32 Background 0.0942375 * * * 

33 Beta(1) 0 * * * 

34 Beta(2) 5.31152e-009 * * * 

35 

36 * - Indicates that this value is not calculated. 

37 

38 

39 

40 Analysis of Deviance Table 

41 

42 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

43 Full model -79.5959 4 

44 Fitted model -81.4737 2 3.75561 2 0.1529 

45 Reduced model -85.3351 1 11.4782 3 0.009402 

46 

47 AIC: 166.947 

48 

49 

50 Goodness of Fit 

51 Scaled 

52 Dose Est._Prob. Expected Observed Size Residual 

53 ------------------------------------------------------------------------ 

54 0.0000 0.0942 6.691 10.000 71 1.344 

55 420.0366 0.0951 4.564 2.000 48 -1.262 

56 1239.6134 0.1016 4.877 4.000 48 -0.419 

57 6117.5662 0.2575 12.876 13.000 50 0.040 

58 

59 Chi^2 = 3.58 d.f. = 2 P-value = 0.1673 

60 

61 

62 Benchmark Dose Computation 

63 

64 Specified effect = 0.01 

65 

66 Risk Type = Extra risk 

67 

68 Confidence level = 0.95 

69 

70 BMD = 1375.56 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-51 —DO NOT CITE OR QUOTE 

1 

2 BMDL = 225.385 

3 

4 BMDU = 2284.92 

5 

6 Taken together, (225.385, 2284.92) is a 90 % two-sided confidence 

7 interval for the BMD 

8 

9 Multistage Cancer Slope Factor = 4.43686e-005 

10 

11 

12 F.1.19. National Toxicology Program (1982): Male Mice, Liver, Hepatocellular Adenoma 

13 or Carcinoma 

14 F.1.19.1. Summary Table of BMDS Modeling Results 

15 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 0.15 0.93 258.55 1.1E+02 7.5E+01 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

1 0.08 0.78 260.48 1.7E+02 7.5E+01 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

1 0.07 0.79 260.47 1.6E+02 7.5E+01 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

16 

17 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-52 —DO NOT CITE OR QUOTE 

1 F.1.19.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.19.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_m_liver_aden_carc.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_mice_m_liver_aden_carc.plt 

13 Mon Nov 23 15:48:23 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the probability function is: 

20 

21 P[response] = background + (1-background)*[1-EXP( 

22 -beta1*dose^1)] 

23 

24 The parameter betas are restricted to be positive 

25 

26 

27 Dependent variable = Mean 

28 Independent variable = Dose 

29 

30 Total number of observations = 4 

31 Total number of records with missing values = 0 

32 Total number of parameters in model = 2 

33 Total number of specified parameters = 0 

34 Degree of polynomial = 1 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 1000 2000 3000 4000 5000 6000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:48 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-53 —DO NOT CITE OR QUOTE 

1 

2 

3 Maximum number of iterations = 250 

4 Relative Function Convergence has been set to: 1e-008 

5 Parameter Convergence has been set to: 1e-008 

6 

7 

8 

9 Default Initial Parameter Values 

10 Background = 0.201516 

11 Beta(1) = 8.94392e-005 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 Background Beta(1) 

17 

18 Background 1 -0.53 

19 

20 Beta(1) -0.53 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0.204153 * * * 

29 Beta(1) 8.75513e-005 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -127.199 4 

39 Fitted model -127.274 2 0.151061 2 0.9273 

40 Reduced model -135.589 1 16.7801 3 0.0007843 

41 

42 AIC: 258.549 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.2042 14.903 15.000 73 0.028 

50 420.0366 0.2329 11.412 12.000 49 0.199 

51 1239.6134 0.2860 14.014 13.000 49 -0.321 

52 6117.5662 0.5342 26.709 27.000 50 0.083 

53 

54 Chi^2 = 0.15 d.f. = 2 P-value = 0.9278 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 114.794 

66 

67 BMDL = 74.9717 

68 

69 BMDU = 208.915 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-54 —DO NOT CITE OR QUOTE 

1 Taken together, (74.9717, 208.915) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 0.000133384 

5 

6 

7 F.1.20. National Toxicology Program (2006): Liver, Cholangiocarcinoma 

8 F.1.20.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degree 

5 20.87 0.00 138.46 5.2E+02 3.9E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

5 5.09 0.40 119.37 2.3E+03 1.6E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degreeb

5 0.47 0.99 113.51 4.2E+03 2.3E+03 betas restricted ≥0 

a

 Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-55 —DO NOT CITE OR QUOTE 

1 F.1.20.2. Figure for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.20.3. Output File for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc3_ngkgd_liv_cho-carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc3_ngkgd_liv_cho-carc.plt 

12 Mon Nov 23 15:48:43 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2-beta3*dose^3)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 4 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 3 

34 

35 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:48 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-56 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0 

10 Beta(2) = 0 

11 Beta(3) = 1.46324e-013 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 ( *** The model parameter(s) -Background -Beta(1) -Beta(2) 

17 have been estimated at a boundary point, or have been specified by the user, 

18 and do not appear in the correlation matrix ) 

19 

20 Beta(3) 

21 

22 Beta(3) 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 Background 0 * * * 

31 Beta(1) 0 * * * 

32 Beta(2) 0 * * * 

33 Beta(3) 1.38296e-013 * * * 

34 

35 * - Indicates that this value is not calculated. 

36 

37 

38 

39 Analysis of Deviance Table 

40 

41 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

42 Full model -55.408 6 

43 Fitted model -55.7539 1 0.691685 5 0.9834 

44 Reduced model -96.9934 1 83.1708 5 <.0001 

45 

46 AIC: 113.508 

47 

48 

49 Goodness of Fit 

50 Scaled 

51 Dose Est._Prob. Expected Observed Size Residual 

52 ------------------------------------------------------------------------ 

53 0.0000 0.0000 0.000 0.000 49 0.000 

54 1408.4504 0.0004 0.019 0.000 48 -0.136 

55 3137.0446 0.0043 0.196 0.000 46 -0.444 

56 5392.9593 0.0215 1.073 1.000 50 -0.071 

57 9128.8027 0.0999 4.893 4.000 49 -0.426 

58 16361.0000 0.4543 24.078 25.000 53 0.254 

59 

60 Chi^2 = 0.47 d.f. = 5 P-value = 0.9933 

61 

62 

63 Benchmark Dose Computation 

64 

65 Specified effect = 0.01 

66 

67 Risk Type = Extra risk 

68 

69 Confidence level = 0.95 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-57 —DO NOT CITE OR QUOTE 

1 BMD = 4173.08 

2 

3 BMDL = 2277.15 

4 

5 BMDU = 4642.18 

6 

7 Taken together, (2277.15, 4642.18) is a 90 % two-sided confidence 

8 interval for the BMD 

9 

10 Multistage Cancer Slope Factor = 4.39145e-006 

11 

12 

13 F.1.21. National Toxicology Program (2006): Liver, Hepatocellular Adenoma 

14 F.1.21.1. Summary Table of BMDS Modeling Results 

15 

Model Degrees of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) 

Model 

Notes 

Multistage 

cancer, 

1-degree 

5 12.73 0.03 87.02 1.2E+03 8.0E+02 

betas 

restricted 

≥0 

Multistage 

cancer, 

2-degree 

5 4.29 0.51 76.98 3.6E+03 2.4E+03 

betas 

restricted 

≥0 

Multistag

e cancer, 

3-degreeb

5 1.32 0.93 72.78 5.6E+03 3.6E+03 

betas 

restricted 

≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

16 

17 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-58 —DO NOT CITE OR QUOTE 

1 F.1.21.2. Figure for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.21.3. Output File for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc3_ngkgd_liv_hepat_ad.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc3_ngkgd_liv_hepat_ad.plt 

12 Mon Nov 23 15:49:03 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2-beta3*dose^3)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 4 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 3 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:49 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-59 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0 

10 Beta(2) = 0 

11 Beta(3) = 6.51095e-014 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 ( *** The model parameter(s) -Background -Beta(1) -Beta(2) 

17 have been estimated at a boundary point, or have been specified by the user, 

18 and do not appear in the correlation matrix ) 

19 

20 Beta(3) 

21 

22 Beta(3) 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 Background 0 * * * 

31 Beta(1) 0 * * * 

32 Beta(2) 0 * * * 

33 Beta(3) 5.62766e-014 * * * 

34 

35 * - Indicates that this value is not calculated. 

36 

37 

38 

39 Analysis of Deviance Table 

40 

41 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

42 Full model -34.4075 6 

43 Fitted model -35.3908 1 1.96651 5 0.8538 

44 Reduced model -56.3333 1 43.8515 5 <.0001 

45 

46 AIC: 72.7815 

47 

48 

49 Goodness of Fit 

50 Scaled 

51 Dose Est._Prob. Expected Observed Size Residual 

52 ------------------------------------------------------------------------ 

53 0.0000 0.0000 0.000 0.000 49 0.000 

54 1408.4504 0.0002 0.008 0.000 48 -0.087 

55 3137.0446 0.0017 0.080 0.000 46 -0.283 

56 5392.9593 0.0088 0.439 0.000 50 -0.666 

57 9128.8027 0.0419 2.054 1.000 49 -0.751 

58 16361.0000 0.2184 11.577 13.000 53 0.473 

59 

60 Chi^2 = 1.32 d.f. = 5 P-value = 0.9330 

61 

62 

63 Benchmark Dose Computation 

64 

65 Specified effect = 0.01 

66 

67 Risk Type = Extra risk 

68 

69 Confidence level = 0.95 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-60 —DO NOT CITE OR QUOTE 

1 BMD = 5631.42 

2 

3 BMDL = 3596.03 

4 

5 BMDU = 6597.97 

6 

7 Taken together, (3596.03, 6597.97) is a 90 % two-sided confidence 

8 interval for the BMD 

9 

10 Multistage Cancer Slope Factor = 2.78084e-006 

11 

12 

13 F.1.22. National Toxicology Program (2006): Oral mucosa, Squamous Cell Carcinoma 

14 F.1.22.1. Summary Table of BMDS Modeling Results 

15 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) 

Model Notes 

Multistage 

cancer, 1-degree 4 4.15 0.39 125.48 4.8E+00 3.0E+00 betas restricted ≥0 

Multistage cancer, 

2-degreeb 4 2.83 0.59 123.25 1.6E+01 3.8E+00 betas restricted ≥0, bound hit 

Multistage cancer, 

3-degree 4 2.83 0.59 123.25 1.6E+01 3.8E+00 betas restricted ≥0, bound hit 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

16 

17 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-61 —DO NOT CITE OR QUOTE 

1 F.1.22.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0, 

2 Bound Hit 

3 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:11 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation

4 

5 

6 

7 F.1.22.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0, 

8 Bound Hit 

9 

10 

11 ==================================================================== 

12 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

13 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_oral_carc.(d) 

14 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_oral_carc.plt 

15 Mon Nov 23 15:11:37 2009 

16 ==================================================================== 

17 

18 0 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the probability function is: 

22 

23 P[response] = background + (1-background)*[1-EXP( 

24 -beta1*dose^1)] 

25 

26 The parameter betas are restricted to be positive 

27 

28 

29 Dependent variable = Mean 

30 Independent variable = Dose 

31 

32 Total number of observations = 6 

33 Total number of records with missing values = 0 

34 Total number of parameters in model = 2 

35 Total number of specified parameters = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-62 —DO NOT CITE OR QUOTE 

1 Degree of polynomial = 1 

2 

3 

4 Maximum number of iterations = 250 

5 Relative Function Convergence has been set to: 1e-008 

6 Parameter Convergence has been set to: 1e-008 

7 

8 

9 

10 Default Initial Parameter Values 

11 Background = 0.00607545 

12 Beta(1) = 0.00265195 

13 

14 

15 Asymptotic Correlation Matrix of Parameter Estimates 

16 

17 Background Beta(1) 

18 

19 Background 1 -0.6 

20 

21 Beta(1) -0.6 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0.0171416 * * * 

30 Beta(1) 0.00211536 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -57.5353 6 

40 Fitted model -60.7418 2 6.41293 4 0.1704 

41 Reduced model -67.7782 1 20.4858 5 0.001013 

42 

43 AIC: 125.484 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0171 0.840 1.000 49 0.176 

51 2.1400 0.0216 1.036 2.000 48 0.958 

52 7.1400 0.0319 1.466 1.000 46 -0.391 

53 15.7000 0.0492 2.462 0.000 50 -1.609 

54 32.9000 0.0832 4.078 4.000 49 -0.040 

55 71.4000 0.1549 8.211 10.000 53 0.679 

56 

57 Chi^2 = 4.15 d.f. = 4 P-value = 0.3855 

58 

59 

60 Benchmark Dose Computation 

61 

62 Specified effect = 0.01 

63 

64 Risk Type = Extra risk 

65 

66 Confidence level = 0.95 

67 

68 BMD = 4.75111 

69 

70 BMDL = 2.9556 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-63 —DO NOT CITE OR QUOTE 

1 

2 BMDU = 9.19454 

3 

4 Taken together, (2.9556 , 9.19454) is a 90 % two-sided confidence 

5 interval for the BMD 

6 

7 Multistage Cancer Slope Factor = 0.0033834 

8 

9 

10 F.1.23. National Toxicology Program (2006): Pancreas, Adenoma or Carcinoma 

11 F.1.23.1. Summary Table of BMDS Modeling Results 

12 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

5 3.39 0.64 29.37 5.8E+03 2.6E+03 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

5 1.36 0.93 27.06 8.0E+03 4.0E+03 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

5 0.64 0.99 25.97 9.6E+03 5.2E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

13 

14 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-64 —DO NOT CITE OR QUOTE 

1 F.1.23.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.23.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_panc_ad_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_panc_ad_carc.plt 

12 Mon Nov 23 15:49:45 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:49 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-65 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 3.46905e-006 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 1.73461e-006 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -11.4096 6 

39 Fitted model -13.6863 1 4.55338 5 0.4728 

40 Reduced model -16.7086 1 10.598 5 0.05996 

41 

42 AIC: 29.3726 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 48 0.000 

50 1408.4504 0.0024 0.117 0.000 48 -0.343 

51 3137.0446 0.0054 0.250 0.000 46 -0.501 

52 5392.9593 0.0093 0.466 0.000 50 -0.686 

53 9128.8027 0.0157 0.754 0.000 48 -0.875 

54 16361.0000 0.0280 1.427 3.000 51 1.336 

55 

56 Chi^2 = 3.39 d.f. = 5 P-value = 0.6404 

57 

58 

59 Benchmark Dose Computation 

60 

61 Specified effect = 0.01 

62 

63 Risk Type = Extra risk 

64 

65 Confidence level = 0.95 

66 

67 BMD = 5794 

68 

69 BMDL = 2550.9 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-66 —DO NOT CITE OR QUOTE 

1 BMDU = 18101.1 

2 

3 Taken together, (2550.9 , 18101.1) is a 90 % two-sided confidence 

4 interval for the BMD 

5 

6 Multistage Cancer Slope Factor = 3.92019e-006 

7 

8 

9 F.1.24. National Toxicology Program (2006): Lung, Cystic Keratinizing Epithelioma 

10 F.1.24.1. Summary Table of BMDS Modeling Results 

11 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degree 

5 10.52 0.06 64.03 1.9E+03 1.1E+03 betas restricted ≥0 

Multistage 

cancer, 

2-degreeb

5 4.30 0.51 56.94 4.6E+03 2.9E+03 betas restricted 

≥0 

Multistage 

cancer, 

3-degree 

5 2.03 0.84 53.56 6.6E+03 4.3E+03 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

12 

13 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-67 —DO NOT CITE OR QUOTE 

1 F.1.24.2. Figure for Selected Model: Multistage Cancer, 2-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.24.3. Output File for Selected Model: Multistage Cancer, 2-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc2_ngkgd_lung_epith.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc2_ngkgd_lung_epith.plt 

12 Mon Nov 23 15:50:07 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 3 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 2 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0 2000 4000 6000 8000 10000 12000 14000 16000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:50 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-68 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0 

10 Beta(2) = 7.12912e-010 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background -Beta(1) 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(2) 

20 

21 Beta(2) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 0 * * * 

31 Beta(2) 4.80115e-010 * * * 

32 

33 * - Indicates that this value is not calculated. 

34 

35 

36 

37 Analysis of Deviance Table 

38 

39 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

40 Full model -23.958 6 

41 Fitted model -27.4714 1 7.02665 5 0.2187 

42 Reduced model -40.2069 1 32.4976 5 <.0001 

43 

44 AIC: 56.9427 

45 

46 

47 Goodness of Fit 

48 Scaled 

49 Dose Est._Prob. Expected Observed Size Residual 

50 ------------------------------------------------------------------------ 

51 0.0000 0.0000 0.000 0.000 49 0.000 

52 1408.4504 0.0010 0.046 0.000 48 -0.214 

53 3137.0446 0.0047 0.217 0.000 46 -0.467 

54 5392.9593 0.0139 0.679 0.000 49 -0.830 

55 9128.8027 0.0392 1.922 0.000 49 -1.414 

56 16361.0000 0.1206 6.271 9.000 52 1.162 

57 

58 Chi^2 = 4.30 d.f. = 5 P-value = 0.5067 

59 

60 

61 Benchmark Dose Computation 

62 

63 Specified effect = 0.01 

64 

65 Risk Type = Extra risk 

66 

67 Confidence level = 0.95 

68 

69 BMD = 4575.28 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-69 —DO NOT CITE OR QUOTE 

1 BMDL = 2889.79 

2 

3 BMDU = 6187.18 

4 

5 Taken together, (2889.79, 6187.18) is a 90 % two-sided confidence 

6 interval for the BMD 

7 

8 Multistage Cancer Slope Factor = 3.46046e-006 

9 

10 

11 F.1.25. Toth et al. (1978): 1YR, Liver, Tumors 

12 F.1.25.1. Summary Table of BMDS Modeling Results 

13 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

1 1.10 0.29 155.74 2.0E+02 1.2E+02 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

1 1.10 0.29 155.74 2.0E+02 1.2E+02 betas restricted ≥0 

Multistage 

cancer, 

0-degree 

 0.29 -999.00 error error betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

14 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-70 —DO NOT CITE OR QUOTE 

1 F.1.25.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.1.25.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adr_cor_1yr.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\msc1_ngkgd_adr_cor_1yr.plt 

12 Mon Nov 23 17:29:16 2009 

13 ==================================================================== 

14 

15 Table 1 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 3 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 1000 2000 3000 4000 5000 6000 7000 8000

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

17:29 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-71 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.234944 

10 Beta(1) = 4.90901e-005 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.55 

18 

19 Beta(1) -0.55 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.235288 * * * 

28 Beta(1) 4.96192e-005 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -75.3127 3 

38 Fitted model -75.8701 2 1.11477 1 0.291 

39 Reduced model -79.4897 1 8.35401 2 0.01534 

40 

41 AIC: 155.74 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.2353 8.941 7.000 38 -0.742 

49 315.4949 0.2472 10.875 13.000 44 0.743 

50 7814.0188 0.4811 21.167 21.000 44 -0.050 

51 

52 Chi^2 = 1.10 d.f. = 1 P-value = 0.2932 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 202.549 

64 

65 BMDL = 115.257 

66 

67 BMDU = 555.609 

68 

69 Taken together, (115.257, 555.609) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-72 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 8.67623e-005 

3 

4 

5 F.2. ADMINISTERED DOSE BMDS RESULTS 

6 F.2.1. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma of Hard Palate 

7 or Nasal Turbinates 

8 F.2.1.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.46 0.93 30.75 1.3E+01 6.5E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.04 1.00 29.96 3.5E+01 7.2E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.00 1.00 29.89 4.9E+01 7.3E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-73 —DO NOT CITE OR QUOTE 

1 F.2.1.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.1.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_palate_nasal.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_palate_nasal.plt 

12 Mon Nov 23 15:04:28 2009 

13 ==================================================================== 

14 

15 Source - Table 4 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:04 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-74 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0.000858074 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 0.00074801 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -13.9385 4 

39 Fitted model -14.3726 1 0.868297 3 0.8331 

40 Reduced model -20.2589 1 12.6409 3 0.005481 

41 

42 AIC: 30.7452 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 85 0.000 

50 1.0000 0.0007 0.037 0.000 50 -0.193 

51 10.0000 0.0075 0.373 0.000 50 -0.613 

52 100.0000 0.0721 3.604 4.000 50 0.217 

53 

54 Chi^2 = 0.46 d.f. = 3 P-value = 0.9276 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 13.4361 

66 

67 BMDL = 6.51522 

68 

69 BMDU = 34.829 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-75 —DO NOT CITE OR QUOTE 

1 Taken together, (6.51522, 34.829 ) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 0.00153487 

5 

6 

7 F.2.2. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma of Tongue 

8 F.2.2.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 1.59 0.45 48.37 1.7E+01 7.1E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 1.59 0.45 48.37 1.7E+01 7.1E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 1.59 0.45 48.37 1.7E+01 7.1E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-76 —DO NOT CITE OR QUOTE 

1 F.2.2.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.2.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_tongue.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_tongue.plt 

12 Mon Nov 23 15:04:49 2009 

13 ==================================================================== 

14 

15 Source - Table 4 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:04 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-77 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.0113883 

9 Beta(1) = 0.000508703 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.52 

17 

18 Beta(1) -0.52 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.00809154 * * * 

27 Beta(1) 0.000576915 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -21.1523 4 

37 Fitted model -22.1838 2 2.06309 2 0.3565 

38 Reduced model -24.1972 1 6.08976 3 0.1073 

39 

40 AIC: 48.3677 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0081 0.688 0.000 85 -0.833 

48 1.0000 0.0087 0.433 1.000 50 0.865 

49 10.0000 0.0138 0.690 1.000 50 0.376 

50 100.0000 0.0637 3.185 3.000 50 -0.107 

51 

52 Chi^2 = 1.59 d.f. = 2 P-value = 0.4506 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 17.4208 

64 

65 BMDL = 7.14637 

66 

67 BMDU = 3.20359e+006 

68 

69 Taken together, (7.14637, 3.20359e+006) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-78 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.00139931 

3 

4 

5 F.2.3. Kociba et al. (1978): Female. Adenoma of Adrenal Cortex 

6 F.2.3.1. Summary Table of BMDS Modeling Results 

7 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 3.11 0.38 53.52 7.6E+00 4.3E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 3.11 0.38 53.52 7.6E+00 4.3E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 3.11 0.38 53.52 7.6E+00 4.3E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

8 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-79 —DO NOT CITE OR QUOTE 

1 F.2.3.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.3.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adre_adenoma.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adre_adenoma.plt 

12 Mon Nov 23 15:05:10 2009 

13 ==================================================================== 

14 

15 Source - Table 5 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:05 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-80 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.00927818 

9 Beta(1) = 0.00098105 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 0.00132464 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -24.6514 4 

39 Fitted model -25.759 1 2.2152 3 0.529 

40 Reduced model -31.4904 1 13.6781 3 0.003378 

41 

42 AIC: 53.5179 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 85 0.000 

50 1.0000 0.0013 0.066 0.000 50 -0.257 

51 10.0000 0.0132 0.658 2.000 50 1.666 

52 100.0000 0.1241 6.203 5.000 50 -0.516 

53 

54 Chi^2 = 3.11 d.f. = 3 P-value = 0.3755 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 7.58722 

66 

67 BMDL = 4.31737 

68 

69 BMDU = 17.638 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-81 —DO NOT CITE OR QUOTE 

1 Taken together, (4.31737, 17.638 ) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 0.00231623 

5 

6 

7 F.2.4. Kociba et al. (1978): Female, Hepatocellular Adenoma(S) or Carcinoma(s) 

8 F.2.4.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 6.77 0.03 146.20 1.8E+00 1.2E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 6.77 0.03 146.20 1.8E+00 1.2E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 6.77 0.03 146.20 1.8E+00 1.2E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-82 —DO NOT CITE OR QUOTE 

1 F.2.4.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.4.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_liver_ad_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_liver_ad_carc.plt 

12 Mon Nov 23 15:05:31 2009 

13 ==================================================================== 

14 

15 Source - Table 1 in Goodman and Sauer 1992 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:05 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-83 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.0591902 

9 Beta(1) = 0.00458516 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.47 

17 

18 Beta(1) -0.47 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.0328755 * * * 

27 Beta(1) 0.00568299 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -68.2561 4 

37 Fitted model -71.0993 2 5.68634 2 0.05824 

38 Reduced model -89.1983 1 41.8843 3 <.0001 

39 

40 AIC: 146.199 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0329 2.827 2.000 86 -0.500 

48 1.0000 0.0384 1.918 1.000 50 -0.676 

49 10.0000 0.0863 4.315 9.000 50 2.359 

50 100.0000 0.4521 20.346 18.000 45 -0.703 

51 

52 Chi^2 = 6.77 d.f. = 2 P-value = 0.0339 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 1.7685 

64 

65 BMDL = 1.22517 

66 

67 BMDU = 2.77641 

68 

69 Taken together, (1.22517, 2.77641) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-84 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.00816214 

3 

4 

5 F.2.5. Kociba et al. (1978): Female, Stratified Squamous Cell Carcinoma of Hard Palate 

6 or Nasal Turbinates 

7 F.2.5.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.46 0.93 30.75 1.3E+01 6.5E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.04 1.00 29.96 3.5E+01 7.2E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.00 1.00 29.89 4.9E+01 7.3E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-85 —DO NOT CITE OR QUOTE 

1 F.2.5.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.5.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_nasal.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_nasal.plt 

12 Mon Nov 23 15:05:50 2009 

13 ==================================================================== 

14 

15 Source - Table 5 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:05 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-86 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.00343283 

10 Beta(1) = 0.000825276 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(1) 

20 

21 Beta(1) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 0.000953868 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -18.7562 4 

40 Fitted model -19.0532 1 0.594034 3 0.8978 

41 Reduced model -24.1972 1 10.882 3 0.01238 

42 

43 AIC: 40.1064 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0000 0.000 0.000 86 0.000 

51 1.0000 0.0010 0.048 0.000 50 -0.218 

52 10.0000 0.0095 0.475 1.000 50 0.766 

53 100.0000 0.0910 4.458 4.000 49 -0.227 

54 

55 Chi^2 = 0.69 d.f. = 3 P-value = 0.8764 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.01 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 10.5364 

67 

68 BMDL = 5.46907 

69 

70 BMDU = 25.864 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-87 —DO NOT CITE OR QUOTE 

1 

2 Taken together, (5.46907, 25.864 ) is a 90 % two-sided confidence 

3 interval for the BMD 

4 

5 Multistage Cancer Slope Factor = 0.00182846 

6 

7 

8 F.2.6. Kociba et al. (1978): Female, Keratinizing Squamous Cell Carcinoma of Lung 

9 F.2.6.1. Summary Table of BMDS Modeling Results 

10 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.85 0.84 43.79 7.3E+00 4.2E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.08 0.99 42.35 2.6E+01 4.9E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.01 1.00 42.21 4.0E+01 5.0E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

11 

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-88 —DO NOT CITE OR QUOTE 

1 F.2.6.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.6.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_kera_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_kera_carc.plt 

12 Mon Nov 23 15:06:12 2009 

13 ==================================================================== 

14 

15 Source - Table 5 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:06 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-89 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0.00158635 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 0.0013747 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -20.0957 4 

39 Fitted model -20.8959 1 1.60041 3 0.6593 

40 Reduced model -31.4904 1 22.7894 3 <.0001 

41 

42 AIC: 43.7918 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 86 0.000 

50 1.0000 0.0014 0.069 0.000 50 -0.262 

51 10.0000 0.0137 0.683 0.000 50 -0.832 

52 100.0000 0.1284 6.294 7.000 49 0.302 

53 

54 Chi^2 = 0.85 d.f. = 3 P-value = 0.8370 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 7.31091 

66 

67 BMDL = 4.15929 

68 

69 BMDU = 14.6306 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-90 —DO NOT CITE OR QUOTE 

1 Taken together, (4.15929, 14.6306) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 0.00240426 

5 

6 

7 F.2.7. National Toxicology Program (1982): Female Rats, Subcutaneous Tissue, 

8 Fibrosarcoma 

9 F.2.7.1. Summary Table of BMDS Modeling Results 

10 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

11 

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-91 —DO NOT CITE OR QUOTE 

1 F.2.7.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.7.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_sub_fibro.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_sub_fibro.plt 

12 Mon Nov 23 15:06:33 2009 

13 ==================================================================== 

14 

15 Source - Table 10 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:06 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-92 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.030595 

9 Beta(1) = 0.000799545 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.54 

17 

18 Beta(1) -0.54 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.0231556 * * * 

27 Beta(1) 0.00102962 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -33.5998 4 

37 Fitted model -36.1883 2 5.17698 2 0.07513 

38 Reduced model -37.7465 1 8.29346 3 0.04032 

39 

40 AIC: 76.3766 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0232 1.737 0.000 75 -1.333 

48 1.4000 0.0246 1.228 2.000 50 0.705 

49 7.1000 0.0303 1.514 3.000 50 1.227 

50 71.0000 0.0920 4.509 4.000 49 -0.252 

51 

52 Chi^2 = 3.84 d.f. = 2 P-value = 0.1463 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 9.76124 

64 

65 BMDL = 3.96354 

66 

67 BMDU = 1.03301e+006 

68 

69 Taken together, (3.96354, 1.03301e+006) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-93 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.002523 

3 

4 

5 F.2.8. National Toxicology Program (1982): Female Rats, Liver, Neoplastic Nodule or 

6 Hepatocellular Carcinoma 

7 F.2.8.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.37 0.40 133.83 2.6E+00 1.6E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.03 0.50 133.44 1.3E+01 1.7E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.00 0.50 133.44 1.3E+01 1.7E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-94 —DO NOT CITE OR QUOTE 

1 F.2.8.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.8.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_liver_nod.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_liver_nod.plt 

12 Mon Nov 23 15:07:55 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:07 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-95 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0 

10 Beta(1) = 0.000900399 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(1) 

20 

21 Beta(1) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 0.000775683 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -11.3484 4 

40 Fitted model -11.6976 1 0.698469 3 0.8736 

41 Reduced model -15.9189 1 9.14109 3 0.02747 

42 

43 AIC: 25.3952 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0000 0.000 0.000 74 0.000 

51 1.4000 0.0011 0.054 0.000 50 -0.233 

52 7.1000 0.0055 0.275 0.000 50 -0.525 

53 71.0000 0.0536 2.679 3.000 50 0.201 

54 

55 Chi^2 = 0.37 d.f. = 3 P-value = 0.9462 

56 

57 

58 Benchmark Dose Computation 

59 

60 Specified effect = 0.01 

61 

62 Risk Type = Extra risk 

63 

64 Confidence level = 0.95 

65 

66 BMD = 12.9568 

67 

68 BMDL = 5.70369 

69 

70 BMDU = 39.9878 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-96 —DO NOT CITE OR QUOTE 

1 

2 Taken together, (5.70369, 39.9878) is a 90 % two-sided confidence 

3 interval for the BMD 

4 

5 Multistage Cancer Slope Factor = 0.00175325 

6 

7 

8 F.2.9. National Toxicology Program (1982): Female Rats, Adrenal, Cortical Adenoma, or 

9 Carcinoma or Adenoma, NOS 

10 F.2.9.1. Summary Table of BMDS Modeling Results 

11 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 1.81 0.40 203.38 3.7E+00 1.9E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 1.38 0.50 202.89 1.6E+01 2.0E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 1.33 0.51 202.83 2.6E+01 2.0E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

12 

13 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-97 —DO NOT CITE OR QUOTE 

1 F.2.9.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.9.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adre_cort_ad_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adre_cort_ad_carc.plt 

12 Mon Nov 23 15:07:15 2009 

13 ==================================================================== 

14 

15 Source - Table 10 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:07 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-98 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.140663 

9 Beta(1) = 0.00289845 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.48 

17 

18 Beta(1) -0.48 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.143284 * * * 

27 Beta(1) 0.00273674 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -98.7282 4 

37 Fitted model -99.6898 2 1.92318 2 0.3823 

38 Reduced model -102.201 1 6.94636 3 0.07363 

39 

40 AIC: 203.38 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.1433 10.460 11.000 73 0.180 

48 1.4000 0.1466 7.181 9.000 49 0.735 

49 7.1000 0.1598 7.829 5.000 49 -1.103 

50 71.0000 0.2946 13.551 14.000 46 0.145 

51 

52 Chi^2 = 1.81 d.f. = 2 P-value = 0.4046 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 3.67237 

64 

65 BMDL = 1.87133 

66 

67 BMDU = 15.4002 

68 

69 Taken together, (1.87133, 15.4002) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-99 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.00534381 

3 

4 

5 F.2.10. National Toxicology Program (1982): Female Rats, Thyroid, Follicular-Cell 

6 Adenoma 

7 F.2.10.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 0.83 0.66 92.02 7.6E+00 3.5E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 0.53 0.77 91.64 2.3E+01 3.7E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 0.49 0.78 91.60 3.3E+01 3.7E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-100 —DO NOT CITE OR QUOTE 

1 F.2.10.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.10.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_thy_ad.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_thy_ad.plt 

12 Mon Nov 23 15:07:34 2009 

13 ==================================================================== 

14 

15 Source - Table 10 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:07 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-101 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.032089 

9 Beta(1) = 0.00143599 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.5 

17 

18 Beta(1) -0.5 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.0345958 * * * 

27 Beta(1) 0.00132742 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -43.5264 4 

37 Fitted model -44.0098 2 0.966786 2 0.6167 

38 Reduced model -46.2299 1 5.40699 3 0.1443 

39 

40 AIC: 92.0196 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0346 2.525 3.000 73 0.304 

48 1.4000 0.0364 1.637 2.000 45 0.289 

49 7.1000 0.0437 2.139 1.000 49 -0.796 

50 71.0000 0.1214 5.707 6.000 47 0.131 

51 

52 Chi^2 = 0.83 d.f. = 2 P-value = 0.6614 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 7.57131 

64 

65 BMDL = 3.48815 

66 

67 BMDU = 964541 

68 

69 Taken together, (3.48815, 964541 ) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-102 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.00286685 

3 

4 

5 F.2.11. National Toxicology Program (1982): Male Rats, Liver, Neoplastic Nodule or 

6 Hepatocellular Carcinoma 

7 F.2.11.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

3 0.37 0.40 133.83 2.6E+00 1.6E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

3 0.03 0.50 133.44 1.3E+01 1.7E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

3 0.00 0.50 133.44 1.3E+01 1.7E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-103 —DO NOT CITE OR QUOTE 

1 F.2.11.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.11.3. Output File for selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_liver_nod.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_liver_nod.plt 

12 Mon Nov 23 15:07:55 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:07 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-104 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0.000900399 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 0.000775683 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -11.3484 4 

39 Fitted model -11.6976 1 0.698469 3 0.8736 

40 Reduced model -15.9189 1 9.14109 3 0.02747 

41 

42 AIC: 25.3952 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 74 0.000 

50 1.4000 0.0011 0.054 0.000 50 -0.233 

51 7.1000 0.0055 0.275 0.000 50 -0.525 

52 71.0000 0.0536 2.679 3.000 50 0.201 

53 

54 Chi^2 = 0.37 d.f. = 3 P-value = 0.9462 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 0.01 

60 

61 Risk Type = Extra risk 

62 

63 Confidence level = 0.95 

64 

65 BMD = 12.9568 

66 

67 BMDL = 5.70369 

68 

69 BMDU = 39.9878 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-105 —DO NOT CITE OR QUOTE 

1 Taken together, (5.70369, 39.9878) is a 90 % two-sided confidence 

2 interval for the BMD 

3 

4 Multistage Cancer Slope Factor = 0.00175325 

5 

6 

7 F.2.12. National Toxicology Program (1982): Male Rats, Thyroid, Follicular-Cell 

8 Adenoma or Carcinoma 

9 F.2.12.1. Summary Table of BMDS Modeling Results 

10 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 7.14 0.03 151.22 3.5E+00 1.9E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 7.14 0.03 151.22 3.5E+00 1.9E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 7.14 0.03 151.22 3.5E+00 1.9E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

11 

12 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-106 —DO NOT CITE OR QUOTE 

1 F.2.12.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 F.2.12.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

5 

6 

7 ==================================================================== 

8 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

9 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_thyroid.(d) 

10 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_thyroid.plt 

11 Mon Nov 23 15:08:16 2009 

12 ==================================================================== 

13 

14 Source - Table 9 

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

16 

17 The form of the probability function is: 

18 

19 P[response] = background + (1-background)*[1-EXP( 

20 -beta1*dose^1)] 

21 

22 The parameter betas are restricted to be positive 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 

28 Total number of observations = 4 

29 Total number of records with missing values = 0 

30 Total number of parameters in model = 2 

31 Total number of specified parameters = 0 

32 Degree of polynomial = 1 

33 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:08 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-107 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.0867382 

9 Beta(1) = 0.00232055 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.53 

17 

18 Beta(1) -0.53 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.0704713 * * * 

27 Beta(1) 0.00285481 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -69.5946 4 

37 Fitted model -73.6119 2 8.03468 2 0.018 

38 Reduced model -77.5267 1 15.8643 3 0.001209 

39 

40 AIC: 151.224 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0705 4.863 1.000 69 -1.817 

48 1.4000 0.0742 3.561 5.000 48 0.793 

49 7.1000 0.0891 4.456 8.000 50 1.759 

50 71.0000 0.2410 12.051 11.000 50 -0.347 

51 

52 Chi^2 = 7.14 d.f. = 2 P-value = 0.0281 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 3.5205 

64 

65 BMDL = 1.91558 

66 

67 BMDU = 9.76663 

68 

69 Taken together, (1.91558, 9.76663) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-108 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.00522034 

3 

4 

5 F.2.13. National Toxicology Program (1982): Male Rats, Adrenal cortex, Adenoma 

6 F.2.13.1. Summary Table of BMDS Modeling Results 

7 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 5.83 0.05 199.67 1.4E+01 3.4E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 5.83 0.05 199.67 1.4E+01 3.4E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 5.83 0.05 199.67 1.4E+01 3.4E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

8 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-109 —DO NOT CITE OR QUOTE 

1 F.2.13.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.13.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adre_cort.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adre_cort.plt 

12 Mon Nov 23 15:08:35 2009 

13 ==================================================================== 

14 

15 Source - Table 9 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:08 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-110 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.168444 

9 Beta(1) = 0.000395949 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.53 

17 

18 Beta(1) -0.53 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.153096 * * * 

27 Beta(1) 0.000718012 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -94.8672 4 

37 Fitted model -97.8359 2 5.93732 2 0.05137 

38 Reduced model -98.0432 1 6.35197 3 0.09569 

39 

40 AIC: 199.672 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.1531 11.023 6.000 72 -1.644 

48 1.4000 0.1539 7.697 9.000 50 0.510 

49 7.1000 0.1574 7.713 12.000 49 1.682 

50 71.0000 0.1952 9.564 9.000 49 -0.203 

51 

52 Chi^2 = 5.83 d.f. = 2 P-value = 0.0541 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 13.9974 

64 

65 BMDL = 3.4443 

66 

67 

68 BMDU did not converge for BMR = 0.010000 

69 BMDU calculation failed 

70 BMDU = Inf 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-111 —DO NOT CITE OR QUOTE 

1 

2 

3 F.2.14. National Toxicology Program (1982): Female Mice, Subcutaneous Tissue, 

4 Fibrosarcoma 

5 F.2.14.1. Summary Table of BMDS Modeling Results 

6 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

7 

8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-112 —DO NOT CITE OR QUOTE 

1 F.2.14.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.14.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_subcu_fibro.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_subcu_fibro.plt 

12 Mon Nov 23 15:08:56 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

36 Maximum number of iterations = 250 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 50 100 150 200 250 300

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:08 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-113 —DO NOT CITE OR QUOTE 

1 Relative Function Convergence has been set to: 1e-008 

2 Parameter Convergence has been set to: 1e-008 

3 

4 

5 

6 Default Initial Parameter Values 

7 Background = 0.0143554 

8 Beta(1) = 0.000341874 

9 

10 

11 Asymptotic Correlation Matrix of Parameter Estimates 

12 

13 Background Beta(1) 

14 

15 Background 1 -0.5 

16 

17 Beta(1) -0.5 1 

18 

19 

20 

21 Parameter Estimates 

22 

23 95.0% Wald Confidence Interval 

24 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

25 Background 0.0145028 * * * 

26 Beta(1) 0.000338561 * * * 

27 

28 * - Indicates that this value is not calculated. 

29 

30 

31 

32 Analysis of Deviance Table 

33 

34 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

35 Full model -30.9876 4 

36 Fitted model -31.0199 2 0.0645971 2 0.9682 

37 Reduced model -34.3291 1 6.68308 3 0.08272 

38 

39 AIC: 66.0397 

40 

41 

42 Goodness of Fit 

43 Scaled 

44 Dose Est._Prob. Expected Observed Size Residual 

45 ------------------------------------------------------------------------ 

46 0.0000 0.0145 1.073 1.000 74 -0.071 

47 5.7000 0.0164 0.820 1.000 50 0.200 

48 28.6000 0.0240 1.152 1.000 48 -0.143 

49 286.0000 0.1055 4.956 5.000 47 0.021 

50 

51 Chi^2 = 0.07 d.f. = 2 P-value = 0.9675 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 0.01 

57 

58 Risk Type = Extra risk 

59 

60 Confidence level = 0.95 

61 

62 BMD = 29.6855 

63 

64 BMDL = 14.3524 

65 

66 BMDU = 100.382 

67 

68 Taken together, (14.3524, 100.382) is a 90 % two-sided confidence 

69 interval for the BMD 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-114 —DO NOT CITE OR QUOTE 

1 Multistage Cancer Slope Factor = 0.000696747 

2 

3 

4 F.2.15. National Toxicology Program (1982): Female Mice, Hematopoietic System, 

5 Lymphoma 

6 F.2.15.1. Summary Table of BMDS Modeling Results 

7 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 0.03 0.99 261.43 1.0E+01 5.5E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 0.03 0.99 261.43 1.0E+01 5.5E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 0.03 0.99 261.43 1.0E+01 5.5E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

8 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-115 —DO NOT CITE OR QUOTE 

1 F.2.15.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.15.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_f_lymphoma.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_f_lymphoma.plt 

12 Mon Nov 23 15:09:17 2009 

13 ==================================================================== 

14 

15 Table 15 page 64 Hematopoietic System Lymphoma or Leukemia 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 50 100 150 200 250 300

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:09 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-116 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.242959 

9 Beta(1) = 0.000967723 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.48 

17 

18 Beta(1) -0.48 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.242712 * * * 

27 Beta(1) 0.000971954 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -128.699 4 

37 Fitted model -128.712 2 0.0264819 2 0.9868 

38 Reduced model -131.412 1 5.42487 3 0.1432 

39 

40 AIC: 261.425 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.2427 17.961 18.000 74 0.011 

48 5.7000 0.2469 12.345 12.000 50 -0.113 

49 28.6000 0.2635 12.647 13.000 48 0.116 

50 286.0000 0.4265 20.045 20.000 47 -0.013 

51 

52 Chi^2 = 0.03 d.f. = 2 P-value = 0.9868 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 10.3403 

64 

65 BMDL = 5.45599 

66 

67 BMDU = 38.9139 

68 

69 Taken together, (5.45599, 38.9139) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-117 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.00183285 

3 

4 

5 F.2.16. National Toxicology Program (1982): Female Mice, Liver, Hepatocellular 

6 Adenoma or Carcinoma 

7 F.2.16.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 2.82 0.24 156.00 1.5E+01 7.8E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 2.82 0.24 156.00 1.5E+01 7.8E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 2.82 0.24 156.00 1.5E+01 7.8E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-118 —DO NOT CITE OR QUOTE 

1 F.2.16.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.16.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_f_liv_aden_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_f_liv_aden_carc.plt 

12 Mon Nov 23 15:09:36 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 50 100 150 200 250 300

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:09 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-119 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.0888873 

10 Beta(1) = 0.000616931 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.5 

18 

19 Beta(1) -0.5 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.0788077 * * * 

28 Beta(1) 0.000689385 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -74.5177 4 

38 Fitted model -76.0006 2 2.96597 2 0.227 

39 Reduced model -79.6703 1 10.3053 3 0.01614 

40 

41 AIC: 156.001 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0788 5.753 3.000 73 -1.196 

49 5.7000 0.0824 4.121 6.000 50 0.966 

50 28.6000 0.0968 4.646 6.000 48 0.661 

51 286.0000 0.2436 11.452 11.000 47 -0.153 

52 

53 Chi^2 = 2.82 d.f. = 2 P-value = 0.2436 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 14.5787 

65 

66 BMDL = 7.82902 

67 

68 BMDU = 42.4536 

69 

70 Taken together, (7.82902, 42.4536) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-120 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 0.0012773 

4 

5 

6 F.2.17. National Toxicology Program (1982): Female Mice, Thyroid Follicular Cell 

7 Adenoma 

8 F.2.17.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.84 0.15 76.38 9.8E+00 4.0E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-121 —DO NOT CITE OR QUOTE 

1 F.2.17.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.17.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_f_thyroid_aden.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_f_thyroid_aden.plt 

12 Mon Nov 23 15:09:56 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0 50 100 150 200 250 300

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:09 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-122 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.02405 

9 Beta(1) = 0.000315564 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.51 

17 

18 Beta(1) -0.51 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.0207192 * * * 

27 Beta(1) 0.000331835 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -32.0017 4 

37 Fitted model -34.6122 2 5.22112 2 0.07349 

38 Reduced model -37.2405 1 10.4776 3 0.01491 

39 

40 AIC: 73.2245 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.0207 1.430 0.000 69 -1.208 

48 5.7000 0.0226 1.128 3.000 50 1.782 

49 28.6000 0.0300 1.409 1.000 47 -0.350 

50 286.0000 0.1094 5.032 5.000 46 -0.015 

51 

52 Chi^2 = 4.76 d.f. = 2 P-value = 0.0927 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 30.2871 

64 

65 BMDL = 13.993 

66 

67 BMDU = 130.014 

68 

69 Taken together, (13.993 , 130.014) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-123 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.000714641 

3 

4 

5 F.2.18. National Toxicology Program (1982): Male Mice, Lung, Alveolar/Bronchiolar 

6 Adenoma or Carcinoma 

7 F.2.18.1. Summary Table of BMDS Modeling Results 

8 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 3.97 0.14 167.34 3.7E+00 2.0E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 3.41 0.18 166.81 1.6E+01 2.1E+00 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 3.38 0.18 166.78 2.6E+01 2.1E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

9 

10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-124 —DO NOT CITE OR QUOTE 

1 F.2.18.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.18.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_lung_aden_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_lung_aden_carc.plt 

12 Mon Nov 23 15:10:17 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:10 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-125 —DO NOT CITE OR QUOTE 

1 

2 Maximum number of iterations = 250 

3 Relative Function Convergence has been set to: 1e-008 

4 Parameter Convergence has been set to: 1e-008 

5 

6 

7 

8 Default Initial Parameter Values 

9 Background = 0.0827179 

10 Beta(1) = 0.00298266 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 Background Beta(1) 

16 

17 Background 1 -0.49 

18 

19 Beta(1) -0.49 1 

20 

21 

22 

23 Parameter Estimates 

24 

25 95.0% Wald Confidence Interval 

26 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

27 Background 0.0925449 * * * 

28 Beta(1) 0.00271189 * * * 

29 

30 * - Indicates that this value is not calculated. 

31 

32 

33 

34 Analysis of Deviance Table 

35 

36 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

37 Full model -79.5959 4 

38 Fitted model -81.6704 2 4.14885 2 0.1256 

39 Reduced model -85.3351 1 11.4782 3 0.009402 

40 

41 AIC: 167.341 

42 

43 

44 Goodness of Fit 

45 Scaled 

46 Dose Est._Prob. Expected Observed Size Residual 

47 ------------------------------------------------------------------------ 

48 0.0000 0.0925 6.571 10.000 71 1.404 

49 1.4000 0.0960 4.607 2.000 48 -1.278 

50 7.1000 0.1099 5.273 4.000 48 -0.588 

51 71.0000 0.2515 12.574 13.000 50 0.139 

52 

53 Chi^2 = 3.97 d.f. = 2 P-value = 0.1375 

54 

55 

56 Benchmark Dose Computation 

57 

58 Specified effect = 0.01 

59 

60 Risk Type = Extra risk 

61 

62 Confidence level = 0.95 

63 

64 BMD = 3.70603 

65 

66 BMDL = 2.0263 

67 

68 BMDU = 10.562 

69 

70 Taken together, (2.0263 , 10.562 ) is a 90 % two-sided confidence 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-126 —DO NOT CITE OR QUOTE 

1 interval for the BMD 

2 

3 Multistage Cancer Slope Factor = 0.0049351 

4 

5 

6 F.2.19. National Toxicology Program (1982): Male Mice, Liver, Hepatocellular Adenoma 

7 or Carcinoma 

8 F.2.19.1. Summary Table of BMDS Modeling Results 

9 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

2 0.17 0.92 258.57 1.3E+00 8.6E-01 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

2 0.17 0.92 258.57 1.3E+00 8.6E-01 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

2 0.17 0.92 258.57 1.3E+00 8.6E-01 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

10 

11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-127 —DO NOT CITE OR QUOTE 

1 F.2.19.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.19.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_m_liver_aden_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_mice_m_liver_aden_carc.plt 

12 Mon Nov 23 15:10:37 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 4 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0.7

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:10 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-128 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.22264 

9 Beta(1) = 0.0074005 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.46 

17 

18 Beta(1) -0.46 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.219315 * * * 

27 Beta(1) 0.00750879 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -127.199 4 

37 Fitted model -127.286 2 0.174343 2 0.9165 

38 Reduced model -135.589 1 16.7801 3 0.0007843 

39 

40 AIC: 258.572 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.2193 16.010 15.000 73 -0.286 

48 1.4000 0.2275 11.146 12.000 49 0.291 

49 7.1000 0.2598 12.732 13.000 49 0.087 

50 71.0000 0.5419 27.096 27.000 50 -0.027 

51 

52 Chi^2 = 0.17 d.f. = 2 P-value = 0.9164 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 0.01 

58 

59 Risk Type = Extra risk 

60 

61 Confidence level = 0.95 

62 

63 BMD = 1.33848 

64 

65 BMDL = 0.861975 

66 

67 BMDU = 2.4671 

68 

69 Taken together, (0.861975, 2.4671 ) is a 90 % two-sided confidence 

70 interval for the BMD 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-129 —DO NOT CITE OR QUOTE 

1 

2 Multistage Cancer Slope Factor = 0.0116013 

3 

4 

5 F.2.20. National Toxicology Program (2006): Liver, Cholangiocarcinoma 

6 F.2.20.1. Summary Table of BMDS Modeling Results 

7 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degree 

5 12.91 0.02 129.07 1.9E+00 1.4E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

5 1.18 0.95 114.35 9.4E+00 5.3E+00 betas restricted ≥0 

Multistag

e cancer, 

3-degreeb

4 0.22 0.99 115.16 1.3E+01 4.5E+00 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

8 

9 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-130 —DO NOT CITE OR QUOTE 

1 F.2.20.2. Figure for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.20.3. Output File for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc3_ngkgd_liv_cho-carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc3_ngkgd_liv_cho-carc.plt 

12 Mon Nov 23 15:10:57 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2-beta3*dose^3)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 4 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 3 

34 

35 

 0

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:10 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-131 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0.000561481 

10 Beta(2) = 1.74365e-005 

11 Beta(3) = 1.40248e-006 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 ( *** The model parameter(s) -Background -Beta(1) 

17 have been estimated at a boundary point, or have been specified by the user, 

18 and do not appear in the correlation matrix ) 

19 

20 Beta(2) Beta(3) 

21 

22 Beta(2) 1 -0.99 

23 

24 Beta(3) -0.99 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 95.0% Wald Confidence Interval 

31 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

32 Background 0 * * * 

33 Beta(1) 0 * * * 

34 Beta(2) 4.35927e-005 * * * 

35 Beta(3) 1.14186e-006 * * * 

36 

37 * - Indicates that this value is not calculated. 

38 

39 

40 

41 Analysis of Deviance Table 

42 

43 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

44 Full model -55.408 6 

45 Fitted model -55.5789 2 0.34181 4 0.987 

46 Reduced model -96.9934 1 83.1708 5 <.0001 

47 

48 AIC: 115.158 

49 

50 

51 Goodness of Fit 

52 Scaled 

53 Dose Est._Prob. Expected Observed Size Residual 

54 ------------------------------------------------------------------------ 

55 0.0000 0.0000 0.000 0.000 49 0.000 

56 2.1400 0.0002 0.010 0.000 48 -0.101 

57 7.1400 0.0026 0.121 0.000 46 -0.349 

58 15.7000 0.0150 0.752 1.000 50 0.288 

59 32.9000 0.0841 4.121 4.000 49 -0.062 

60 71.4000 0.4716 24.994 25.000 53 0.002 

61 

62 Chi^2 = 0.22 d.f. = 4 P-value = 0.9945 

63 

64 

65 Benchmark Dose Computation 

66 

67 Specified effect = 0.01 

68 

69 Risk Type = Extra risk 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-132 —DO NOT CITE OR QUOTE 

1 Confidence level = 0.95 

2 

3 BMD = 13.1014 

4 

5 BMDL = 4.46755 

6 

7 BMDU = 19.1783 

8 

9 Taken together, (4.46755, 19.1783) is a 90 % two-sided confidence 

10 interval for the BMD 

11 

12 Multistage Cancer Slope Factor = 0.00223836 

13 

14 

15 F.2.21. National Toxicology Program (2006): Liver, Hepatocellular Adenoma 

16 F.2.21.1. Summary Table of BMDS Modeling Results 

17 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degree 

5 8.50 0.13 82.31 4.4E+00 2.9E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

5 1.94 0.86 73.66 1.5E+01 8.6E+00 betas restricted ≥0 

Multistag

e cancer, 

3-degreeb

5 0.24 1.00 71.22 2.4E+01 1.2E+01 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded 

18 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-133 —DO NOT CITE OR QUOTE 

1 F.2.21.2. Figure for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.21.3. Output File for Selected Model: Multistage Cancer, 3-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc3_ngkgd_liv_hepat_ad.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc3_ngkgd_liv_hepat_ad.plt 

12 Mon Nov 23 15:11:17 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2-beta3*dose^3)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 4 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 3 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0.4

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:11 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-134 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0 

10 Beta(2) = 0 

11 Beta(3) = 7.77141e-007 

12 

13 

14 Asymptotic Correlation Matrix of Parameter Estimates 

15 

16 ( *** The model parameter(s) -Background -Beta(1) -Beta(2) 

17 have been estimated at a boundary point, or have been specified by the user, 

18 and do not appear in the correlation matrix ) 

19 

20 Beta(3) 

21 

22 Beta(3) 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 Background 0 * * * 

31 Beta(1) 0 * * * 

32 Beta(2) 0 * * * 

33 Beta(3) 7.46408e-007 * * * 

34 

35 * - Indicates that this value is not calculated. 

36 

37 

38 

39 Analysis of Deviance Table 

40 

41 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

42 Full model -34.4075 6 

43 Fitted model -34.6078 1 0.40065 5 0.9953 

44 Reduced model -56.3333 1 43.8515 5 <.0001 

45 

46 AIC: 71.2156 

47 

48 

49 Goodness of Fit 

50 Scaled 

51 Dose Est._Prob. Expected Observed Size Residual 

52 ------------------------------------------------------------------------ 

53 0.0000 0.0000 0.000 0.000 49 0.000 

54 2.1400 0.0000 0.000 0.000 48 -0.019 

55 7.1400 0.0003 0.012 0.000 46 -0.112 

56 15.7000 0.0029 0.144 0.000 50 -0.380 

57 32.9000 0.0262 1.285 1.000 49 -0.255 

58 71.4000 0.2379 12.609 13.000 53 0.126 

59 

60 Chi^2 = 0.24 d.f. = 5 P-value = 0.9986 

61 

62 

63 Benchmark Dose Computation 

64 

65 Specified effect = 0.01 

66 

67 Risk Type = Extra risk 

68 

69 Confidence level = 0.95 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-135 —DO NOT CITE OR QUOTE 

1 BMD = 23.7904 

2 

3 BMDL = 11.5343 

4 

5 BMDU = 27.8755 

6 

7 Taken together, (11.5343, 27.8755) is a 90 % two-sided confidence 

8 interval for the BMD 

9 

10 Multistage Cancer Slope Factor = 0.000866978 

11 

12 

13 F.2.22. National Toxicology Program (2006): Oral Mucosa, Squamous Cell Carcinoma 

14 F.2.22.1. Summary Table of BMDS Modeling Results 

15 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD 

(ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

multistage 

cancer, 

1-degree 

4 4.15 0.39 125.48 4.8E+00 3.0E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degreeb

4 2.83 0.59 123.25 1.6E+01 3.8E+00 betas restricted ≥0, 

bound hit 

Multistage 

cancer, 

3-degree 

4 2.83 0.59 123.25 1.6E+01 3.8E+00 betas restricted ≥0, 

bound hit 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

 Best-fitting model as assessed by lowest-AIC criterion, bolded.

16 

17 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-136 —DO NOT CITE OR QUOTE 

1 F.2.22.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0, 

2 Bound Hit 

3 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0.35

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:11 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation

4 

5 

6 

7 F.2.22.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0, 

8 Bound Hit 

9 

10 

11 ==================================================================== 

12 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

13 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_oral_carc.(d) 

14 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_oral_carc.plt 

15 Mon Nov 23 15:11:37 2009 

16 ==================================================================== 

17 

18 0 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the probability function is: 

22 

23 P[response] = background + (1-background)*[1-EXP( 

24 -beta1*dose^1)] 

25 

26 The parameter betas are restricted to be positive 

27 

28 

29 Dependent variable = Mean 

30 Independent variable = Dose 

31 

32 Total number of observations = 6 

33 Total number of records with missing values = 0 

34 Total number of parameters in model = 2 

35 Total number of specified parameters = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-137 —DO NOT CITE OR QUOTE 

1 Degree of polynomial = 1 

2 

3 

4 Maximum number of iterations = 250 

5 Relative Function Convergence has been set to: 1e-008 

6 Parameter Convergence has been set to: 1e-008 

7 

8 

9 

10 Default Initial Parameter Values 

11 Background = 0.00607545 

12 Beta(1) = 0.00265195 

13 

14 

15 Asymptotic Correlation Matrix of Parameter Estimates 

16 

17 Background Beta(1) 

18 

19 Background 1 -0.6 

20 

21 Beta(1) -0.6 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0.0171416 * * * 

30 Beta(1) 0.00211536 * * * 

31 

32 * - Indicates that this value is not calculated. 

33 

34 

35 

36 Analysis of Deviance Table 

37 

38 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

39 Full model -57.5353 6 

40 Fitted model -60.7418 2 6.41293 4 0.1704 

41 Reduced model -67.7782 1 20.4858 5 0.001013 

42 

43 AIC: 125.484 

44 

45 

46 Goodness of Fit 

47 Scaled 

48 Dose Est._Prob. Expected Observed Size Residual 

49 ------------------------------------------------------------------------ 

50 0.0000 0.0171 0.840 1.000 49 0.176 

51 2.1400 0.0216 1.036 2.000 48 0.958 

52 7.1400 0.0319 1.466 1.000 46 -0.391 

53 15.7000 0.0492 2.462 0.000 50 -1.609 

54 32.9000 0.0832 4.078 4.000 49 -0.040 

55 71.4000 0.1549 8.211 10.000 53 0.679 

56 

57 Chi^2 = 4.15 d.f. = 4 P-value = 0.3855 

58 

59 

60 Benchmark Dose Computation 

61 

62 Specified effect = 0.01 

63 

64 Risk Type = Extra risk 

65 

66 Confidence level = 0.95 

67 

68 BMD = 4.75111 

69 

70 BMDL = 2.9556 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-138 —DO NOT CITE OR QUOTE 

1 

2 BMDU = 9.19454 

3 

4 Taken together, (2.9556 , 9.19454) is a 90 % two-sided confidence 

5 interval for the BMD 

6 

7 Multistage Cancer Slope Factor = 0.0033834 

8 

9 

10 F.2.23. National Toxicology Program (2006): Pancreas, Adenoma or Carcinoma 

11 F.2.23.1. Summary Table of BMDS Modeling Results 

12 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degreeb

5 2.37 0.80 28.32 2.1E+01 9.3E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degree 

5 0.80 0.98 26.23 3.3E+01 1.4E+01 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

5 0.32 1.00 25.43 4.1E+01 1.8E+01 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

13 

14 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-139 —DO NOT CITE OR QUOTE 

1 F.2.23.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.23.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_panc_ad_carc.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_panc_ad_carc.plt 

12 Mon Nov 23 15:11:58 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0

 0.05

 0.1

 0.15

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:11 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-140 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0.000817541 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 ( *** The model parameter(s) -Background 

15 have been estimated at a boundary point, or have been specified by the user, 

16 and do not appear in the correlation matrix ) 

17 

18 Beta(1) 

19 

20 Beta(1) 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 Background 0 * * * 

29 Beta(1) 0.000474004 * * * 

30 

31 * - Indicates that this value is not calculated. 

32 

33 

34 

35 Analysis of Deviance Table 

36 

37 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

38 Full model -11.4096 6 

39 Fitted model -13.1581 1 3.49702 5 0.6238 

40 Reduced model -16.7086 1 10.598 5 0.05996 

41 

42 AIC: 28.3163 

43 

44 

45 Goodness of Fit 

46 Scaled 

47 Dose Est._Prob. Expected Observed Size Residual 

48 ------------------------------------------------------------------------ 

49 0.0000 0.0000 0.000 0.000 48 0.000 

50 2.1400 0.0010 0.049 0.000 48 -0.221 

51 7.1400 0.0034 0.155 0.000 46 -0.395 

52 15.7000 0.0074 0.371 0.000 50 -0.611 

53 32.9000 0.0155 0.743 0.000 48 -0.869 

54 71.4000 0.0333 1.697 3.000 51 1.017 

55 

56 Chi^2 = 2.37 d.f. = 5 P-value = 0.7964 

57 

58 

59 Benchmark Dose Computation 

60 

61 Specified effect = 0.01 

62 

63 Risk Type = Extra risk 

64 

65 Confidence level = 0.95 

66 

67 BMD = 21.2031 

68 

69 BMDL = 9.33481 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-141 —DO NOT CITE OR QUOTE 

1 BMDU = 65.4351 

2 

3 Taken together, (9.33481, 65.4351) is a 90 % two-sided confidence 

4 interval for the BMD 

5 

6 Multistage Cancer Slope Factor = 0.00107126 

7 

8 

9 F.2.24. National Toxicology Program (2006): Lung, Cystic Keratinizing Epithelioma 

10 F.2.24.1. Summary Table of BMDS Modeling Results 

11 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

Multistage 

cancer, 

1-degree 

5 7.42 0.19 60.81 6.9E+00 4.2E+00 betas restricted ≥0 

Multistage 

cancer, 

2-degreeb

5 2.54 0.77 54.36 1.9E+01 1.1E+01 betas restricted ≥0 

Multistage 

cancer, 

3-degree 

5 1.02 0.96 51.85 2.8E+01 1.6E+01 betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

12 

13 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-142 —DO NOT CITE OR QUOTE 

1 F.2.24.2. Figure for Selected Model: Multistage Cancer, 2-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.24.3. Output File for Selected Model: Multistage Cancer, 2-Degree, Betas Restricted ≥0

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc2_ngkgd_lung_epith.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc2_ngkgd_lung_epith.plt 

12 Mon Nov 23 15:12:20 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1-beta2*dose^2)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 6 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 3 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 2 

34 

35 

 0

 0.05

 0.1

 0.15

 0.2

 0.25

 0.3

 0 10 20 30 40 50 60 70

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

15:12 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-143 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0 

9 Beta(1) = 0 

10 Beta(2) = 3.77591e-005 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 ( *** The model parameter(s) -Background -Beta(1) 

16 have been estimated at a boundary point, or have been specified by the user, 

17 and do not appear in the correlation matrix ) 

18 

19 Beta(2) 

20 

21 Beta(2) 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 Background 0 * * * 

30 Beta(1) 0 * * * 

31 Beta(2) 2.91011e-005 * * * 

32 

33 * - Indicates that this value is not calculated. 

34 

35 

36 

37 Analysis of Deviance Table 

38 

39 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

40 Full model -23.958 6 

41 Fitted model -26.1815 1 4.44693 5 0.487 

42 Reduced model -40.2069 1 32.4976 5 <.0001 

43 

44 AIC: 54.363 

45 

46 

47 Goodness of Fit 

48 Scaled 

49 Dose Est._Prob. Expected Observed Size Residual 

50 ------------------------------------------------------------------------ 

51 0.0000 0.0000 0.000 0.000 49 0.000 

52 2.1400 0.0001 0.006 0.000 48 -0.080 

53 7.1400 0.0015 0.068 0.000 46 -0.261 

54 15.7000 0.0071 0.350 0.000 49 -0.594 

55 32.9000 0.0310 1.519 0.000 49 -1.252 

56 71.4000 0.1379 7.170 9.000 52 0.736 

57 

58 Chi^2 = 2.54 d.f. = 5 P-value = 0.7708 

59 

60 

61 Benchmark Dose Computation 

62 

63 Specified effect = 0.01 

64 

65 Risk Type = Extra risk 

66 

67 Confidence level = 0.95 

68 

69 BMD = 18.5839 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-144 —DO NOT CITE OR QUOTE 

1 BMDL = 10.6878 

2 

3 BMDU = 25.1324 

4 

5 Taken together, (10.6878, 25.1324) is a 90 % two-sided confidence 

6 interval for the BMD 

7 

8 Multistage Cancer Slope Factor = 0.000935646 

9 

10 

11 F.2.25. Toth et al. (1978): 1YR, Liver, Tumors 

12 F.2.25.1. Summary Table of BMDS Modeling Results 

13 

Model 

Degrees 

of 

Freedom 

χ 2 Test 

Statistic 

χ 2

p-Valuea AIC BMD (ng/kg-day) 

BMDL 

(ng/kg-day) Model Notes 

multistage 

cancer, 

1-degreeb

1 1.30 0.25 155.95 2.7E+00 1.5E+00 betas restricted ≥0 

multistage 

cancer, 

2-degree 

1 1.30 0.25 155.95 2.7E+00 1.5E+00 betas restricted ≥0 

multistage 

cancer, 

0-degree 

 0.25 -999.00 error error betas restricted ≥0 

a

Values <0.1 fail to meet BMDS goodness-of-fit criteria. 

b

Best-fitting model as assessed by lowest-AIC criterion, bolded. 

14 

15 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-145 —DO NOT CITE OR QUOTE 

1 F.2.25.2. Figure for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

2 

3 

4 

5 F.2.25.3. Output File for Selected Model: Multistage Cancer, 1-Degree, Betas Restricted ≥0 

6 

7 

8 ==================================================================== 

9 Multistage Cancer Model. (Version: 1.7; Date: 05/16/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adr_cor_1yr.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\msc1_ngkgd_adr_cor_1yr.plt 

12 Mon Nov 23 17:30:17 2009 

13 ==================================================================== 

14 

15 Table 1 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the probability function is: 

19 

20 P[response] = background + (1-background)*[1-EXP( 

21 -beta1*dose^1)] 

22 

23 The parameter betas are restricted to be positive 

24 

25 

26 Dependent variable = Mean 

27 Independent variable = Dose 

28 

29 Total number of observations = 3 

30 Total number of records with missing values = 0 

31 Total number of parameters in model = 2 

32 Total number of specified parameters = 0 

33 Degree of polynomial = 1 

34 

35 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 20 40 60 80 100

Fraction Affected

dose

Multistage Cancer Model with 0.95 Confidence Level

17:30 11/23 2009

BMDL BMD

 

Multistage Cancer

Linear extrapolation
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-146 —DO NOT CITE OR QUOTE 

1 Maximum number of iterations = 250 

2 Relative Function Convergence has been set to: 1e-008 

3 Parameter Convergence has been set to: 1e-008 

4 

5 

6 

7 Default Initial Parameter Values 

8 Background = 0.240176 

9 Beta(1) = 0.00374745 

10 

11 

12 Asymptotic Correlation Matrix of Parameter Estimates 

13 

14 Background Beta(1) 

15 

16 Background 1 -0.53 

17 

18 Beta(1) -0.53 1 

19 

20 

21 

22 Parameter Estimates 

23 

24 95.0% Wald Confidence Interval 

25 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

26 Background 0.2418 * * * 

27 Beta(1) 0.00373791 * * * 

28 

29 * - Indicates that this value is not calculated. 

30 

31 

32 

33 Analysis of Deviance Table 

34 

35 Model Log(likelihood) # Param's Deviance Test d.f. P-value 

36 Full model -75.3127 3 

37 Fitted model -75.9728 2 1.3201 1 0.2506 

38 Reduced model -79.4897 1 8.35401 2 0.01534 

39 

40 AIC: 155.946 

41 

42 

43 Goodness of Fit 

44 Scaled 

45 Dose Est._Prob. Expected Observed Size Residual 

46 ------------------------------------------------------------------------ 

47 0.0000 0.2418 9.188 7.000 38 -0.829 

48 1.0000 0.2446 10.764 13.000 44 0.784 

49 100.0000 0.4783 21.044 21.000 44 -0.013 

50 

51 Chi^2 = 1.30 d.f. = 1 P-value = 0.2537 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 0.01 

57 

58 Risk Type = Extra risk 

59 

60 Confidence level = 0.95 

61 

62 BMD = 2.68876 

63 

64 BMDL = 1.52183 

65 

66 BMDU = 7.54263 

67 

68 Taken together, (1.52183, 7.54263) is a 90 % two-sided confidence 

69 interval for the BMD 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-147 —DO NOT CITE OR QUOTE 

1 Multistage Cancer Slope Factor = 0.00657103 

2 
This document is a draft for review purposes only and does not constitute Agency policy

1/15/10 F-148 DRAFT: DO NOT CITE OR QUOTE F.3. HUMAN EQUIVALENT DOSES FOR 1, 5, AND 10% EXTRA RISK Comparison of Human Equivalent Doses from Benchmark Dose Modeling Assuming 1%, 5%, and 

BMD01 HED BMDL01 HED BMD05 HED BM

H

Study Species Sex Morphology: topography (ng/kg- day) (ng/kg- day) (ng/kg- day) (n

Stratified squamous cell carcinoma of hard palate or nasal turbinates 4.7E-01 1.6E-01 4.6E+00 1.7Stratified squamous cell carcinoma of tongue 5.1E-01 1.4E-01 4.9E+00 1.6

Male Adenoma of adrenal cortex 2.0E-01 8.5E-02 2.1E+00 9.

Hepatocellular adenoma(s) or carcinoma(s) 1.9E-02 1.2E-02 2.3E-01 1.Stratified squamous cell carcinoma of hard palate or nasal turbinates 3.3E-01 1.2E-01 3.3E+00 1.3

Kociba, 1978 Rat Female Keratinizing squamous cell carcinoma of lung 1.9E-01 8.0E-02 2.0E+00 9.

Subcutaneous tissue: fibrosarcoma 1.8E-01 5.3E-02 2.0E+00 6.Liver: neoplastic nodule or hepatocellular carcinoma 4.2E-02 2.1E-02 4.9E-01 2.Adrenal: cortical adenoma, or carcinoma or adenoma, NOS 6.8E-02 2.4E-02 7.8E-01 2.

Female Thyroid: follicular-cell adenoma 2.1E-01 6.4E-02 2.2E+00 7.

Liver: neoplastic nodule or hepatocellular carcinoma 5.1E-01 1.5E-01 4.9E+00 1.6Thyroid: follicular-cell adenoma or carcinoma 4.3E-02 1.9E-02 5.1E-01 2.

Rat Male Adrenal cortex: adenoma 2.6E-01 4.4E-02 2.8E+00 5.

Subcutaneous tissue: fibrosarcoma 2.1E-01 7.2E-02 2.2E+00 8.Hematopoietic system: lymphoma or leukemia 4.0E-02 1.5E-02 4.7E-01 1.Liver: hepatocellular adenoma or carcinoma 5.9E-02 2.4E-02 6.9E-01 2.

Female Thyroid: follicular-cell adenoma 1.8E-01 5.6E-02 1.9E+00 6.

Lung: alveolar/bronchiolar adenoma or carcinoma 1.3E-01 8.6E-03 4.6E-01 1.

NTP, 1982 Mouse Male Liver: hepatocellular adenoma or carcinoma 3.1E-03 1.7E-03 3.7E-02 1.

Liver: cholangiocarcinoma 7.0E-01 2.9E-01 1.5E+00 1.2Liver: hepatocellular adenoma 1.1E+00 5.6E-01 2.3E+00 1.Oral mucosa: squamous cell carcinoma 1.1E-01 5.5E-02 1.2E+00 6.Pancreas: adenoma or carcinoma 1.1E+00 3.4E-01 5.3E+00 3.

NTP, 2006 Rat Female Lung: cystic keratinizing epithelioma 8.0E-01 4.1E-01 2.5E+00 1.Toth, 1979 Mouse Male Liver: tumors 5.1E-03 1.9E-03 6.7E-02 2.
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT F-149 —DO NOT CITE OR QUOTE 

F.4. REFERENCES 

1 Goodman, DG; Sauer, RM. (1992) Hepatotoxicity and carcinogenicity in female Sprague-Dawley rats treated with 

2 2,3,7,8-tetrachlorordibenzo-p-dioxin (TCDD): a Pathology Working Group reevaluation. Regul Toxicol Pharmacol 

3 15:245–252. 

4 Kociba, RJ; Keyes, DG; Beyer, JE; et al. (1978) Results of a two-year chronic toxicity and oncogenicity study of 

5 2,3,7,8-tetrachlorodibenzo-p-dioxin in rats. Toxicol Appl Pharmacol 46(2):279–303. 

6 NTP (National Toxicology Program). (1982) Bioassay of 2,3,7,8-tetrachlorodibenzo-p-dioxin for possible 

7 carcinogenicity (gavage study). Tech. Rept. Ser. No. 201. U.S. Department of Health and Human Services, Public 

8 Health Service, Research Triangle Park, NC. 

9 NTP (National Toxicology Program). (2006) Studies of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in female 

10 Harlan Sprague-Dawley rats (gavage studies) Tech. Rep. Ser. No. 521. U.S. Department of Health and Human 

11 Services, Public Health Service, Research Triangle Park, NC. 

12 Toth, KJ; Sugar, S; Somfai-Relle S; et al. (1978) Carcinogenic bioassay of the herbicide 2,4,5-trichlorphenoxy 

13 ethanol (TCPE) with Swiss mice. Prog Biochem Pharmacol 14:82–93. 

DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX G 

Endpoints Excluded From Reference Dose 

Derivation Based on Toxicological Relevance 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 G-1 DRAFT—DO NOT CITE OR QUOTE 

1 APPENDIX G. ENDPOINTS EXCLUDED FROM REFERENCE DOSE DERIVATION 

2 BASED ON TOXICOLOGICAL RELEVANCE 

3

4

5 The National Academy of Sciences (NAS) committee commented on the low dose model 

6 predictions and the need to discuss the biological significance of the noncancer health effects 

7 modeled in the 2003 Reassessment. In selecting point of departure (POD) candidates from the 

8 animal bioassays for derivation of the reference dose (RfD), U.S. Environmental Protection 

9 Agency (EPA) had to consider the toxicological relevance of the identified endpoint(s) from any 

10 given study. Often endpoints/effects may be sensitive, but lack general toxicological 

11 significance due to not being clearly adverse (defined in the Integrated Risk Information System 

12 (IRIS) glossary as a biochemical change, functional impairment, or pathologic lesion that affects 

13 the performance of the whole organism, or reduces an organism’s ability to respond to an 

14 additional environmental challenge), being an adaptive response, or not being clearly linked to 

15 downstream functional or pathological alterations. It is standard EPA RfD derivation policy not 

16 to base a reference value on endpoints that are not adverse or not obvious precursors to an 

17 adverse effect. For select studies, a rationale for lack of toxicological relevance of particular 

18 endpoints reported is listed here. These endpoints were not considered for derivation of the RfD. 

19 Kitchin and Woods (1979) administered female Sprague-Dawley rats a single gavage 

20 dose of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and measured cytochrome P450 levels and 

21 benzo(a)pyrene hydroxylase (BPH) activity as a marker of hepatic microsomal cytochrome 

22 P448-mediated enzyme activity. They found a statistically significant increase in BPH at doses 

23 ≥2 ng/kg and a significant increase in cytochrome P450 levels at doses ≥600 ng/kg. Aryl 

24 hydrocarbon hydrolase and EROD were both significantly increased 3 months after exposure; 

25 however the elevation did not maintain statistical significance at 6 months. No other indicators 

26 of hepatic effects were analyzed. CYP induction alone is not considered a significant 

27 toxicologically adverse effect given that CYPs are induced as a means of hepatic processing of 

28 xenobiotic agents. Additionally, the role of CYP induction in hepatotoxicity and carcinogenicity 

29 of TCDD is unknown, and CYP induction is not considered a relevant POD without obvious 

30 pathological significance. 

31 In multiple studies by Hassoun et al. (1998, 2000, 2002, 2003), various indicators of 

32 oxidative stress were measured in hepatic and brain tissue of female B6C3F1 mice and Sprague-
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 G-2 DRAFT—DO NOT CITE OR QUOTE 

1 Dawley rats following 13 or 30 weeks of TCDD gavage dosing (5 days a week). Biomarkers for 

2 oxidative stress included production superoxide anion, lipid peroxidation, and DNA single-strand 

3 breaks. The authors report a statistically significant effect on several oxidative stress markers as 

4 a result of TCDD exposure, the lowest dose producing an effect being 0.32 ng/kg-day (Hassoun 

5 et al., 1998). In this study, all oxidative stress markers were significantly effected, but no other 

6 indicators of brain pathology were assessed. Thus, it is impracticable to link the markers of 

7 oxidative stress to a toxicological outcome in the brain, and this study and its endpoints are not 

8 considered relevant POD candidates. 

9 Burleson et al. (1996) analyzed the effect of a TCDD on viral host resistance following a 

10 single gavage dose of TCDD by measuring mortality mediated by influenza virus challenge in 

11 B6C3F1 female mice. The study authors found that TCDD at ≥10 ng/kg-day increased 

12 influenza-induced mortality. The experimental design calls for a 30% mortality in untreated 

13 animals (15% was achieved); mortality, itself, is not a direct result of TCDD exposure. None of 

14 the other immunologically-relevant measures were affected by TCDD treatment in this study, 

15 and no other effects were reported. The interpretation of these results with respect to humans is 

16 problematic. Furthermore, the findings were not reproduced by Nohara et al. (2002) using the 

17 same experimental design (see Section 2.4.2). Therefore, this endpoint is not considered relevant 

18 as a POD candidate. 

19 To examine the central nervous system response to TCDD, Kuchiiwa et al (2002) 

20 analyzed the effect of in utero and lactational TCDD exposure on the serotonergic system in the 

21 brainstem of male ddY mice. Female mice were administered TCDD by oral gavage once a 

22 week for 8 weeks prior to pregnancy and, using an immunocytochemical detection method, the 

23 raphe nuclei in the brainstem of male offspring was monitored for serotogergic neurons. TCDD 

24 at 0.7 ng/kg-day caused a 25−50% reduction in the immunostaining of serotonin, however there 

25 were no differences in external morphology, birth or postnatal body weights between 

26 TCDD-exposed and control offspring. The authors suggest that these findings may indicate that 

27 TCDD acts as a neuroteratogen by mediating long-term alterations in neuronal serotonin 

28 synthesis and serotonergic function. However, no other relevant neurotoxicity endpoints were 

29 examined or reported. Thus, reduced serotonin is not an adverse endpoint of toxicological 

30 significance in and of itself, and this study is deemed unsuitable as a POD candidate. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 G-3 DRAFT—DO NOT CITE OR QUOTE 

1 Mally and Chipman (2002) evaluated the effect of TCDD on gap junctions, 

2 hypothesizing that as a nongenotoxic carcinogen, TCDD may induce tumor formation by 

3 disturbing tissue homeostasis. Female F344 rats were dosed with TCDD by oral gavage for 

4 either 3 consecutive days or 2 days a week for 28 days. Gap junction connexin (Cx) plaque 

5 expression and hepatocyte proliferation was measured. The study authors report a decrease in 

6 Cx32 plaque number and area in the liver of rats exposed to 0.7 ng/kg-day and higher, however 

7 they did not find an associated increase in hepatocyte proliferation. No clinical signs of toxicity 

8 were observed, and histological examination of the liver revealed no abnormalities. In the 

9 absence of additional indicators of hepatotoxicity, a decrease in Cx32 plaque formation is not 

10 clearly linked to TCDD-mediated hepatotoxicity or hepatocarcinogenicty, nor is it considered an 

11 adverse effect. This endpoint is not considered a toxicologically relevant POD. 

12 Vanden Heuvel et al. (1994) analyzed changes in hepatic mRNA following a single 

13 administration of TCDD to female Sprague-Dawley rats by oral gavage. Four days after 

14 treatment, animals were sacrificed and livers were excised. Using reverse transcriptase15 polymerase chain reaction (RT-PCR) on hepatic RNA, they compared levels of “dioxin 

16 responsive” mRNA’s (CYP1A1, UDP-glucuronosyltransferase I, plasminogen activator inhibitor 

17 2, and transforming growth factor α) at various doses of TCDD and at control (baseline) levels. 

18 They determined that CYP1A1 elicited the most sensitive response to TCDD, with a statistically 

19 significant increase (3-fold) in mRNA from rat livers exposed to 1 ng/kg-day TCDD. Induction 

20 of CYP1A1 expression is not considered an adverse effect, as the role of CYP1A1 in 

21 TCDD-mediated carcinogenicity is unsettled. Therefore, in the absence of other indicators of 

22 hepatoxicity, increases in liver CYP1A1 cannot be considered toxicologically relevant for a POD 

23 candidate. 

24 Devito et al. (1994) assessed the activity of CYP1A1 and CYP1A2, the amount of 

25 phosphorylation of phosphotyrosyl proteins (pp32, pp34, and pp38), and the levels of estrogen 

26 receptor in the liver, uterus, lung and skin tissue of female B6C3F1 mice administered TCDD for 

27 5 days a week for 13 weeks. The authors hypothesized that these measurements may be 

28 sensitive biomarkers for exposure to TCDD. Body weights were also recorded weekly. 

29 Induction of CY1A1 and CYP1A2, as well as increased phosphorylated forms of pp32, pp34, 

30 and pp38 were sensitive indicators of TCDD exposure, with statistically significant changes seen 

31 at 1.07 ng/kg-day. EROD activity in the ling, skin, and liver was also observed with significant 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 G-4 DRAFT—DO NOT CITE OR QUOTE 

1 increases at this dose. However, the authors did not find a change in rat body or terminal organ 

2 weights, nor did they note any pathology in the animals at this dose level. The role of CYPs and 

3 phosphorylated pp32, pp34, and pp38 in TCDD-mediated toxicity is unknown, and changes in 

4 the activity or function of these proteins are not considered adverse. Therefore, these endpoints 

5 are not considered suitable as PODs. 

6 Because TCDD had been detected in the soil of contaminated locations, determining the 

7 bioavailability of TCDD from ingested soil may be important to the calculation of safe exposure 

8 levels. Lucier et al. (1986) fed adult female Sprague-Dawley rats TCDD contaminated soil or 

9 gave them TCDD in corn oil at various doses and compared the effects of TCDD on biochemical 

10 parameters from liver tissue. They found that equivalent doses of TCDD in corn oil and soil 

11 produced similar increases in hepatic aryl hydrocarbon hydroxylase activity (AHH) and UDP 

12 glucuronyltransferase activity. They determined that AHH was statistically induced 1.8-fold at 

13 15 ng/kg in corn oil and 40 ng/kg in soil. Cytochrome P450 was significantly increased at higher 

14 doses. No clinical signs of acute toxicity or changes in body weight were observed. The 

15 association between AHH activity and TCDD-mediated hepatotoxicity is unknown and no 

16 adverse endpoints were measured. Thus, this endpoint is not suitable as a POD candidate. 

17 Sugita-Konishi et al. (2003) investigated the change in host resistance of mice offspring 

18 lactationally exposed to TCDD. Pregnant C57BL/6NCji mice were administered TCDD via 

19 drinking water from parturition to weaning of the offspring (17 days). One group of offspring 

20 was then infected with Listeria monocytogenes and blood and spleen samples were collected 

21 various time points post infection. Uninfected, TCDD exposed offspring were weighed and their 

22 spleens and thymuses removed for assay of cellular content and protein expression. TCDD 

23 exposure caused a statistically-significant decrease in relative spleen weight and a statistically24 significant increase in thymic CD4+ cells in the high-dose group (11.3 ng/kg-day). Offspring 

25 infected with Listeria following TCDD exposure exhibited a statistically significant increase in 

26 serum tumor necrosis factor alpha (TNF-α) 2 days after infection in both sexes in the low27 (1.14 ng/kg-day) and high-dose groups. The authors conclude that exposure to TCDD disrupted 

28 the host resistance of the offspring at the lowest dose tested, despite the primary immune 

29 parameters being unaffected. Without an obvious association between TCDD and immune 

30 function, however, this endpoint is not suitable for identification of a LOAEL. Thus, the 

31 LOAEL for this study is 11.3 ng/kg-day, and the NOAEL is 1.14 ng/kg-day. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 G-5 DRAFT—DO NOT CITE OR QUOTE 

1 Sewall et al. (1993) investigated alterations in the epidermal growth factor receptor 

2 (EGFR) pathway in a two-stage initiation promotion model of TCDD hepatic cancer. EGFR 

3 signaling has been implicated in the altered cell growth induction by tumor promoters. Female 

4 Sprague-Dawley rats were administered TCDD biweekly by oral gavage for 30 weeks following 

5 initiation by a single dose of diethylnitrosamine (DEN). A group also received TCDD without 

6 prior DEN initiation. Livers were harvested and fixed from sacrificed animals and sections 

7 tested for EGFR binding, autophosphorylation, immunolocalization, and hepatic cell 

8 proliferation. The authors report a significant dose-dependent decrease in plasma membrane 

9 EGFR maximum binding capacity in TCDD-exposed rats beginning at 3.5 ng/kg-day. However, 

10 at this same dose, the authors note a statistically significant decrease in cell proliferation (as 

11 measured by DNA replication labeling), with increases in proliferation only occurring at higher 

12 doses (125 ng/kg-day). No other indicators of hepatic toxicity or tumorigenicity were assessed. 

13 The role of EGFR in TCDD-mediated hepatotoxicity and hepatocarcinogenicity is unknown, and 

14 as such, this endpoint cannot be unequivocally linked to TCDD-induced hepatic effects nor 

15 labeled as adverse. Thus, it is not suitable as a POD candidate. 

16

17 G.1. REFERENCES 

18 Burleson, GR; Lebrec, H; Yang, YG; et al. (1996) Effect of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) on 

19 influenza virus host resistance in mice. Fund Appl Toxicol 29:40−47. 

20 Devito, MJ; Ma, X; Babish, JG; et al. (1994) Dose-response relationships in mice following subchronic exposure to 

21 2,3,7,8-tetrachlorodibenzo-p-dioxin: CYP1A1, CYP1A2, estrogen receptor, and protein tyrosine phosphoylation. 

22 Toxicol Appl Pharmacol 124:82–90. 

23 Hassoun, EA; Wilt, SC; DeVito, MJ; et al. (1998) Induction of oxidative stress in brain tissues of mice after 

24 subchronic exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin. Toxicol Sci 42:23−27. 

25 Hassoun, EA; Li, F; Abushaban, A; et al. (2000) The relative abilities of TCDD and its congeners to induce 

26 oxidative stress in the hepatic and brain tissues of rats after subchronic exposure. Toxicology 145:103−113. 

27 Hassoun, EA; Wang, H; Abushaban, A. (2002) Induction of oxidative stress following chronic exposure to TCDD, 

28 2,3,4,7,8-pentachlorodibenzofuran, and 2,3’,4,4’,5-pentachlorobiphenyl. J Toxicol Environ Health A 65:825−842. 

29 Hassoun, EA; Al-Ghafri, M; Abushaban, A. (2003) The role of antioxidant enzymes in TCDD-induced oxidative 

30 stress in various brain regions of rats after subchronic exposure. Free Rad Biol Medicine 35(9):1028−1036. 

31 Kitchin, KT; Woods, JS. (1979) 2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) effects on hepatic microsomal 

32 cytochrome P-448-mediated enzyme activities. Toxicol Appl Pharmacol 47:537−546. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 G-6 DRAFT—DO NOT CITE OR QUOTE 

1 Kuchiiwa, S; Cheng, S-B; Nagatomo, I; et al. (2002) In utero and lactational exposure to 2,3,7,8-tetrachlorodibenso2 p-dioxin decreases serotonin-immunoreactive neurons in raphe nuclei of male mouse offspring. Neurosci Lett 

3 317:73−76. 

4 Lucier, GW; Rumbaugh, RC; McCoy, Z; et al. (1986) Ingestion of soil contaminated with 2,3,7,8-tetrachloro5 dibenzo-p-dioxin (TCDD) alters hepatic enzyme activities in rats. Fund Appl Toxicol 6:364–371. 

6 Mally, A; Chipman, JK. (2002) Non-genotoxic carcinogens: early effects on gap junctions, cell proliferation and 

7 apoptosis in the rat. Toxicology 180:233–248. 

8 Nohara, K; Izumi, H; Tamura, S; et al. (2002) Effect of low-dose 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) on 

9 influenza A virus-induced mortality in mice. Toxicology 170:131–138. 

10 Sewall, CH; Lucier, GW; Tritscher, AM; et al. (1993) TCDD-mediated changes in hepatic epidermal growth factor 

11 receptor may be a critical event in the hepatocarcinogenic action of TCDD. Carcinogenesis 14:1885–1893. 

12 Sugita-Konishi, Y; Kobayashi, K; Naito, H; et al. (2003) Effect of lactational exposure to 2,3,7,8-

13 tetrachlorodibenzo-p-dioxin on the susceptibility to Listeria infection. Biosci Biotechnol Biochem 67(1):89−93. 

14 U.S. EPA. (2003) Exposure and human health reassessment of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and 

15 related compounds [NAS review draft]. Volumes 1−3. National Center for Environmental Assessment, Washington, 

16 DC; EPA/600/P-00/001 Cb. Available at: http://www.epa.gov/nceawww1/pdfs/dioxin/nas-review/. 

17 Vanden Heuvel, JP; Clark, GC; Tritscher, A; et al. (1994) Accumulation of polychlorinated dibenzo-p-dioxins and 

18 dibenzofurans in liver of control laboratory rats. Fundam Appl Toxicol 23:465–469. 

 19

DRAFT 

DO NOT CITE OR QUOTE January 2010 

Agency/Interagency Review Draft 

APPENDIX H 

Cancer Precursor Benchmark Dose Modeling 

NOTICE 

THIS DOCUMENT IS AN AGENCY/INTERAGENCY REVIEW DRAFT. It has not been 

formally released by the U.S. Environmental Protection Agency and should not at this stage be 

construed to represent Agency policy. It is being circulated for comment on its technical 

accuracy and policy implications. 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Cincinnati, OH 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-ii —DO NOT CITE OR QUOTE 

CONTENTS—APPENDIX H: Cancer Precursor Benchmark Dose Modeling 

APPENDIX H. CANCER PRECURSOR BENCHMARK DOSE MODELING.......................1 

H.1. BMDS INPUT TABLES .........................................................................................1 

H.1.1. Hassoun et al. (2000) ................................................................................1 

H.1.2. Kitchin et al. (1979) ..................................................................................1 

H.1.3. National Toxicology Program. (2006), 31 Week Exposure .....................2 

H.1.4. National Toxicology Program (2006), 53 Week Exposure ......................2 

H.1.5. National Toxicology Program (2006), 2 Year Exposure..........................2 

H.1.6. Van Birgelen et al. (1995a, b)...................................................................3 

H.1.7. Vanden Heuvel et al. (1994) .....................................................................3 

H.2. ALTERNATE DOSE: BLOOD SERUM BMDS RESULTS ................................3 

H.2.1. Hassoun et al. (2000): CytC liver ............................................................3 

H.2.1.1. Summary Table of BMDS Modeling Results............................3 

H.2.1.2. Figure for Selected Model: Exponential (M5), Constant 

Variance, Power Restricted ≥1 ..................................................5 

H.2.1.3. Output File for Selected Model: Exponential (M5), 

Constant Variance, Power Restricted ≥1 ...................................5 

H.2.1.4. Figure for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted.....................................8 

H.2.1.5. Output file for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted.....................................8 

H.2.1.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted..............................................................................11 

H.2.1.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted ..........................................................11 

H.2.1.8. Figure for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ..................................................14 

H.2.1.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ..................................................14 

H.2.2. Hassoun et al. (2000): DNA SSB ..........................................................17 

H.2.2.1. Summary Table of BMDS Modeling Results..........................17 

H.2.2.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1 ................................................18 

H.2.2.3. Output File For Selected Model: Exponential (M4), 

Constant Variance, Power Restricted ≥1 .................................18 

H.2.2.4. Figure for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted...................................21 

H.2.2.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted...................................21 

H.2.2.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted..............................................................................24 

H.2.2.7. Output File For Unrestricted Model: Hill, Constant 

Variance, n Unrestricted ..........................................................24 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-iii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.2.2.8. Figure for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ..................................................27 

H.2.2.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ..................................................27 

H.2.3. Hassoun et al. (2000): TBARs Liver .....................................................30 

H.2.3.1. Summary Table of BMDS Modeling Results..........................30 

H.2.3.2. Figure for Selected Model: Exponential (M5), Constant 

Variance, Power Unrestricted ..................................................31 

H.2.3.3. Output File for Selected Model: Exponential (M5), 

Constant Variance, Power Unrestricted...................................31 

H.2.3.4. Figure for Unrestricted Model: Hill, Constant Variance, n 

Restricted >1 ............................................................................34 

H.2.3.5. Output File for Unrestricted Model: Hill, Constant 

Variance, n Restricted >1.........................................................34 

H.2.3.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted..............................................................................37 

H.2.3.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted ..........................................................37 

H.2.3.8. Figure for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ..................................................40 

H.2.3.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ..................................................40 

H.2.4. Kitchin et al. (1979): BaP Hydrolase Activity.......................................43 

H.2.4.1. Summary Table of BMDS Modeling Results..........................43 

H.2.4.2. Figure for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 ...........................44 

H.2.4.3. Output File for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 ...........................44 

H.2.4.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................47 

H.2.4.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................47 

H.2.4.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................50 

H.2.4.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................51 

H.2.4.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ..................................................53 

H.2.4.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ..................................................53 

H.2.5. National Toxicology Program. (2006): EROD Liver Week 53.............57 

H.2.5.1. Summary Table of BMDS Modeling Results..........................57 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-iv —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.2.5.2. Figure for Selected Model: Hill, Nonconstant Variance, n 

Restricted >1 ............................................................................58 

H.2.5.3. Output file for Selected Model: Hill, Nonconstant 

Variance, n Restricted >1.........................................................58 

H.2.5.4. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................61 

H.2.5.5. Output file for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................61 

H.2.6. National Toxicology Program. (2006): Lung EROD Week 31 .............64 

H.2.6.1. Summary Table of BMDS Modeling Results..........................64 

H.2.6.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 ...........................65 

H.2.6.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 ...........................65 

H.2.6.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................68 

H.2.6.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................68 

H.2.6.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................71 

H.2.6.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................71 

H.2.6.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ..................................................74 

H.2.6.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ..................................................74 

H.2.7. National Toxicology Program. (2006): Lung EROD Week 53 .............77 

H.2.7.1. Summary Table of BMDS Modeling Results..........................77 

H.2.7.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 ...........................78 

H.2.7.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 ...........................78 

H.2.7.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................81 

H.2.7.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................81 

H.2.7.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................84 

H.2.7.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ..........................................................84 

H.2.7.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ..................................................87 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-v —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.2.7.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ..................................................87 

H.2.8. National Toxicology Program. (2006): Tbl11 Index Week 31..............90 

H.2.8.1. Summary Table of BMDS Modeling Results..........................90 

H.2.8.2. Figure for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1 ...........................91 

H.2.8.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1 ...........................91 

H.2.9. Van Birgelen et al. (1995b): T4 UGT....................................................94 

H.2.9.1. Summary Table of BMDS Modeling Results..........................94 

H.2.9.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 ...........................95 

H.2.9.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 ...........................95 

H.2.9.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................98 

H.2.9.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted.............................98 

H.2.9.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................101 

H.2.9.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................101 

H.2.9.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................105 

H.2.9.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................105 

H.2.10. Van Birgelen et al. (1995b): UGT 1A1 ...............................................108 

H.2.10.1. Summary Table of BMDS Modeling Results........................108 

H.2.10.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................109 

H.2.10.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................109 

H.2.10.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................112 

H.2.10.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................112 

H.2.10.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................115 

H.2.10.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................115 

H.2.10.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................118 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-vi —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.2.10.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................118 

H.2.11. Vanden Heuvel et al. (1994): Hepatic CYP1A1 mRNA Expression...121 

H.2.11.1. Summary Table of BMDS Modeling Results........................121 

H.2.11.2. Figure for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 .........................122 

H.2.11.3. Output File for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 .........................122 

H.3. ADMINISTERED DOSE BMDS RESULTS .....................................................125 

H.3.1. Hassoun et al. (2000): CytC Liver .......................................................125 

H.3.1.1. Summary Table of BMDS Modeling Results........................125 

H.3.1.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1 ..............................................126 

H.3.1.3. Output File for Selected Model: Exponential (M4), 

Constant Variance, Power Restricted ≥1 ...............................126 

H.3.1.4. Figure for Unrestricted Model: Exponential (M5), Constant 

Variance, Power Unrestricted ................................................129 

H.3.1.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted.................................129 

H.3.1.6. Figure for Unrestricted Model: Hill, Constant Variance, n 

Unrestricted............................................................................132 

H.3.1.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted ........................................................132 

H.3.1.8. Figure for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ................................................135 

H.3.1.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ................................................135 

H.3.2. Hassoun et al. (2000): DNA SSB ........................................................138 

H.3.2.1. Summary Table of BMDS Modeling Results........................138 

H.3.2.2. Figure for Selected Model: Exponential (M5), Constant 

Variance, Power Unrestricted ................................................139 

H.3.2.3. Output File for Selected Model: Exponential (M5), 

Constant Variance, Power Unrestricted.................................139 

H.3.2.4. Figure for Unrestricted Model: Hill, Constant Variance, n 

Restricted >1, Bound Hit .......................................................142 

H.3.2.5. Output File for Unrestricted Model: Hill, Constant 

Variance, n Restricted >1, Bound Hit....................................142 

H.3.2.6. Figure for Unrestricted Model: Hill, Constant Variance, 

n Unrestricted.........................................................................145 

H.3.2.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted ........................................................145 

H.3.2.8. Figure for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ................................................148 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-vii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.3.2.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ................................................148 

H.3.3. Hassoun et al. (2000): TBARs Liver ...................................................151 

H.3.3.1. Summary Table of BMDS Modeling Results........................151 

H.3.3.2. Figure for Selected Model: Exponential (M4), Constant 

Variance, Power Restricted ≥1 ..............................................152 

H.3.3.3. Output File for Selected Model: Exponential (M4), 

Constant Variance, Power Restricted ≥1 ...............................152 

H.3.3.4. Figure for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted.................................155 

H.3.3.5. Output File for Unrestricted Model: Exponential (M5), 

Constant Variance, Power Unrestricted.................................155 

H.3.3.6. Figure for Unrestricted Model: Hill, Constant Variance, 

n Unrestricted.........................................................................158 

H.3.3.7. Output File for Unrestricted Model: Hill, Constant 

Variance, n Unrestricted ........................................................158 

H.3.3.8. Figure for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ................................................161 

H.3.3.9. Output File for Unrestricted Model: Power, Constant 

Variance, Power Unrestricted ................................................161 

H.3.4. Kitchin et al. (1979): BaP Hydrolase Activity.....................................164 

H.3.4.1. Summary Table of BMDS Modeling Results........................164 

H.3.4.2. Figure for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 .........................165 

H.3.4.3. Output File for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 .........................165 

H.3.4.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................168 

H.3.4.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................168 

H.3.4.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................171 

H.3.4.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................172 

H.3.4.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................174 

H.3.4.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................175 

H.3.5. National Toxicology Program. (2006): EROD Liver Week 53...........177 

H.3.5.1. Summary Table of BMDS Modeling Results........................177 

H.3.5.2. Figure for Selected Model: Hill, Nonconstant Variance, 

n Restricted >1 .......................................................................178 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-viii —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.3.5.3. Output File for Selected Model: Hill, Nonconstant 

Variance, n Restricted >1.......................................................179 

H.3.5.4. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................181 

H.3.5.5. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................181 

H.3.6. National Toxicology Program. (2006): Lung EROD Week 31 ...........184 

H.3.6.1. Summary Table of BMDS Modeling Results........................184 

H.3.6.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................185 

H.3.6.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................185 

H.3.6.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................188 

H.3.6.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................188 

H.3.6.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................191 

H.3.6.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................191 

H.3.6.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................194 

H.3.6.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................194 

H.3.7. National Toxicology Program. (2006): Lung EROD Week 53 ...........197 

H.3.7.1. Summary Table of BMDS Modeling Results........................197 

H.3.7.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................198 

H.3.7.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................198 

H.3.7.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................201 

H.3.7.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................201 

H.3.7.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................204 

H.3.7.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................204 

H.3.7.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................207 

H.3.7.9. Output File for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................207 

H.3.8. National Toxicology Program. (2006): Tbl11 Index Week 31............210 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-ix —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.3.8.1. Summary Table of BMDS Modeling Results........................210 

H.3.8.2. Figure for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1 .........................211 

H.3.8.3. Output File for Selected Model: Exponential (M2), 

Nonconstant Variance, Power Restricted ≥1 .........................211 

H.3.9. Van Birgelen et al. (1995b): T4 UGT..................................................214 

H.3.9.1. Summary Table of BMDS Modeling Results........................214 

H.3.9.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................215 

H.3.9.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................215 

H.3.9.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................218 

H.3.9.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................218 

H.3.9.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................221 

H.3.9.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................221 

H.3.9.8. Figure for Unrestricted Model: Power, Nonconstant 

Variance, Power Unrestricted ................................................224 

H.3.9.9. Output File for Unrestricted Model: Power, 

Nonconstant Variance, Power Unrestricted...........................224 

H.3.10. Van Birgelen et al. (1995b): UGT 1A1 ...............................................227 

H.3.10.1. Summary Table of BMDS Modeling Results........................227 

H.3.10.2. Figure for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................228 

H.3.10.3. Output File for Selected Model: Exponential (M4), 

Nonconstant Variance, Power Restricted ≥1 .........................228 

H.3.10.4. Figure for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................231 

H.3.10.5. Output File for Unrestricted Model: Exponential (M5), 

Nonconstant Variance, Power Unrestricted...........................231 

H.3.10.6. Figure for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................234 

H.3.10.7. Output File for Unrestricted Model: Hill, Nonconstant 

Variance, n Unrestricted ........................................................234 

H.3.10.8. Figure for Unrestricted Model: Power, Nonconstant Variance, 

Power Unrestricted.................................................................237 

H.3.10.9. Output File for Unrestricted Model: Power, 

Nonconstant Variance, Power Unrestricted...........................237 

H.3.11. Vanden Heuvel et al. (1994): Hepatic CYP1A1 mRNA 

Expression ........................................................................................240 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-x —DO NOT CITE OR QUOTE 

CONTENTS (continued) 

H.3.11.1. Summary Table of BMDS Modeling Results........................240 

H.3.11.2. Figure for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 .........................241 

H.3.11.3. Output File for Selected Model: Exponential (M5), 

Nonconstant Variance, Power Restricted ≥1 .........................241 

H.4. REFERENCES ....................................................................................................244 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-1 —DO NOT CITE OR QUOTE 

1 APPENDIX H. CANCER PRECURSOR BENCHMARK DOSE MODELING 

 2 

 3 

4 H.1. BMDS INPUT TABLES 

5 H.1.1. Hassoun et al. (2000) 

Administered Dose (ng/kg-day) 

0 3 10 22 46 100 

Internal Dose (ng/kg blood) a

0 1,068 2,542 4,489 7,718 13,960 

Endpoint n = 6 n = 6 n = 6 n = 6 n = 6 n = 6 

CytC liver 0.15 ± 0.07 0.18 ± 0.05 b 0.19 ± 0.06 0.27 ± 0.06 c 0.39 ± 0.06 c 0.44 ± 0.11 c

DNA SSB 7.41 ± 1.54 10.78 ± 1.25 b,c 13.6 ± 1.69 c 15.3 ± 1.71 c 20.4 ± 2.25 c 23.5 ± 1.37 c

TBARs liver 1.47 ± 0.29 1.55 ± 0.54 b 2.15 ± 0.36 c 2.28 ± 0.25 c 2.62 ± 0.52 c 2.29 ± 0.49 c

a

From the Emond PRPK model described in 3.3. 

b

LOEL for selected endpoint.

c

Statistically significant as compared to control (p < 0.05). 

 6 

 7 

8 H.1.2. Kitchin et al. (1979) 

Administered Dose (ng/kg-day) 

0 0.2 0.667 1.33 6.67 20 

Internal Dose (ng/kg blood) a

0 70 232 463 2,318 6,949 

Endpoint n = 9 n = 4 n = 4 n = 4 n = 4 n = 4 

BaP hydrolase activity 

(continued on next line) 4.9 ± 1.11 4.9 ± 1.18 b 6.7 ± 1.4 c,d 7.2 ± 1.8 d 8.3 ± 0.26 e 14 ± 5 e

Administered Dose (ng/kg-day) 

66.7 200 667 1,670 6,670 

Internal Dose (ng/kg blood) a

23,185 69,657 232,550 581,930 2,332,100 

Endpoint n = 4 n = 4 n = 4 n = 4 n = 4 

BaP hydrolase activity 

(continued) 59 ± 6.8 e 96 ± 46 e 155 ± 16.4 e 182 ± 26 e 189 ± 26 e 

a

From the Emond PRPK model described in 3.3. 

b

NOEL for selected endpoint. 

c

LOEL for selected endpoint. 

d

Statistically significant as compared to control (p < 0.05). e

Statistically significant as compared to control (p < 0.001). 

 9 

 10 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-2 —DO NOT CITE OR QUOTE 

1 H.1.3. National Toxicology Program. (2006), 31 Week Exposure 

Administered Dose (ng/kg-day) 

0 2.14 7.14 15.7 32.9 71.4 

Internal Dose (ng/kg blood) a

0 1,284 2,932 5,075 8,629 15,503 

Endpoint n = 9 n = 10 n = 10 n = 10 n = 10 n = 10 

Tbl11 Index ,week 31 0.33 ± 0.19 0.85 ± 0.65 b 0.96 ± 0.74 b 0.79 ± 0.46 b 1.33 ± 1.12 b 3.85 ± 3.08 b

Lung EROD, week 31 2.07 ± 0.97 25.34 ± 2.55 c 30.39 ± 5.83 c 50.19 ± 8.68 c 49.07 ± 13.91 c 48.42 ± 8.93 c

a

From the Emond PRPK model described in 3.3. 

b

Statistically significant as compared to control (p < 0.05). c

Statistically significant as compared to control (p < 0.01). 

 2 

 3 

4 H.1.4. National Toxicology Program (2006), 53 Week Exposure 

Administered Dose (ng/kg-day) 

0 2.14 7.14 15.7 32.9 71.4 

Internal Dose (ng/kg blood) a

0 1,354 3,056 5,259 8,918 16,001 

Endpoint n = 8 n = 8 n = 8 n = 8 n = 8 n = 8 

Liver EROD, week 53 3.61 ± 0.49 7.27 ± 0.56 b 14.76 ± 1.61 b 17.28 ± 1.59 b 20.58 ± 3.05 b 21.21 ± 3.82 b

Lung EROD, week 53 3.01 ± 1.58 27.15 ± 5.27 b 42.85 ± 11.15 b 36.57 ± 12.99 b 43.75 ± 18.55 b 43.71 ± 6.32 b

a

From the Emond PRPK model described in 3.3. 

b

Statistically significant as compared to control (p < 0.01).

 5 

 6 

7 H.1.5. National Toxicology Program (2006), 2 Year Exposure 

Administered Dose (ng/kg-day) 

0 2.14 7.14 15.7 32.9 71.4 

Internal Dose (ng/kg blood) a

0 1,408 3,137 5,393 9,129 16,361 

Endpoint n = 53 n = 54 n = 53 n = 53 n = 53 n = 53 

Toxic Hepatopathy 0/53 (0%) 2/54 (0%) 8/53 (20%) b 30/53 (60%) b 45/53 (80%) b 53/53 (100%) b

a

From the Emond PRPK model described in 3.3. 

b

Statistically significant as compared to control (p < 0.01).

 8 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-3 —DO NOT CITE OR QUOTE 

1 H.1.6. Van Birgelen et al. (1995a, b) 

Administered Dose (ng/kg-day) 

0 14 26 47 320 1,024 

Internal Dose (ng/kg blood) a

0 3,969 6,479 9,968 47,606 137,820 

Endpoint n = 8 n = 8 n = 8 n = 8 n = 8 n = 8 

T4 UGT 0.33 ± 0.2 0.6 ± 0.42 0.64 ± 0.45 b 0.87 ± 0.91 b 2.08 ± 1.33 b 2.59 ± 0.88 b

UGT 1A1 101 ± 15.59 194 ± 36.37 b Not reported. 304 ± 17.32 b 452 ± 48.5 b 296 ± 148.96 b

a

From the Emond PRPK model described in 3.3. 

b

Statistically significant as compared to control (p < 0.05). 

 2 

 3 

4 H.1.7. Vanden Heuvel et al. (1994) 

Administered Dose (ng/kg-day) 

0 0.1 1 10 100 1,000 10,000 

Internal Dose (ng/kg blood) a

0 4 36 302 2,149 14,301 114,690 

Endpoint 

n = 13 n = 5 n = 12 n = 7 n = 7 n = 11 n = 5 

Hepatic CYP1A1 

mRNA Expression 5.4 ± 3.61 7.2 ± 5.59 14.8 ± 14.9 b 12.8 ± 4.5 b 536 ± 320.14 b 18000 ± 15223.31 b

36700 ± 

22137.07 b

a

From the Emond PRPK model described in 3.3. 

b

Statistically significant as compared to control (p < 0.05).

 5 

 6 

7 H.2. ALTERNATE DOSE: BLOOD SERUM BMDS RESULTS 

8 H.2.1. Hassoun et al. (2000): CytC liver 

9 H.2.1.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 0.39 10.22 0.04 -145.92 3.5E+03 2.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.39 10.22 0.04 -145.92 3.5E+03 2.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.39 3.38 0.34 -150.76 1.6E+03 9.7E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.39 0.56 0.76 -151.58 3.0E+03 1.4E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.39 0.56 0.76 -151.58 3.0E+03 1.4E+03 nonconstant variance, 

power unrestricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-4 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

Hill 2 0.39 0.66 0.72 -151.47 3.1E+03 error nonconstant variance, 

n restricted >1 

Hill 2 0.39 0.66 0.72 -151.47 3.1E+03 error nonconstant variance, 

n unrestricted 

linear 4 0.39 4.68 0.32 -151.45 2.1E+03 1.4E+03 nonconstant variance 

polynomial 4 0.39 4.68 0.32 -151.45 2.1E+03 1.4E+03 nonconstant variance 

power 4 0.39 4.68 0.32 -151.45 2.1E+03 1.4E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.39 4.26 0.23 -149.87 1.6E+03 6.8E+02 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.39 12.17 0.02 -143.33 5.1E+03 4.3E+03 constant variance, 

power restricted ≥1 

exponential (M3) 4 0.39 12.17 0.02 -143.33 5.1E+03 4.3E+03 constant variance, 

power restricted ≥1 

exponential (M4) 3 0.39 3.37 0.34 -150.14 1.9E+03 1.2E+03 constant variance, 

power restricted ≥1 

exponential (M5) c 2 0.39 0.48 0.79 -151.03 3.3E+03 1.7E+03 constant variance, 

power restricted ≥1 

exponential (M5) d 2 0.39 0.48 0.79 -151.03 3.3E+03 1.7E+03 constant variance, 

power unrestricted 

Hill 2 0.39 0.59 0.74 -150.91 3.4E+03 1.8E+03 constant variance, n 

restricted >1 

Hill d 2 0.39 0.59 0.74 -150.91 3.4E+03 1.8E+03 constant variance, n 

unrestricted 

linear 4 0.39 6.42 0.17 -149.09 3.1E+03 2.4E+03 constant variance 

polynomial 4 0.39 6.42 0.17 -149.09 3.1E+03 2.4E+03 constant variance 

power 4 0.39 6.42 0.17 -149.09 3.1E+03 2.4E+03 

constant variance, 

power restricted ≥1, 

bound hit 

power d 3 0.39 4.84 0.18 -148.66 1.8E+03 7.4E+02 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix d

Alternate model also presented in this appendix 

1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-5 —DO NOT CITE OR QUOTE 

1 H.2.1.2. Figure for Selected Model: Exponential (M5), Constant Variance, Power Restricted 

2 ≥1 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Exponential

3 

 4 

 5 

6 H.2.1.3. Output File for Selected Model: Exponential (M5), Constant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Exp_CV_BMR1_CytC_Liver.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 23 12:51:43 2009 

15 ==================================================================== 

16 

17 TBARs, liver only (Table 2) 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-6 —DO NOT CITE OR QUOTE 

1 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

2 rho is set to 0. 

3 A constant variance model is fit. 

4 

5 Total number of dose groups = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 5 

17 -------- -------- 

18 lnalpha -5.48625 

19 rho(S) 0 

20 a 0.1387 

21 b 4.08913e-005 

22 c 6.40231 

23 d 1 

24 

25 (S) = Specified 

26 

27 

28 

29 Parameter Estimates 

30 

31 Variable Model 5 

32 -------- ------- 

33 lnalpha -5.47298 

34 rho 0 

35 a 0.156024 

36 b 0.00016181 

37 c 2.85354 

38 d 2.14237 

39 

40 

41 Table of Stats From Input Data 

42 

43 Dose N Obs Mean Obs Std Dev 

44 ----- --- ---------- ------------- 

45 0 6 0.146 0.06614 

46 1068 6 0.177 0.05389 

47 2542 6 0.191 0.05634 

48 4489 6 0.271 0.05634 

49 7718 6 0.388 0.06369 

50 1.396e+004 6 0.444 0.1102 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 0.156 0.0648 -0.3789 

58 1068 0.1627 0.0648 0.5416 

59 2542 0.1961 0.0648 -0.1919 

60 4489 0.2705 0.0648 0.01767 

61 7718 0.3874 0.0648 0.02225 

62 1.396e+004 0.4443 0.0648 -0.0107 

63 

64 

65 

66 Other models for which likelihoods are calculated: 

67 

68 Model A1: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-7 —DO NOT CITE OR QUOTE 

1 Model A2: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = Sigma(i)^2 

3 

4 Model A3: Yij = Mu(i) + e(ij) 

5 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

6 

7 Model R: Yij = Mu + e(i) 

8 Var{e(ij)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) DF AIC 

14 ------- ----------------- ---- ------------ 

15 A1 80.75258 7 -147.5052 

16 A2 83.37355 12 -142.7471 

17 A3 80.75258 7 -147.5052 

18 R 55.82002 2 -107.64 

19 5 80.51365 5 -151.0273 

20 

21 

22 Additive constant for all log-likelihoods = -33.08. This constant added to the 

23 above values gives the log-likelihood including the term that does not 

24 depend on the model parameters. 

25 

26 

27 Explanation of Tests 

28 

29 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

30 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

31 Test 3: Are variances adequately modeled? (A2 vs. A3) 

32 

33 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

34 

35 

36 Tests of Interest 

37 

38 Test -2*log(Likelihood Ratio) D. F. p-value 

39 -------- ------------------------ ------ -------------- 

40 Test 1 55.11 10 < 0.0001 

41 Test 2 5.242 5 0.3871 

42 Test 3 5.242 5 0.3871 

43 Test 7a 0.4779 2 0.7875 

44 

45 

46 The p-value for Test 1 is less than .05. There appears to be a 

47 difference between response and/or variances among the dose 

48 levels, it seems appropriate to model the data. 

49 

50 The p-value for Test 2 is greater than .1. A homogeneous 

51 variance model appears to be appropriate here. 

52 

53 The p-value for Test 3 is greater than .1. The modeled 

54 variance appears to be appropriate here. 

55 

56 The p-value for Test 7a is greater than .1. Model 5 seems 

57 to adequately describe the data. 

58 

59 

60 Benchmark Dose Computations: 

61 

62 Specified Effect = 1.000000 

63 

64 Risk Type = Estimated standard deviations from control 

65 

66 Confidence Level = 0.950000 

67 

68 BMD = 3257.85 

69 

70 BMDL = 1709.28 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-8 —DO NOT CITE OR QUOTE 

1 H.2.1.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

2 Unrestricted

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Exponential

3 

 4 

 5 

6 H.2.1.5. Output file for Unrestricted Model: Exponential (M5), Constant Variance, Power 

7 Unrestricted 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Exp_CV_Unrest_BMR1_CytC_Liver.(d) 

13 Gnuplot Plotting File: 

14 Mon Nov 23 12:51:49 2009 

15 ==================================================================== 

16 

17 TBARs, liver only (Table 2) 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-9 —DO NOT CITE OR QUOTE 

1 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

2 rho is set to 0. 

3 A constant variance model is fit. 

4 

5 Total number of dose groups = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 MLE solution provided: Exact 

12 

13 

14 Initial Parameter Values 

15 

16 Variable Model 5 

17 -------- -------- 

18 lnalpha -5.48625 

19 rho(S) 0 

20 a 0.1387 

21 b 4.08913e-005 

22 c 6.40231 

23 d 1 

24 

25 (S) = Specified 

26 

27 

28 

29 Parameter Estimates 

30 

31 Variable Model 5 

32 -------- ------- 

33 lnalpha -5.47298 

34 rho 0 

35 a 0.156024 

36 b 0.00016181 

37 c 2.85354 

38 d 2.14237 

39 

40 

41 Table of Stats From Input Data 

42 

43 Dose N Obs Mean Obs Std Dev 

44 ----- --- ---------- ------------- 

45 0 6 0.146 0.06614 

46 1068 6 0.177 0.05389 

47 2542 6 0.191 0.05634 

48 4489 6 0.271 0.05634 

49 7718 6 0.388 0.06369 

50 1.396e+004 6 0.444 0.1102 

51 

52 

53 Estimated Values of Interest 

54 

55 Dose Est Mean Est Std Scaled Residual 

56 ------ ---------- --------- ---------------- 

57 0 0.156 0.0648 -0.3789 

58 1068 0.1627 0.0648 0.5416 

59 2542 0.1961 0.0648 -0.1919 

60 4489 0.2705 0.0648 0.01767 

61 7718 0.3874 0.0648 0.02225 

62 1.396e+004 0.4443 0.0648 -0.0107 

63 

64 

65 Other models for which likelihoods are calculated: 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-10 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

5 

6 Model R: Yij = Mu + e(i) 

7 Var{e(ij)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) DF AIC 

13 ------- ----------------- ---- ------------ 

14 A1 80.75258 7 -147.5052 

15 A2 83.37355 12 -142.7471 

16 A3 80.75258 7 -147.5052 

17 R 55.82002 2 -107.64 

18 5 80.51365 5 -151.0273 

19 

20 

21 Additive constant for all log-likelihoods = -33.08. This constant added to the 

22 above values gives the log-likelihood including the term that does not 

23 depend on the model parameters. 

24 

25 

26 Explanation of Tests 

27 

28 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

29 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

30 Test 3: Are variances adequately modeled? (A2 vs. A3) 

31 

32 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

33 

34 Tests of Interest 

35 

36 Test -2*log(Likelihood Ratio) D. F. p-value 

37 -------- ------------------------ ------ -------------- 

38 Test 1 55.11 10 < 0.0001 

39 Test 2 5.242 5 0.3871 

40 Test 3 5.242 5 0.3871 

41 Test 7a 0.4779 2 0.7875 

42 

43 

44 The p-value for Test 1 is less than .05. There appears to be a 

45 difference between response and/or variances among the dose 

46 levels, it seems appropriate to model the data. 

47 

48 The p-value for Test 2 is greater than .1. A homogeneous 

49 variance model appears to be appropriate here. 

50 

51 The p-value for Test 3 is greater than .1. The modeled 

52 variance appears to be appropriate here. 

53 

54 The p-value for Test 7a is greater than .1. Model 5 seems 

55 to adequately describe the data. 

56 

57 

58 Benchmark Dose Computations: 

59 

60 Specified Effect = 1.000000 

61 

62 Risk Type = Estimated standard deviations from control 

63 

64 Confidence Level = 0.950000 

65 

66 BMD = 3257.85 

67 

68 BMDL = 1709.28 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-11 —DO NOT CITE OR QUOTE 

1 H.2.1.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Hill

2 

 3 

 4 

5 H.2.1.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_Unrest_BMR1_CytC_Liver.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_Unrest_BMR1_CytC_Liver.plt 

12 Mon Nov 23 12:51:51 2009 

13 ==================================================================== 

14 

15 TBARs, liver only (Table 2) 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 Power parameter is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 alpha = 0.004972 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-12 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 intercept = 0.146 

3 v = 0.298 

4 n = 18 

5 k = 10285.5 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 ( *** The model parameter(s) -rho 

11 have been estimated at a boundary point, or have been specified by the user, 

12 and do not appear in the correlation matrix ) 

13 

14 alpha intercept v n k 

15 

16 alpha 1 -2.4e-008 4.5e-008 -5.6e-008 2.4e-008 

17 

18 intercept -2.4e-008 1 -0.61 0.52 0.098 

19 

20 v 4.5e-008 -0.61 1 -0.83 0.6 

21 

22 n -5.6e-008 0.52 -0.83 1 -0.48 

23 

24 k 2.4e-008 0.098 0.6 -0.48 1 

25 

26 

27 

28 Parameter Estimates 

29 

30 95.0% Wald Confidence Interval 

31 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

32 alpha 0.00421237 0.000992864 0.00226639 0.00615834 

33 intercept 0.159647 0.0202575 0.119943 0.199351 

34 v 0.303055 0.0583218 0.188746 0.417363 

35 n 2.91267 1.3832 0.201656 5.62369 

36 k 5344.44 923.736 3533.95 7154.93 

37 

38 

39 

40 Table of Data and Estimated Values of Interest 

41 

42 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

43 ------ --- -------- -------- ----------- ----------- ---------- 

44 

45 0 6 0.146 0.16 0.0661 0.0649 -0.515 

46 1068 6 0.177 0.162 0.0539 0.0649 0.551 

47 2542 6 0.191 0.191 0.0563 0.0649 0.00541 

48 4489 6 0.271 0.273 0.0563 0.0649 -0.0938 

49 7718 6 0.388 0.385 0.0637 0.0649 0.101 

50 1.396e+004 6 0.444 0.445 0.11 0.0649 -0.0481 

51 

52 

53 

54 Model Descriptions for likelihoods calculated 

55 

56 

57 Model A1: Yij = Mu(i) + e(ij) 

58 Var{e(ij)} = Sigma^2 

59 

60 Model A2: Yij = Mu(i) + e(ij) 

61 Var{e(ij)} = Sigma(i)^2 

62 

63 Model A3: Yij = Mu(i) + e(ij) 

64 Var{e(ij)} = Sigma^2 

65 Model A3 uses any fixed variance parameters that 

66 were specified by the user 

67 

68 Model R: Yi = Mu + e(i) 

69 Var{e(i)} = Sigma^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-13 —DO NOT CITE OR QUOTE 

1 

2 Likelihoods of Interest 

3 

4 Model Log(likelihood) # Param's AIC 

5 A1 80.752584 7 -147.505168 

6 A2 83.373547 12 -142.747094 

7 A3 80.752584 7 -147.505168 

8 fitted 80.455153 5 -150.910305 

9 R 55.820023 2 -107.640047 

10 

11 

12 Explanation of Tests 

13 

14 Test 1: Do responses and/or variances differ among Dose levels? 

15 (A2 vs. R) 

16 Test 2: Are Variances Homogeneous? (A1 vs A2) 

17 Test 3: Are variances adequately modeled? (A2 vs. A3) 

18 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

19 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

20 

21 Tests of Interest 

22 

23 Test -2*log(Likelihood Ratio) Test df p-value 

24 

25 Test 1 55.107 10 <.0001 

26 Test 2 5.24193 5 0.3871 

27 Test 3 5.24193 5 0.3871 

28 Test 4 0.594862 2 0.7427 

29 

30 The p-value for Test 1 is less than .05. There appears to be a 

31 difference between response and/or variances among the dose levels 

32 It seems appropriate to model the data 

33 

34 The p-value for Test 2 is greater than .1. A homogeneous variance 

35 model appears to be appropriate here 

36 

37 

38 The p-value for Test 3 is greater than .1. The modeled variance appears 

39 to be appropriate here 

40 

41 The p-value for Test 4 is greater than .1. The model chosen seems 

42 to adequately describe the data 

43 

44 

45 Benchmark Dose Computation 

46 

47 Specified effect = 1 

48 

49 Risk Type = Estimated standard deviations from the control mean 

50 

51 Confidence level = 0.95 

52 

53 BMD = 3420.29 

54 

55 BMDL = 1757.33 

56 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-14 —DO NOT CITE OR QUOTE 

1 H.2.1.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 0.1

 0.2

 0.3

 0.4

 0.5

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Power

2 

 3 

 4 

5 H.2.1.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 6 

7 

8 ==================================================================== 

9 Power Model. (Version: 2.15; Date: 04/07/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Pwr_CV_Unrest_BMR1_CytC_Liver.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Pwr_CV_Unrest_BMR1_CytC_Liver.plt 

12 Mon Nov 23 12:51:51 2009 

13 ==================================================================== 

14 

15 TBARs, liver only (Table 2) 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = control + slope * dose^power 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 The power is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 alpha = 0.004972 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-15 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 control = 0.146 

3 slope = 2.56594e-005 

4 power = 0.980719 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -rho 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 alpha control slope power 

14 

15 alpha 1 4.5e-009 -1.5e-009 1.3e-009 

16 

17 control 4.5e-009 1 -0.71 0.68 

18 

19 slope -1.5e-009 -0.71 1 -1 

20 

21 power 1.3e-009 0.68 -1 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 alpha 0.00474021 0.00111728 0.00255039 0.00693004 

30 control 0.13485 0.0248098 0.0862235 0.183476 

31 slope 0.000217707 0.000332694 -0.000434363 0.000869776 

32 power 0.766684 0.157896 0.457213 1.07615 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 6 0.146 0.135 0.0661 0.0688 0.397 

42 1068 6 0.177 0.181 0.0539 0.0688 -0.126 

43 2542 6 0.191 0.224 0.0563 0.0688 -1.16 

44 4489 6 0.271 0.272 0.0563 0.0688 -0.0436 

45 7718 6 0.388 0.343 0.0637 0.0688 1.6 

46 1.396e+004 6 0.444 0.463 0.11 0.0688 -0.666 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = Sigma^2 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-16 —DO NOT CITE OR QUOTE 

1 A1 80.752584 7 -147.505168 

2 A2 83.373547 12 -142.747094 

3 A3 80.752584 7 -147.505168 

4 fitted 78.330124 4 -148.660249 

5 R 55.820023 2 -107.640047 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 55.107 10 <.0001 

22 Test 2 5.24193 5 0.3871 

23 Test 3 5.24193 5 0.3871 

24 Test 4 4.84492 3 0.1835 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is greater than .1. A homogeneous variance 

31 model appears to be appropriate here 

32 

33 

34 The p-value for Test 3 is greater than .1. The modeled variance appears 

35 to be appropriate here 

36 

37 The p-value for Test 4 is greater than .1. The model chosen seems 

38 to adequately describe the data 

39 

40 

41 Benchmark Dose Computation 

42 

43 Specified effect = 1 

44 

45 Risk Type = Estimated standard deviations from the control mean 

46 

47 Confidence level = 0.95 

48 

49 BMD = 1823.19 

50 

51 

52 BMDL = 743.833 

53 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-17 —DO NOT CITE OR QUOTE 

1 H.2.2. Hassoun et al. (2000): DNA SSB 

2 H.2.2.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 0.75 39.08 <0.0001 112.91 4.1E+03 2.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.75 39.08 <0.0001 112.91 4.1E+03 2.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.75 4.29 0.23 80.12 5.6E+02 3.6E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.75 4.29 0.23 80.12 5.6E+02 3.6E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.75 4.29 0.23 80.12 5.6E+02 3.6E+02 nonconstant variance, 

power unrestricted 

Hill 3 0.75 4.16 0.25 79.99 5.0E+02 3.9E+02 nonconstant variance, n 

restricted >1, bound hit 

Hill 2 0.75 3.82 0.15 81.65 3.7E+02 1.3E+02 nonconstant variance, n 

unrestricted 

linear 4 0.75 25.42 <.0001 99.26 1.6E+03 9.6E+02 nonconstant variance 

polynomial 4 0.75 25.42 <.0001 99.26 1.6E+03 9.6E+02 nonconstant variance 

power 4 0.75 25.42 <.0001 99.26 1.6E+03 9.6E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.75 5.14 0.16 80.98 1.9E+02 7.4E+01 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.75 38.85 <0.0001 111.13 3.6E+03 3.0E+03 constant variance, 

power restricted ≥1 

exponential (M3) 4 0.75 38.85 <0.0001 111.13 3.6E+03 3.0E+03 constant variance, 

power restricted ≥1 

exponential (M4) c 3 0.75 4.30 0.23 78.59 6.6E+02 5.0E+02 constant variance, 

power restricted ≥1 

exponential (M5) 3 0.75 4.30 0.23 78.59 6.6E+02 5.0E+02 constant variance, 

power restricted ≥1 

exponential (M5) d 3 0.75 4.30 0.23 78.59 6.6E+02 5.0E+02 constant variance, 

power unrestricted 

Hill 3 0.75 4.31 0.23 78.59 6.0E+02 4.4E+02 constant variance, n 

restricted >1, bound hit 

Hill d 2 0.75 4.09 0.13 80.38 4.8E+02 1.5E+02 constant variance, n 

unrestricted 

linear 4 0.75 25.33 <.0001 97.62 2.0E+03 1.6E+03 constant variance 

polynomial 4 0.75 25.33 <.0001 97.62 2.0E+03 1.6E+03 constant variance 

power 4 0.75 25.33 <.0001 97.62 2.0E+03 1.6E+03 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-18 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power d 3 0.75 5.61 0.13 79.89 2.5E+02 1.1E+02 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.2.2.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

4 ≥1 

 5

 10

 15

 20

 25

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:50 11/23 2009

BMDL BMD

 

Exponential

5 

 6 

 7 

8 H.2.2.3. Output File For Selected Model: Exponential (M4), Constant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Exp_CV_BMR1_DNA_SSB.(d) 

15 Gnuplot Plotting File: 

16 Mon Nov 23 12:50:08 2009 

17 ==================================================================== 

18 

19 DNA single-strand breaks, liver only (Table 3) 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-19 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 rho is set to 0. 

20 A constant variance model is fit. 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 4 

34 -------- -------- 

35 lnalpha 0.841244 

36 rho(S) 0 

37 a 7.0395 

38 b 0.000187891 

39 c 3.50522 

40 d 1 

41 

42 (S) = Specified 

43 

44 

45 

46 Parameter Estimates 

47 

48 Variable Model 4 

49 -------- ------- 

50 lnalpha 0.960792 

51 rho 0 

52 a 7.75279 

53 b 0.000136903 

54 c 3.39666 

55 d 1 

56 

57 

58 Table of Stats From Input Data 

59 

60 Dose N Obs Mean Obs Std Dev 

61 ----- --- ---------- ------------- 

62 0 6 7.41 1.543 

63 1068 6 10.78 1.249 

64 2542 6 13.6 1.69 

65 4489 6 15.3 1.715 

66 7718 6 20.4 2.254 

67 1.396e+004 6 23.5 1.372 

68 

69 

70 Estimated Values of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-20 —DO NOT CITE OR QUOTE 

1 

2 Dose Est Mean Est Std Scaled Residual 

3 ------ ---------- --------- ---------------- 

4 0 7.753 1.617 -0.5194 

5 1068 10.28 1.617 0.7575 

6 2542 13.21 1.617 0.5853 

7 4489 16.28 1.617 -1.49 

8 7718 19.87 1.617 0.7958 

9 1.396e+004 23.59 1.617 -0.1293 

10 

11 

12 

13 Other models for which likelihoods are calculated: 

14 

15 Model A1: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma^2 

17 

18 Model A2: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma(i)^2 

20 

21 Model A3: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

23 

24 Model R: Yij = Mu + e(i) 

25 Var{e(ij)} = Sigma^2 

26 

27 

28 Likelihoods of Interest 

29 

30 Model Log(likelihood) DF AIC 

31 ------- ----------------- ---- ------------ 

32 A1 -33.14239 7 80.28478 

33 A2 -31.81197 12 87.62394 

34 A3 -33.14239 7 80.28478 

35 R -80.44209 2 164.8842 

36 4 -35.29426 4 78.58852 

37 

38 

39 Additive constant for all log-likelihoods = -33.08. This constant added to the 

40 above values gives the log-likelihood including the term that does not 

41 depend on the model parameters. 

42 

43 

44 Explanation of Tests 

45 

46 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

47 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

48 Test 3: Are variances adequately modeled? (A2 vs. A3) 

49 

50 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

51 

52 

53 Tests of Interest 

54 

55 Test -2*log(Likelihood Ratio) D. F. p-value 

56 -------- ------------------------ ------ -------------- 

57 Test 1 97.26 10 < 0.0001 

58 Test 2 2.661 5 0.7521 

59 Test 3 2.661 5 0.7521 

60 Test 6a 4.304 3 0.2305 

61 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose 

65 levels, it seems appropriate to model the data. 

66 

67 The p-value for Test 2 is greater than .1. A homogeneous 

68 variance model appears to be appropriate here. 

69 

70 The p-value for Test 3 is greater than .1. The modeled 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-21 —DO NOT CITE OR QUOTE 

1 variance appears to be appropriate here. 

2 

3 The p-value for Test 6a is greater than .1. Model 4 seems 

4 to adequately describe the data. 

5 

6 

7 Benchmark Dose Computations: 

8 

9 Specified Effect = 1.000000 

10 

11 Risk Type = Estimated standard deviations from control 

12 

13 Confidence Level = 0.950000 

14 

15 BMD = 664.925 

16 

17 BMDL = 504.974 

18 

19 

20 

21 H.2.2.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

22 Unrestricted

 5

 10

 15

 20

 25

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:50 11/23 2009

BMDL BMD

 

Exponential

23 

 24 

 25 

26 H.2.2.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

27 Unrestricted 

28 

29 

30 ==================================================================== 

31 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

32 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Exp_CV_Unrest_BMR1_DNA_SSB.(d) 

33 Gnuplot Plotting File: 

34 Mon Nov 23 12:50:16 2009 

35 ==================================================================== 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-22 —DO NOT CITE OR QUOTE 

1 DNA single-strand breaks, liver only (Table 3) 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the response function by Model: 

5 Model 2: Y[dose] = a * exp{sign * b * dose} 

6 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

7 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

8 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

9 

10 Note: Y[dose] is the median response for exposure = dose; 

11 sign = +1 for increasing trend in data; 

12 sign = -1 for decreasing trend. 

13 

14 Model 2 is nested within Models 3 and 4. 

15 Model 3 is nested within Model 5. 

16 Model 4 is nested within Model 5. 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Data are assumed to be distributed: normally 

22 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

23 rho is set to 0. 

24 A constant variance model is fit. 

25 

26 Total number of dose groups = 6 

27 Total number of records with missing values = 0 

28 Maximum number of iterations = 250 

29 Relative Function Convergence has been set to: 1e-008 

30 Parameter Convergence has been set to: 1e-008 

31 

32 MLE solution provided: Exact 

33 

34 

35 Initial Parameter Values 

36 

37 Variable Model 5 

38 -------- -------- 

39 lnalpha 0.841244 

40 rho(S) 0 

41 a 7.0395 

42 b 0.000187891 

43 c 3.50522 

44 d 1 

45 

46 (S) = Specified 

47 

48 

49 

50 Parameter Estimates 

51 

52 Variable Model 5 

53 -------- ------- 

54 lnalpha 0.960792 

55 rho 0 

56 a 7.75279 

57 b 0.000136903 

58 c 3.39666 

59 d 1 

60 

61 

62 Table of Stats From Input Data 

63 

64 Dose N Obs Mean Obs Std Dev 

65 ----- --- ---------- ------------- 

66 0 6 7.41 1.543 

67 1068 6 10.78 1.249 

68 2542 6 13.6 1.69 

69 4489 6 15.3 1.715 

70 7718 6 20.4 2.254 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-23 —DO NOT CITE OR QUOTE 

1 1.396e+004 6 23.5 1.372 

2 

3 

4 Estimated Values of Interest 

5 

6 Dose Est Mean Est Std Scaled Residual 

7 ------ ---------- --------- ---------------- 

8 0 7.753 1.617 -0.5194 

9 1068 10.28 1.617 0.7575 

10 2542 13.21 1.617 0.5853 

11 4489 16.28 1.617 -1.49 

12 7718 19.87 1.617 0.7958 

13 1.396e+004 23.59 1.617 -0.1293 

14 

15 

16 

17 Other models for which likelihoods are calculated: 

18 

19 Model A1: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = Sigma^2 

21 

22 Model A2: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma(i)^2 

24 

25 Model A3: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

27 

28 Model R: Yij = Mu + e(i) 

29 Var{e(ij)} = Sigma^2 

30 

31 

32 Likelihoods of Interest 

33 

34 Model Log(likelihood) DF AIC 

35 ------- ----------------- ---- ------------ 

36 A1 -33.14239 7 80.28478 

37 A2 -31.81197 12 87.62394 

38 A3 -33.14239 7 80.28478 

39 R -80.44209 2 164.8842 

40 5 -35.29426 4 78.58852 

41 

42 

43 Additive constant for all log-likelihoods = -33.08. This constant added to the 

44 above values gives the log-likelihood including the term that does not 

45 depend on the model parameters. 

46 

47 

48 Explanation of Tests 

49 

50 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

51 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

52 Test 3: Are variances adequately modeled? (A2 vs. A3) 

53 

54 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

55 

56 

57 Tests of Interest 

58 

59 Test -2*log(Likelihood Ratio) D. F. p-value 

60 -------- ------------------------ ------ -------------- 

61 Test 1 97.26 10 < 0.0001 

62 Test 2 2.661 5 0.7521 

63 Test 3 2.661 5 0.7521 

64 Test 7a 4.304 3 0.2305 

65 

66 

67 The p-value for Test 1 is less than .05. There appears to be a 

68 difference between response and/or variances among the dose 

69 levels, it seems appropriate to model the data. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-24 —DO NOT CITE OR QUOTE 

1 The p-value for Test 2 is greater than .1. A homogeneous 

2 variance model appears to be appropriate here. 

3 

4 The p-value for Test 3 is greater than .1. The modeled 

5 variance appears to be appropriate here. 

6 

7 The p-value for Test 7a is greater than .1. Model 5 seems 

8 to adequately describe the data. 

9 

10 

11 Benchmark Dose Computations: 

12 

13 Specified Effect = 1.000000 

14 

15 Risk Type = Estimated standard deviations from control 

16 

17 Confidence Level = 0.950000 

18 

19 BMD = 664.925 

20 

21 BMDL = 504.974 

22 

23 

24 

25 H.2.2.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 5

 10

 15

 20

 25

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:50 11/23 2009

BMDL BMD

 

Hill

26 

 27 

 28 

29 H.2.2.7. Output File For Unrestricted Model: Hill, Constant Variance, n Unrestricted 30 

31 

32 ==================================================================== 

33 Hill Model. (Version: 2.14; Date: 06/26/2008) 

34 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_Unrest_BMR1_DNA_SSB.(d) 

35 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_Unrest_BMR1_DNA_SSB.plt 

36 Mon Nov 23 12:50:18 2009 

37 ==================================================================== 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-25 —DO NOT CITE OR QUOTE 

1 

2 DNA single-strand breaks, liver only (Table 3) 

3 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

4 

5 The form of the response function is: 

6 

7 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

8 

9 

10 Dependent variable = Mean 

11 Independent variable = Dose 

12 rho is set to 0 

13 Power parameter is not restricted 

14 A constant variance model is fit 

15 

16 Total number of dose groups = 6 

17 Total number of records with missing values = 0 

18 Maximum number of iterations = 250 

19 Relative Function Convergence has been set to: 1e-008 

20 Parameter Convergence has been set to: 1e-008 

21 

22 

23 

24 Default Initial Parameter Values 

25 alpha = 2.7831 

26 rho = 0 Specified 

27 intercept = 7.41 

28 v = 16.09 

29 n = 0.235041 

30 k = 10849.8 

31 

32 

33 Asymptotic Correlation Matrix of Parameter Estimates 

34 

35 ( *** The model parameter(s) -rho 

36 have been estimated at a boundary point, or have been specified by the user, 

37 and do not appear in the correlation matrix ) 

38 

39 alpha intercept v n k 

40 

41 alpha 1 -2.8e-008 7.4e-008 -6.3e-008 7.2e-008 

42 

43 intercept -2.8e-008 1 -0.34 0.47 -0.28 

44 

45 v 7.4e-008 -0.34 1 -0.95 1 

46 

47 n -6.3e-008 0.47 -0.95 1 -0.95 

48 

49 k 7.2e-008 -0.28 1 -0.95 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 alpha 2.59837 0.612441 1.398 3.79873 

58 intercept 7.4823 0.666037 6.17689 8.78771 

59 v 32.65 17.9338 -2.49963 67.7997 

60 n 0.876148 0.260495 0.365588 1.38671 

61 k 14136.3 16730.5 -18654.9 46927.4 

62 

63 

64 

65 Table of Data and Estimated Values of Interest 

66 

67 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

68 ------ --- -------- -------- ----------- ----------- ---------- 

69 

70 0 6 7.41 7.48 1.54 1.61 -0.11 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-26 —DO NOT CITE OR QUOTE 

1 1068 6 10.8 10.6 1.25 1.61 0.336 

2 2542 6 13.6 13.4 1.69 1.61 0.27 

3 4489 6 15.3 16.2 1.71 1.61 -1.41 

4 7718 6 20.4 19.6 2.25 1.61 1.25 

5 1.396e+004 6 23.5 23.7 1.37 1.61 -0.331 

6 

7 

8 

9 Model Descriptions for likelihoods calculated 

10 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma^2 

20 Model A3 uses any fixed variance parameters that 

21 were specified by the user 

22 

23 Model R: Yi = Mu + e(i) 

24 Var{e(i)} = Sigma^2 

25 

26 

27 Likelihoods of Interest 

28 

29 Model Log(likelihood) # Param's AIC 

30 A1 -33.142389 7 80.284779 

31 A2 -31.811970 12 87.623940 

32 A3 -33.142389 7 80.284779 

33 fitted -35.187895 5 80.375790 

34 R -80.442086 2 164.884172 

35 

36 

37 Explanation of Tests 

38 

39 Test 1: Do responses and/or variances differ among Dose levels? 

40 (A2 vs. R) 

41 Test 2: Are Variances Homogeneous? (A1 vs A2) 

42 Test 3: Are variances adequately modeled? (A2 vs. A3) 

43 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

44 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

45 

46 Tests of Interest 

47 

48 Test -2*log(Likelihood Ratio) Test df p-value 

49 

50 Test 1 97.2602 10 <.0001 

51 Test 2 2.66084 5 0.7521 

52 Test 3 2.66084 5 0.7521 

53 Test 4 4.09101 2 0.1293 

54 

55 The p-value for Test 1 is less than .05. There appears to be a 

56 difference between response and/or variances among the dose levels 

57 It seems appropriate to model the data 

58 

59 The p-value for Test 2 is greater than .1. A homogeneous variance 

60 model appears to be appropriate here 

61 

62 

63 The p-value for Test 3 is greater than .1. The modeled variance appears 

64 to be appropriate here 

65 

66 The p-value for Test 4 is greater than .1. The model chosen seems 

67 to adequately describe the data 

68 

69 

70 Benchmark Dose Computation 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-27 —DO NOT CITE OR QUOTE 

1 

2 Specified effect = 1 

3 

4 Risk Type = Estimated standard deviations from the control mean 

5 

6 Confidence level = 0.95 

7 

8 BMD = 483.289 

9 

10 BMDL = 153.678 

11 

12 

13 

14 H.2.2.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 5

 10

 15

 20

 25

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:50 11/23 2009

BMDL BMD

 

Power

15 

 16 

 17 

18 H.2.2.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 19 

20 

21 ==================================================================== 

22 Power Model. (Version: 2.15; Date: 04/07/2008) 

23 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Pwr_CV_Unrest_BMR1_DNA_SSB.(d) 

24 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Pwr_CV_Unrest_BMR1_DNA_SSB.plt 

25 Mon Nov 23 12:50:18 2009 

26 ==================================================================== 

27 

28 DNA single-strand breaks, liver only (Table 3) 

29 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

30 

31 The form of the response function is: 

32 

33 Y[dose] = control + slope * dose^power 

34 

35 

36 Dependent variable = Mean 

37 Independent variable = Dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-28 —DO NOT CITE OR QUOTE 

1 rho is set to 0 

2 The power is not restricted 

3 A constant variance model is fit 

4 

5 Total number of dose groups = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 

12 

13 Default Initial Parameter Values 

14 alpha = 2.7831 

15 rho = 0 Specified 

16 control = 7.41 

17 slope = 0.0433022 

18 power = 0.620052 

19 

20 

21 Asymptotic Correlation Matrix of Parameter Estimates 

22 

23 ( *** The model parameter(s) -rho 

24 have been estimated at a boundary point, or have been specified by the user, 

25 and do not appear in the correlation matrix ) 

26 

27 alpha control slope power 

28 

29 alpha 1 2.5e-009 -5.4e-009 5.7e-009 

30 

31 control 2.5e-009 1 -0.71 0.66 

32 

33 slope -5.4e-009 -0.71 1 -1 

34 

35 power 5.7e-009 0.66 -1 1 

36 

37 

38 

39 Parameter Estimates 

40 

41 95.0% Wald Confidence Interval 

42 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

43 alpha 2.71023 0.638807 1.45819 3.96226 

44 control 7.26415 0.64416 6.00162 8.52668 

45 slope 0.0685886 0.0392449 -0.00833 0.145507 

46 power 0.575949 0.0589672 0.460375 0.691523 

47 

48 

49 

50 Table of Data and Estimated Values of Interest 

51 

52 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

53 ------ --- -------- -------- ----------- ----------- ---------- 

54 

55 0 6 7.41 7.26 1.54 1.65 0.217 

56 1068 6 10.8 11.1 1.25 1.65 -0.433 

57 2542 6 13.6 13.5 1.69 1.65 0.094 

58 4489 6 15.3 16 1.71 1.65 -0.993 

59 7718 6 20.4 19.2 2.25 1.65 1.85 

60 1.396e+004 6 23.5 24 1.37 1.65 -0.735 

61 

62 

63 

64 Model Descriptions for likelihoods calculated 

65 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-29 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = Sigma^2 

5 Model A3 uses any fixed variance parameters that 

6 were specified by the user 

7 

8 Model R: Yi = Mu + e(i) 

9 Var{e(i)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) # Param's AIC 

15 A1 -33.142389 7 80.284779 

16 A2 -31.811970 12 87.623940 

17 A3 -33.142389 7 80.284779 

18 fitted -35.946581 4 79.893162 

19 R -80.442086 2 164.884172 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Do responses and/or variances differ among Dose levels? 

25 (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A1 vs A2) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

29 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) Test df p-value 

34 

35 Test 1 97.2602 10 <.0001 

36 Test 2 2.66084 5 0.7521 

37 Test 3 2.66084 5 0.7521 

38 Test 4 5.60838 3 0.1323 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose levels 

42 It seems appropriate to model the data 

43 

44 The p-value for Test 2 is greater than .1. A homogeneous variance 

45 model appears to be appropriate here 

46 

47 

48 The p-value for Test 3 is greater than .1. The modeled variance appears 

49 to be appropriate here 

50 

51 The p-value for Test 4 is greater than .1. The model chosen seems 

52 to adequately describe the data 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 1 

58 

59 Risk Type = Estimated standard deviations from the control mean 

60 

61 Confidence level = 0.95 

62 

63 BMD = 249.162 

64 

65 

66 BMDL = 111.676 

67 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-30 —DO NOT CITE OR QUOTE 

1 H.2.3. Hassoun et al. (2000): TBARs Liver 

2 H.2.3.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 0.33 17.56 0.00 -7.04 7.4E+03 3.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.33 17.56 0.00 -7.04 7.4E+03 3.9E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.33 4.35 0.23 -18.26 1.0E+03 5.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.33 2.78 0.25 -17.82 1.6E+03 6.5E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.33 2.78 0.25 -17.82 1.6E+03 6.5E+02 nonconstant variance, 

power unrestricted 

Hill 2 0.33 2.52 0.28 -18.09 1.7E+03 8.1E+02 nonconstant variance, 

n restricted >1 

Hill 2 0.33 2.52 0.28 -18.09 1.7E+03 8.1E+02 nonconstant variance, 

n unrestricted 

linear 4 0.33 15.72 0.00 -8.88 5.1E+03 2.4E+03 nonconstant variance 

polynomial 4 0.33 15.72 0.00 -8.88 5.1E+03 2.4E+03 nonconstant variance 

power 4 0.33 15.72 0.00 -8.88 5.1E+03 2.4E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.33 8.40 0.04 -14.21 5.3E+02 8.3E+00 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.33 18.02 0.00 -8.52 9.6E+03 6.7E+03 constant variance, 

power restricted ≥1 

exponential (M3) 4 0.33 18.02 0.00 -8.52 9.6E+03 6.7E+03 constant variance, 

power restricted ≥1 

exponential (M4) 3 0.33 4.79 0.19 -19.75 1.2E+03 6.3E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.33 2.86 0.24 -19.68 1.9E+03 8.4E+02 constant variance, 

power restricted ≥1 

exponential (M5) d 2 0.33 2.86 0.24 -19.68 1.9E+03 8.4E+02 constant variance, 

power unrestricted 

Hill c 2 0.33 2.60 0.27 -19.93 1.8E+03 9.6E+02 constant variance, n 

restricted >1 

Hill d 2 0.33 2.60 0.27 -19.93 1.8E+03 9.6E+02 constant variance, n 

unrestricted 

linear 4 0.33 16.75 0.00 -9.79 8.0E+03 5.3E+03 constant variance 

polynomial 4 0.33 16.75 0.00 -9.79 8.0E+03 5.3E+03 constant variance 

power 4 0.33 16.75 0.00 -9.79 8.0E+03 5.3E+03 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-31 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power d 3 0.33 9.75 0.02 -14.79 1.0E+03 5.7E+01 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.2.3.2. Figure for Selected Model: Exponential (M5), Constant Variance, Power 

4 Unrestricted

 1

 1.5

 2

 2.5

 3

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Exponential

5 

 6 

 7 

8 H.2.3.3. Output File for Selected Model: Exponential (M5), Constant Variance, Power 

9 Unrestricted

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Exp_CV_Unrest_BMR1_TBARs_Liver.(d) 

15 Gnuplot Plotting File: 

16 Mon Nov 23 12:51:02 2009 

17 ==================================================================== 

18 

19 TBARs, liver only (Table 2) 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-32 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 rho is set to 0. 

20 A constant variance model is fit. 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 5 

34 -------- -------- 

35 lnalpha -1.90388 

36 rho(S) 0 

37 a 1.39555 

38 b 0.000142164 

39 c 1.97051 

40 d 1 

41 

42 (S) = Specified 

43 

44 

45 

46 Parameter Estimates 

47 

48 Variable Model 5 

49 -------- ------- 

50 lnalpha -1.82448 

51 rho 0 

52 a 1.46526 

53 b 0.000431089 

54 c 1.63651 

55 d 2.96871 

56 

57 

58 Table of Stats From Input Data 

59 

60 Dose N Obs Mean Obs Std Dev 

61 ----- --- ---------- ------------- 

62 0 6 1.469 0.2915 

63 1068 6 1.549 0.5389 

64 2542 6 2.15 0.3625 

65 4489 6 2.28 0.2474 

66 7718 6 2.619 0.5168 

67 1.396e+004 6 2.292 0.4874 

68 

69 

70 Estimated Values of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-33 —DO NOT CITE OR QUOTE 

1 

2 Dose Est Mean Est Std Scaled Residual 

3 ------ ---------- --------- ---------------- 

4 0 1.465 0.4016 0.0228 

5 1068 1.554 0.4016 -0.03039 

6 2542 2.147 0.4016 0.01965 

7 4489 2.397 0.4016 -0.7145 

8 7718 2.398 0.4016 1.348 

9 1.396e+004 2.398 0.4016 -0.646 

10 

11 

12 

13 Other models for which likelihoods are calculated: 

14 

15 Model A1: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma^2 

17 

18 Model A2: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma(i)^2 

20 

21 Model A3: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

23 

24 Model R: Yij = Mu + e(i) 

25 Var{e(ij)} = Sigma^2 

26 

27 

28 Likelihoods of Interest 

29 

30 Model Log(likelihood) DF AIC 

31 ------- ----------------- ---- ------------ 

32 A1 16.26977 7 -18.53954 

33 A2 19.12783 12 -14.25565 

34 A3 16.26977 7 -18.53954 

35 R 2.44294 2 -0.8858799 

36 5 14.84065 5 -19.6813 

37 

38 

39 Additive constant for all log-likelihoods = -33.08. This constant added to the 

40 above values gives the log-likelihood including the term that does not 

41 depend on the model parameters. 

42 

43 

44 Explanation of Tests 

45 

46 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

47 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

48 Test 3: Are variances adequately modeled? (A2 vs. A3) 

49 

50 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

51 

52 

53 Tests of Interest 

54 

55 Test -2*log(Likelihood Ratio) D. F. p-value 

56 -------- ------------------------ ------ -------------- 

57 Test 1 33.37 10 0.000236 

58 Test 2 5.716 5 0.3348 

59 Test 3 5.716 5 0.3348 

60 Test 7a 2.858 2 0.2395 

61 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose 

65 levels, it seems appropriate to model the data. 

66 

67 The p-value for Test 2 is greater than .1. A homogeneous 

68 variance model appears to be appropriate here. 

69 

70 The p-value for Test 3 is greater than .1. The modeled 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-34 —DO NOT CITE OR QUOTE 

1 variance appears to be appropriate here. 

2 

3 The p-value for Test 7a is greater than .1. Model 5 seems 

4 to adequately describe the data. 

5 

6 

7 Benchmark Dose Computations: 

8 

9 Specified Effect = 1.000000 

10 

11 Risk Type = Estimated standard deviations from control 

12 

13 Confidence Level = 0.950000 

14 

15 BMD = 1911.82 

16 

17 BMDL = 840.487 

18 

19 

20 

21 H.2.3.4. Figure for Unrestricted Model: Hill, Constant Variance, n Restricted >1 

 1

 1.5

 2

 2.5

 3

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:50 11/23 2009

BMDL BMD

 

Hill

22 

 23 

 24 

25 H.2.3.5. Output File for Unrestricted Model: Hill, Constant Variance, n Restricted >1 26 

27 

28 ==================================================================== 

29 Hill Model. (Version: 2.14; Date: 06/26/2008) 

30 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_BMR1_TBARs_Liver.(d) 

31 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_BMR1_TBARs_Liver.plt 

32 Mon Nov 23 12:50:58 2009 

33 ==================================================================== 

34 

35 TBARs, liver only (Table 2) 

36 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-35 —DO NOT CITE OR QUOTE 

1 The form of the response function is: 

2 

3 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

4 

5 

6 Dependent variable = Mean 

7 Independent variable = Dose 

8 rho is set to 0 

9 Power parameter restricted to be greater than 1 

10 A constant variance model is fit 

11 

12 Total number of dose groups = 6 

13 Total number of records with missing values = 0 

14 Maximum number of iterations = 250 

15 Relative Function Convergence has been set to: 1e-008 

16 Parameter Convergence has been set to: 1e-008 

17 

18 

19 

20 Default Initial Parameter Values 

21 alpha = 0.178788 

22 rho = 0 Specified 

23 intercept = 1.469 

24 v = 1.15 

25 n = 1.27851 

26 k = 2801.9 

27 

28 

29 Asymptotic Correlation Matrix of Parameter Estimates 

30 

31 ( *** The model parameter(s) -rho 

32 have been estimated at a boundary point, or have been specified by the user, 

33 and do not appear in the correlation matrix ) 

34 

35 alpha intercept v n k 

36 

37 alpha 1 1.1e-007 -1.4e-007 1.2e-007 -7.6e-009 

38 

39 intercept 1.1e-007 1 -0.82 0.48 0.52 

40 

41 v -1.4e-007 -0.82 1 -0.61 -0.22 

42 

43 n 1.2e-007 0.48 -0.61 1 0.29 

44 

45 k -7.6e-009 0.52 -0.22 0.29 1 

46 

47 

48 

49 Parameter Estimates 

50 

51 95.0% Wald Confidence Interval 

52 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

53 alpha 0.16017 0.0377524 0.0861764 0.234163 

54 intercept 1.46138 0.152797 1.1619 1.76086 

55 v 0.963032 0.20228 0.56657 1.35949 

56 n 3.44649 2.43475 -1.32553 8.21851 

57 k 2002.3 562.074 900.655 3103.95 

58 

59 

60 

61 Table of Data and Estimated Values of Interest 

62 

63 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

64 ------ --- -------- -------- ----------- ----------- ---------- 

65 

66 0 6 1.47 1.46 0.291 0.4 0.0466 

67 1068 6 1.55 1.56 0.539 0.4 -0.0697 

68 2542 6 2.15 2.13 0.363 0.4 0.12 

69 4489 6 2.28 2.37 0.247 0.4 -0.54 

70 7718 6 2.62 2.42 0.517 0.4 1.25 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-36 —DO NOT CITE OR QUOTE 

1 1.396e+004 6 2.29 2.42 0.487 0.4 -0.803 

2 

3 

4 

5 Model Descriptions for likelihoods calculated 

6 

7 

8 Model A1: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma^2 

10 

11 Model A2: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma(i)^2 

13 

14 Model A3: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma^2 

16 Model A3 uses any fixed variance parameters that 

17 were specified by the user 

18 

19 Model R: Yi = Mu + e(i) 

20 Var{e(i)} = Sigma^2 

21 

22 

23 Likelihoods of Interest 

24 

25 Model Log(likelihood) # Param's AIC 

26 A1 16.269770 7 -18.539539 

27 A2 19.127827 12 -14.255654 

28 A3 16.269770 7 -18.539539 

29 fitted 14.967385 5 -19.934770 

30 R 2.442940 2 -0.885880 

31 

32 

33 Explanation of Tests 

34 

35 Test 1: Do responses and/or variances differ among Dose levels? 

36 (A2 vs. R) 

37 Test 2: Are Variances Homogeneous? (A1 vs A2) 

38 Test 3: Are variances adequately modeled? (A2 vs. A3) 

39 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

40 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

41 

42 Tests of Interest 

43 

44 Test -2*log(Likelihood Ratio) Test df p-value 

45 

46 Test 1 33.3698 10 0.000236 

47 Test 2 5.71611 5 0.3348 

48 Test 3 5.71611 5 0.3348 

49 Test 4 2.60477 2 0.2719 

50 

51 The p-value for Test 1 is less than .05. There appears to be a 

52 difference between response and/or variances among the dose levels 

53 It seems appropriate to model the data 

54 

55 The p-value for Test 2 is greater than .1. A homogeneous variance 

56 model appears to be appropriate here 

57 

58 

59 The p-value for Test 3 is greater than .1. The modeled variance appears 

60 to be appropriate here 

61 

62 The p-value for Test 4 is greater than .1. The model chosen seems 

63 to adequately describe the data 

64 

65 

66 Benchmark Dose Computation 

67 

68 Specified effect = 1 

69 

70 Risk Type = Estimated standard deviations from the control mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-37 —DO NOT CITE OR QUOTE 

1 

2 Confidence level = 0.95 

3 

4 BMD = 1813.69 

5 

6 BMDL = 957.252 

7 

8 

9 

10 H.2.3.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 1

 1.5

 2

 2.5

 3

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Hill

11 

 12 

 13 

14 H.2.3.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 15 

16 

17 ==================================================================== 

18 Hill Model. (Version: 2.14; Date: 06/26/2008) 

19 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_Unrest_BMR1_TBARs_Liver.(d) 

20 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Hill_CV_Unrest_BMR1_TBARs_Liver.plt 

21 Mon Nov 23 12:51:04 2009 

22 ==================================================================== 

23 

24 TBARs, liver only (Table 2) 

25 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

26 

27 The form of the response function is: 

28 

29 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

30 

31 

32 Dependent variable = Mean 

33 Independent variable = Dose 

34 rho is set to 0 

35 Power parameter is not restricted 

36 A constant variance model is fit 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-38 —DO NOT CITE OR QUOTE 

1 Total number of dose groups = 6 

2 Total number of records with missing values = 0 

3 Maximum number of iterations = 250 

4 Relative Function Convergence has been set to: 1e-008 

5 Parameter Convergence has been set to: 1e-008 

6 

7 

8 

9 Default Initial Parameter Values 

10 alpha = 0.178788 

11 rho = 0 Specified 

12 intercept = 1.469 

13 v = 1.15 

14 n = 1.27851 

15 k = 2801.9 

16 

17 

18 Asymptotic Correlation Matrix of Parameter Estimates 

19 

20 ( *** The model parameter(s) -rho 

21 have been estimated at a boundary point, or have been specified by the user, 

22 and do not appear in the correlation matrix ) 

23 

24 alpha intercept v n k 

25 

26 alpha 1 1.1e-007 -1.4e-007 1.2e-007 -7.6e-009 

27 

28 intercept 1.1e-007 1 -0.82 0.48 0.52 

29 

30 v -1.4e-007 -0.82 1 -0.61 -0.22 

31 

32 n 1.2e-007 0.48 -0.61 1 0.29 

33 

34 k -7.6e-009 0.52 -0.22 0.29 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 95.0% Wald Confidence Interval 

41 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

42 alpha 0.16017 0.0377524 0.0861764 0.234163 

43 intercept 1.46138 0.152797 1.1619 1.76086 

44 v 0.963032 0.20228 0.56657 1.35949 

45 n 3.44649 2.43475 -1.32553 8.21851 

46 k 2002.3 562.074 900.655 3103.95 

47 

48 

49 

50 Table of Data and Estimated Values of Interest 

51 

52 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

53 ------ --- -------- -------- ----------- ----------- ---------- 

54 

55 0 6 1.47 1.46 0.291 0.4 0.0466 

56 1068 6 1.55 1.56 0.539 0.4 -0.0697 

57 2542 6 2.15 2.13 0.363 0.4 0.12 

58 4489 6 2.28 2.37 0.247 0.4 -0.54 

59 7718 6 2.62 2.42 0.517 0.4 1.25 

60 1.396e+004 6 2.29 2.42 0.487 0.4 -0.803 

61 

62 

63 

64 Model Descriptions for likelihoods calculated 

65 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-39 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = Sigma^2 

5 Model A3 uses any fixed variance parameters that 

6 were specified by the user 

7 

8 Model R: Yi = Mu + e(i) 

9 Var{e(i)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) # Param's AIC 

15 A1 16.269770 7 -18.539539 

16 A2 19.127827 12 -14.255654 

17 A3 16.269770 7 -18.539539 

18 fitted 14.967385 5 -19.934770 

19 R 2.442940 2 -0.885880 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Do responses and/or variances differ among Dose levels? 

25 (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A1 vs A2) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

29 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) Test df p-value 

34 

35 Test 1 33.3698 10 0.000236 

36 Test 2 5.71611 5 0.3348 

37 Test 3 5.71611 5 0.3348 

38 Test 4 2.60477 2 0.2719 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose levels 

42 It seems appropriate to model the data 

43 

44 The p-value for Test 2 is greater than .1. A homogeneous variance 

45 model appears to be appropriate here 

46 

47 

48 The p-value for Test 3 is greater than .1. The modeled variance appears 

49 to be appropriate here 

50 

51 The p-value for Test 4 is greater than .1. The model chosen seems 

52 to adequately describe the data 

53 

54 

55 Benchmark Dose Computation 

56 

57 Specified effect = 1 

58 

59 Risk Type = Estimated standard deviations from the control mean 

60 

61 Confidence level = 0.95 

62 

63 BMD = 1813.69 

64 

65 BMDL = 957.252 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-40 —DO NOT CITE OR QUOTE 

1 H.2.3.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 1

 1.5

 2

 2.5

 3

 0 2000 4000 6000 8000 10000 12000 14000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:51 11/23 2009

BMDL BMD

 

Power

2 

 3 

 4 

5 H.2.3.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 6 

7 

8 ==================================================================== 

9 Power Model. (Version: 2.15; Date: 04/07/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Blood\Pwr_CV_Unrest_BMR1_TBARs_Liver.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Blood\Pwr_CV_Unrest_BMR1_TBARs_Liver.plt 

12 Mon Nov 23 12:51:05 2009 

13 ==================================================================== 

14 

15 TBARs, liver only (Table 2) 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = control + slope * dose^power 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 The power is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 alpha = 0.178788 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-41 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 control = 1.469 

3 slope = 0.000328724 

4 power = 0.885141 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -rho 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 alpha control slope power 

14 

15 alpha 1 3.9e-011 -2.9e-010 3.6e-010 

16 

17 control 3.9e-011 1 -0.59 0.47 

18 

19 slope -2.9e-010 -0.59 1 -0.99 

20 

21 power 3.6e-010 0.47 -0.99 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 alpha 0.195332 0.0460403 0.105095 0.28557 

30 control 1.42145 0.17171 1.0849 1.75799 

31 slope 0.0382805 0.0492936 -0.0583331 0.134894 

32 power 0.353387 0.132966 0.0927779 0.613996 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 6 1.47 1.42 0.291 0.442 0.264 

42 1068 6 1.55 1.87 0.539 0.442 -1.79 

43 2542 6 2.15 2.03 0.363 0.442 0.649 

44 4489 6 2.28 2.17 0.247 0.442 0.616 

45 7718 6 2.62 2.33 0.517 0.442 1.62 

46 1.396e+004 6 2.29 2.54 0.487 0.442 -1.36 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = Sigma^2 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-42 —DO NOT CITE OR QUOTE 

1 A1 16.269770 7 -18.539539 

2 A2 19.127827 12 -14.255654 

3 A3 16.269770 7 -18.539539 

4 fitted 11.394946 4 -14.789892 

5 R 2.442940 2 -0.885880 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 33.3698 10 0.000236 

22 Test 2 5.71611 5 0.3348 

23 Test 3 5.71611 5 0.3348 

24 Test 4 9.74965 3 0.02082 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is greater than .1. A homogeneous variance 

31 model appears to be appropriate here 

32 

33 

34 The p-value for Test 3 is greater than .1. The modeled variance appears 

35 to be appropriate here 

36 

37 The p-value for Test 4 is less than .1. You may want to try a different 

38 model 

39 

40 

41 Benchmark Dose Computation 

42 

43 Specified effect = 1 

44 

45 Risk Type = Estimated standard deviations from the control mean 

46 

47 Confidence level = 0.95 

48 

49 BMD = 1014.75 

50 

51 

52 BMDL = 56.7719 

53 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-43 —DO NOT CITE OR QUOTE 

1 H.2.4. Kitchin et al. (1979): BaP Hydrolase Activity 

2 H.2.4.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 9 <0.0001 247.10 <0.0001 452.74 9.3E+05 4.3E+05 nonconstant variance, 

power restricted ≥1 

exponential (M3) 9 <0.0001 247.10 <0.0001 452.74 9.3E+05 4.3E+05 nonconstant variance, 

power restricted ≥1 

exponential (M4) 8 <0.0001 18.95 0.02 226.59 6.3E+02 4.8E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) c 7 <0.0001 16.76 0.02 226.41 1.2E+03 5.6E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 7 <0.0001 16.76 0.02 226.41 1.2E+03 5.6E+02 nonconstant variance, 

power unrestricted 

Hill 7 <.0001 296.88 <.0001 506.53 error error nonconstant variance, n 

restricted >1 

Hill d 7 <.0001 296.88 <.0001 506.53 error error nonconstant variance, n 

unrestricted 

linear 9 <.0001 94.23 <.0001 299.87 9.6E+02 6.9E+02 nonconstant variance 

polynomial 9 <.0001 -197.64 <.0001 8.00 error error nonconstant variance 

power 9 <.0001 94.23 <.0001 299.87 9.6E+02 6.9E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 8 <.0001 63.63 <.0001 271.27 1.0E+02 4.4E+01 nonconstant variance, 

power unrestricted 

exponential (M2) 9 <0.0001 129.40 <0.0001 451.64 1.3E+06 1.1E+06 constant variance, 

power restricted ≥1 

exponential (M3) 9 <0.0001 129.40 <0.0001 451.64 1.3E+06 1.1E+06 constant variance, 

power restricted ≥1 

exponential (M4) 8 <0.0001 6.96 0.54 331.23 9.5E+03 7.3E+03 constant variance, 

power restricted ≥1 

exponential (M5) 8 <0.0001 6.96 0.54 331.23 9.5E+03 7.3E+03 constant variance, 

power restricted ≥1 

exponential (M5) 8 <0.0001 6.96 0.54 331.23 9.5E+03 7.3E+03 constant variance, 

power unrestricted 

Hill 7 <.0001 35.69 <.0001 361.95 6.3E+04 2.6E+03 constant variance, n 

restricted >1 

Hill 7 <.0001 35.69 <.0001 361.95 6.3E+04 3.0E+02 constant variance, n 

unrestricted 

linear 9 <.0001 120.38 <.0001 442.64 6.6E+05 5.1E+05 constant variance 

polynomial 9 <.0001 120.38 <.0001 442.64 6.6E+05 5.1E+05 constant variance 

power 9 <.0001 120.38 <.0001 442.64 6.6E+05 5.1E+05 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-44 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 8 <.0001 51.09 <.0001 375.35 4.1E+02 8.6E+01 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 H.2.4.2. Figure for Selected Model: Exponential (M5), Nonconstant Variance, Power 

3 Restricted ≥1 

 0

 50

 100

 150

 200

 250

 0 500000 1e+006 1.5e+006 2e+006

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:25 11/20 2009

BMDBMDL

 

Exponential

4 

 5 

 6 

7 H.2.4.3. Output File for Selected Model: Exponential (M5), Nonconstant Variance, Power 

8 Restricted ≥1 

9 

10 

11 ==================================================================== 

12 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

13 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_BaP_hydro_act.(d) 

14 Gnuplot Plotting File: 

15 Fri Nov 20 13:25:02 2009 

16 ==================================================================== 

17 

18 Kitchin 1979, Tbl3, BaP hydrolase activity 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the response function by Model: 

22 Model 2: Y[dose] = a * exp{sign * b * dose} 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-45 —DO NOT CITE OR QUOTE 

1 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

2 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

3 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

4 

5 Note: Y[dose] is the median response for exposure = dose; 

6 sign = +1 for increasing trend in data; 

7 sign = -1 for decreasing trend. 

8 

9 Model 2 is nested within Models 3 and 4. 

10 Model 3 is nested within Model 5. 

11 Model 4 is nested within Model 5. 

12 

13 

14 Dependent variable = Mean 

15 Independent variable = Dose 

16 Data are assumed to be distributed: normally 

17 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

18 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

19 

20 Total number of dose groups = 11 

21 Total number of records with missing values = 0 

22 Maximum number of iterations = 250 

23 Relative Function Convergence has been set to: 1e-008 

24 Parameter Convergence has been set to: 1e-008 

25 

26 MLE solution provided: Exact 

27 

28 

29 Initial Parameter Values 

30 

31 Variable Model 5 

32 -------- -------- 

33 lnalpha -3.27793 

34 rho 1.92227 

35 a 4.655 

36 b 1.52141e-006 

37 c 42.6316 

38 d 1 

39 

40 

41 

42 Parameter Estimates 

43 

44 Variable Model 5 

45 -------- ------- 

46 lnalpha -2.64351 

47 rho 1.93772 

48 a 5.43367 

49 b 1.65224e-005 

50 c 31.204 

51 d 1.21424 

52 

53 

54 Table of Stats From Input Data 

55 

56 Dose N Obs Mean Obs Std Dev 

57 ----- --- ---------- ------------- 

58 0 9 4.9 1.11 

59 69.5 4 4.9 1.18 

60 232 4 6.7 1.4 

61 463 4 7.2 1.8 

62 2318 4 8.3 0.26 

63 6949 4 14 5 

64 2.319e+004 4 59 6.8 

65 6.966e+004 4 96 46 

66 2.326e+005 4 155 16.4 

67 5.819e+005 4 182 26 

68 2.332e+006 4 189 26 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-46 —DO NOT CITE OR QUOTE 

1 Estimated Values of Interest 

2 

3 Dose Est Mean Est Std Scaled Residual 

4 ------ ---------- --------- ---------------- 

5 0 5.434 1.375 -1.165 

6 69.5 5.478 1.385 -0.8342 

7 232 5.625 1.421 1.513 

8 463 5.875 1.483 1.787 

9 2318 8.529 2.127 -0.2151 

10 6949 16.87 4.119 -1.392 

11 2.319e+004 49.41 11.67 1.644 

12 6.966e+004 119.4 27.44 -1.708 

13 2.326e+005 168.6 38.32 -0.7087 

14 5.819e+005 169.6 38.53 0.6461 

15 2.332e+006 169.6 38.53 1.009 

16 

17 

18 

19 Other models for which likelihoods are calculated: 

20 

21 Model A1: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = Sigma^2 

23 

24 Model A2: Yij = Mu(i) + e(ij) 

25 Var{e(ij)} = Sigma(i)^2 

26 

27 Model A3: Yij = Mu(i) + e(ij) 

28 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

29 

30 Model R: Yij = Mu + e(i) 

31 Var{e(ij)} = Sigma^2 

32 

33 

34 Likelihoods of Interest 

35 

36 Model Log(likelihood) DF AIC 

37 ------- ----------------- ---- ------------ 

38 A1 -158.1306 12 340.2613 

39 A2 -84.80028 22 213.6006 

40 A3 -98.82189 13 223.6438 

41 R -234.6252 2 473.2504 

42 5 -107.2031 6 226.4062 

43 

44 

45 Additive constant for all log-likelihoods = -45.03. This constant added to the 

46 above values gives the log-likelihood including the term that does not 

47 depend on the model parameters. 

48 

49 

50 Explanation of Tests 

51 

52 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

53 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

54 Test 3: Are variances adequately modeled? (A2 vs. A3) 

55 

56 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

57 

58 

59 Tests of Interest 

60 

61 Test -2*log(Likelihood Ratio) D. F. p-value 

62 -------- ------------------------ ------ -------------- 

63 Test 1 299.6 20 < 0.0001 

64 Test 2 146.7 10 < 0.0001 

65 Test 3 28.04 9 0.0009381 

66 Test 7a 16.76 7 0.01899 

67 

68 

69 The p-value for Test 1 is less than .05. There appears to be a 

70 difference between response and/or variances among the dose 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-47 —DO NOT CITE OR QUOTE 

1 levels, it seems appropriate to model the data. 

2 

3 The p-value for Test 2 is less than .1. A non-homogeneous 

4 variance model appears to be appropriate. 

5 

6 The p-value for Test 3 is less than .1. You may want to 

7 consider a different variance model. 

8 

9 The p-value for Test 7a is less than .1. Model 5 may not adequately 

10 describe the data; you may want to consider another model. 

11 

12 

13 Benchmark Dose Computations: 

14 

15 Specified Effect = 1.000000 

16 

17 Risk Type = Estimated standard deviations from control 

18 

19 Confidence Level = 0.950000 

20 

21 BMD = 1182.79 

22 

23 BMDL = 556.132 

24 

25 

26 

27 H.2.4.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

28 Unrestricted

 0

 50

 100

 150

 200

 250

 0 500000 1e+006 1.5e+006 2e+006

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:25 11/20 2009

BMDBMDL

 

Exponential

29 

 30 

 31 

32 H.2.4.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

33 Power Unrestricted 

34 

35 

36 ==================================================================== 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-48 —DO NOT CITE OR QUOTE 

1 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

2 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_BaP_hydro_act.(d) 

3 Gnuplot Plotting File: 

4 Fri Nov 20 13:25:17 2009 

5 ==================================================================== 

6 

7 Kitchin 1979, Tbl3, BaP hydrolase activity 

8 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

9 

10 The form of the response function by Model: 

11 Model 2: Y[dose] = a * exp{sign * b * dose} 

12 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

13 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

14 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

15 

16 Note: Y[dose] is the median response for exposure = dose; 

17 sign = +1 for increasing trend in data; 

18 sign = -1 for decreasing trend. 

19 

20 Model 2 is nested within Models 3 and 4. 

21 Model 3 is nested within Model 5. 

22 Model 4 is nested within Model 5. 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 Data are assumed to be distributed: normally 

28 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

29 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

30 

31 Total number of dose groups = 11 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 

37 MLE solution provided: Exact 

38 

39 

40 Initial Parameter Values 

41 

42 Variable Model 5 

43 -------- -------- 

44 lnalpha -3.27793 

45 rho 1.92227 

46 a 4.655 

47 b 1.52141e-006 

48 c 42.6316 

49 d 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 Variable Model 5 

56 -------- ------- 

57 lnalpha -2.64351 

58 rho 1.93772 

59 a 5.43367 

60 b 1.65224e-005 

61 c 31.204 

62 d 1.21424 

63 

64 

65 Table of Stats From Input Data 

66 

67 Dose N Obs Mean Obs Std Dev 

68 ----- --- ---------- ------------- 

69 0 9 4.9 1.11 

70 69.5 4 4.9 1.18 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-49 —DO NOT CITE OR QUOTE 

1 232 4 6.7 1.4 

2 463 4 7.2 1.8 

3 2318 4 8.3 0.26 

4 6949 4 14 5 

5 2.319e+004 4 59 6.8 

6 6.966e+004 4 96 46 

7 2.326e+005 4 155 16.4 

8 5.819e+005 4 182 26 

9 2.332e+006 4 189 26 

10 

11 

12 Estimated Values of Interest 

13 

14 Dose Est Mean Est Std Scaled Residual 

15 ------ ---------- --------- ---------------- 

16 0 5.434 1.375 -1.165 

17 69.5 5.478 1.385 -0.8342 

18 232 5.625 1.421 1.513 

19 463 5.875 1.483 1.787 

20 2318 8.529 2.127 -0.2151 

21 6949 16.87 4.119 -1.392 

22 2.319e+004 49.41 11.67 1.644 

23 6.966e+004 119.4 27.44 -1.708 

24 2.326e+005 168.6 38.32 -0.7087 

25 5.819e+005 169.6 38.53 0.6461 

26 2.332e+006 169.6 38.53 1.009 

27 

28 

29 

30 Other models for which likelihoods are calculated: 

31 

32 Model A1: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma^2 

34 

35 Model A2: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = Sigma(i)^2 

37 

38 Model A3: Yij = Mu(i) + e(ij) 

39 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

40 

41 Model R: Yij = Mu + e(i) 

42 Var{e(ij)} = Sigma^2 

43 

44 

45 Likelihoods of Interest 

46 

47 Model Log(likelihood) DF AIC 

48 ------- ----------------- ---- ------------ 

49 A1 -158.1306 12 340.2613 

50 A2 -84.80028 22 213.6006 

51 A3 -98.82189 13 223.6438 

52 R -234.6252 2 473.2504 

53 5 -107.2031 6 226.4062 

54 

55 

56 Additive constant for all log-likelihoods = -45.03. This constant added to the 

57 above values gives the log-likelihood including the term that does not 

58 depend on the model parameters. 

59 

60 

61 Explanation of Tests 

62 

63 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

64 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

65 Test 3: Are variances adequately modeled? (A2 vs. A3) 

66 

67 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

68 

69 

70 Tests of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-50 —DO NOT CITE OR QUOTE 

1 

2 Test -2*log(Likelihood Ratio) D. F. p-value 

3 -------- ------------------------ ------ -------------- 

4 Test 1 299.6 20 < 0.0001 

5 Test 2 146.7 10 < 0.0001 

6 Test 3 28.04 9 0.0009381 

7 Test 7a 16.76 7 0.01899 

8 

9 

10 The p-value for Test 1 is less than .05. There appears to be a 

11 difference between response and/or variances among the dose 

12 levels, it seems appropriate to model the data. 

13 

14 The p-value for Test 2 is less than .1. A non-homogeneous 

15 variance model appears to be appropriate. 

16 

17 The p-value for Test 3 is less than .1. You may want to 

18 consider a different variance model. 

19 

20 The p-value for Test 7a is less than .1. Model 5 may not adequately 

21 describe the data; you may want to consider another model. 

22 

23 

24 Benchmark Dose Computations: 

25 

26 Specified Effect = 1.000000 

27 

28 Risk Type = Estimated standard deviations from control 

29 

30 Confidence Level = 0.950000 

31 

32 BMD = 1182.79 

33 

34 BMDL = 556.132 

35 

36 H.2.4.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 50

 100

 150

 200

 250

 0 500000 1e+006 1.5e+006 2e+006

Mean Response

dose

Hill Model

13:25 11/20 2009

BMD

Hill

37 

 38 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-51 —DO NOT CITE OR QUOTE 

 1 

2 H.2.4.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 3 

4 

5 ==================================================================== 

6 Hill Model. (Version: 2.14; Date: 06/26/2008) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_BaP_hydro_act.(d) 

8 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_BaP_hydro_act.plt 

9 Fri Nov 20 13:25:18 2009 

10 ==================================================================== 

11 

12 Kitchin 1979, Tbl3, BaP hydrolase activity 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function is: 

16 

17 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

18 

19 

20 Dependent variable = Mean 

21 Independent variable = Dose 

22 Power parameter is not restricted 

23 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

24 

25 Total number of dose groups = 11 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 

32 

33 Default Initial Parameter Values 

34 lalpha = 5.70855 

35 rho = 0 

36 intercept = 4.9 

37 v = 184.1 

38 n = 18 

39 k = 392820 

40 

41 

42 Asymptotic Correlation Matrix of Parameter Estimates 

43 

44 lalpha rho intercept v n k 

45 

46 lalpha NA NA NA NA NA NA 

47 

48 rho NA NA NA NA NA NA 

49 

50 intercept NA NA 1 NA 0.28 0.1 

51 

52 v NA NA NA NA NA NA 

53 

54 n NA NA 0.28 NA 1 -0.98 

55 

56 k NA NA 0.1 NA -0.98 1 

57 

58 

59 

60 Parameter Estimates 

61 

62 95.0% Wald Confidence Interval 

63 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

64 lalpha 10.1833 NA NA NA 

65 rho 0.0839751 NA NA NA 

66 intercept -2.28069e-006 NA NA NA 

67 v 184.001 NA NA NA 

68 n 17.9976 NA NA NA 

69 k 1.41183e+007 NA NA NA 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-52 —DO NOT CITE OR QUOTE 

1 

2 At least some variance estimates are negative. 

3 THIS USUALLY MEANS THE MODEL HAS NOT CONVERGED! 

4 Try again from another starting point. 

5 

6 

7 

8 Table of Data and Estimated Values of Interest 

9 

10 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

11 ------ --- -------- -------- ----------- ----------- ---------- 

12 

13 0 9 4.9 -2.28e-006 1.11 94.3 0.156 

14 69.5 4 4.9 -2.28e-006 1.18 94.3 0.104 

15 232 4 6.7 -2.28e-006 1.4 94.3 0.142 

16 463 4 7.2 -2.28e-006 1.8 94.3 0.153 

17 2318 4 8.3 -2.28e-006 0.26 94.3 0.176 

18 6949 4 14 -2.28e-006 5 94.3 0.297 

19 2.319e+004 4 59 -2.28e-006 6.8 94.3 1.25 

20 6.966e+004 4 96 -2.28e-006 46 94.3 2.04 

21 2.326e+005 4 155 -2.28e-006 16.4 94.3 3.29 

22 5.819e+005 4 182 -2.28e-006 26 94.3 3.86 

23 2.332e+006 4 189 -2.28e-006 26 94.3 4.01 

24 

25 

26 

27 Model Descriptions for likelihoods calculated 

28 

29 

30 Model A1: Yij = Mu(i) + e(ij) 

31 Var{e(ij)} = Sigma^2 

32 

33 Model A2: Yij = Mu(i) + e(ij) 

34 Var{e(ij)} = Sigma(i)^2 

35 

36 Model A3: Yij = Mu(i) + e(ij) 

37 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

38 Model A3 uses any fixed variance parameters that 

39 were specified by the user 

40 

41 Model R: Yi = Mu + e(i) 

42 Var{e(i)} = Sigma^2 

43 

44 

45 Likelihoods of Interest 

46 

47 Model Log(likelihood) # Param's AIC 

48 A1 -158.130647 12 340.261294 

49 A2 -84.800279 22 213.600558 

50 A3 -98.821893 13 223.643786 

51 fitted -247.263464 6 506.526929 

52 R -234.625213 2 473.250426 

53 

54 

55 Explanation of Tests 

56 

57 Test 1: Do responses and/or variances differ among Dose levels? 

58 (A2 vs. R) 

59 Test 2: Are Variances Homogeneous? (A1 vs A2) 

60 Test 3: Are variances adequately modeled? (A2 vs. A3) 

61 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

62 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

63 

64 Tests of Interest 

65 

66 Test -2*log(Likelihood Ratio) Test df p-value 

67 

68 Test 1 299.65 20 <.0001 

69 Test 2 146.661 10 <.0001 

70 Test 3 28.0432 9 0.0009381 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-53 —DO NOT CITE OR QUOTE 

1 Test 4 296.883 7 <.0001 

2 

3 The p-value for Test 1 is less than .05. There appears to be a 

4 difference between response and/or variances among the dose levels 

5 It seems appropriate to model the data 

6 

7 The p-value for Test 2 is less than .1. A non-homogeneous variance 

8 model appears to be appropriate 

9 

10 The p-value for Test 3 is less than .1. You may want to consider a 

11 different variance model 

12 

13 The p-value for Test 4 is less than .1. You may want to try a different 

14 model 

15 

16 

17 Benchmark Dose Computation 

18 

19 Specified effect = 1 

20 

21 Risk Type = Estimated standard deviations from the control mean 

22 

23 Confidence level = 0.95 

24 

25 BMD = 1.#QNAN 

26 

27 

28 BMDL computation failed. 

29 

30 H.2.4.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 50

 100

 150

 200

 250

 0 500000 1e+006 1.5e+006 2e+006

Mean Response

dose

Power Model with 0.95 Confidence Level

13:25 11/20 2009

BMDBMDL

 

Power

31 

 32 

 33 

34 H.2.4.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

35 Unrestricted

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-54 —DO NOT CITE OR QUOTE 

1 ==================================================================== 

2 Power Model. (Version: 2.15; Date: 04/07/2008) 

3 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_BaP_hydro_act.(d) 

4 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_BaP_hydro_act.plt 

5 Fri Nov 20 13:25:19 2009 

6 ==================================================================== 

7 

8 Kitchin 1979, Tbl3, BaP hydrolase activity 

9 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

10 

11 The form of the response function is: 

12 

13 Y[dose] = control + slope * dose^power 

14 

15 

16 Dependent variable = Mean 

17 Independent variable = Dose 

18 The power is not restricted 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 11 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 

28 

29 Default Initial Parameter Values 

30 lalpha = 5.70855 

31 rho = 0 

32 control = 4.9 

33 slope = 0.0304965 

34 power = 0.593743 

35 

36 

37 Asymptotic Correlation Matrix of Parameter Estimates 

38 

39 lalpha rho control slope power 

40 

41 lalpha 1 -0.9 -0.45 0.25 -0.23 

42 

43 rho -0.9 1 0.35 -0.18 0.12 

44 

45 control -0.45 0.35 1 -0.44 0.42 

46 

47 slope 0.25 -0.18 -0.44 1 -0.98 

48 

49 power -0.23 0.12 0.42 -0.98 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 95.0% Wald Confidence Interval 

56 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

57 lalpha -3.42042 0.570798 -4.53917 -2.30168 

58 rho 2.42941 0.164247 2.10749 2.75133 

59 control 4.52558 0.315791 3.90665 5.14452 

60 slope 0.0642178 0.0318952 0.00170434 0.126731 

61 power 0.619697 0.0482017 0.525223 0.71417 

62 

63 

64 

65 Table of Data and Estimated Values of Interest 

66 

67 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

68 ------ --- -------- -------- ----------- ----------- ---------- 

69 

70 0 9 4.9 4.53 1.11 1.13 0.993 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-55 —DO NOT CITE OR QUOTE 

1 69.5 4 4.9 5.42 1.18 1.41 -0.732 

2 232 4 6.7 6.4 1.4 1.72 0.344 

3 463 4 7.2 7.41 1.8 2.06 -0.2 

4 2318 4 8.3 12.3 0.26 3.83 -2.11 

5 6949 4 14 20 5 6.86 -1.74 

6 2.319e+004 4 59 37.1 6.8 14.6 3.01 

7 6.966e+004 4 96 68.9 46 30.9 1.75 

8 2.326e+005 4 155 140 16.4 73.4 0.397 

9 5.819e+005 4 182 244 26 144 -0.868 

10 2.332e+006 4 189 572 26 404 -1.89 

11 

12 

13 

14 Model Descriptions for likelihoods calculated 

15 

16 

17 Model A1: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma^2 

19 

20 Model A2: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma(i)^2 

22 

23 Model A3: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

25 Model A3 uses any fixed variance parameters that 

26 were specified by the user 

27 

28 Model R: Yi = Mu + e(i) 

29 Var{e(i)} = Sigma^2 

30 

31 

32 Likelihoods of Interest 

33 

34 Model Log(likelihood) # Param's AIC 

35 A1 -158.130647 12 340.261294 

36 A2 -84.800279 22 213.600558 

37 A3 -98.821893 13 223.643786 

38 fitted -130.634662 5 271.269325 

39 R -234.625213 2 473.250426 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Do responses and/or variances differ among Dose levels? 

45 (A2 vs. R) 

46 Test 2: Are Variances Homogeneous? (A1 vs A2) 

47 Test 3: Are variances adequately modeled? (A2 vs. A3) 

48 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

49 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) Test df p-value 

54 

55 Test 1 299.65 20 <.0001 

56 Test 2 146.661 10 <.0001 

57 Test 3 28.0432 9 0.0009381 

58 Test 4 63.6255 8 <.0001 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose levels 

62 It seems appropriate to model the data 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous variance 

65 model appears to be appropriate 

66 

67 The p-value for Test 3 is less than .1. You may want to consider a 

68 different variance model 

69 

70 The p-value for Test 4 is less than .1. You may want to try a different 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-56 —DO NOT CITE OR QUOTE 

1 model 

2 

3 

4 Benchmark Dose Computation 

5 

6 Specified effect = 1 

7 

8 Risk Type = Estimated standard deviations from the control mean 

9 

10 Confidence level = 0.95 

11 

12 BMD = 102.508 

13 

14 

15 BMDL = 44.1703 

16 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-57 —DO NOT CITE OR QUOTE 

1 H.2.5. National Toxicology Program. (2006): EROD Liver Week 53 

2 H.2.5.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 113.40 <0.0001 203.18 7.6E+03 5.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 113.40 <0.0001 203.18 7.6E+03 5.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 20.95 0.00 112.76 1.2E+02 8.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 6.69 0.04 100.50 3.1E+02 2.0E+02 nonconstant variance, 

power restricted ≥1 

Hill c 2 <.0001 3.09 0.21 96.90 4.2E+02 3.0E+02 nonconstant variance, 

n restricted >1 

Hill d 2 <.0001 3.09 0.21 96.90 4.2E+02 3.0E+02 nonconstant variance, n 

unrestricted 

linear 4 <.0001 73.05 <.0001 162.86 1.5E+02 1.1E+02 nonconstant variance 

polynomial 4 <.0001 -81.81 <.0001 8.00 6.0E-08 error nonconstant variance 

power 4 <.0001 73.05 <.0001 162.86 1.5E+02 1.1E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 4 <0.0001 77.17 <0.0001 201.35 7.0E+03 5.9E+03 constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 77.17 <0.0001 201.35 7.0E+03 5.9E+03 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 7.36 0.06 133.54 4.6E+02 3.6E+02 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 4.20 0.12 132.37 7.3E+02 4.5E+02 constant variance, 

power restricted ≥1 

Hill 2 <.0001 2.31 0.31 130.49 9.1E+02 6.1E+02 constant variance, n 

restricted >1 

Hill 2 <.0001 2.31 0.31 130.49 9.1E+02 6.1E+02 constant variance, n 

unrestricted 

linear 4 <.0001 64.69 <.0001 188.86 4.0E+03 3.2E+03 constant variance 

polynomial 4 <.0001 64.69 <.0001 188.86 4.0E+03 3.2E+03 constant variance 

power 4 <.0001 64.69 <.0001 188.86 4.0E+03 3.2E+03 

constant variance, 

power restricted ≥1, 

bound hit a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-58 —DO NOT CITE OR QUOTE 

1 H.2.5.2. Figure for Selected Model: Hill, Nonconstant Variance, n Restricted >1 

 5

 10

 15

 20

 25

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Hill Model with 0.95 Confidence Level

11:23 11/19 2009

BMDL BMD

 

Hill

2 

 3 

 4 

5 H.2.5.3. Output file for Selected Model: Hill, Nonconstant Variance, n Restricted >1 6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_BMR1_Tbl12_wk53_EROD_liv.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\AD\Blood\Hill_BMR1_Tbl12_wk53_EROD_liv.plt 

12 Thu Nov 19 11:23:04 2009 

13 ==================================================================== 

14 

15 0 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 Power parameter restricted to be greater than 1 

26 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

27 

28 Total number of dose groups = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 

35 

36 Default Initial Parameter Values 

37 lalpha = 1.59547 

38 rho = 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-59 —DO NOT CITE OR QUOTE 

1 intercept = 3.614 

2 v = 17.599 

3 n = 2.06282 

4 k = 3589.94 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 lalpha rho intercept v n k 

10 

11 lalpha 1 -0.96 -0.16 0.088 -0.06 0.042 

12 

13 rho -0.96 1 0.15 -0.12 0.062 -0.045 

14 

15 intercept -0.16 0.15 1 -0.18 0.13 0.073 

16 

17 v 0.088 -0.12 -0.18 1 -0.7 0.82 

18 

19 n -0.06 0.062 0.13 -0.7 1 -0.78 

20 

21 k 0.042 -0.045 0.073 0.82 -0.78 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 lalpha -4.86517 0.742003 -6.31947 -3.41087 

30 rho 2.26994 0.287404 1.70664 2.83324 

31 intercept 3.62886 0.133846 3.36652 3.89119 

32 v 17.8693 0.946035 16.0151 19.7235 

33 n 2.12332 0.238762 1.65535 2.59128 

34 k 2573.21 216.955 2147.99 2998.43 

35 

36 

37 

38 Table of Data and Estimated Values of Interest 

39 

40 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

41 ------ --- -------- -------- ----------- ----------- ---------- 

42 

43 0 8 3.61 3.63 0.486 0.379 -0.111 

44 1354 8 7.27 7.27 0.557 0.834 0.013 

45 3056 8 14.8 14.2 1.61 1.78 0.925 

46 5259 8 17.3 18.3 1.59 2.38 -1.19 

47 8918 8 20.6 20.3 3.05 2.68 0.29 

48 1.6e+004 8 21.2 21.1 3.82 2.8 0.077 

49 

50 

51 

52 Model Descriptions for likelihoods calculated 

53 

54 

55 Model A1: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma^2 

57 

58 Model A2: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma(i)^2 

60 

61 Model A3: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

63 Model A3 uses any fixed variance parameters that 

64 were specified by the user 

65 

66 Model R: Yi = Mu + e(i) 

67 Var{e(i)} = Sigma^2 

68 

69 

70 Likelihoods of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-60 —DO NOT CITE OR QUOTE 

1 

2 Model Log(likelihood) # Param's AIC 

3 A1 -59.086537 7 132.173073 

4 A2 -37.515858 12 99.031716 

5 A3 -40.906180 8 97.812359 

6 fitted -42.452016 6 96.904031 

7 R -116.710291 2 237.420582 

8 

9 

10 Explanation of Tests 

11 

12 Test 1: Do responses and/or variances differ among Dose levels? 

13 (A2 vs. R) 

14 Test 2: Are Variances Homogeneous? (A1 vs A2) 

15 Test 3: Are variances adequately modeled? (A2 vs. A3) 

16 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

17 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

18 

19 Tests of Interest 

20 

21 Test -2*log(Likelihood Ratio) Test df p-value 

22 

23 Test 1 158.389 10 <.0001 

24 Test 2 43.1414 5 <.0001 

25 Test 3 6.78064 4 0.1479 

26 Test 4 3.09167 2 0.2131 

27 

28 The p-value for Test 1 is less than .05. There appears to be a 

29 difference between response and/or variances among the dose levels 

30 It seems appropriate to model the data 

31 

32 The p-value for Test 2 is less than .1. A non-homogeneous variance 

33 model appears to be appropriate 

34 

35 The p-value for Test 3 is greater than .1. The modeled variance appears 

36 to be appropriate here 

37 

38 The p-value for Test 4 is greater than .1. The model chosen seems 

39 to adequately describe the data 

40 

41 

42 Benchmark Dose Computation 

43 

44 Specified effect = 1 

45 

46 Risk Type = Estimated standard deviations from the control mean 

47 

48 Confidence level = 0.95 

49 

50 BMD = 423.477 

51 

52 BMDL = 304.577 

53 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-61 —DO NOT CITE OR QUOTE 

1 H.2.5.4. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 5

 10

 15

 20

 25

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Hill Model with 0.95 Confidence Level

11:23 11/19 2009

BMDL BMD

 

Hill

2 

 3 

 4 

5 H.2.5.5. Output file for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 6 

7 

8 ==================================================================== 

9 Hill Model. (Version: 2.14; Date: 06/26/2008) 

10 Input Data File: C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_Tbl12_wk53_EROD_liv.(d) 

11 Gnuplot Plotting File: 

12 C:\USEPA\BMDS21\AD\Blood\Hill_Unrest_BMR1_Tbl12_wk53_EROD_liv.plt 

13 Thu Nov 19 11:23:13 2009 

14 ==================================================================== 

15 

16 0 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 Power parameter is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 lalpha = 1.59547 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-62 —DO NOT CITE OR QUOTE 

1 rho = 0 

2 intercept = 3.614 

3 v = 17.599 

4 n = 2.06282 

5 k = 3589.94 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho intercept v n k 

11 

12 lalpha 1 -0.96 -0.16 0.088 -0.06 0.042 

13 

14 rho -0.96 1 0.15 -0.12 0.062 -0.045 

15 

16 intercept -0.16 0.15 1 -0.18 0.13 0.073 

17 

18 v 0.088 -0.12 -0.18 1 -0.7 0.82 

19 

20 n -0.06 0.062 0.13 -0.7 1 -0.78 

21 

22 k 0.042 -0.045 0.073 0.82 -0.78 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 95.0% Wald Confidence Interval 

29 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

30 lalpha -4.86517 0.742003 -6.31947 -3.41087 

31 rho 2.26994 0.287404 1.70664 2.83324 

32 intercept 3.62886 0.133846 3.36652 3.89119 

33 v 17.8693 0.946034 16.0151 19.7235 

34 n 2.12332 0.238762 1.65535 2.59128 

35 k 2573.21 216.955 2147.99 2998.43 

36 

37 

38 

39 Table of Data and Estimated Values of Interest 

40 

41 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

42 ------ --- -------- -------- ----------- ----------- ---------- 

43 

44 0 8 3.61 3.63 0.486 0.379 -0.111 

45 1354 8 7.27 7.27 0.557 0.834 0.013 

46 3056 8 14.8 14.2 1.61 1.78 0.925 

47 5259 8 17.3 18.3 1.59 2.38 -1.19 

48 8918 8 20.6 20.3 3.05 2.68 0.29 

49 1.6e+004 8 21.2 21.1 3.82 2.8 0.077 

50 

51 

52 

53 Model Descriptions for likelihoods calculated 

54 

55 

56 Model A1: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma^2 

58 

59 Model A2: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = Sigma(i)^2 

61 

62 Model A3: Yij = Mu(i) + e(ij) 

63 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

64 Model A3 uses any fixed variance parameters that 

65 were specified by the user 

66 

67 Model R: Yi = Mu + e(i) 

68 Var{e(i)} = Sigma^2 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-63 —DO NOT CITE OR QUOTE 

1 Likelihoods of Interest 

2 

3 Model Log(likelihood) # Param's AIC 

4 A1 -59.086537 7 132.173073 

5 A2 -37.515858 12 99.031716 

6 A3 -40.906180 8 97.812359 

7 fitted -42.452016 6 96.904032 

8 R -116.710291 2 237.420582 

9 

10 

11 Explanation of Tests 

12 

13 Test 1: Do responses and/or variances differ among Dose levels? 

14 (A2 vs. R) 

15 Test 2: Are Variances Homogeneous? (A1 vs A2) 

16 Test 3: Are variances adequately modeled? (A2 vs. A3) 

17 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

18 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

19 

20 Tests of Interest 

21 

22 Test -2*log(Likelihood Ratio) Test df p-value 

23 

24 Test 1 158.389 10 <.0001 

25 Test 2 43.1414 5 <.0001 

26 Test 3 6.78064 4 0.1479 

27 Test 4 3.09167 2 0.2131 

28 

29 The p-value for Test 1 is less than .05. There appears to be a 

30 difference between response and/or variances among the dose levels 

31 It seems appropriate to model the data 

32 

33 The p-value for Test 2 is less than .1. A non-homogeneous variance 

34 model appears to be appropriate 

35 

36 The p-value for Test 3 is greater than .1. The modeled variance appears 

37 to be appropriate here 

38 

39 The p-value for Test 4 is greater than .1. The model chosen seems 

40 to adequately describe the data 

41 

42 

43 Benchmark Dose Computation 

44 

45 Specified effect = 1 

46 

47 Risk Type = Estimated standard deviations from the control mean 

48 

49 Confidence level = 0.95 

50 

51 BMD = 423.477 

52 

53 BMDL = 304.577 

54 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-64 —DO NOT CITE OR QUOTE 

1 H.2.6. National Toxicology Program. (2006): Lung EROD Week 31 

2 H.2.6.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 123.80 <0.0001 390.99 1.2E+04 8.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 123.80 <0.0001 390.99 1.2E+04 8.1E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 13.01 0.00 282.20 4.1E+01 2.9E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 13.01 0.00 282.20 4.1E+01 2.9E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 <0.0001 13.01 0.00 282.20 4.1E+01 2.9E+01 nonconstant variance, 

power unrestricted 

Hill 4 <.0001 59.49 <.0001 326.67 1.3E-11 1.3E-11 nonconstant variance, n 

restricted >1, bound hit 

Hill d 4 <.0001 59.49 <.0001 326.67 1.3E-11 1.3E-11 nonconstant variance, n 

unrestricted 

linear 4 <.0001 116.14 <.0001 383.32 4.1E+03 1.5E+03 nonconstant variance 

polynomial 4 <.0001 123.25 <.0001 390.43 1.3E+04 7.5E+01 nonconstant variance 

power 4 <.0001 116.14 <.0001 383.32 4.1E+03 1.5E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 23.64 <.0001 292.82 4.5E-02 4.5E-02 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 80.66 <0.0001 390.82 9.0E+03 7.5E+03 constant variance, power 

restricted ≥1 

exponential (M3) 4 <0.0001 80.66 <0.0001 390.82 9.0E+03 7.5E+03 constant variance, power 

restricted ≥1 

exponential (M4) 3 <0.0001 12.08 0.01 324.24 4.6E+02 3.4E+02 constant variance, power 

restricted ≥1 

exponential (M5) 2 <0.0001 12.08 0.00 326.24 4.6E+02 3.4E+02 constant variance, power 

restricted ≥1 

exponential (M5) 2 <0.0001 12.08 0.00 326.24 4.6E+02 3.4E+02 constant variance, power 

unrestricted 

Hill 2 <.0001 14.17 0.00 328.33 5.1E+02 2.4E+02 constant variance, n 

restricted >1 

Hill 2 <.0001 14.17 0.00 328.33 5.1E+02 1.9E+02 constant variance, n 

unrestricted 

linear 4 <.0001 71.44 <.0001 381.60 5.6E+03 4.4E+03 constant variance 

polynomial 4 <.0001 71.44 <.0001 381.60 5.6E+03 4.4E+03 constant variance 

power 4 <.0001 71.44 <.0001 381.60 5.6E+03 4.4E+03 constant variance, power 

restricted ≥1, bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-65 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 3 <.0001 23.14 <.0001 335.30 2.0E+01 2.0E+00 constant variance, power 

unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.2.6.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 10

 20

 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:16 11/20 2009

BMDLBMD

 

Exponential

5 

 6 

 7 

8 H.2.6.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_Lung_EROD_wk31.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 13:16:38 2009 

17 ==================================================================== 

18 

19 Tbl 12, Week 31, Lung Microsomes EROD 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-66 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 6 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 4 

33 -------- -------- 

34 lnalpha -1.42653 

35 rho 1.46168 

36 a 1.96745 

37 b 0.000226755 

38 c 26.7857 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 4 

46 -------- ------- 

47 lnalpha -1.47384 

48 rho 1.57432 

49 a 2.11972 

50 b 0.000440068 

51 c 23.6215 

52 d 1 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 10 2.071 0.9708 

60 1284 10 25.34 2.549 

61 2932 10 30.39 5.831 

62 5075 10 50.19 8.68 

63 8629 10 49.07 13.91 

64 1.55e+004 10 48.42 8.933 

65 

66 

67 Estimated Values of Interest 

68 

69 Dose Est Mean Est Std Scaled Residual 

70 ------ ---------- --------- ---------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-67 —DO NOT CITE OR QUOTE 

1 0 2.12 0.8646 -0.1782 

2 1284 22.82 5.612 1.423 

3 2932 36.88 8.189 -2.506 

4 5075 44.93 9.567 1.738 

5 8629 49 10.24 0.02179 

6 1.55e+004 50.02 10.41 -0.4854 

7 

8 

9 

10 Other models for which likelihoods are calculated: 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

20 

21 Model R: Yij = Mu + e(i) 

22 Var{e(ij)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) DF AIC 

28 ------- ----------------- ---- ------------ 

29 A1 -152.0793 7 318.1586 

30 A2 -123.367 12 270.734 

31 A3 -129.5911 8 275.1823 

32 R -206.5175 2 417.0349 

33 4 -136.0978 5 282.1956 

34 

35 

36 Additive constant for all log-likelihoods = -55.14. This constant added to the 

37 above values gives the log-likelihood including the term that does not 

38 depend on the model parameters. 

39 

40 

41 Explanation of Tests 

42 

43 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

44 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

45 Test 3: Are variances adequately modeled? (A2 vs. A3) 

46 

47 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

48 

49 

50 Tests of Interest 

51 

52 Test -2*log(Likelihood Ratio) D. F. p-value 

53 -------- ------------------------ ------ -------------- 

54 Test 1 166.3 10 < 0.0001 

55 Test 2 57.42 5 < 0.0001 

56 Test 3 12.45 4 0.01431 

57 Test 6a 13.01 3 0.004608 

58 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose 

62 levels, it seems appropriate to model the data. 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous 

65 variance model appears to be appropriate. 

66 

67 The p-value for Test 3 is less than .1. You may want to 

68 consider a different variance model. 

69 

70 The p-value for Test 6a is less than .1. Model 4 may not adequately 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-68 —DO NOT CITE OR QUOTE 

1 describe the data; you may want to consider another model. 

2 

3 

4 Benchmark Dose Computations: 

5 

6 Specified Effect = 1.000000 

7 

8 Risk Type = Estimated standard deviations from control 

9 

10 Confidence Level = 0.950000 

11 

12 BMD = 41.3446 

13 

14 BMDL = 28.8946 

15 

16 

17 

18 H.2.6.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

19 Unrestricted

 0

 10

 20

 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:16 11/20 2009

BMDLBMD

 

Exponential

20 

 21 

 22 

23 H.2.6.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

24 Power Unrestricted 

25 

26 

27 ==================================================================== 

28 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

29 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_Lung_EROD_wk31.(d) 

30 Gnuplot Plotting File: 

31 Fri Nov 20 13:16:45 2009 

32 ==================================================================== 

33 

34 Tbl 12, Week 31, Lung Microsomes EROD 

35 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-69 —DO NOT CITE OR QUOTE 

1 The form of the response function by Model: 

2 Model 2: Y[dose] = a * exp{sign * b * dose} 

3 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

4 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

5 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

6 

7 Note: Y[dose] is the median response for exposure = dose; 

8 sign = +1 for increasing trend in data; 

9 sign = -1 for decreasing trend. 

10 

11 Model 2 is nested within Models 3 and 4. 

12 Model 3 is nested within Model 5. 

13 Model 4 is nested within Model 5. 

14 

15 

16 Dependent variable = Mean 

17 Independent variable = Dose 

18 Data are assumed to be distributed: normally 

19 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

20 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 5 

34 -------- -------- 

35 lnalpha -1.42653 

36 rho 1.46168 

37 a 1.96745 

38 b 0.000226755 

39 c 26.7857 

40 d 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 Variable Model 5 

47 -------- ------- 

48 lnalpha -1.47384 

49 rho 1.57432 

50 a 2.11972 

51 b 0.000440068 

52 c 23.6215 

53 d 1 

54 

55 

56 Table of Stats From Input Data 

57 

58 Dose N Obs Mean Obs Std Dev 

59 ----- --- ---------- ------------- 

60 0 10 2.071 0.9708 

61 1284 10 25.34 2.549 

62 2932 10 30.39 5.831 

63 5075 10 50.19 8.68 

64 8629 10 49.07 13.91 

65 1.55e+004 10 48.42 8.933 

66 

67 

68 Estimated Values of Interest 

69 

70 Dose Est Mean Est Std Scaled Residual 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-70 —DO NOT CITE OR QUOTE 

1 ------ ---------- --------- ---------------- 

2 0 2.12 0.8646 -0.1782 

3 1284 22.82 5.612 1.423 

4 2932 36.88 8.189 -2.506 

5 5075 44.93 9.567 1.738 

6 8629 49 10.24 0.02179 

7 1.55e+004 50.02 10.41 -0.4854 

8 

9 

10 

11 Other models for which likelihoods are calculated: 

12 

13 Model A1: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma^2 

15 

16 Model A2: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma(i)^2 

18 

19 Model A3: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

21 

22 Model R: Yij = Mu + e(i) 

23 Var{e(ij)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) DF AIC 

29 ------- ----------------- ---- ------------ 

30 A1 -152.0793 7 318.1586 

31 A2 -123.367 12 270.734 

32 A3 -129.5911 8 275.1823 

33 R -206.5175 2 417.0349 

34 5 -136.0978 5 282.1956 

35 

36 

37 Additive constant for all log-likelihoods = -55.14. This constant added to the 

38 above values gives the log-likelihood including the term that does not 

39 depend on the model parameters. 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

45 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

46 Test 3: Are variances adequately modeled? (A2 vs. A3) 

47 

48 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

49 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) D. F. p-value 

54 -------- ------------------------ ------ -------------- 

55 Test 1 166.3 10 < 0.0001 

56 Test 2 57.42 5 < 0.0001 

57 Test 3 12.45 4 0.01431 

58 Test 7a 13.01 3 0.004608 

59 

60 

61 The p-value for Test 1 is less than .05. There appears to be a 

62 difference between response and/or variances among the dose 

63 levels, it seems appropriate to model the data. 

64 

65 The p-value for Test 2 is less than .1. A non-homogeneous 

66 variance model appears to be appropriate. 

67 

68 The p-value for Test 3 is less than .1. You may want to 

69 consider a different variance model. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-71 —DO NOT CITE OR QUOTE 

1 The p-value for Test 7a is less than .1. Model 5 may not adequately 

2 describe the data; you may want to consider another model. 

3 

4 

5 Benchmark Dose Computations: 

6 

7 Specified Effect = 1.000000 

8 

9 Risk Type = Estimated standard deviations from control 

10 

11 Confidence Level = 0.950000 

12 

13 BMD = 41.3446 

14 

15 BMDL = 28.8946 

16 

17 

18 

19 H.2.6.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 10

 20

 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:16 11/20 2009

BMDBMDL

 

Hill

20 

 21 

 22 

23 H.2.6.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 24 

25 

26 ==================================================================== 

27 Hill Model. (Version: 2.14; Date: 06/26/2008) 

28 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_Lung_EROD_wk31.(d) 

29 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_Lung_EROD_wk31.plt 

30 Fri Nov 20 13:16:47 2009 

31 ==================================================================== 

32 

33 Tbl 12, Week 31, Lung Microsomes EROD 

34 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

35 

36 The form of the response function is: 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-72 —DO NOT CITE OR QUOTE 

1 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

2 

3 

4 Dependent variable = Mean 

5 Independent variable = Dose 

6 Power parameter is not restricted 

7 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

8 

9 Total number of dose groups = 6 

10 Total number of records with missing values = 0 

11 Maximum number of iterations = 250 

12 Relative Function Convergence has been set to: 1e-008 

13 Parameter Convergence has been set to: 1e-008 

14 

15 

16 

17 Default Initial Parameter Values 

18 lalpha = 4.17467 

19 rho = 0 

20 intercept = 2.071 

21 v = 48.119 

22 n = 18 

23 k = 4322.89 

24 

25 

26 Asymptotic Correlation Matrix of Parameter Estimates 

27 

28 ( *** The model parameter(s) -n -k 

29 have been estimated at a boundary point, or have been specified by the user, 

30 and do not appear in the correlation matrix ) 

31 

32 lalpha rho intercept v 

33 

34 lalpha 1 -0.95 -0.49 0.11 

35 

36 rho -0.95 1 0.45 -0.22 

37 

38 intercept -0.49 0.45 1 -0.15 

39 

40 v 0.11 -0.22 -0.15 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 95.0% Wald Confidence Interval 

47 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

48 lalpha -1.47774 0.642044 -2.73613 -0.219359 

49 rho 1.8037 0.187436 1.43633 2.17107 

50 intercept 2.071 0.291246 1.50017 2.64183 

51 v 38.6102 1.9322 34.8232 42.3972 

52 n 18 NA 

53 k 1.5503e-011 NA 

54 

55 NA - Indicates that this parameter has hit a bound 

56 implied by some inequality constraint and thus 

57 has no standard error. 

58 

59 

60 

61 Table of Data and Estimated Values of Interest 

62 

63 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

64 ------ --- -------- -------- ----------- ----------- ---------- 

65 

66 0 10 2.07 2.07 0.971 0.921 -2.27e-007 

67 1284 10 25.3 40.7 2.55 13.5 -3.59 

68 2932 10 30.4 40.7 5.83 13.5 -2.41 

69 5075 10 50.2 40.7 8.68 13.5 2.23 

70 8629 10 49.1 40.7 13.9 13.5 1.96 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-73 —DO NOT CITE OR QUOTE 

1 1.55e+004 10 48.4 40.7 8.93 13.5 1.81 

2 

3 

4 

5 Model Descriptions for likelihoods calculated 

6 

7 

8 Model A1: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma^2 

10 

11 Model A2: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma(i)^2 

13 

14 Model A3: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

16 Model A3 uses any fixed variance parameters that 

17 were specified by the user 

18 

19 Model R: Yi = Mu + e(i) 

20 Var{e(i)} = Sigma^2 

21 

22 Likelihoods of Interest 

23 

24 Model Log(likelihood) # Param's AIC 

25 A1 -152.079318 7 318.158637 

26 A2 -123.366985 12 270.733969 

27 A3 -129.591134 8 275.182269 

28 fitted -159.335928 4 326.671856 

29 R -206.517459 2 417.034919 

30 

31 

32 Explanation of Tests 

33 

34 Test 1: Do responses and/or variances differ among Dose levels? 

35 (A2 vs. R) 

36 Test 2: Are Variances Homogeneous? (A1 vs A2) 

37 Test 3: Are variances adequately modeled? (A2 vs. A3) 

38 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

39 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

40 

41 Tests of Interest 

42 

43 Test -2*log(Likelihood Ratio) Test df p-value 

44 

45 Test 1 166.301 10 <.0001 

46 Test 2 57.4247 5 <.0001 

47 Test 3 12.4483 4 0.01431 

48 Test 4 59.4896 4 <.0001 

49 

50 The p-value for Test 1 is less than .05. There appears to be a 

51 difference between response and/or variances among the dose levels 

52 It seems appropriate to model the data 

53 

54 The p-value for Test 2 is less than .1. A non-homogeneous variance 

55 model appears to be appropriate 

56 

57 The p-value for Test 3 is less than .1. You may want to consider a 

58 different variance model 

59 

60 The p-value for Test 4 is less than .1. You may want to try a different 

61 model 

62 

63 

64 Benchmark Dose Computation 

65 

66 Specified effect = 1 

67 

68 Risk Type = Estimated standard deviations from the control mean 

69 

70 Confidence level = 0.95 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-74 —DO NOT CITE OR QUOTE 

1 

2 BMD = 1.26143e-011 

3 

4 BMDL = 1.26143e-011 

5 

6 H.2.6.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 10

 20

 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Power Model with 0.95 Confidence Level

13:16 11/20 2009

BMDBMDL

 

Power

7 

 8 

 9 

10 H.2.6.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

11 Unrestricted

12 

13 

14 ==================================================================== 

15 Power Model. (Version: 2.15; Date: 04/07/2008) 

16 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_Lung_EROD_wk31.(d) 

17 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_Lung_EROD_wk31.plt 

18 Fri Nov 20 13:16:48 2009 

19 ==================================================================== 

20 

21 Tbl 12, Week 31, Lung Microsomes EROD 

22 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

23 

24 The form of the response function is: 

25 

26 Y[dose] = control + slope * dose^power 

27 

28 

29 Dependent variable = Mean 

30 Independent variable = Dose 

31 The power is not restricted 

32 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

33 

34 Total number of dose groups = 6 

35 Total number of records with missing values = 0 

36 Maximum number of iterations = 250 

37 Relative Function Convergence has been set to: 1e-008 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-75 —DO NOT CITE OR QUOTE 

1 Parameter Convergence has been set to: 1e-008 

2 

3 

4 

5 Default Initial Parameter Values 

6 lalpha = 4.17467 

7 rho = 0 

8 control = 2.071 

9 slope = 2.58483 

10 power = 0.313845 

11 

12 

13 Asymptotic Correlation Matrix of Parameter Estimates 

14 

15 lalpha rho control slope power 

16 

17 lalpha 1 -0.94 -0.42 0.14 -0.14 

18 

19 rho -0.94 1 0.38 -0.17 0.15 

20 

21 control -0.42 0.38 1 -0.11 0.094 

22 

23 slope 0.14 -0.17 -0.11 1 -1 

24 

25 power -0.14 0.15 0.094 -1 1 

26 

27 

28 

29 Parameter Estimates 

30 

31 95.0% Wald Confidence Interval 

32 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

33 lalpha -1.53087 0.573913 -2.65572 -0.406018 

34 rho 1.64612 0.167167 1.31848 1.97376 

35 control 2.1082 0.270802 1.57744 2.63896 

36 slope 2.35281 0.945551 0.499559 4.20605 

37 power 0.325737 0.0465627 0.234476 0.416998 

38 

39 

40 

41 Table of Data and Estimated Values of Interest 

42 

43 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

44 ------ --- -------- -------- ----------- ----------- ---------- 

45 

46 0 10 2.07 2.11 0.971 0.859 -0.137 

47 1284 10 25.3 26.3 2.55 6.86 -0.453 

48 2932 10 30.4 33.8 5.83 8.43 -1.28 

49 5075 10 50.2 40 8.68 9.69 3.33 

50 8629 10 49.1 47.2 13.9 11.1 0.545 

51 1.55e+004 10 48.4 56.6 8.93 12.9 -2.01 

52 

53 

54 

55 Model Descriptions for likelihoods calculated 

56 

57 

58 Model A1: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = Sigma^2 

60 

61 Model A2: Yij = Mu(i) + e(ij) 

62 Var{e(ij)} = Sigma(i)^2 

63 

64 Model A3: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

66 Model A3 uses any fixed variance parameters that 

67 were specified by the user 

68 

69 Model R: Yi = Mu + e(i) 

70 Var{e(i)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-76 —DO NOT CITE OR QUOTE 

1 

2 

3 Likelihoods of Interest 

4 

5 Model Log(likelihood) # Param's AIC 

6 A1 -152.079318 7 318.158637 

7 A2 -123.366985 12 270.733969 

8 A3 -129.591134 8 275.182269 

9 fitted -141.409222 5 292.818443 

10 R -206.517459 2 417.034919 

11 

12 

13 Explanation of Tests 

14 

15 Test 1: Do responses and/or variances differ among Dose levels? 

16 (A2 vs. R) 

17 Test 2: Are Variances Homogeneous? (A1 vs A2) 

18 Test 3: Are variances adequately modeled? (A2 vs. A3) 

19 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

20 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

21 

22 Tests of Interest 

23 

24 Test -2*log(Likelihood Ratio) Test df p-value 

25 

26 Test 1 166.301 10 <.0001 

27 Test 2 57.4247 5 <.0001 

28 Test 3 12.4483 4 0.01431 

29 Test 4 23.6362 3 <.0001 

30 

31 The p-value for Test 1 is less than .05. There appears to be a 

32 difference between response and/or variances among the dose levels 

33 It seems appropriate to model the data 

34 

35 The p-value for Test 2 is less than .1. A non-homogeneous variance 

36 model appears to be appropriate 

37 

38 The p-value for Test 3 is less than .1. You may want to consider a 

39 different variance model 

40 

41 The p-value for Test 4 is less than .1. You may want to try a different 

42 model 

43 

44 

45 Benchmark Dose Computation 

46 

47 Specified effect = 1 

48 

49 Risk Type = Estimated standard deviations from the control mean 

50 

51 Confidence level = 0.95 

52 

53 BMD = 0.0454117 

54 

55 

56 BMDL = 0.0454112 

57 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-77 —DO NOT CITE OR QUOTE 

1 H.2.7. National Toxicology Program. (2006): Lung EROD Week 53 

2 H.2.7.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 64.02 <0.0001 314.33 1.8E+04 1.1E+04 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 64.02 <0.0001 314.33 1.8E+04 1.1E+04 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 3.63 0.30 255.94 5.3E+01 3.3E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 2.58 0.28 256.88 5.8E+02 3.6E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 2 <0.0001 2.58 0.28 256.88 5.8E+02 3.6E+01 nonconstant variance, 

power unrestricted 

Hill 3 <.0001 16.10 0.00 268.40 1.7E-05 1.7E-05 nonconstant variance, n 

restricted >1 

Hill d 3 <.0001 16.10 0.00 268.40 1.7E-05 1.7E-05 nonconstant variance, n 

unrestricted 

linear 4 <.0001 62.93 <.0001 313.23 1.5E+04 6.9E+03 nonconstant variance 

polynomial 5 <.0001 81.88 <.0001 330.18 error 2.0E+03 nonconstant variance 

power 4 <.0001 62.93 <.0001 313.23 1.5E+04 6.9E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 8.76 0.03 261.07 1.1E-04 1.1E-04 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 39.91 <0.0001 316.45 1.1E+04 8.8E+03 constant variance, power 

restricted ≥1 

exponential (M3) 4 <0.0001 39.91 <0.0001 316.45 1.1E+04 8.8E+03 constant variance, power 

restricted ≥1 

exponential (M4) 3 <0.0001 3.69 0.30 282.22 4.0E+02 2.4E+02 constant variance, power 

restricted ≥1 

exponential (M5) 2 <0.0001 2.71 0.26 283.24 1.1E+03 2.7E+02 constant variance, power 

restricted ≥1 

exponential (M5) 2 <0.0001 2.71 0.26 283.24 1.1E+03 2.7E+02 constant variance, power 

unrestricted 

Hill 3 <.0001 2.71 0.44 281.24 1.2E+03 1.6E+02 constant variance, n 

restricted >1, bound hit 

Hill 3 <.0001 2.71 0.44 281.24 1.2E+03 3.8E+01 constant variance, n 

unrestricted 

linear 4 <.0001 36.71 <.0001 313.25 8.3E+03 5.9E+03 constant variance 

polynomial 4 <.0001 36.71 <.0001 313.25 8.3E+03 5.9E+03 constant variance 

power 4 <.0001 36.71 <.0001 313.25 8.3E+03 5.9E+03 constant variance, power 

restricted ≥1, bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-78 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 3 <.0001 6.08 0.11 284.61 2.8E+00 9.6E-05 constant variance, power 

unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.2.7.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 10

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 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:27 11/20 2009

BMDLBMD

 

Exponential

5 

 6 

 7 

8 H.2.7.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_Lung_EROD_wk53.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 12:27:08 2009 

17 ==================================================================== 

18 

19 Tbl 12, Week 53, Lung Microsomes EROD 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-79 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 6 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 4 

33 -------- -------- 

34 lnalpha -0.80064 

35 rho 1.47683 

36 a 2.86045 

37 b 0.000243673 

38 c 16.0581 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 4 

46 -------- ------- 

47 lnalpha -1.14118 

48 rho 1.62714 

49 a 3.06882 

50 b 0.000715169 

51 c 13.702 

52 d 3.78652 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 8 3.011 1.584 

60 1354 8 27.15 5.269 

61 3056 8 42.85 11.15 

62 5259 8 36.57 12.99 

63 8918 8 43.75 18.55 

64 1.6e+004 8 43.71 6.322 

65 

66 

67 Estimated Values of Interest 

68 

69 Dose Est Mean Est Std Scaled Residual 

70 ------ ---------- --------- ---------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-80 —DO NOT CITE OR QUOTE 

1 0 3.061 1.408 -0.1008 

2 1354 27.14 8.377 0.001867 

3 3056 38.19 11.07 1.191 

4 5259 42.16 12.01 -1.317 

5 8918 43.23 12.25 0.1192 

6 1.6e+004 43.33 12.28 0.08869 

7 

8 

9 

10 Other models for which likelihoods are calculated: 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

20 

21 Model R: Yij = Mu + e(i) 

22 Var{e(ij)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) DF AIC 

28 ------- ----------------- ---- ------------ 

29 A1 -135.2677 7 284.5353 

30 A2 -115.6885 12 255.3771 

31 A3 -121.1517 8 258.3034 

32 R -162.0902 2 328.1805 

33 4 -122.9684 5 255.9369 

34 

35 

36 Additive constant for all log-likelihoods = -44.11. This constant added to the 

37 above values gives the log-likelihood including the term that does not 

38 depend on the model parameters. 

39 

40 

41 Explanation of Tests 

42 

43 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

44 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

45 Test 3: Are variances adequately modeled? (A2 vs. A3) 

46 

47 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

48 

49 

50 Tests of Interest 

51 

52 Test -2*log(Likelihood Ratio) D. F. p-value 

53 -------- ------------------------ ------ -------------- 

54 Test 1 92.8 10 < 0.0001 

55 Test 2 39.16 5 < 0.0001 

56 Test 3 10.93 4 0.0274 

57 Test 6a 3.633 3 0.3039 

58 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose 

62 levels, it seems appropriate to model the data. 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous 

65 variance model appears to be appropriate. 

66 

67 The p-value for Test 3 is less than .1. You may want to 

68 consider a different variance model. 

69 

70 The p-value for Test 6a is greater than .1. Model 4 seems 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-81 —DO NOT CITE OR QUOTE 

1 to adequately describe the data. 

2 

3 

4 Benchmark Dose Computations: 

5 

6 Specified Effect = 1.000000 

7 

8 Risk Type = Estimated standard deviations from control 

9 

10 Confidence Level = 0.950000 

11 

12 BMD = 52.8515 

13 

14 BMDL = 32.5706 

15 

16 

17 

18 H.2.7.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

19 Unrestricted

 0

 10

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 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:27 11/20 2009

BMDL BMD

 

Exponential

20 

 21 

 22 

23 H.2.7.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

24 Power Unrestricted 

25 

26 

27 ==================================================================== 

28 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

29 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_Lung_EROD_wk53.(d) 

30 Gnuplot Plotting File: 

31 Fri Nov 20 12:27:17 2009 

32 ==================================================================== 

33 

34 Tbl 12, Week 53, Lung Microsomes EROD 

35 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-82 —DO NOT CITE OR QUOTE 

1 The form of the response function by Model: 

2 Model 2: Y[dose] = a * exp{sign * b * dose} 

3 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

4 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

5 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

6 

7 Note: Y[dose] is the median response for exposure = dose; 

8 sign = +1 for increasing trend in data; 

9 sign = -1 for decreasing trend. 

10 

11 Model 2 is nested within Models 3 and 4. 

12 Model 3 is nested within Model 5. 

13 Model 4 is nested within Model 5. 

14 

15 

16 Dependent variable = Mean 

17 Independent variable = Dose 

18 Data are assumed to be distributed: normally 

19 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

20 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 5 

34 -------- -------- 

35 lnalpha -0.80064 

36 rho 1.47683 

37 a 2.86045 

38 b 0.000243673 

39 c 16.0581 

40 d 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 Variable Model 5 

47 -------- ------- 

48 lnalpha -1.14118 

49 rho 1.62714 

50 a 3.06882 

51 b 0.000715169 

52 c 13.702 

53 d 3.78652 

54 

55 

56 Table of Stats From Input Data 

57 

58 Dose N Obs Mean Obs Std Dev 

59 ----- --- ---------- ------------- 

60 0 8 3.011 1.584 

61 1354 8 27.15 5.269 

62 3056 8 42.85 11.15 

63 5259 8 36.57 12.99 

64 8918 8 43.75 18.55 

65 1.6e+004 8 43.71 6.322 

66 

67 

68 Estimated Values of Interest 

69 

70 Dose Est Mean Est Std Scaled Residual 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-83 —DO NOT CITE OR QUOTE 

1 ------ ---------- --------- ---------------- 

2 0 3.069 1.407 -0.1162 

3 1354 25.95 7.993 0.4234 

4 3056 42.05 11.84 0.1907 

5 5259 42.05 11.84 -1.309 

6 8918 42.05 11.84 0.4055 

7 1.6e+004 42.05 11.84 0.3976 

8 

9 

10 

11 Other models for which likelihoods are calculated: 

12 

13 Model A1: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma^2 

15 

16 Model A2: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma(i)^2 

18 

19 Model A3: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

21 

22 Model R: Yij = Mu + e(i) 

23 Var{e(ij)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) DF AIC 

29 ------- ----------------- ---- ------------ 

30 A1 -135.2677 7 284.5353 

31 A2 -115.6885 12 255.3771 

32 A3 -121.1517 8 258.3034 

33 R -162.0902 2 328.1805 

34 5 -122.4411 6 256.8821 

35 

36 

37 Additive constant for all log-likelihoods = -44.11. This constant added to the 

38 above values gives the log-likelihood including the term that does not 

39 depend on the model parameters. 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

45 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

46 Test 3: Are variances adequately modeled? (A2 vs. A3) 

47 

48 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

49 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) D. F. p-value 

54 -------- ------------------------ ------ -------------- 

55 Test 1 92.8 10 < 0.0001 

56 Test 2 39.16 5 < 0.0001 

57 Test 3 10.93 4 0.0274 

58 Test 7a 2.579 2 0.2755 

59 

60 

61 The p-value for Test 1 is less than .05. There appears to be a 

62 difference between response and/or variances among the dose 

63 levels, it seems appropriate to model the data. 

64 

65 The p-value for Test 2 is less than .1. A non-homogeneous 

66 variance model appears to be appropriate. 

67 

68 The p-value for Test 3 is less than .1. You may want to 

69 consider a different variance model. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-84 —DO NOT CITE OR QUOTE 

1 The p-value for Test 7a is greater than .1. Model 5 seems 

2 to adequately describe the data. 

3 

4 

5 Benchmark Dose Computations: 

6 

7 Specified Effect = 1.000000 

8 

9 Risk Type = Estimated standard deviations from control 

10 

11 Confidence Level = 0.950000 

12 

13 BMD = 584.449 

14 

15 BMDL = 36.2497 

16 

17 

18 

19 H.2.7.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 10

 20

 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:27 11/20 2009

BMDBMDL

 

Hill

20 

 21 

 22 

23 H.2.7.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 24 

25 

26 ==================================================================== 

27 Hill Model. (Version: 2.14; Date: 06/26/2008) 

28 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_Lung_EROD_wk53.(d) 

29 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_Lung_EROD_wk53.plt 

30 Fri Nov 20 12:27:19 2009 

31 ==================================================================== 

32 

33 Tbl 12, Week 53, Lung Microsomes EROD 

34 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

35 

36 The form of the response function is: 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-85 —DO NOT CITE OR QUOTE 

1 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

2 

3 

4 Dependent variable = Mean 

5 Independent variable = Dose 

6 Power parameter is not restricted 

7 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

8 

9 Total number of dose groups = 6 

10 Total number of records with missing values = 0 

11 Maximum number of iterations = 250 

12 Relative Function Convergence has been set to: 1e-008 

13 Parameter Convergence has been set to: 1e-008 

14 

15 

16 

17 Default Initial Parameter Values 

18 lalpha = 4.76968 

19 rho = 0 

20 intercept = 3.011 

21 v = 40.735 

22 n = 2.49974 

23 k = 1565.11 

24 

25 

26 Asymptotic Correlation Matrix of Parameter Estimates 

27 

28 ( *** The model parameter(s) -k 

29 have been estimated at a boundary point, or have been specified by the user, 

30 and do not appear in the correlation matrix ) 

31 

32 lalpha rho intercept v n 

33 

34 lalpha 1 -0.96 -0.5 0.17 NA 

35 

36 rho -0.96 1 0.47 -0.25 NA 

37 

38 intercept -0.5 0.47 1 -0.25 NA 

39 

40 v 0.17 -0.25 -0.25 1 NA 

41 

42 n NA NA NA NA NA 

43 

44 

45 NA - This parameter's variance has been estimated as zero or less. 

46 THE MODEL HAS PROBABLY NOT CONVERGED!!! 

47 

48 

49 

50 Parameter Estimates 

51 

52 95.0% Wald Confidence Interval 

53 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

54 lalpha -1.07501 NA NA NA 

55 rho 1.68859 NA NA NA 

56 intercept 3.011 NA NA NA 

57 v 35.7938 NA NA NA 

58 n 5.85653 NA NA NA 

59 k 2.91999e-005 NA 

60 

61 At least some variance estimates are negative. 

62 THIS USUALLY MEANS THE MODEL HAS NOT CONVERGED! 

63 Try again from another starting point. 

64 

65 

66 

67 Table of Data and Estimated Values of Interest 

68 

69 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

70 ------ --- -------- -------- ----------- ----------- ---------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-86 —DO NOT CITE OR QUOTE 

1 

2 0 8 3.01 3.01 1.58 1.48 -2.78e-009 

3 1354 8 27.1 38.8 5.27 12.8 -2.57 

4 3056 8 42.8 38.8 11.2 12.8 0.891 

5 5259 8 36.6 38.8 13 12.8 -0.493 

6 8918 8 43.7 38.8 18.5 12.8 1.09 

7 1.6e+004 8 43.7 38.8 6.32 12.8 1.08 

8 

9 

10 

11 Model Descriptions for likelihoods calculated 

12 

13 

14 Model A1: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma^2 

16 

17 Model A2: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma(i)^2 

19 

20 Model A3: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

22 Model A3 uses any fixed variance parameters that 

23 were specified by the user 

24 

25 Model R: Yi = Mu + e(i) 

26 Var{e(i)} = Sigma^2 

27 

28 

29 Likelihoods of Interest 

30 

31 Model Log(likelihood) # Param's AIC 

32 A1 -135.267662 7 284.535325 

33 A2 -115.688533 12 255.377067 

34 A3 -121.151707 8 258.303413 

35 fitted -129.200555 5 268.401110 

36 R -162.090242 2 328.180484 

37 

38 

39 Explanation of Tests 

40 

41 Test 1: Do responses and/or variances differ among Dose levels? 

42 (A2 vs. R) 

43 Test 2: Are Variances Homogeneous? (A1 vs A2) 

44 Test 3: Are variances adequately modeled? (A2 vs. A3) 

45 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

46 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

47 

48 Tests of Interest 

49 

50 Test -2*log(Likelihood Ratio) Test df p-value 

51 

52 Test 1 92.8034 10 <.0001 

53 Test 2 39.1583 5 <.0001 

54 Test 3 10.9263 4 0.0274 

55 Test 4 16.0977 3 0.001083 

56 

57 The p-value for Test 1 is less than .05. There appears to be a 

58 difference between response and/or variances among the dose levels 

59 It seems appropriate to model the data 

60 

61 The p-value for Test 2 is less than .1. A non-homogeneous variance 

62 model appears to be appropriate 

63 

64 The p-value for Test 3 is less than .1. You may want to consider a 

65 different variance model 

66 

67 The p-value for Test 4 is less than .1. You may want to try a different 

68 model 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-87 —DO NOT CITE OR QUOTE 

1 Benchmark Dose Computation 

2 

3 Specified effect = 1 

4 

5 Risk Type = Estimated standard deviations from the control mean 

6 

7 Confidence level = 0.95 

8 

9 BMD = 1.70749e-005 

10 

11 BMDL = 1.70749e-005 

12 

13 

14 

15 H.2.7.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 10

 20

 30

 40

 50

 60

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:27 11/20 2009

BMDBMDL

 

Power

16 

 17 

 18 

19 H.2.7.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

20 Unrestricted

21 

22 

23 ==================================================================== 

24 Power Model. (Version: 2.15; Date: 04/07/2008) 

25 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_Lung_EROD_wk53.(d) 

26 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_Lung_EROD_wk53.plt 

27 Fri Nov 20 12:27:20 2009 

28 ==================================================================== 

29 

30 Tbl 12, Week 53, Lung Microsomes EROD 

31 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

32 

33 The form of the response function is: 

34 

35 Y[dose] = control + slope * dose^power 

36 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-88 —DO NOT CITE OR QUOTE 

1 Dependent variable = Mean 

2 Independent variable = Dose 

3 The power is not restricted 

4 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

5 

6 Total number of dose groups = 6 

7 Total number of records with missing values = 0 

8 Maximum number of iterations = 250 

9 Relative Function Convergence has been set to: 1e-008 

10 Parameter Convergence has been set to: 1e-008 

11 

12 

13 

14 Default Initial Parameter Values 

15 lalpha = 4.76968 

16 rho = 0 

17 control = 3.011 

18 slope = 7.10636 

19 power = 0.187655 

20 

21 

22 Asymptotic Correlation Matrix of Parameter Estimates 

23 

24 lalpha rho control slope power 

25 

26 lalpha 1 -0.96 -0.49 0.062 -0.046 

27 

28 rho -0.96 1 0.45 -0.074 0.051 

29 

30 control -0.49 0.45 1 -0.075 0.049 

31 

32 slope 0.062 -0.074 -0.075 1 -1 

33 

34 power -0.046 0.051 0.049 -1 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 95.0% Wald Confidence Interval 

41 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

42 lalpha -1.02691 0.818371 -2.63089 0.577065 

43 rho 1.6303 0.240525 1.15888 2.10172 

44 control 3.01554 0.519298 1.99773 4.03334 

45 slope 7.64061 4.22038 -0.631172 15.9124 

46 power 0.18001 0.0639858 0.0546001 0.30542 

47 

48 

49 

50 Table of Data and Estimated Values of Interest 

51 

52 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

53 ------ --- -------- -------- ----------- ----------- ---------- 

54 

55 0 8 3.01 3.02 1.58 1.47 -0.00872 

56 1354 8 27.1 31 5.27 9.83 -1.11 

57 3056 8 42.8 35.4 11.2 11 1.92 

58 5259 8 36.6 38.7 13 11.8 -0.52 

59 8918 8 43.7 42.3 18.5 12.7 0.323 

60 1.6e+004 8 43.7 46.7 6.32 13.7 -0.607 

61 

62 

63 

64 Model Descriptions for likelihoods calculated 

65 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-89 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

5 Model A3 uses any fixed variance parameters that 

6 were specified by the user 

7 

8 Model R: Yi = Mu + e(i) 

9 Var{e(i)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) # Param's AIC 

15 A1 -135.267662 7 284.535325 

16 A2 -115.688533 12 255.377067 

17 A3 -121.151707 8 258.303413 

18 fitted -125.533162 5 261.066325 

19 R -162.090242 2 328.180484 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Do responses and/or variances differ among Dose levels? 

25 (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A1 vs A2) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

29 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) Test df p-value 

34 

35 Test 1 92.8034 10 <.0001 

36 Test 2 39.1583 5 <.0001 

37 Test 3 10.9263 4 0.0274 

38 Test 4 8.76291 3 0.03261 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose levels 

42 It seems appropriate to model the data 

43 

44 The p-value for Test 2 is less than .1. A non-homogeneous variance 

45 model appears to be appropriate 

46 

47 The p-value for Test 3 is less than .1. You may want to consider a 

48 different variance model 

49 

50 The p-value for Test 4 is less than .1. You may want to try a different 

51 model 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 1 

57 

58 Risk Type = Estimated standard deviations from the control mean 

59 

60 Confidence level = 0.95 

61 

62 BMD = 0.000106161 

63 

64 

65 BMDL = 0.000106161 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-90 —DO NOT CITE OR QUOTE 

1 H.2.8. National Toxicology Program. (2006): Tbl11 Index Week 31 

2 H.2.8.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) c 4 <0.0001 20.59 0.00 46.55 4.8E+03 3.8E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 20.59 0.00 46.55 4.8E+03 3.8E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 23.01 <0.0001 50.97 1.7E+03 1.0E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 23.01 <0.0001 50.97 1.7E+03 1.0E+03 nonconstant variance, 

power restricted ≥1 

Hill 3 <0.0001 23.01 <0.0001 50.97 1.7E+03 error nonconstant variance, n 

restricted >1, bound hit 

linear 4 <0.0001 23.01 0.00 48.97 1.7E+03 1.0E+03 nonconstant variance 

polynomial 3 <0.0001 22.24 <.0001 50.20 3.4E+03 1.1E+03 nonconstant variance 

power 4 <0.0001 23.01 0.00 48.97 1.7E+03 1.0E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 4 <0.0001 1.20 0.88 101.67 1.0E+04 9.0E+03 constant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 0.97 0.81 103.44 1.1E+04 9.0E+03 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 5.31 0.15 107.78 6.8E+03 5.2E+03 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 1.08 0.58 105.55 1.1E+04 7.5E+03 constant variance, 

power restricted ≥1 

Hill 2 <0.0001 1.08 0.58 105.55 1.1E+04 7.5E+03 constant variance, n 

restricted >1 

linear 4 <0.0001 5.31 0.26 105.78 6.8E+03 5.2E+03 constant variance 

polynomial 4 <0.0001 1.44 0.84 101.91 1.0E+04 8.9E+03 constant variance 

power 3 <0.0001 1.08 0.78 103.55 1.1E+04 7.5E+03 constant variance, 

power restricted ≥1 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-91 —DO NOT CITE OR QUOTE 

1 H.2.8.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 1

 2

 3

 4

 5

 6

 0 2000 4000 6000 8000 10000 12000 14000 16000

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

11:23 11/19 2009

BMDL BMD

 

Exponential

3 

 4 

 5 

6 H.2.8.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_BMR1_Tbl11_31wk.(d) 

13 Gnuplot Plotting File: 

14 Thu Nov 19 11:23:48 2009 

15 ==================================================================== 

16 

17 Tbl 11, 31wk, Hep Cell Proliferation Labeling Index 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-92 —DO NOT CITE OR QUOTE 

1 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

2 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

3 

4 Total number of dose groups = 6 

5 Total number of records with missing values = 0 

6 Maximum number of iterations = 250 

7 Relative Function Convergence has been set to: 1e-008 

8 Parameter Convergence has been set to: 1e-008 

9 

10 MLE solution provided: Exact 

11 

12 

13 Initial Parameter Values 

14 

15 Variable Model 2 

16 -------- -------- 

17 lnalpha -0.674004 

18 rho 2.29189 

19 a 0.31065 

20 b 3.44963e-005 

21 c 24.761 

22 d 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 Variable Model 2 

29 -------- ------- 

30 lnalpha -0.467457 

31 rho 2.1664 

32 a 0.394038 

33 b 5.38146e-009 

34 c 78344.1 

35 d 1 

36 

37 

38 Table of Stats From Input Data 

39 

40 Dose N Obs Mean Obs Std Dev 

41 ----- --- ---------- ------------- 

42 0 9 0.327 0.189 

43 1284 10 0.852 0.6514 

44 2932 10 0.956 0.7368 

45 5075 10 0.792 0.4617 

46 8629 10 1.333 1.123 

47 1.55e+004 10 3.846 3.08 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 0.5305 0.4275 -1.428 

55 1284 0.6219 0.4983 1.46 

56 2932 0.7627 0.6067 1.007 

57 5075 0.9946 0.7837 -0.8176 

58 8629 1.545 1.198 -0.5587 

59 1.55e+004 3.619 2.722 0.2635 

60 

61 

62 

63 Other models for which likelihoods are calculated: 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-93 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

3 

4 Model R: Yij = Mu + e(i) 

5 Var{e(ij)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) DF AIC 

11 ------- ----------------- ---- ------------ 

12 A1 -47.23498 7 108.47 

13 A2 -8.679256 12 41.35851 

14 A3 -8.980651 8 33.9613 

15 R -63.44829 2 130.8966 

16 2 -19.27346 4 46.54692 

17 

18 

19 Additive constant for all log-likelihoods = -54.22. This constant added to the 

20 above values gives the log-likelihood including the term that does not 

21 depend on the model parameters. 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

27 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

28 Test 3: Are variances adequately modeled? (A2 vs. A3) 

29 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

30 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) D. F. p-value 

35 -------- ------------------------ ------ -------------- 

36 Test 1 109.5 10 < 0.0001 

37 Test 2 77.11 5 < 0.0001 

38 Test 3 0.6028 4 0.9628 

39 Test 4 20.59 4 0.0003826 

40 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose 

44 levels, it seems appropriate to model the data. 

45 

46 The p-value for Test 2 is less than .1. A non-homogeneous 

47 variance model appears to be appropriate. 

48 

49 The p-value for Test 3 is greater than .1. The modeled 

50 variance appears to be appropriate here. 

51 

52 The p-value for Test 4 is less than .1. Model 2 may not adequately 

53 describe the data; you may want to consider another model. 

54 

55 

56 Benchmark Dose Computations: 

57 

58 Specified Effect = 1.000000 

59 

60 Risk Type = Estimated standard deviations from control 

61 

62 Confidence Level = 0.950000 

63 

64 BMD = 4772.05 

65 

66 BMDL = 3816.47 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-94 —DO NOT CITE OR QUOTE 

1 H.2.9. Van Birgelen et al. (1995b): T4 UGT 

2 H.2.9.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 33.51 <0.0001 36.92 6.3E+04 4.4E+04 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 33.51 <0.0001 36.92 6.3E+04 4.4E+04 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 1.50 0.68 6.90 2.7E+03 1.5E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 1.14 0.57 8.55 3.5E+03 1.6E+03 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 2 <0.0001 1.14 0.57 8.55 3.5E+03 1.6E+03 nonconstant variance, 

power unrestricted 

Hill 2 <.0001 1.22 0.54 8.63 3.7E+03 1.7E+03 nonconstant variance, n 

restricted >1 

Hill d 2 <.0001 1.22 0.54 8.63 3.7E+03 1.5E+03 nonconstant variance, n 

unrestricted 

linear 4 <.0001 19.72 0.00 23.13 1.8E+04 9.1E+03 nonconstant variance 

polynomial 4 <.0001 19.72 0.00 23.13 1.8E+04 9.1E+03 nonconstant variance 

power 4 <.0001 19.72 0.00 23.13 1.8E+04 9.1E+03 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 6.02 0.11 11.42 1.3E+03 2.1E+02 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 13.46 0.01 38.87 8.2E+04 6.9E+04 constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 13.46 0.01 38.87 8.2E+04 6.9E+04 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 0.11 0.99 27.51 1.3E+04 6.7E+03 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 0.07 0.97 29.47 1.5E+04 6.8E+03 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 0.07 0.97 29.47 1.5E+04 6.8E+03 constant variance, 

power unrestricted 

Hill 2 <.0001 0.10 0.95 29.50 1.4E+04 5.6E+03 constant variance, n 

restricted >1 

Hill 2 <.0001 0.10 0.95 29.50 1.4E+04 5.1E+03 constant variance, n 

unrestricted 

linear 4 <.0001 8.58 0.07 33.98 5.1E+04 3.9E+04 constant variance 

polynomial 4 <.0001 8.58 0.07 33.98 5.1E+04 3.9E+04 constant variance 

power 4 <.0001 8.58 0.07 33.98 5.1E+04 3.9E+04 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-95 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 3 <.0001 2.70 0.44 30.10 1.1E+04 2.6E+03 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.2.9.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:32 11/20 2009

BMDL BMD

 

Exponential

5 

 6 

 7 

8 H.2.9.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_T4_UGT.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 12:32:06 2009 

17 ==================================================================== 

18 

19 Tbl2, T4 UGT 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-96 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 6 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 4 

33 -------- -------- 

34 lnalpha -0.937573 

35 rho 1.54913 

36 a 0.3135 

37 b 2.19381e-005 

38 c 8.67464 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 4 

46 -------- ------- 

47 lnalpha -0.934825 

48 rho 1.69365 

49 a 0.293644 

50 b 5.48685e-005 

51 c 7.66316 

52 d 1.27403 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 8 0.33 0.198 

60 3969 8 0.6 0.4243 

61 6479 8 0.64 0.4525 

62 9968 8 0.87 0.9051 

63 4.761e+004 8 2.08 1.329 

64 1.378e+005 8 2.59 0.8768 

65 

66 

67 Estimated Values of Interest 

68 

69 Dose Est Mean Est Std Scaled Residual 

70 ------ ---------- --------- ---------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-97 —DO NOT CITE OR QUOTE 

1 0 0.2841 0.2186 0.594 

2 3969 0.5945 0.4063 0.03836 

3 6479 0.7663 0.5029 -0.7106 

4 9968 0.9778 0.6171 -0.4939 

5 4.761e+004 2.062 1.155 0.04516 

6 1.378e+005 2.351 1.289 0.5245 

7 

8 

9 

10 Other models for which likelihoods are calculated: 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

20 

21 Model R: Yij = Mu + e(i) 

22 Var{e(ij)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) DF AIC 

28 ------- ----------------- ---- ------------ 

29 A1 -9.701316 7 33.40263 

30 A2 4.934967 12 14.13007 

31 A3 2.296438 8 11.40712 

32 R -29.51921 2 63.03841 

33 4 1.548351 5 6.903297 

34 

35 

36 Additive constant for all log-likelihoods = -44.11. This constant added to the 

37 above values gives the log-likelihood including the term that does not 

38 depend on the model parameters. 

39 

40 

41 Explanation of Tests 

42 

43 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

44 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

45 Test 3: Are variances adequately modeled? (A2 vs. A3) 

46 

47 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

48 

49 

50 Tests of Interest 

51 

52 Test -2*log(Likelihood Ratio) D. F. p-value 

53 -------- ------------------------ ------ -------------- 

54 Test 1 68.91 10 < 0.0001 

55 Test 2 29.27 5 < 0.0001 

56 Test 3 5.277 4 0.26 

57 Test 6a 1.496 3 0.6832 

58 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose 

62 levels, it seems appropriate to model the data. 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous 

65 variance model appears to be appropriate. 

66 

67 The p-value for Test 3 is greater than .1. The modeled 

68 variance appears to be appropriate here. 

69 

70 The p-value for Test 6a is greater than .1. Model 4 seems 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-98 —DO NOT CITE OR QUOTE 

1 to adequately describe the data. 

2 

3 

4 Benchmark Dose Computations: 

5 

6 Specified Effect = 1.000000 

7 

8 Risk Type = Estimated standard deviations from control 

9 

10 Confidence Level = 0.950000 

11 

12 BMD = 2726.3 

13 

14 BMDL = 1491.73 

15 

16 

17 

18 H.2.9.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

19 Unrestricted

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:32 11/20 2009

BMDL BMD

 

Exponential

20 

 21 

 22 

23 H.2.9.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

24 Power Unrestricted 

25 

26 

27 ==================================================================== 

28 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

29 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_T4_UGT.(d) 

30 Gnuplot Plotting File: 

31 Fri Nov 20 12:32:13 2009 

32 ==================================================================== 

33 

34 Tbl2, T4 UGT 

35 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-99 —DO NOT CITE OR QUOTE 

1 The form of the response function by Model: 

2 Model 2: Y[dose] = a * exp{sign * b * dose} 

3 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

4 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

5 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

6 

7 Note: Y[dose] is the median response for exposure = dose; 

8 sign = +1 for increasing trend in data; 

9 sign = -1 for decreasing trend. 

10 

11 Model 2 is nested within Models 3 and 4. 

12 Model 3 is nested within Model 5. 

13 Model 4 is nested within Model 5. 

14 

15 

16 Dependent variable = Mean 

17 Independent variable = Dose 

18 Data are assumed to be distributed: normally 

19 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

20 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 5 

34 -------- -------- 

35 lnalpha -0.937573 

36 rho 1.54913 

37 a 0.3135 

38 b 2.19381e-005 

39 c 8.67464 

40 d 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 Variable Model 5 

47 -------- ------- 

48 lnalpha -0.934825 

49 rho 1.69365 

50 a 0.293644 

51 b 5.48685e-005 

52 c 7.66316 

53 d 1.27403 

54 

55 

56 Table of Stats From Input Data 

57 

58 Dose N Obs Mean Obs Std Dev 

59 ----- --- ---------- ------------- 

60 0 8 0.33 0.198 

61 3969 8 0.6 0.4243 

62 6479 8 0.64 0.4525 

63 9968 8 0.87 0.9051 

64 4.761e+004 8 2.08 1.329 

65 1.378e+005 8 2.59 0.8768 

66 

67 

68 Estimated Values of Interest 

69 

70 Dose Est Mean Est Std Scaled Residual 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-100 —DO NOT CITE OR QUOTE 

1 ------ ---------- --------- ---------------- 

2 0 0.2936 0.222 0.4632 

3 3969 0.555 0.3806 0.334 

4 6479 0.7533 0.4929 -0.6498 

5 9968 1.019 0.6369 -0.6636 

6 4.761e+004 2.185 1.215 -0.2441 

7 1.378e+005 2.25 1.245 0.7717 

8 

9 

10 

11 Other models for which likelihoods are calculated: 

12 

13 Model A1: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma^2 

15 

16 Model A2: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma(i)^2 

18 

19 Model A3: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

21 

22 Model R: Yij = Mu + e(i) 

23 Var{e(ij)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) DF AIC 

29 ------- ----------------- ---- ------------ 

30 A1 -9.701316 7 33.40263 

31 A2 4.934967 12 14.13007 

32 A3 2.296438 8 11.40712 

33 R -29.51921 2 63.03841 

34 5 1.725713 6 8.548574 

35 

36 

37 Additive constant for all log-likelihoods = -44.11. This constant added to the 

38 above values gives the log-likelihood including the term that does not 

39 depend on the model parameters. 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

45 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

46 Test 3: Are variances adequately modeled? (A2 vs. A3) 

47 

48 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

49 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) D. F. p-value 

54 -------- ------------------------ ------ -------------- 

55 Test 1 68.91 10 < 0.0001 

56 Test 2 29.27 5 < 0.0001 

57 Test 3 5.277 4 0.26 

58 Test 7a 1.141 2 0.5651 

59 

60 

61 The p-value for Test 1 is less than .05. There appears to be a 

62 difference between response and/or variances among the dose 

63 levels, it seems appropriate to model the data. 

64 

65 The p-value for Test 2 is less than .1. A non-homogeneous 

66 variance model appears to be appropriate. 

67 

68 The p-value for Test 3 is greater than .1. The modeled 

69 variance appears to be appropriate here. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-101 —DO NOT CITE OR QUOTE 

1 The p-value for Test 7a is greater than .1. Model 5 seems 

2 to adequately describe the data. 

3 

4 

5 Benchmark Dose Computations: 

6 

7 Specified Effect = 1.000000 

8 

9 Risk Type = Estimated standard deviations from control 

10 

11 Confidence Level = 0.950000 

12 

13 BMD = 3460.45 

14 

15 BMDL = 1550.03 

16 

17 

18 

19 H.2.9.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:32 11/20 2009

BMDL BMD

 

Hill

20 

 21 

 22 

23 H.2.9.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 24 

25 

26 ==================================================================== 

27 Hill Model. (Version: 2.14; Date: 06/26/2008) 

28 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_T4_UGT.(d) 

29 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_T4_UGT.plt 

30 Fri Nov 20 12:32:14 2009 

31 ==================================================================== 

32 

33 Tbl2, T4 UGT 

34 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

35 

36 The form of the response function is: 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-102 —DO NOT CITE OR QUOTE 

1 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

2 

3 

4 Dependent variable = Mean 

5 Independent variable = Dose 

6 Power parameter is not restricted 

7 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

8 

9 Total number of dose groups = 6 

10 Total number of records with missing values = 0 

11 Maximum number of iterations = 250 

12 Relative Function Convergence has been set to: 1e-008 

13 Parameter Convergence has been set to: 1e-008 

14 

15 

16 

17 Default Initial Parameter Values 

18 lalpha = -0.462247 

19 rho = 0 

20 intercept = 0.33 

21 v = 2.26 

22 n = 0.525864 

23 k = 66891.8 

24 

25 

26 Asymptotic Correlation Matrix of Parameter Estimates 

27 

28 lalpha rho intercept v n k 

29 

30 lalpha 1 0.035 -0.26 -0.18 -0.017 0.038 

31 

32 rho 0.035 1 0.48 -0.49 0.023 -0.21 

33 

34 intercept -0.26 0.48 1 -0.37 0.26 -0.14 

35 

36 v -0.18 -0.49 -0.37 1 -0.59 0.77 

37 

38 n -0.017 0.023 0.26 -0.59 1 -0.84 

39 

40 k 0.038 -0.21 -0.14 0.77 -0.84 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 95.0% Wald Confidence Interval 

47 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

48 lalpha -0.933225 0.25643 -1.43582 -0.430632 

49 rho 1.68188 0.441442 0.816665 2.54709 

50 intercept 0.294743 0.0705015 0.156563 0.432924 

51 v 2.10713 0.497534 1.13198 3.08228 

52 n 1.51694 0.601141 0.33872 2.69515 

53 k 14931.4 7059.91 1094.23 28768.6 

54 

55 

56 

57 Table of Data and Estimated Values of Interest 

58 

59 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

60 ------ --- -------- -------- ----------- ----------- ---------- 

61 

62 0 8 0.33 0.295 0.198 0.224 0.444 

63 3969 8 0.6 0.544 0.424 0.376 0.424 

64 6479 8 0.64 0.758 0.453 0.497 -0.672 

65 9968 8 0.87 1.04 0.905 0.646 -0.723 

66 4.761e+004 8 2.08 2.09 1.33 1.17 -0.0297 

67 1.378e+005 8 2.59 2.33 0.877 1.28 0.571 

68 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-103 —DO NOT CITE OR QUOTE 

1 Model Descriptions for likelihoods calculated 

2 

3 

4 Model A1: Yij = Mu(i) + e(ij) 

5 Var{e(ij)} = Sigma^2 

6 

7 Model A2: Yij = Mu(i) + e(ij) 

8 Var{e(ij)} = Sigma(i)^2 

9 

10 Model A3: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

12 Model A3 uses any fixed variance parameters that 

13 were specified by the user 

14 

15 Model R: Yi = Mu + e(i) 

16 Var{e(i)} = Sigma^2 

17 

18 

19 Likelihoods of Interest 

20 

21 Model Log(likelihood) # Param's AIC 

22 A1 -9.701316 7 33.402631 

23 A2 4.934967 12 14.130066 

24 A3 2.296438 8 11.407124 

25 fitted 1.684209 6 8.631582 

26 R -29.519205 2 63.038411 

27 

28 

29 Explanation of Tests 

30 

31 Test 1: Do responses and/or variances differ among Dose levels? 

32 (A2 vs. R) 

33 Test 2: Are Variances Homogeneous? (A1 vs A2) 

34 Test 3: Are variances adequately modeled? (A2 vs. A3) 

35 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

36 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

37 

38 Tests of Interest 

39 

40 Test -2*log(Likelihood Ratio) Test df p-value 

41 

42 Test 1 68.9083 10 <.0001 

43 Test 2 29.2726 5 <.0001 

44 Test 3 5.27706 4 0.26 

45 Test 4 1.22446 2 0.5421 

46 

47 The p-value for Test 1 is less than .05. There appears to be a 

48 difference between response and/or variances among the dose levels 

49 It seems appropriate to model the data 

50 

51 The p-value for Test 2 is less than .1. A non-homogeneous variance 

52 model appears to be appropriate 

53 

54 The p-value for Test 3 is greater than .1. The modeled variance appears 

55 to be appropriate here 

56 

57 The p-value for Test 4 is greater than .1. The model chosen seems 

58 to adequately describe the data 

59 

60 

61 Benchmark Dose Computation 

62 

63 Specified effect = 1 

64 

65 Risk Type = Estimated standard deviations from the control mean 

66 

67 Confidence level = 0.95 

68 

69 BMD = 3674.98 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-104 —DO NOT CITE OR QUOTE 

1 BMDL = 1463.66 

2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-105 —DO NOT CITE OR QUOTE 

1 H.2.9.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:32 11/20 2009

BMDL BMD

 

Power

2 

 3 

 4 

5 H.2.9.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_T4_UGT.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_T4_UGT.plt 

13 Fri Nov 20 12:32:14 2009 

14 ==================================================================== 

15 

16 Tbl2, T4 UGT 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-106 —DO NOT CITE OR QUOTE 

1 lalpha = -0.462247 

2 rho = 0 

3 control = 0.33 

4 slope = 0.00102277 

5 power = 0.650735 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho control slope power 

11 

12 lalpha 1 0.031 -0.26 -0.13 0.074 

13 

14 rho 0.031 1 0.58 0.11 -0.18 

15 

16 control -0.26 0.58 1 -0.13 0.067 

17 

18 slope -0.13 0.11 -0.13 1 -0.99 

19 

20 power 0.074 -0.18 0.067 -0.99 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 lalpha -0.836884 0.261303 -1.34903 -0.324739 

29 rho 1.68473 0.453932 0.795038 2.57442 

30 control 0.2748 0.0676712 0.142167 0.407433 

31 slope 0.00549254 0.00532631 -0.00494685 0.0159319 

32 power 0.516485 0.0924979 0.335192 0.697777 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 8 0.33 0.275 0.198 0.222 0.704 

42 3969 8 0.6 0.671 0.424 0.471 -0.43 

43 6479 8 0.64 0.786 0.453 0.537 -0.767 

44 9968 8 0.87 0.913 0.905 0.61 -0.2 

45 4.761e+004 8 2.08 1.71 1.33 1.03 1.02 

46 1.378e+005 8 2.59 2.75 0.877 1.54 -0.299 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-107 —DO NOT CITE OR QUOTE 

1 A1 -9.701316 7 33.402631 

2 A2 4.934967 12 14.130066 

3 A3 2.296438 8 11.407124 

4 fitted -0.712209 5 11.424417 

5 R -29.519205 2 63.038411 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 68.9083 10 <.0001 

22 Test 2 29.2726 5 <.0001 

23 Test 3 5.27706 4 0.26 

24 Test 4 6.01729 3 0.1108 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is less than .1. A non-homogeneous variance 

31 model appears to be appropriate 

32 

33 The p-value for Test 3 is greater than .1. The modeled variance appears 

34 to be appropriate here 

35 

36 The p-value for Test 4 is greater than .1. The model chosen seems 

37 to adequately describe the data 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 1286.41 

49 

50 

51 BMDL = 212.264 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-108 —DO NOT CITE OR QUOTE 

1 H.2.10. Van Birgelen et al. (1995b): UGT 1A1 

2 H.2.10.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 3 0.00 29.05 <0.0001 166.85 8.1E+04 2.4E+04 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.00 29.05 <0.0001 166.85 8.1E+04 2.4E+04 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 2 0.00 1.04 0.60 140.83 4.0E+02 2.2E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 1 0.00 0.97 0.32 142.77 5.0E+02 2.2E+02 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 1 0.00 0.97 0.32 142.77 5.0E+02 2.2E+02 nonconstant variance, 

power unrestricted 

Hill 1 0.00 1.27 0.26 143.07 8.2E+02 error nonconstant variance, n 

restricted >1 

Hill d 1 0.00 1.27 0.26 143.07 8.2E+02 error nonconstant variance, n 

unrestricted 

linear 3 0.00 26.47 <.0001 164.27 1.8E+04 5.3E+02 nonconstant variance 

polynomial 3 0.00 31.07 <.0001 168.87 3.5E+05 4.9E+02 nonconstant variance 

power 3 0.00 26.47 <.0001 164.27 1.8E+04 5.3E+02 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 2 0.00 5.95 0.05 145.75 3.8E+00 2.3E-04 nonconstant variance, 

power unrestricted 

exponential (M2) 3 0.00 22.21 <0.0001 165.71 1.6E+05 8.3E+04 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.00 22.21 <0.0001 165.71 1.6E+05 8.3E+04 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.00 8.05 0.02 153.55 2.6E+03 1.2E+03 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.00 7.88 0.00 155.38 3.3E+03 1.2E+03 constant variance, 

power restricted ≥1 

exponential (M5) 1 0.00 7.88 0.00 155.38 3.3E+03 1.2E+03 constant variance, 

power unrestricted 

Hill 1 0.00 8.12 0.00 155.61 3.7E+03 9.6E+02 constant variance, n 

restricted >1 

Hill 1 0.00 8.12 0.00 155.61 3.7E+03 8.8E+02 constant variance, n 

unrestricted 

linear 3 0.00 21.83 <.0001 165.32 1.3E+05 6.2E+04 constant variance 

polynomial 3 0.00 21.83 <.0001 165.32 1.3E+05 6.2E+04 constant variance 

power 3 0.00 21.83 <.0001 165.32 1.3E+05 6.2E+04 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-109 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 2 0.00 13.23 0.00 158.73 7.2E+01 1.6E-06 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 H.2.10.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

3 Restricted ≥1 

-100

 0

 100

 200

 300

 400

 500

 600

 700

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

12:43 11/20 2009

BMDLBMD

 

Exponential

4 

 5 

 6 

7 H.2.10.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

8 Restricted ≥1 

9 

10 

11 ==================================================================== 

12 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

13 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_BMR1_UGT_1A1.(d) 

14 Gnuplot Plotting File: 

15 Fri Nov 20 12:43:51 2009 

16 ==================================================================== 

17 

18 Tbl2, UGT_1A1 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the response function by Model: 

22 Model 2: Y[dose] = a * exp{sign * b * dose} 

23 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-110 —DO NOT CITE OR QUOTE 

1 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

2 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

3 

4 Note: Y[dose] is the median response for exposure = dose; 

5 sign = +1 for increasing trend in data; 

6 sign = -1 for decreasing trend. 

7 

8 Model 2 is nested within Models 3 and 4. 

9 Model 3 is nested within Model 5. 

10 Model 4 is nested within Model 5. 

11 

12 

13 Dependent variable = Mean 

14 Independent variable = Dose 

15 Data are assumed to be distributed: normally 

16 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

17 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

18 

19 Total number of dose groups = 5 

20 Total number of records with missing values = 0 

21 Maximum number of iterations = 250 

22 Relative Function Convergence has been set to: 1e-008 

23 Parameter Convergence has been set to: 1e-008 

24 

25 MLE solution provided: Exact 

26 

27 

28 Initial Parameter Values 

29 

30 Variable Model 4 

31 -------- -------- 

32 lnalpha -1.53604 

33 rho 1.59958 

34 a 95.95 

35 b 1.15499e-005 

36 c 4.94633 

37 d 1 

38 

39 

40 

41 Parameter Estimates 

42 

43 Variable Model 4 

44 -------- ------- 

45 lnalpha -10.3642 

46 rho 3.29138 

47 a 101.591 

48 b 0.000102786 

49 c 3.84125 

50 d 1.08913 

51 

52 

53 Table of Stats From Input Data 

54 

55 Dose N Obs Mean Obs Std Dev 

56 ----- --- ---------- ------------- 

57 0 3 101 15.59 

58 3969 3 194 36.37 

59 9968 3 304 17.32 

60 4.761e+004 3 452 48.5 

61 1.378e+005 3 296 149 

62 

63 

64 Estimated Values of Interest 

65 

66 Dose Est Mean Est Std Scaled Residual 

67 ------ ---------- --------- ---------------- 

68 0 101.5 11.18 -0.07335 

69 3969 194.7 32.89 -0.03837 

70 9968 282.1 60.75 0.6236 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-111 —DO NOT CITE OR QUOTE 

1 4.761e+004 389.3 103.5 1.049 

2 1.378e+005 392.1 104.7 -1.589 

3 

4 

5 

6 Other models for which likelihoods are calculated: 

7 

8 Model A1: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma^2 

10 

11 Model A2: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma(i)^2 

13 

14 Model A3: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

16 

17 Model R: Yij = Mu + e(i) 

18 Var{e(ij)} = Sigma^2 

19 

20 

21 Likelihoods of Interest 

22 

23 Model Log(likelihood) DF AIC 

24 ------- ----------------- ---- ------------ 

25 A1 -68.74833 6 149.4967 

26 A2 -58.69126 10 137.3825 

27 A3 -64.89907 7 143.7981 

28 R -80.72265 2 165.4453 

29 4 -65.41669 5 140.8334 

30 

31 

32 Additive constant for all log-likelihoods = -13.78. This constant added to the 

33 above values gives the log-likelihood including the term that does not 

34 depend on the model parameters. 

35 

36 

37 Explanation of Tests 

38 

39 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

40 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

41 Test 3: Are variances adequately modeled? (A2 vs. A3) 

42 

43 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

44 

45 

46 Tests of Interest 

47 

48 Test -2*log(Likelihood Ratio) D. F. p-value 

49 -------- ------------------------ ------ -------------- 

50 Test 1 44.06 8 < 0.0001 

51 Test 2 20.11 4 0.0004741 

52 Test 3 12.42 3 0.006087 

53 Test 6a 1.035 2 0.5959 

54 

55 

56 The p-value for Test 1 is less than .05. There appears to be a 

57 difference between response and/or variances among the dose 

58 levels, it seems appropriate to model the data. 

59 

60 The p-value for Test 2 is less than .1. A non-homogeneous 

61 variance model appears to be appropriate. 

62 

63 The p-value for Test 3 is less than .1. You may want to 

64 consider a different variance model. 

65 

66 The p-value for Test 6a is greater than .1. Model 4 seems 

67 to adequately describe the data. 

68 

69 

70 Benchmark Dose Computations: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-112 —DO NOT CITE OR QUOTE 

1 

2 Specified Effect = 1.000000 

3 

4 Risk Type = Estimated standard deviations from control 

5 

6 Confidence Level = 0.950000 

7 

8 BMD = 402.539 

9 

10 BMDL = 221.776 

 11 

12 H.2.10.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

13 Unrestricted

-100

 0

 100

 200

 300

 400

 500

 600

 700

 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

12:44 11/20 2009

BMDLBMD

 

Exponential

14 

 15 

 16 

17 H.2.10.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

18 Power Unrestricted 

19 

20 

21 ==================================================================== 

22 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

23 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Exp_Unrest_BMR1_UGT_1A1.(d) 

24 Gnuplot Plotting File: 

25 Fri Nov 20 12:44:01 2009 

26 ==================================================================== 

27 

28 Tbl2, UGT_1A1 

29 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

30 

31 The form of the response function by Model: 

32 Model 2: Y[dose] = a * exp{sign * b * dose} 

33 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

34 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

35 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-113 —DO NOT CITE OR QUOTE 

1 Note: Y[dose] is the median response for exposure = dose; 

2 sign = +1 for increasing trend in data; 

3 sign = -1 for decreasing trend. 

4 

5 Model 2 is nested within Models 3 and 4. 

6 Model 3 is nested within Model 5. 

7 Model 4 is nested within Model 5. 

8 

9 

10 Dependent variable = Mean 

11 Independent variable = Dose 

12 Data are assumed to be distributed: normally 

13 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

14 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

15 

16 Total number of dose groups = 5 

17 Total number of records with missing values = 0 

18 Maximum number of iterations = 250 

19 Relative Function Convergence has been set to: 1e-008 

20 Parameter Convergence has been set to: 1e-008 

21 

22 MLE solution provided: Exact 

23 

24 

25 Initial Parameter Values 

26 

27 Variable Model 5 

28 -------- -------- 

29 lnalpha -1.53604 

30 rho 1.59958 

31 a 95.95 

32 b 1.15499e-005 

33 c 4.94633 

34 d 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 Variable Model 5 

41 -------- ------- 

42 lnalpha -10.3642 

43 rho 3.29138 

44 a 101.591 

45 b 0.000102786 

46 c 3.84125 

47 d 1.08913 

48 

49 

50 Table of Stats From Input Data 

51 

52 Dose N Obs Mean Obs Std Dev 

53 ----- --- ---------- ------------- 

54 0 3 101 15.59 

55 3969 3 194 36.37 

56 9968 3 304 17.32 

57 4.761e+004 3 452 48.5 

58 1.378e+005 3 296 149 

59 

60 

61 Estimated Values of Interest 

62 

63 Dose Est Mean Est Std Scaled Residual 

64 ------ ---------- --------- ---------------- 

65 0 101.6 11.28 -0.09081 

66 3969 192.2 32.19 0.09829 

67 9968 286.9 62.23 0.4773 

68 4.761e+004 389.2 102.8 1.058 

69 1.378e+005 390.2 103.3 -1.581 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-114 —DO NOT CITE OR QUOTE 

1 

2 

3 Other models for which likelihoods are calculated: 

4 

5 Model A1: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 

8 Model A2: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma(i)^2 

10 

11 Model A3: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

13 

14 Model R: Yij = Mu + e(i) 

15 Var{e(ij)} = Sigma^2 

16 

17 

18 Likelihoods of Interest 

19 

20 Model Log(likelihood) DF AIC 

21 ------- ----------------- ---- ------------ 

22 A1 -68.74833 6 149.4967 

23 A2 -58.69126 10 137.3825 

24 A3 -64.89907 7 143.7981 

25 R -80.72265 2 165.4453 

26 5 -65.38628 6 142.7726 

27 

28 

29 Additive constant for all log-likelihoods = -13.78. This constant added to the 

30 above values gives the log-likelihood including the term that does not 

31 depend on the model parameters. 

32 

33 

34 Explanation of Tests 

35 

36 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

37 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

38 Test 3: Are variances adequately modeled? (A2 vs. A3) 

39 

40 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

41 

42 

43 Tests of Interest 

44 

45 Test -2*log(Likelihood Ratio) D. F. p-value 

46 -------- ------------------------ ------ -------------- 

47 Test 1 44.06 8 < 0.0001 

48 Test 2 20.11 4 0.0004741 

49 Test 3 12.42 3 0.006087 

50 Test 7a 0.9744 1 0.3236 

51 

52 

53 The p-value for Test 1 is less than .05. There appears to be a 

54 difference between response and/or variances among the dose 

55 levels, it seems appropriate to model the data. 

56 

57 The p-value for Test 2 is less than .1. A non-homogeneous 

58 variance model appears to be appropriate. 

59 

60 The p-value for Test 3 is less than .1. You may want to 

61 consider a different variance model. 

62 

63 The p-value for Test 7a is greater than .1. Model 5 seems 

64 to adequately describe the data. 

65 

66 

67 Benchmark Dose Computations: 

68 

69 Specified Effect = 1.000000 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-115 —DO NOT CITE OR QUOTE 

1 Risk Type = Estimated standard deviations from control 

2 

3 Confidence Level = 0.950000 

4 

5 BMD = 504.638 

6 

7 BMDL = 223.156 

8 

9 

10 

11 H.2.10.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

-100

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 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Hill Model

12:44 11/20 2009

BMD

Hill

12 

 13 

 14 

15 H.2.10.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 16 

17 

18 ==================================================================== 

19 Hill Model. (Version: 2.14; Date: 06/26/2008) 

20 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_UGT_1A1.(d) 

21 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Hill_Unrest_BMR1_UGT_1A1.plt 

22 Fri Nov 20 12:44:02 2009 

23 ==================================================================== 

24 

25 Tbl2, UGT_1A1 

26 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

27 

28 The form of the response function is: 

29 

30 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

31 

32 

33 Dependent variable = Mean 

34 Independent variable = Dose 

35 Power parameter is not restricted 

36 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-116 —DO NOT CITE OR QUOTE 

1 Total number of dose groups = 5 

2 Total number of records with missing values = 0 

3 Maximum number of iterations = 250 

4 Relative Function Convergence has been set to: 1e-008 

5 Parameter Convergence has been set to: 1e-008 

6 

7 

8 

9 Default Initial Parameter Values 

10 lalpha = 8.57191 

11 rho = 0 

12 intercept = 101 

13 v = 351 

14 n = 0.350477 

15 k = 11467.2 

16 

17 

18 Asymptotic Correlation Matrix of Parameter Estimates 

19 

20 lalpha rho intercept v n k 

21 

22 lalpha 1 -0.99 -0.19 0.14 0.12 -0.0083 

23 

24 rho -0.99 1 0.18 -0.17 -0.12 -0.0038 

25 

26 intercept -0.19 0.18 1 -0.12 0.031 0.1 

27 

28 v 0.14 -0.17 -0.12 1 -0.57 0.79 

29 

30 n 0.12 -0.12 0.031 -0.57 1 -0.73 

31 

32 k -0.0083 -0.0038 0.1 0.79 -0.73 1 

33 

34 

35 

36 Parameter Estimates 

37 

38 95.0% Wald Confidence Interval 

39 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

40 lalpha -10.4997 3.7002 -17.752 -3.24748 

41 rho 3.31877 0.67548 1.99485 4.64269 

42 intercept 101.641 6.48455 88.9319 114.351 

43 v 296.324 52.8989 192.644 400.003 

44 n 1.52651 0.645076 0.262182 2.79084 

45 k 6852.92 2333.57 2279.2 11426.6 

46 

47 

48 

49 Table of Data and Estimated Values of Interest 

50 

51 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

52 ------ --- -------- -------- ----------- ----------- ---------- 

53 

54 0 3 101 102 15.6 11.2 -0.0989 

55 3969 3 194 191 36.4 32.1 0.141 

56 9968 3 304 291 17.3 64.4 0.348 

57 4.761e+004 3 452 383 48.5 102 1.17 

58 1.378e+005 3 296 395 149 107 -1.6 

59 

60 

61 

62 Model Descriptions for likelihoods calculated 

63 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-117 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

3 Model A3 uses any fixed variance parameters that 

4 were specified by the user 

5 

6 Model R: Yi = Mu + e(i) 

7 Var{e(i)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) # Param's AIC 

13 A1 -68.748326 6 149.496653 

14 A2 -58.691256 10 137.382511 

15 A3 -64.899072 7 143.798144 

16 fitted -65.536514 6 143.073028 

17 R -80.722651 2 165.445302 

18 

19 

20 Explanation of Tests 

21 

22 Test 1: Do responses and/or variances differ among Dose levels? 

23 (A2 vs. R) 

24 Test 2: Are Variances Homogeneous? (A1 vs A2) 

25 Test 3: Are variances adequately modeled? (A2 vs. A3) 

26 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

27 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

28 

29 Tests of Interest 

30 

31 Test -2*log(Likelihood Ratio) Test df p-value 

32 

33 Test 1 44.0628 8 <.0001 

34 Test 2 20.1141 4 0.0004741 

35 Test 3 12.4156 3 0.006087 

36 Test 4 1.27488 1 0.2589 

37 

38 The p-value for Test 1 is less than .05. There appears to be a 

39 difference between response and/or variances among the dose levels 

40 It seems appropriate to model the data 

41 

42 The p-value for Test 2 is less than .1. A non-homogeneous variance 

43 model appears to be appropriate 

44 

45 The p-value for Test 3 is less than .1. You may want to consider a 

46 different variance model 

47 

48 The p-value for Test 4 is greater than .1. The model chosen seems 

49 to adequately describe the data 

50 

51 

52 Benchmark Dose Computation 

53 

54 Specified effect = 1 

55 

56 Risk Type = Estimated standard deviations from the control mean 

57 

58 Confidence level = 0.95 

59 

60 BMD = 823.8 

61 

62 

63 BMDL computation failed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-118 —DO NOT CITE OR QUOTE 

1 H.2.10.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

-100

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 0 20000 40000 60000 80000 100000 120000 140000

Mean Response

dose

Power Model with 0.95 Confidence Level

12:44 11/20 2009

BMDBMDL

 

Power

2 

 3 

 4 

5 H.2.10.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_UGT_1A1.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Blood\Pwr_Unrest_BMR1_UGT_1A1.plt 

13 Fri Nov 20 12:44:03 2009 

14 ==================================================================== 

15 

16 Tbl2, UGT_1A1 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-119 —DO NOT CITE OR QUOTE 

1 lalpha = 8.57191 

2 rho = 0 

3 control = 101 

4 slope = 19.8524 

5 power = 0.225107 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho control slope power 

11 

12 lalpha 1 -0.99 -0.22 0.0058 0.021 

13 

14 rho -0.99 1 0.21 0.024 -0.057 

15 

16 control -0.22 0.21 1 -0.14 0.11 

17 

18 slope 0.0058 0.024 -0.14 1 -0.99 

19 

20 power 0.021 -0.057 0.11 -0.99 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 lalpha -11.5995 3.46108 -18.3831 -4.81588 

29 rho 3.55351 0.629824 2.31908 4.78795 

30 control 101.406 6.37341 88.9147 113.898 

31 slope 7.06329 7.31729 -7.27833 21.4049 

32 power 0.337328 0.106575 0.128444 0.546212 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 3 101 101 15.6 11.1 -0.0634 

42 3969 3 194 217 36.4 42.9 -0.928 

43 9968 3 304 259 17.3 58.8 1.32 

44 4.761e+004 3 452 369 48.5 110 1.31 

45 1.378e+005 3 296 484 149 178 -1.82 

46 

47 

48 

49 Model Descriptions for likelihoods calculated 

50 

51 

52 Model A1: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = Sigma^2 

54 

55 Model A2: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma(i)^2 

57 

58 Model A3: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

60 Model A3 uses any fixed variance parameters that 

61 were specified by the user 

62 

63 Model R: Yi = Mu + e(i) 

64 Var{e(i)} = Sigma^2 

65 

66 

67 Likelihoods of Interest 

68 

69 Model Log(likelihood) # Param's AIC 

70 A1 -68.748326 6 149.496653 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-120 —DO NOT CITE OR QUOTE 

1 A2 -58.691256 10 137.382511 

2 A3 -64.899072 7 143.798144 

3 fitted -67.875596 5 145.751193 

4 R -80.722651 2 165.445302 

5 

6 

7 Explanation of Tests 

8 

9 Test 1: Do responses and/or variances differ among Dose levels? 

10 (A2 vs. R) 

11 Test 2: Are Variances Homogeneous? (A1 vs A2) 

12 Test 3: Are variances adequately modeled? (A2 vs. A3) 

13 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

14 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

15 

16 Tests of Interest 

17 

18 Test -2*log(Likelihood Ratio) Test df p-value 

19 

20 Test 1 44.0628 8 <.0001 

21 Test 2 20.1141 4 0.0004741 

22 Test 3 12.4156 3 0.006087 

23 Test 4 5.95305 2 0.05097 

24 

25 The p-value for Test 1 is less than .05. There appears to be a 

26 difference between response and/or variances among the dose levels 

27 It seems appropriate to model the data 

28 

29 The p-value for Test 2 is less than .1. A non-homogeneous variance 

30 model appears to be appropriate 

31 

32 The p-value for Test 3 is less than .1. You may want to consider a 

33 different variance model 

34 

35 The p-value for Test 4 is less than .1. You may want to try a different 

36 model 

37 

38 

39 Benchmark Dose Computation 

40 

41 Specified effect = 1 

42 

43 Risk Type = Estimated standard deviations from the control mean 

44 

45 Confidence level = 0.95 

46 

47 BMD = 3.82374 

48 

49 

50 BMDL = 0.000231902 

51 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-121 —DO NOT CITE OR QUOTE 

1 H.2.11. Vanden Heuvel et al. (1994): Hepatic CYP1A1 mRNA Expression 

2 H.2.11.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 5 <0.0001 518.90 <0.0001 1114.48 4.2E+03 3.2E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 5 <0.0001 518.90 <0.0001 1114.48 4.2E+03 3.2E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 4 <0.0001 71.31 <0.0001 668.92 2.2E+01 1.0E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) c 3 <0.0001 35.23 <0.0001 634.84 4.5E+02 3.3E+02 nonconstant variance, 

power restricted ≥1 

Hill 3 <.0001 33.65 <.0001 633.26 5.3E+02 error nonconstant variance, 

n restricted >1 

linear 5 <.0001 79.92 <.0001 675.53 1.6E+01 8.5E+00 nonconstant variance 

polynomial 5 <.0001 235.66 <.0001 831.27 1.4E+05 3.0E+02 nonconstant variance 

power 4 <.0001 77.35 <.0001 674.96 2.1E+01 1.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M2) 5 <0.0001 27.27 <0.0001 1178.21 6.7E+04 5.9E+04 constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 62.38 <0.0001 1215.33 1.6E+09 6.0E+06 constant variance, 

power restricted ≥1 

exponential (M4) 4 <0.0001 0.86 0.93 1153.81 5.8E+03 4.1E+03 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 0.00 1.00 1154.95 9.0E+03 4.4E+03 constant variance, 

power restricted ≥1 

Hill 3 <.0001 0.00 1.00 1154.95 8.4E+03 3.5E+03 constant variance, n 

restricted >1 

linear 5 <.0001 19.42 0.00 1170.37 3.0E+04 2.4E+04 constant variance 

polynomial 5 <.0001 26.27 <.0001 1177.21 2.4E+04 2.1E+04 constant variance 

power 5 <.0001 19.32 0.00 1170.27 3.1E+04 2.4E+04 

constant variance, 

power restricted ≥1, 

bound hit 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-122 —DO NOT CITE OR QUOTE 

1 H.2.11.2. Figure for Selected Model: Exponential (M5), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 10000

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 50000

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 70000

 0 20000 40000 60000 80000 100000 120000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

11:31 11/19 2009

BMDLBMD

 

Exponential

3 

 4 

 5 

6 H.2.11.3. Output File for Selected Model: Exponential (M5), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\AD\Blood\Exp_BMR1_hepatic_CYP1A1_mRNA_expression.(d) 

13 Gnuplot Plotting File: 

14 Thu Nov 19 11:31:49 2009 

15 ==================================================================== 

16 

17 [insert study notes] 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-123 —DO NOT CITE OR QUOTE 

1 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

2 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

3 

4 Total number of dose groups = 7 

5 Total number of records with missing values = 0 

6 Maximum number of iterations = 250 

7 Relative Function Convergence has been set to: 1e-008 

8 Parameter Convergence has been set to: 1e-008 

9 

10 MLE solution provided: Exact 

11 

12 

13 Initial Parameter Values 

14 

15 Variable Model 5 

16 -------- -------- 

17 lnalpha -0.89532 

18 rho 2.01401 

19 a 5.13 

20 b 2.68046e-005 

21 c 7511.7 

22 d 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 Variable Model 5 

29 -------- ------- 

30 lnalpha 0.166401 

31 rho 1.90534 

32 a 9.80088 

33 b 7.30524e-005 

34 c 3246.67 

35 d 2.37353 

36 

37 

38 Table of Stats From Input Data 

39 

40 Dose N Obs Mean Obs Std Dev 

41 ----- --- ---------- ------------- 

42 0 13 5.4 3.606 

43 3.805 5 7.2 5.59 

44 35.91 12 14.8 14.9 

45 301.9 7 12.8 4.498 

46 2149 7 536 320.1 

47 1.43e+004 11 1.8e+004 1.522e+004 

48 1.147e+005 5 3.67e+004 2.214e+004 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 9.801 9.561 -1.66 

56 3.805 9.801 9.561 -0.6083 

57 35.91 9.825 9.583 1.799 

58 301.9 13.52 12.99 -0.1474 

59 2149 400.1 327.4 1.099 

60 1.43e+004 2.133e+004 1.446e+004 -0.7638 

61 1.147e+005 3.182e+004 2.117e+004 0.5154 

62 

63 

64 

65 Other models for which likelihoods are calculated: 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-124 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

5 

6 Model R: Yij = Mu + e(i) 

7 Var{e(ij)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) DF AIC 

13 ------- ----------------- ---- ------------ 

14 A1 -572.4744 8 1160.949 

15 A2 -290.7965 14 609.5929 

16 A3 -293.806 9 605.6119 

17 R -603.6646 2 1211.329 

18 5 -311.4203 6 634.8406 

19 

20 

21 Additive constant for all log-likelihoods = -55.14. This constant added to the 

22 above values gives the log-likelihood including the term that does not 

23 depend on the model parameters. 

24 

25 

26 Explanation of Tests 

27 

28 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

29 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

30 Test 3: Are variances adequately modeled? (A2 vs. A3) 

31 

32 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

33 

34 

35 Tests of Interest 

36 

37 Test -2*log(Likelihood Ratio) D. F. p-value 

38 -------- ------------------------ ------ -------------- 

39 Test 1 625.7 12 < 0.0001 

40 Test 2 563.4 6 < 0.0001 

41 Test 3 6.019 5 0.3044 

42 Test 7a 35.23 3 < 0.0001 

43 

44 

45 The p-value for Test 1 is less than .05. There appears to be a 

46 difference between response and/or variances among the dose 

47 levels, it seems appropriate to model the data. 

48 

49 The p-value for Test 2 is less than .1. A non-homogeneous 

50 variance model appears to be appropriate. 

51 

52 The p-value for Test 3 is greater than .1. The modeled 

53 variance appears to be appropriate here. 

54 

55 The p-value for Test 7a is less than .1. Model 5 may not adequately 

56 describe the data; you may want to consider another model. 

57 

58 

59 Benchmark Dose Computations: 

60 

61 Specified Effect = 1.000000 

62 

63 Risk Type = Estimated standard deviations from control 

64 

65 Confidence Level = 0.950000 

66 

67 BMD = 449.252 

68 

69 BMDL = 332.057 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-125 —DO NOT CITE OR QUOTE 

1 H.3. ADMINISTERED DOSE BMDS RESULTS 

2 H.3.1. Hassoun et al. (2000): CytC Liver 

3 H.3.1.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 0.39 15.15 0.00 -140.98 2.8E+01 1.9E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.39 15.15 0.00 -140.98 2.8E+01 1.9E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.39 1.73 0.63 -152.40 7.5E+00 4.6E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.39 0.56 0.76 -151.57 1.2E+01 5.2E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.39 0.56 0.76 -151.57 1.2E+01 5.2E+00 nonconstant variance, 

power unrestricted 

Hill 2 0.39 0.67 0.72 -151.46 1.3E+01 error nonconstant variance, n 

restricted >1 

Hill 2 0.39 0.67 0.72 -151.46 1.3E+01 4.5E+00 nonconstant variance, n 

unrestricted 

linear 4 0.39 7.87 0.10 -148.27 1.5E+01 1.0E+01 nonconstant variance 

polynomial 4 0.39 7.87 0.10 -148.27 1.5E+01 1.0E+01 nonconstant variance 

power 4 0.39 7.87 0.10 -148.27 1.5E+01 1.0E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.39 3.95 0.27 -150.18 5.6E+00 1.7E+00 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.39 16.43 0.00 -139.08 3.9E+01 3.3E+01 constant variance, power 

restricted ≥1 

exponential (M3) 4 0.39 16.43 0.00 -139.08 3.9E+01 3.3E+01 constant variance, power 

restricted ≥1 

exponential (M4) c 3 0.39 1.70 0.64 -151.81 9.1E+00 5.9E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.39 0.48 0.79 -151.02 1.4E+01 6.5E+00 constant variance, power 

restricted ≥1 

exponential (M5) d 2 0.39 0.48 0.79 -151.02 1.4E+01 6.5E+00 constant variance, power 

unrestricted 

Hill 2 0.39 0.60 0.74 -150.90 1.5E+01 6.3E+00 constant variance, n 

restricted >1 

Hill d 2 0.39 0.60 0.74 -150.90 1.5E+01 5.9E+00 constant variance, n 

unrestricted 

linear 4 0.39 10.56 0.03 -144.95 2.5E+01 1.9E+01 constant variance 

polynomial 4 0.39 10.56 0.03 -144.95 2.5E+01 1.9E+01 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-126 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 4 0.39 10.56 0.03 -144.95 2.5E+01 1.9E+01 constant variance, power 

restricted ≥1, bound hit 

power d 3 0.39 4.52 0.21 -148.99 6.6E+00 2.0E+00 constant variance, power 

unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.1.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

4 ≥1 

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:45 11/23 2009

BMDL BMD

 

Exponential

5 

 6 

 7 

8 H.3.1.3. Output File for Selected Model: Exponential (M4), Constant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov23\Exp_CV_BMR1_CytC_Liver.(d) 

15 Gnuplot Plotting File: 

16 Mon Nov 23 13:45:24 2009 

17 ==================================================================== 

18 

19 TBARs, liver only (Table 2) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-127 —DO NOT CITE OR QUOTE 

1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

2 

3 The form of the response function by Model: 

4 Model 2: Y[dose] = a * exp{sign * b * dose} 

5 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

6 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

7 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

8 

9 Note: Y[dose] is the median response for exposure = dose; 

10 sign = +1 for increasing trend in data; 

11 sign = -1 for decreasing trend. 

12 

13 Model 2 is nested within Models 3 and 4. 

14 Model 3 is nested within Model 5. 

15 Model 4 is nested within Model 5. 

16 

17 

18 Dependent variable = Mean 

19 Independent variable = Dose 

20 Data are assumed to be distributed: normally 

21 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

22 rho is set to 0. 

23 A constant variance model is fit. 

24 

25 Total number of dose groups = 6 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 MLE solution provided: Exact 

32 

33 

34 Initial Parameter Values 

35 

36 Variable Model 4 

37 -------- -------- 

38 lnalpha -5.48625 

39 rho(S) 0 

40 a 0.1387 

41 b 0.027423 

42 c 3.36121 

43 d 1 

44 

45 (S) = Specified 

46 

47 

48 

49 Parameter Estimates 

50 

51 Variable Model 4 

52 -------- ------- 

53 lnalpha -5.47287 

54 rho 0 

55 a 0.156285 

56 b 0.0293581 

57 c 2.85125 

58 d 1.56807 

59 

60 

61 Table of Stats From Input Data 

62 

63 Dose N Obs Mean Obs Std Dev 

64 ----- --- ---------- ------------- 

65 0 6 0.146 0.06614 

66 3 6 0.177 0.05389 

67 10 6 0.191 0.05634 

68 22 6 0.271 0.05634 

69 46 6 0.388 0.06369 

70 100 6 0.444 0.1102 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-128 —DO NOT CITE OR QUOTE 

1 

2 

3 Estimated Values of Interest 

4 

5 Dose Est Mean Est Std Scaled Residual 

6 ------ ---------- --------- ---------------- 

7 0 0.1413 0.06591 0.1762 

8 3 0.1646 0.06591 0.4609 

9 10 0.2131 0.06591 -0.8196 

10 22 0.2796 0.06591 -0.3199 

11 46 0.3676 0.06591 0.7587 

12 100 0.4509 0.06591 -0.2564 

13 

14 

15 

16 Other models for which likelihoods are calculated: 

17 

18 Model A1: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma^2 

20 

21 Model A2: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = Sigma(i)^2 

23 

24 Model A3: Yij = Mu(i) + e(ij) 

25 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

26 

27 Model R: Yij = Mu + e(i) 

28 Var{e(ij)} = Sigma^2 

29 

30 

31 Likelihoods of Interest 

32 

33 Model Log(likelihood) DF AIC 

34 ------- ----------------- ---- ------------ 

35 A1 80.75258 7 -147.5052 

36 A2 83.37355 12 -142.7471 

37 A3 80.75258 7 -147.5052 

38 R 55.82002 2 -107.64 

39 4 79.90337 4 -151.8067 

40 

41 

42 Additive constant for all log-likelihoods = -33.08. This constant added to the 

43 above values gives the log-likelihood including the term that does not 

44 depend on the model parameters. 

45 

46 

47 Explanation of Tests 

48 

49 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

50 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

51 Test 3: Are variances adequately modeled? (A2 vs. A3) 

52 

53 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

54 

55 

56 Tests of Interest 

57 

58 Test -2*log(Likelihood Ratio) D. F. p-value 

59 -------- ------------------------ ------ -------------- 

60 Test 1 55.11 10 < 0.0001 

61 Test 2 5.242 5 0.3871 

62 Test 3 5.242 5 0.3871 

63 Test 6a 1.698 3 0.6373 

64 

65 

66 The p-value for Test 1 is less than .05. There appears to be a 

67 difference between response and/or variances among the dose 

68 levels, it seems appropriate to model the data. 

69 

70 The p-value for Test 2 is greater than .1. A homogeneous 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-129 —DO NOT CITE OR QUOTE 

1 variance model appears to be appropriate here. 

2 

3 The p-value for Test 3 is greater than .1. The modeled 

4 variance appears to be appropriate here. 

5 

6 The p-value for Test 6a is greater than .1. Model 4 seems 

7 to adequately describe the data. 

8 

9 

10 Benchmark Dose Computations: 

11 

12 Specified Effect = 1.000000 

13 

14 Risk Type = Estimated standard deviations from control 

15 

16 Confidence Level = 0.950000 

17 

18 BMD = 9.0851 

19 

20 BMDL = 5.88612 

21 

22 

23 H.3.1.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

24 Unrestricted

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:45 11/23 2009

BMDL BMD

 

Exponential

25 

26 

27 H.3.1.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

28 Unrestricted 

29 

30 

31 ==================================================================== 

32 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

33 Input Data File: C:\USEPA\BMDS21\Nov23\Exp_CV_Unrest_BMR1_CytC_Liver.(d) 

34 Gnuplot Plotting File: 

35 Mon Nov 23 13:45:31 2009 

36 ==================================================================== 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-130 —DO NOT CITE OR QUOTE 

1 TBARs, liver only (Table 2) 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the response function by Model: 

5 Model 2: Y[dose] = a * exp{sign * b * dose} 

6 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

7 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

8 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

9 

10 Note: Y[dose] is the median response for exposure = dose; 

11 sign = +1 for increasing trend in data; 

12 sign = -1 for decreasing trend. 

13 

14 Model 2 is nested within Models 3 and 4. 

15 Model 3 is nested within Model 5. 

16 Model 4 is nested within Model 5. 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Data are assumed to be distributed: normally 

22 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

23 rho is set to 0. 

24 A constant variance model is fit. 

25 

26 Total number of dose groups = 6 

27 Total number of records with missing values = 0 

28 Maximum number of iterations = 250 

29 Relative Function Convergence has been set to: 1e-008 

30 Parameter Convergence has been set to: 1e-008 

31 

32 MLE solution provided: Exact 

33 

34 

35 Initial Parameter Values 

36 

37 Variable Model 5 

38 -------- -------- 

39 lnalpha -5.48625 

40 rho(S) 0 

41 a 0.1387 

42 b 0.027423 

43 c 3.36121 

44 d 1 

45 

46 (S) = Specified 

47 

48 

49 

50 Parameter Estimates 

51 

52 Variable Model 5 

53 -------- ------- 

54 lnalpha -5.47287 

55 rho 0 

56 a 0.156285 

57 b 0.0293581 

58 c 2.85125 

59 d 1.56807 

60 

61 

62 Table of Stats From Input Data 

63 

64 Dose N Obs Mean Obs Std Dev 

65 ----- --- ---------- ------------- 

66 0 6 0.146 0.06614 

67 3 6 0.177 0.05389 

68 10 6 0.191 0.05634 

69 22 6 0.271 0.05634 

70 46 6 0.388 0.06369 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-131 —DO NOT CITE OR QUOTE 

1 100 6 0.444 0.1102 

2 

3 

4 Estimated Values of Interest 

5 

6 Dose Est Mean Est Std Scaled Residual 

7 ------ ---------- --------- ---------------- 

8 0 0.1563 0.0648 -0.3888 

9 3 0.1626 0.0648 0.5434 

10 10 0.1957 0.0648 -0.1766 

11 22 0.2708 0.0648 0.007576 

12 46 0.3873 0.0648 0.02644 

13 100 0.4443 0.0648 -0.01203 

14 

15 

16 

17 Other models for which likelihoods are calculated: 

18 

19 Model A1: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = Sigma^2 

21 

22 Model A2: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma(i)^2 

24 

25 Model A3: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

27 

28 Model R: Yij = Mu + e(i) 

29 Var{e(ij)} = Sigma^2 

30 

31 

32 Likelihoods of Interest 

33 

34 Model Log(likelihood) DF AIC 

35 ------- ----------------- ---- ------------ 

36 A1 80.75258 7 -147.5052 

37 A2 83.37355 12 -142.7471 

38 A3 80.75258 7 -147.5052 

39 R 55.82002 2 -107.64 

40 5 80.51171 5 -151.0234 

41 

42 

43 Additive constant for all log-likelihoods = -33.08. This constant added to the 

44 above values gives the log-likelihood including the term that does not 

45 depend on the model parameters. 

46 

47 

48 Explanation of Tests 

49 

50 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

51 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

52 Test 3: Are variances adequately modeled? (A2 vs. A3) 

53 

54 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

55 

56 

57 Tests of Interest 

58 

59 Test -2*log(Likelihood Ratio) D. F. p-value 

60 -------- ------------------------ ------ -------------- 

61 Test 1 55.11 10 < 0.0001 

62 Test 2 5.242 5 0.3871 

63 Test 3 5.242 5 0.3871 

64 Test 7a 0.4817 2 0.7859 

65 

66 

67 The p-value for Test 1 is less than .05. There appears to be a 

68 difference between response and/or variances among the dose 

69 levels, it seems appropriate to model the data. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-132 —DO NOT CITE OR QUOTE 

1 The p-value for Test 2 is greater than .1. A homogeneous 

2 variance model appears to be appropriate here. 

3 

4 The p-value for Test 3 is greater than .1. The modeled 

5 variance appears to be appropriate here. 

6 

7 The p-value for Test 7a is greater than .1. Model 5 seems 

8 to adequately describe the data. 

9 

10 

11 Benchmark Dose Computations: 

12 

13 Specified Effect = 1.000000 

14 

15 Risk Type = Estimated standard deviations from control 

16 

17 Confidence Level = 0.950000 

18 

19 BMD = 14.1987 

20 

21 BMDL = 6.53738 

22 

23 

24 H.3.1.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 0.1

 0.2

 0.3

 0.4

 0.5

 0.6

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:45 11/23 2009

BMDL BMD

 

Hill

25 

 26 

 27 

28 H.3.1.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 29 

30 

31 ==================================================================== 

32 Hill Model. (Version: 2.14; Date: 06/26/2008) 

33 Input Data File: C:\USEPA\BMDS21\Nov23\Hill_CV_Unrest_BMR1_CytC_Liver.(d) 

34 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Hill_CV_Unrest_BMR1_CytC_Liver.plt 

35 Mon Nov 23 13:45:33 2009 

36 ==================================================================== 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-133 —DO NOT CITE OR QUOTE 

1 TBARs, liver only (Table 2) 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the response function is: 

5 

6 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

7 

8 

9 Dependent variable = Mean 

10 Independent variable = Dose 

11 rho is set to 0 

12 Power parameter is not restricted 

13 A constant variance model is fit 

14 

15 Total number of dose groups = 6 

16 Total number of records with missing values = 0 

17 Maximum number of iterations = 250 

18 Relative Function Convergence has been set to: 1e-008 

19 Parameter Convergence has been set to: 1e-008 

20 

21 

22 

23 Default Initial Parameter Values 

24 alpha = 0.004972 

25 rho = 0 Specified 

26 intercept = 0.146 

27 v = 0.298 

28 n = 17.5689 

29 k = 65.0769 

30 

31 

32 Asymptotic Correlation Matrix of Parameter Estimates 

33 

34 ( *** The model parameter(s) -rho 

35 have been estimated at a boundary point, or have been specified by the user, 

36 and do not appear in the correlation matrix ) 

37 

38 alpha intercept v n k 

39 

40 alpha 1 8.6e-008 -3.4e-008 3.4e-008 8.6e-008 

41 

42 intercept 8.6e-008 1 -0.61 0.53 0.069 

43 

44 v -3.4e-008 -0.61 1 -0.84 0.64 

45 

46 n 3.4e-008 0.53 -0.84 1 -0.52 

47 

48 k 8.6e-008 0.069 0.64 -0.52 1 

49 

50 

51 

52 Parameter Estimates 

53 

54 95.0% Wald Confidence Interval 

55 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

56 alpha 0.00421303 0.00099302 0.00226674 0.00615931 

57 intercept 0.159748 0.0202818 0.119997 0.1995 

58 v 0.305175 0.0615956 0.18445 0.4259 

59 n 2.11196 1.024 0.104959 4.11895 

60 k 28.1195 6.8986 14.5985 41.6405 

61 

62 

63 

64 Table of Data and Estimated Values of Interest 

65 

66 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

67 ------ --- -------- -------- ----------- ----------- ---------- 

68 

69 0 6 0.146 0.16 0.0661 0.0649 -0.519 

70 3 6 0.177 0.162 0.0539 0.0649 0.55 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-134 —DO NOT CITE OR QUOTE 

1 10 6 0.191 0.191 0.0563 0.0649 0.0134 

2 22 6 0.271 0.274 0.0563 0.0649 -0.1 

3 46 6 0.388 0.385 0.0637 0.0649 0.106 

4 100 6 0.444 0.445 0.11 0.0649 -0.0503 

5 

6 

7 

8 Model Descriptions for likelihoods calculated 

9 

10 

11 Model A1: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma^2 

13 

14 Model A2: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma(i)^2 

16 

17 Model A3: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = Sigma^2 

19 Model A3 uses any fixed variance parameters that 

20 were specified by the user 

21 

22 Model R: Yi = Mu + e(i) 

23 Var{e(i)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) # Param's AIC 

29 A1 80.752584 7 -147.505168 

30 A2 83.373547 12 -142.747094 

31 A3 80.752584 7 -147.505168 

32 fitted 80.452332 5 -150.904663 

33 R 55.820023 2 -107.640047 

34 

35 

36 Explanation of Tests 

37 

38 Test 1: Do responses and/or variances differ among Dose levels? 

39 (A2 vs. R) 

40 Test 2: Are Variances Homogeneous? (A1 vs A2) 

41 Test 3: Are variances adequately modeled? (A2 vs. A3) 

42 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

43 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

44 

45 Tests of Interest 

46 

47 Test -2*log(Likelihood Ratio) Test df p-value 

48 

49 Test 1 55.107 10 <.0001 

50 Test 2 5.24193 5 0.3871 

51 Test 3 5.24193 5 0.3871 

52 Test 4 0.600505 2 0.7406 

53 

54 The p-value for Test 1 is less than .05. There appears to be a 

55 difference between response and/or variances among the dose levels 

56 It seems appropriate to model the data 

57 

58 The p-value for Test 2 is greater than .1. A homogeneous variance 

59 model appears to be appropriate here 

60 

61 

62 The p-value for Test 3 is greater than .1. The modeled variance appears 

63 to be appropriate here 

64 

65 The p-value for Test 4 is greater than .1. The model chosen seems 

66 to adequately describe the data 

67 

68 

69 Benchmark Dose Computation 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-135 —DO NOT CITE OR QUOTE 

1 Specified effect = 1 

2 

3 Risk Type = Estimated standard deviations from the control mean 

4 

5 Confidence level = 0.95 

6 

7 BMD = 15.1313 

8 

9 BMDL = 5.93521 

10 

11 

12 

13 H.3.1.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 0.1

 0.2

 0.3

 0.4

 0.5

 0 20 40 60 80 100

Mean Response

dose

Power Model with 0.95 Confidence Level

13:45 11/23 2009

BMDL BMD

 

Power

14 

 15 

 16 

17 H.3.1.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 18 

19 

20 ==================================================================== 

21 Power Model. (Version: 2.15; Date: 04/07/2008) 

22 Input Data File: C:\USEPA\BMDS21\Nov23\Pwr_CV_Unrest_BMR1_CytC_Liver.(d) 

23 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Pwr_CV_Unrest_BMR1_CytC_Liver.plt 

24 Mon Nov 23 13:45:33 2009 

25 ==================================================================== 

26 

27 TBARs, liver only (Table 2) 

28 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

29 

30 The form of the response function is: 

31 

32 Y[dose] = control + slope * dose^power 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 rho is set to 0 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-136 —DO NOT CITE OR QUOTE 

1 The power is not restricted 

2 A constant variance model is fit 

3 

4 Total number of dose groups = 6 

5 Total number of records with missing values = 0 

6 Maximum number of iterations = 250 

7 Relative Function Convergence has been set to: 1e-008 

8 Parameter Convergence has been set to: 1e-008 

9 

10 

11 

12 Default Initial Parameter Values 

13 alpha = 0.004972 

14 rho = 0 Specified 

15 control = 0.146 

16 slope = 0.0109242 

17 power = 0.717914 

18 

19 

20 Asymptotic Correlation Matrix of Parameter Estimates 

21 

22 ( *** The model parameter(s) -rho 

23 have been estimated at a boundary point, or have been specified by the user, 

24 and do not appear in the correlation matrix ) 

25 

26 alpha control slope power 

27 

28 alpha 1 -8.8e-010 -3.8e-009 4.5e-009 

29 

30 control -8.8e-010 1 -0.77 0.68 

31 

32 slope -3.8e-009 -0.77 1 -0.98 

33 

34 power 4.5e-009 0.68 -0.98 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 95.0% Wald Confidence Interval 

41 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

42 alpha 0.00469717 0.00110713 0.00252723 0.00686711 

43 control 0.135495 0.0246289 0.0872229 0.183766 

44 slope 0.0232652 0.013381 -0.00296103 0.0494915 

45 power 0.573772 0.119032 0.340474 0.80707 

46 

47 

48 

49 Table of Data and Estimated Values of Interest 

50 

51 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

52 ------ --- -------- -------- ----------- ----------- ---------- 

53 

54 0 6 0.146 0.135 0.0661 0.0685 0.375 

55 3 6 0.177 0.179 0.0539 0.0685 -0.0784 

56 10 6 0.191 0.223 0.0563 0.0685 -1.13 

57 22 6 0.271 0.273 0.0563 0.0685 -0.056 

58 46 6 0.388 0.345 0.0637 0.0685 1.54 

59 100 6 0.444 0.462 0.11 0.0685 -0.653 

60 

61 

62 

63 Model Descriptions for likelihoods calculated 

64 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-137 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma^2 

4 Model A3 uses any fixed variance parameters that 

5 were specified by the user 

6 

7 Model R: Yi = Mu + e(i) 

8 Var{e(i)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) # Param's AIC 

14 A1 80.752584 7 -147.505168 

15 A2 83.373547 12 -142.747094 

16 A3 80.752584 7 -147.505168 

17 fitted 78.494318 4 -148.988637 

18 R 55.820023 2 -107.640047 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Do responses and/or variances differ among Dose levels? 

24 (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A1 vs A2) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

28 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) Test df p-value 

33 

34 Test 1 55.107 10 <.0001 

35 Test 2 5.24193 5 0.3871 

36 Test 3 5.24193 5 0.3871 

37 Test 4 4.51653 3 0.2108 

38 

39 The p-value for Test 1 is less than .05. There appears to be a 

40 difference between response and/or variances among the dose levels 

41 It seems appropriate to model the data 

42 

43 The p-value for Test 2 is greater than .1. A homogeneous variance 

44 model appears to be appropriate here 

45 

46 

47 The p-value for Test 3 is greater than .1. The modeled variance appears 

48 to be appropriate here 

49 

50 The p-value for Test 4 is greater than .1. The model chosen seems 

51 to adequately describe the data 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 1 

57 

58 Risk Type = Estimated standard deviations from the control mean 

59 

60 Confidence level = 0.95 

61 

62 BMD = 6.57302 

63 

64 

65 BMDL = 1.96558 

66 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-138 —DO NOT CITE OR QUOTE 

1 H.3.2. Hassoun et al. (2000): DNA SSB 

2 H.3.2.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 0.75 47.92 <0.0001 121.75 3.8E+01 2.5E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.75 47.92 <0.0001 121.75 3.8E+01 2.5E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.75 8.98 0.03 84.81 3.7E+00 2.2E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.75 8.98 0.03 84.81 3.7E+00 2.2E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 0.75 8.98 0.03 84.81 3.7E+00 2.2E+00 nonconstant variance, 

power unrestricted 

Hill 3 0.75 7.46 0.06 83.29 2.6E+00 1.4E+00 nonconstant variance, n 

restricted >1, bound hit 

Hill 2 0.75 3.76 0.15 81.60 6.6E-01 1.8E-01 nonconstant variance, n 

unrestricted 

linear 4 0.75 39.32 <.0001 113.16 1.9E+01 1.0E+01 nonconstant variance 

polynomial 4 0.75 39.32 <.0001 113.16 1.9E+01 1.0E+01 nonconstant variance 

power 4 0.75 39.32 <.0001 113.16 1.9E+01 1.0E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.75 4.68 0.20 80.52 3.0E-01 8.5E-02 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.75 48.54 <0.0001 120.83 3.0E+01 2.5E+01 constant variance, power 

restricted ≥1 

exponential (M3) 4 0.75 48.54 <0.0001 120.83 3.0E+01 2.5E+01 constant variance, power 

restricted ≥1 

exponential (M4) 3 0.75 8.53 0.04 82.81 3.7E+00 2.8E+00 constant variance, power 

restricted ≥1 

exponential (M5) 3 0.75 8.53 0.04 82.81 3.7E+00 2.8E+00 constant variance, power 

restricted ≥1 

exponential (M5) d 3 0.75 8.53 0.04 82.81 3.7E+00 2.8E+00 constant variance, power 

unrestricted 

Hill c 3 0.75 7.12 0.07 81.41 2.9E+00 2.0E+00 constant variance, n 

restricted >1, bound hit

Hill d 2 0.75 4.03 0.13 80.32 9.6E-01 2.1E-01 constant variance, n 

unrestricted 

linear 4 0.75 38.88 <.0001 111.16 1.8E+01 1.5E+01 constant variance 

polynomial 4 0.75 38.88 <.0001 111.16 1.8E+01 1.5E+01 constant variance 

power 4 0.75 38.88 <.0001 111.16 1.8E+01 1.5E+01 constant variance, power 

restricted ≥1, bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-139 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power d 3 0.75 5.10 0.16 79.39 4.4E-01 1.5E-01 constant variance, power 

unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.2.2. Figure for Selected Model: Exponential (M5), Constant Variance, Power 

4 Unrestricted

 5

 10

 15

 20

 25

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:44 11/23 2009

BMDL BMD

 

Exponential

5 

 6 

7 H.3.2.3. Output File for Selected Model: Exponential (M5), Constant Variance, Power 

8 Unrestricted

9 

10 

11 ==================================================================== 

12 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

13 Input Data File: C:\USEPA\BMDS21\Nov23\Exp_CV_Unrest_BMR1_DNA_SSB.(d) 

14 Gnuplot Plotting File: 

15 Mon Nov 23 13:44:02 2009 

16 ==================================================================== 

17 

18 DNA single-strand breaks, liver only (Table 3) 

19 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

20 

21 The form of the response function by Model: 

22 Model 2: Y[dose] = a * exp{sign * b * dose} 

23 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-140 —DO NOT CITE OR QUOTE 

1 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

2 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

3 

4 Note: Y[dose] is the median response for exposure = dose; 

5 sign = +1 for increasing trend in data; 

6 sign = -1 for decreasing trend. 

7 

8 Model 2 is nested within Models 3 and 4. 

9 Model 3 is nested within Model 5. 

10 Model 4 is nested within Model 5. 

11 

12 

13 Dependent variable = Mean 

14 Independent variable = Dose 

15 Data are assumed to be distributed: normally 

16 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

17 rho is set to 0. 

18 A constant variance model is fit. 

19 

20 Total number of dose groups = 6 

21 Total number of records with missing values = 0 

22 Maximum number of iterations = 250 

23 Relative Function Convergence has been set to: 1e-008 

24 Parameter Convergence has been set to: 1e-008 

25 

26 MLE solution provided: Exact 

27 

28 

29 Initial Parameter Values 

30 

31 Variable Model 5 

32 -------- -------- 

33 lnalpha 0.841244 

34 rho(S) 0 

35 a 7.0395 

36 b 0.0279582 

37 c 3.50522 

38 d 1 

39 

40 (S) = Specified 

41 

42 

43 

44 Parameter Estimates 

45 

46 Variable Model 5 

47 -------- ------- 

48 lnalpha 1.07816 

49 rho 0 

50 a 8.47733 

51 b 0.0311513 

52 c 2.84178 

53 d 1 

54 

55 

56 Table of Stats From Input Data 

57 

58 Dose N Obs Mean Obs Std Dev 

59 ----- --- ---------- ------------- 

60 0 6 7.41 1.543 

61 3 6 10.78 1.249 

62 10 6 13.6 1.69 

63 22 6 15.3 1.715 

64 46 6 20.4 2.254 

65 100 6 23.5 1.372 

66 

67 

68 Estimated Values of Interest 

69 

70 Dose Est Mean Est Std Scaled Residual 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-141 —DO NOT CITE OR QUOTE 

1 ------ ---------- --------- ---------------- 

2 0 8.477 1.714 -1.525 

3 3 9.87 1.714 1.3 

4 10 12.66 1.714 1.348 

5 22 16.22 1.714 -1.318 

6 46 20.37 1.714 0.04957 

7 100 23.4 1.714 0.1459 

8 

9 

10 

11 Other models for which likelihoods are calculated: 

12 

13 Model A1: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma^2 

15 

16 Model A2: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma(i)^2 

18 

19 Model A3: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

21 

22 Model R: Yij = Mu + e(i) 

23 Var{e(ij)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) DF AIC 

29 ------- ----------------- ---- ------------ 

30 A1 -33.14239 7 80.28478 

31 A2 -31.81197 12 87.62394 

32 A3 -33.14239 7 80.28478 

33 R -80.44209 2 164.8842 

34 5 -37.40682 4 82.81364 

35 

36 

37 Additive constant for all log-likelihoods = -33.08. This constant added to the 

38 above values gives the log-likelihood including the term that does not 

39 depend on the model parameters. 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

45 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

46 Test 3: Are variances adequately modeled? (A2 vs. A3) 

47 

48 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

49 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) D. F. p-value 

54 -------- ------------------------ ------ -------------- 

55 Test 1 97.26 10 < 0.0001 

56 Test 2 2.661 5 0.7521 

57 Test 3 2.661 5 0.7521 

58 Test 7a 8.529 3 0.03626 

59 

60 

61 The p-value for Test 1 is less than .05. There appears to be a 

62 difference between response and/or variances among the dose 

63 levels, it seems appropriate to model the data. 

64 

65 The p-value for Test 2 is greater than .1. A homogeneous 

66 variance model appears to be appropriate here. 

67 

68 The p-value for Test 3 is greater than .1. The modeled 

69 variance appears to be appropriate here. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-142 —DO NOT CITE OR QUOTE 

1 The p-value for Test 7a is less than .1. Model 5 may not adequately 

2 describe the data; you may want to consider another model. 

3 

4 

5 Benchmark Dose Computations: 

6 

7 Specified Effect = 1.000000 

8 

9 Risk Type = Estimated standard deviations from control 

10 

11 Confidence Level = 0.950000 

12 

13 BMD = 3.73387 

14 

15 BMDL = 2.78339 

16 

17 

18 H.3.2.4. Figure for Unrestricted Model: Hill, Constant Variance, n Restricted >1, Bound 

19 Hit 

 5

 10

 15

 20

 25

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:43 11/23 2009

BMDL BMD

 

Hill

20 

 21 

 22 

23 H.3.2.5. Output File for Unrestricted Model: Hill, Constant Variance, n Restricted >1, 

24 Bound Hit 

25 

26 

27 ==================================================================== 

28 Hill Model. (Version: 2.14; Date: 06/26/2008) 

29 Input Data File: C:\USEPA\BMDS21\Nov23\Hill_CV_BMR1_DNA_SSB.(d) 

30 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Hill_CV_BMR1_DNA_SSB.plt 

31 Mon Nov 23 13:43:57 2009 

32 ==================================================================== 

33 

34 DNA single-strand breaks, liver only (Table 3) 

35 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-143 —DO NOT CITE OR QUOTE 

1 The form of the response function is: 

2 

3 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

4 

5 

6 Dependent variable = Mean 

7 Independent variable = Dose 

8 rho is set to 0 

9 Power parameter restricted to be greater than 1 

10 A constant variance model is fit 

11 

12 Total number of dose groups = 6 

13 Total number of records with missing values = 0 

14 Maximum number of iterations = 250 

15 Relative Function Convergence has been set to: 1e-008 

16 Parameter Convergence has been set to: 1e-008 

17 

18 

19 

20 Default Initial Parameter Values 

21 alpha = 2.7831 

22 rho = 0 Specified 

23 intercept = 7.41 

24 v = 16.09 

25 n = 0.174831 

26 k = 69.2706 

27 

28 

29 Asymptotic Correlation Matrix of Parameter Estimates 

30 

31 ( *** The model parameter(s) -rho -n 

32 have been estimated at a boundary point, or have been specified by the user, 

33 and do not appear in the correlation matrix ) 

34 

35 alpha intercept v k 

36 

37 alpha 1 1.1e-007 1.9e-007 1.9e-007 

38 

39 intercept 1.1e-007 1 0.099 0.61 

40 

41 v 1.9e-007 0.099 1 0.79 

42 

43 k 1.9e-007 0.61 0.79 1 

44 

45 

46 

47 Parameter Estimates 

48 

49 95.0% Wald Confidence Interval 

50 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

51 alpha 2.82659 0.666233 1.5208 4.13238 

52 intercept 8.16404 0.581043 7.02522 9.30286 

53 v 20.1253 1.69013 16.8127 23.4379 

54 n 1 NA 

55 k 31.702 8.35815 15.3203 48.0836 

56 

57 NA - Indicates that this parameter has hit a bound 

58 implied by some inequality constraint and thus 

59 has no standard error. 

60 

61 

62 

63 Table of Data and Estimated Values of Interest 

64 

65 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

66 ------ --- -------- -------- ----------- ----------- ---------- 

67 

68 0 6 7.41 8.16 1.54 1.68 -1.1 

69 3 6 10.8 9.9 1.25 1.68 1.28 

70 10 6 13.6 13 1.69 1.68 0.889 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-144 —DO NOT CITE OR QUOTE 

1 22 6 15.3 16.4 1.71 1.68 -1.62 

2 46 6 20.4 20.1 2.25 1.68 0.469 

3 100 6 23.5 23.4 1.37 1.68 0.0802 

4 

5 

6 

7 Model Descriptions for likelihoods calculated 

8 

9 

10 Model A1: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma^2 

12 

13 Model A2: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma(i)^2 

15 

16 Model A3: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma^2 

18 Model A3 uses any fixed variance parameters that 

19 were specified by the user 

20 

21 Model R: Yi = Mu + e(i) 

22 Var{e(i)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) # Param's AIC 

28 A1 -33.142389 7 80.284779 

29 A2 -31.811970 12 87.623940 

30 A3 -33.142389 7 80.284779 

31 fitted -36.703273 4 81.406545 

32 R -80.442086 2 164.884172 

33 

34 

35 Explanation of Tests 

36 

37 Test 1: Do responses and/or variances differ among Dose levels? 

38 (A2 vs. R) 

39 Test 2: Are Variances Homogeneous? (A1 vs A2) 

40 Test 3: Are variances adequately modeled? (A2 vs. A3) 

41 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

42 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

43 

44 Tests of Interest 

45 

46 Test -2*log(Likelihood Ratio) Test df p-value 

47 

48 Test 1 97.2602 10 <.0001 

49 Test 2 2.66084 5 0.7521 

50 Test 3 2.66084 5 0.7521 

51 Test 4 7.12177 3 0.06812 

52 

53 The p-value for Test 1 is less than .05. There appears to be a 

54 difference between response and/or variances among the dose levels 

55 It seems appropriate to model the data 

56 

57 The p-value for Test 2 is greater than .1. A homogeneous variance 

58 model appears to be appropriate here 

59 

60 

61 The p-value for Test 3 is greater than .1. The modeled variance appears 

62 to be appropriate here 

63 

64 The p-value for Test 4 is less than .1. You may want to try a different 

65 model 

66 

67 

68 Benchmark Dose Computation 

69 

70 Specified effect = 1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-145 —DO NOT CITE OR QUOTE 

1 

2 Risk Type = Estimated standard deviations from the control mean 

3 

4 Confidence level = 0.95 

5 

6 BMD = 2.88976 

7 

8 BMDL = 2.00669 

9 

10 

11 

12 H.3.2.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 5

 10

 15

 20

 25

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:44 11/23 2009

BMDL BMD

 

Hill

13 

 14 

 15 

16 H.3.2.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 17 

18 

19 ==================================================================== 

20 Hill Model. (Version: 2.14; Date: 06/26/2008) 

21 Input Data File: C:\USEPA\BMDS21\Nov23\Hill_CV_Unrest_BMR1_DNA_SSB.(d) 

22 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Hill_CV_Unrest_BMR1_DNA_SSB.plt 

23 Mon Nov 23 13:44:03 2009 

24 ==================================================================== 

25 

26 DNA single-strand breaks, liver only (Table 3) 

27 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

28 

29 The form of the response function is: 

30 

31 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

32 

33 

34 Dependent variable = Mean 

35 Independent variable = Dose 

36 rho is set to 0 

37 Power parameter is not restricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-146 —DO NOT CITE OR QUOTE 

1 A constant variance model is fit 

2 

3 Total number of dose groups = 6 

4 Total number of records with missing values = 0 

5 Maximum number of iterations = 250 

6 Relative Function Convergence has been set to: 1e-008 

7 Parameter Convergence has been set to: 1e-008 

8 

9 

10 

11 Default Initial Parameter Values 

12 alpha = 2.7831 

13 rho = 0 Specified 

14 intercept = 7.41 

15 v = 16.09 

16 n = 0.174831 

17 k = 69.2706 

18 

19 

20 Asymptotic Correlation Matrix of Parameter Estimates 

21 

22 ( *** The model parameter(s) -rho 

23 have been estimated at a boundary point, or have been specified by the user, 

24 and do not appear in the correlation matrix ) 

25 

26 alpha intercept v n k 

27 

28 alpha 1 -2.2e-008 -4.6e-008 8.4e-009 -4.3e-008 

29 

30 intercept -2.2e-008 1 -0.33 0.47 -0.29 

31 

32 v -4.6e-008 -0.33 1 -0.95 1 

33 

34 n 8.4e-009 0.47 -0.95 1 -0.96 

35 

36 k -4.3e-008 -0.29 1 -0.96 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 95.0% Wald Confidence Interval 

43 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

44 alpha 2.5942 0.611459 1.39576 3.79264 

45 intercept 7.47627 0.665055 6.17278 8.77975 

46 v 36.9014 25.5466 -13.1689 86.9718 

47 n 0.612877 0.190055 0.240376 0.985377 

48 k 148.104 303.532 -446.809 743.016 

49 

50 

51 

52 Table of Data and Estimated Values of Interest 

53 

54 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

55 ------ --- -------- -------- ----------- ----------- ---------- 

56 

57 0 6 7.41 7.48 1.54 1.61 -0.101 

58 3 6 10.8 10.6 1.25 1.61 0.313 

59 10 6 13.6 13.4 1.69 1.61 0.286 

60 22 6 15.3 16.2 1.71 1.61 -1.41 

61 46 6 20.4 19.6 2.25 1.61 1.24 

62 100 6 23.5 23.7 1.37 1.61 -0.33 

63 

64 

65 

66 Model Descriptions for likelihoods calculated 

67 

68 

69 Model A1: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-147 —DO NOT CITE OR QUOTE 

1 

2 Model A2: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma(i)^2 

4 

5 Model A3: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 Model A3 uses any fixed variance parameters that 

8 were specified by the user 

9 

10 Model R: Yi = Mu + e(i) 

11 Var{e(i)} = Sigma^2 

12 

13 

14 Likelihoods of Interest 

15 

16 Model Log(likelihood) # Param's AIC 

17 A1 -33.142389 7 80.284779 

18 A2 -31.811970 12 87.623940 

19 A3 -33.142389 7 80.284779 

20 fitted -35.159023 5 80.318046 

21 R -80.442086 2 164.884172 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Do responses and/or variances differ among Dose levels? 

27 (A2 vs. R) 

28 Test 2: Are Variances Homogeneous? (A1 vs A2) 

29 Test 3: Are variances adequately modeled? (A2 vs. A3) 

30 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

31 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

32 

33 Tests of Interest 

34 

35 Test -2*log(Likelihood Ratio) Test df p-value 

36 

37 Test 1 97.2602 10 <.0001 

38 Test 2 2.66084 5 0.7521 

39 Test 3 2.66084 5 0.7521 

40 Test 4 4.03327 2 0.1331 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose levels 

44 It seems appropriate to model the data 

45 

46 The p-value for Test 2 is greater than .1. A homogeneous variance 

47 model appears to be appropriate here 

48 

49 

50 The p-value for Test 3 is greater than .1. The modeled variance appears 

51 to be appropriate here 

52 

53 The p-value for Test 4 is greater than .1. The model chosen seems 

54 to adequately describe the data 

55 

56 

57 Benchmark Dose Computation 

58 

59 Specified effect = 1 

60 

61 Risk Type = Estimated standard deviations from the control mean 

62 

63 Confidence level = 0.95 

64 

65 BMD = 0.961789 

66 

67 BMDL = 0.211403 

68 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-148 —DO NOT CITE OR QUOTE 

1 H.3.2.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 5

 10

 15

 20

 25

 0 20 40 60 80 100

Mean Response

dose

Power Model with 0.95 Confidence Level

13:44 11/23 2009

BMDLBMD

 

Power

2 

 3 

 4 

5 H.3.2.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 6 

7 

8 ==================================================================== 

9 Power Model. (Version: 2.15; Date: 04/07/2008) 

10 Input Data File: C:\USEPA\BMDS21\Nov23\Pwr_CV_Unrest_BMR1_DNA_SSB.(d) 

11 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Pwr_CV_Unrest_BMR1_DNA_SSB.plt 

12 Mon Nov 23 13:44:04 2009 

13 ==================================================================== 

14 

15 DNA single-strand breaks, liver only (Table 3) 

16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

17 

18 The form of the response function is: 

19 

20 Y[dose] = control + slope * dose^power 

21 

22 

23 Dependent variable = Mean 

24 Independent variable = Dose 

25 rho is set to 0 

26 The power is not restricted 

27 A constant variance model is fit 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 

38 alpha = 2.7831 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-149 —DO NOT CITE OR QUOTE 

1 rho = 0 Specified 

2 control = 7.41 

3 slope = 1.99047 

4 power = 0.4538 

5 

6 

7 Asymptotic Correlation Matrix of Parameter Estimates 

8 

9 ( *** The model parameter(s) -rho 

10 have been estimated at a boundary point, or have been specified by the user, 

11 and do not appear in the correlation matrix ) 

12 

13 alpha control slope power 

14 

15 alpha 1 1e-010 3.4e-009 -3.5e-009 

16 

17 control 1e-010 1 -0.79 0.66 

18 

19 slope 3.4e-009 -0.79 1 -0.97 

20 

21 power -3.5e-009 0.66 -0.97 1 

22 

23 

24 

25 Parameter Estimates 

26 

27 95.0% Wald Confidence Interval 

28 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

29 alpha 2.67247 0.629906 1.43787 3.90706 

30 control 7.29122 0.640201 6.03645 8.54599 

31 slope 2.31759 0.501503 1.33466 3.30051 

32 power 0.428335 0.0441267 0.341848 0.514821 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 6 7.41 7.29 1.54 1.63 0.178 

42 3 6 10.8 11 1.25 1.63 -0.332 

43 10 6 13.6 13.5 1.69 1.63 0.142 

44 22 6 15.3 16 1.71 1.63 -1.05 

45 46 6 20.4 19.2 2.25 1.63 1.74 

46 100 6 23.5 24 1.37 1.63 -0.678 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = Sigma^2 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-150 —DO NOT CITE OR QUOTE 

1 A1 -33.142389 7 80.284779 

2 A2 -31.811970 12 87.623940 

3 A3 -33.142389 7 80.284779 

4 fitted -35.694033 4 79.388067 

5 R -80.442086 2 164.884172 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 97.2602 10 <.0001 

22 Test 2 2.66084 5 0.7521 

23 Test 3 2.66084 5 0.7521 

24 Test 4 5.10329 3 0.1644 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is greater than .1. A homogeneous variance 

31 model appears to be appropriate here 

32 

33 

34 The p-value for Test 3 is greater than .1. The modeled variance appears 

35 to be appropriate here 

36 

37 The p-value for Test 4 is greater than .1. The model chosen seems 

38 to adequately describe the data 

39 

40 

41 Benchmark Dose Computation 

42 

43 Specified effect = 1 

44 

45 Risk Type = Estimated standard deviations from the control mean 

46 

47 Confidence level = 0.95 

48 

49 BMD = 0.442709 

50 

51 

52 BMDL = 0.149473 

53 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-151 —DO NOT CITE OR QUOTE 

1 H.3.3. Hassoun et al. (2000): TBARs Liver 

2 H.3.3.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 0.33 20.31 0.00 -4.29 7.0E+01 3.4E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 0.33 20.31 0.00 -4.29 7.0E+01 3.4E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 0.33 3.08 0.38 -19.53 4.3E+00 1.9E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.33 2.78 0.25 -17.82 5.5E+00 2.0E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.33 2.78 0.25 -17.82 5.5E+00 2.0E+00 nonconstant variance, 

power unrestricted 

Hill 2 0.33 2.52 0.28 -18.08 5.7E+00 2.0E+00 nonconstant variance, n 

restricted >1 

Hill 2 0.33 2.52 0.28 -18.08 5.7E+00 error nonconstant variance, n 

unrestricted 

linear 4 0.33 19.16 0.00 -5.44 5.2E+01 2.2E+01 nonconstant variance 

polynomial 4 0.33 19.16 0.00 -5.44 5.2E+01 2.2E+01 nonconstant variance 

power 4 0.33 19.16 0.00 -5.44 5.2E+01 2.2E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power 3 0.33 8.22 0.04 -14.38 1.2E+00 5.2E-03 nonconstant variance, 

power unrestricted 

exponential (M2) 4 0.33 20.40 0.00 -6.14 8.0E+01 5.3E+01 constant variance, 

power restricted ≥1 

exponential (M3) 4 0.33 20.40 0.00 -6.14 8.0E+01 5.3E+01 constant variance, 

power restricted ≥1 

exponential (M4) c 3 0.33 3.36 0.34 -21.18 4.9E+00 2.3E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.33 2.86 0.24 -19.68 6.7E+00 2.5E+00 constant variance, 

power restricted ≥1 

exponential (M5) d 2 0.33 2.86 0.24 -19.68 6.7E+00 2.5E+00 constant variance, 

power unrestricted 

Hill 2 0.33 2.61 0.27 -19.93 6.3E+00 2.6E+00 constant variance, n 

restricted >1 

Hill d 2 0.33 2.61 0.27 -19.93 6.3E+00 2.6E+00 constant variance, n 

unrestricted 

linear 4 0.33 19.52 0.00 -7.02 6.9E+01 4.4E+01 constant variance 

polynomial 4 0.33 19.52 0.00 -7.02 6.9E+01 4.4E+01 constant variance 

power 4 0.33 19.52 0.00 -7.02 6.9E+01 4.4E+01 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-152 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power d 3 0.33 9.55 0.02 -14.99 2.9E+00 6.1E-02 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.3.2. Figure for Selected Model: Exponential (M4), Constant Variance, Power Restricted 

4 ≥1 

 1

 1.5

 2

 2.5

 3

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

13:44 11/23 2009

BMDL BMD

 

Exponential

5 

 6 

 7 

8 H.3.3.3. Output File for Selected Model: Exponential (M4), Constant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov23\Exp_CV_BMR1_TBARs_Liver.(d) 

15 Gnuplot Plotting File: 

16 Mon Nov 23 13:44:41 2009 

17 ==================================================================== 

18 

19 TBARs, liver only (Table 2) 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-153 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 rho is set to 0. 

20 A constant variance model is fit. 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 4 

34 -------- -------- 

35 lnalpha -1.90388 

36 rho(S) 0 

37 a 1.39555 

38 b 0.0194898 

39 c 1.97051 

40 d 1 

41 

42 (S) = Specified 

43 

44 

45 

46 Parameter Estimates 

47 

48 Variable Model 4 

49 -------- ------- 

50 lnalpha -1.82448 

51 rho 0 

52 a 1.46519 

53 b 0.113543 

54 c 1.63661 

55 d 2.13652 

56 

57 

58 Table of Stats From Input Data 

59 

60 Dose N Obs Mean Obs Std Dev 

61 ----- --- ---------- ------------- 

62 0 6 1.469 0.2915 

63 3 6 1.549 0.5389 

64 10 6 2.15 0.3625 

65 22 6 2.28 0.2474 

66 46 6 2.619 0.5168 

67 100 6 2.292 0.4874 

68 

69 

70 Estimated Values of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-154 —DO NOT CITE OR QUOTE 

1 

2 Dose Est Mean Est Std Scaled Residual 

3 ------ ---------- --------- ---------------- 

4 0 1.404 0.4044 0.3915 

5 3 1.674 0.4044 -0.7582 

6 10 2.063 0.4044 0.527 

7 22 2.332 0.4044 -0.3134 

8 46 2.438 0.4044 1.099 

9 100 2.448 0.4044 -0.9458 

10 

11 

12 

13 Other models for which likelihoods are calculated: 

14 

15 Model A1: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma^2 

17 

18 Model A2: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma(i)^2 

20 

21 Model A3: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

23 

24 Model R: Yij = Mu + e(i) 

25 Var{e(ij)} = Sigma^2 

26 

27 

28 Likelihoods of Interest 

29 

30 Model Log(likelihood) DF AIC 

31 ------- ----------------- ---- ------------ 

32 A1 16.26977 7 -18.53954 

33 A2 19.12783 12 -14.25565 

34 A3 16.26977 7 -18.53954 

35 R 2.44294 2 -0.8858799 

36 4 14.5907 4 -21.18141 

37 

38 

39 Additive constant for all log-likelihoods = -33.08. This constant added to the 

40 above values gives the log-likelihood including the term that does not 

41 depend on the model parameters. 

42 

43 

44 Explanation of Tests 

45 

46 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

47 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

48 Test 3: Are variances adequately modeled? (A2 vs. A3) 

49 

50 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

51 

52 

53 Tests of Interest 

54 

55 Test -2*log(Likelihood Ratio) D. F. p-value 

56 -------- ------------------------ ------ -------------- 

57 Test 1 33.37 10 0.000236 

58 Test 2 5.716 5 0.3348 

59 Test 3 5.716 5 0.3348 

60 Test 6a 3.358 3 0.3396 

61 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose 

65 levels, it seems appropriate to model the data. 

66 

67 The p-value for Test 2 is greater than .1. A homogeneous 

68 variance model appears to be appropriate here. 

69 

70 The p-value for Test 3 is greater than .1. The modeled 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-155 —DO NOT CITE OR QUOTE 

1 variance appears to be appropriate here. 

2 

3 The p-value for Test 6a is greater than .1. Model 4 seems 

4 to adequately describe the data. 

5 

6 

7 Benchmark Dose Computations: 

8 

9 Specified Effect = 1.000000 

10 

11 Risk Type = Estimated standard deviations from control 

12 

13 Confidence Level = 0.950000 

14 

15 BMD = 4.91639 

16 

17 BMDL = 2.29952 

18 

19 

20 H.3.3.4. Figure for Unrestricted Model: Exponential (M5), Constant Variance, Power 

21 Unrestricted

 1

 1.5

 2

 2.5

 3

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

13:44 11/23 2009

BMDL BMD

 

Exponential

22 

 23 

 24 

25 H.3.3.5. Output File for Unrestricted Model: Exponential (M5), Constant Variance, Power 

26 Unrestricted 

27 

28 

29 ==================================================================== 

30 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

31 Input Data File: C:\USEPA\BMDS21\Nov23\Exp_CV_Unrest_BMR1_TBARs_Liver.(d) 

32 Gnuplot Plotting File: 

33 Mon Nov 23 13:44:47 2009 

34 ==================================================================== 

35 

36 TBARs, liver only (Table 2) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-156 —DO NOT CITE OR QUOTE 

1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

2 

3 The form of the response function by Model: 

4 Model 2: Y[dose] = a * exp{sign * b * dose} 

5 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

6 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

7 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

8 

9 Note: Y[dose] is the median response for exposure = dose; 

10 sign = +1 for increasing trend in data; 

11 sign = -1 for decreasing trend. 

12 

13 Model 2 is nested within Models 3 and 4. 

14 Model 3 is nested within Model 5. 

15 Model 4 is nested within Model 5. 

16 

17 

18 Dependent variable = Mean 

19 Independent variable = Dose 

20 Data are assumed to be distributed: normally 

21 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

22 rho is set to 0. 

23 A constant variance model is fit. 

24 

25 Total number of dose groups = 6 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 MLE solution provided: Exact 

32 

33 

34 Initial Parameter Values 

35 

36 Variable Model 5 

37 -------- -------- 

38 lnalpha -1.90388 

39 rho(S) 0 

40 a 1.39555 

41 b 0.0194898 

42 c 1.97051 

43 d 1 

44 

45 (S) = Specified 

46 

47 

48 

49 Parameter Estimates 

50 

51 Variable Model 5 

52 -------- ------- 

53 lnalpha -1.82448 

54 rho 0 

55 a 1.46519 

56 b 0.113543 

57 c 1.63661 

58 d 2.13652 

59 

60 

61 Table of Stats From Input Data 

62 

63 Dose N Obs Mean Obs Std Dev 

64 ----- --- ---------- ------------- 

65 0 6 1.469 0.2915 

66 3 6 1.549 0.5389 

67 10 6 2.15 0.3625 

68 22 6 2.28 0.2474 

69 46 6 2.619 0.5168 

70 100 6 2.292 0.4874 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-157 —DO NOT CITE OR QUOTE 

1 

2 

3 Estimated Values of Interest 

4 

5 Dose Est Mean Est Std Scaled Residual 

6 ------ ---------- --------- ---------------- 

7 0 1.465 0.4016 0.02326 

8 3 1.554 0.4016 -0.03103 

9 10 2.147 0.4016 0.02011 

10 22 2.397 0.4016 -0.7145 

11 46 2.398 0.4016 1.348 

12 100 2.398 0.4016 -0.6461 

13 

14 

15 

16 Other models for which likelihoods are calculated: 

17 

18 Model A1: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = Sigma^2 

20 

21 Model A2: Yij = Mu(i) + e(ij) 

22 Var{e(ij)} = Sigma(i)^2 

23 

24 Model A3: Yij = Mu(i) + e(ij) 

25 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

26 

27 Model R: Yij = Mu + e(i) 

28 Var{e(ij)} = Sigma^2 

29 

30 

31 Likelihoods of Interest 

32 

33 Model Log(likelihood) DF AIC 

34 ------- ----------------- ---- ------------ 

35 A1 16.26977 7 -18.53954 

36 A2 19.12783 12 -14.25565 

37 A3 16.26977 7 -18.53954 

38 R 2.44294 2 -0.8858799 

39 5 14.8407 5 -19.68141 

40 

41 

42 Additive constant for all log-likelihoods = -33.08. This constant added to the 

43 above values gives the log-likelihood including the term that does not 

44 depend on the model parameters. 

45 

46 

47 Explanation of Tests 

48 

49 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

50 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

51 Test 3: Are variances adequately modeled? (A2 vs. A3) 

52 

53 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

54 

55 

56 Tests of Interest 

57 

58 Test -2*log(Likelihood Ratio) D. F. p-value 

59 -------- ------------------------ ------ -------------- 

60 Test 1 33.37 10 0.000236 

61 Test 2 5.716 5 0.3348 

62 Test 3 5.716 5 0.3348 

63 Test 7a 2.858 2 0.2395 

64 

65 

66 The p-value for Test 1 is less than .05. There appears to be a 

67 difference between response and/or variances among the dose 

68 levels, it seems appropriate to model the data. 

69 

70 The p-value for Test 2 is greater than .1. A homogeneous 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-158 —DO NOT CITE OR QUOTE 

1 variance model appears to be appropriate here. 

2 

3 The p-value for Test 3 is greater than .1. The modeled 

4 variance appears to be appropriate here. 

5 

6 The p-value for Test 7a is greater than .1. Model 5 seems 

7 to adequately describe the data. 

8 

9 

10 Benchmark Dose Computations: 

11 

12 Specified Effect = 1.000000 

13 

14 Risk Type = Estimated standard deviations from control 

15 

16 Confidence Level = 0.950000 

17 

18 BMD = 6.73152 

19 

20 BMDL = 2.47029 

21 

22 

23 H.3.3.6. Figure for Unrestricted Model: Hill, Constant Variance, n Unrestricted

 1

 1.5

 2

 2.5

 3

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

13:44 11/23 2009

BMDL BMD

 

Hill

24 

 25 

 26 

27 H.3.3.7. Output File for Unrestricted Model: Hill, Constant Variance, n Unrestricted 28 

29 

30 ==================================================================== 

31 Hill Model. (Version: 2.14; Date: 06/26/2008) 

32 Input Data File: C:\USEPA\BMDS21\Nov23\Hill_CV_Unrest_BMR1_TBARs_Liver.(d) 

33 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Hill_CV_Unrest_BMR1_TBARs_Liver.plt 

34 Mon Nov 23 13:44:49 2009 

35 ==================================================================== 

36 

37 TBARs, liver only (Table 2) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-159 —DO NOT CITE OR QUOTE 

1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

2 

3 The form of the response function is: 

4 

5 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

6 

7 

8 Dependent variable = Mean 

9 Independent variable = Dose 

10 rho is set to 0 

11 Power parameter is not restricted 

12 A constant variance model is fit 

13 

14 Total number of dose groups = 6 

15 Total number of records with missing values = 0 

16 Maximum number of iterations = 250 

17 Relative Function Convergence has been set to: 1e-008 

18 Parameter Convergence has been set to: 1e-008 

19 

20 

21 

22 Default Initial Parameter Values 

23 alpha = 0.178788 

24 rho = 0 Specified 

25 intercept = 1.469 

26 v = 1.15 

27 n = 0.921061 

28 k = 11.2346 

29 

30 

31 Asymptotic Correlation Matrix of Parameter Estimates 

32 

33 ( *** The model parameter(s) -rho 

34 have been estimated at a boundary point, or have been specified by the user, 

35 and do not appear in the correlation matrix ) 

36 

37 alpha intercept v n k 

38 

39 alpha 1 4.6e-010 -1.2e-008 2.8e-009 3.8e-009 

40 

41 intercept 4.6e-010 1 -0.82 0.48 0.52 

42 

43 v -1.2e-008 -0.82 1 -0.61 -0.22 

44 

45 n 2.8e-009 0.48 -0.61 1 0.29 

46 

47 k 3.8e-009 0.52 -0.22 0.29 1 

48 

49 

50 

51 Parameter Estimates 

52 

53 95.0% Wald Confidence Interval 

54 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

55 alpha 0.160182 0.0377552 0.0861829 0.23418 

56 intercept 1.4615 0.152914 1.16179 1.76121 

57 v 0.962989 0.202872 0.565367 1.36061 

58 n 2.4861 1.76422 -0.971707 5.94391 

59 k 7.18099 2.79941 1.69424 12.6677 

60 

61 

62 

63 Table of Data and Estimated Values of Interest 

64 

65 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

66 ------ --- -------- -------- ----------- ----------- ---------- 

67 

68 0 6 1.47 1.46 0.291 0.4 0.0459 

69 3 6 1.55 1.56 0.539 0.4 -0.0685 

70 10 6 2.15 2.13 0.363 0.4 0.118 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-160 —DO NOT CITE OR QUOTE 

1 22 6 2.28 2.37 0.247 0.4 -0.541 

2 46 6 2.62 2.42 0.517 0.4 1.25 

3 100 6 2.29 2.42 0.487 0.4 -0.802 

4 

5 

6 

7 Model Descriptions for likelihoods calculated 

8 

9 

10 Model A1: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma^2 

12 

13 Model A2: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma(i)^2 

15 

16 Model A3: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma^2 

18 Model A3 uses any fixed variance parameters that 

19 were specified by the user 

20 

21 Model R: Yi = Mu + e(i) 

22 Var{e(i)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) # Param's AIC 

28 A1 16.269770 7 -18.539539 

29 A2 19.127827 12 -14.255654 

30 A3 16.269770 7 -18.539539 

31 fitted 14.966039 5 -19.932079 

32 R 2.442940 2 -0.885880 

33 

34 

35 Explanation of Tests 

36 

37 Test 1: Do responses and/or variances differ among Dose levels? 

38 (A2 vs. R) 

39 Test 2: Are Variances Homogeneous? (A1 vs A2) 

40 Test 3: Are variances adequately modeled? (A2 vs. A3) 

41 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

42 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

43 

44 Tests of Interest 

45 

46 Test -2*log(Likelihood Ratio) Test df p-value 

47 

48 Test 1 33.3698 10 0.000236 

49 Test 2 5.71611 5 0.3348 

50 Test 3 5.71611 5 0.3348 

51 Test 4 2.60746 2 0.2715 

52 

53 The p-value for Test 1 is less than .05. There appears to be a 

54 difference between response and/or variances among the dose levels 

55 It seems appropriate to model the data 

56 

57 The p-value for Test 2 is greater than .1. A homogeneous variance 

58 model appears to be appropriate here 

59 

60 

61 The p-value for Test 3 is greater than .1. The modeled variance appears 

62 to be appropriate here 

63 

64 The p-value for Test 4 is greater than .1. The model chosen seems 

65 to adequately describe the data 

66 

67 

68 Benchmark Dose Computation 

69 

70 Specified effect = 1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-161 —DO NOT CITE OR QUOTE 

1 

2 Risk Type = Estimated standard deviations from the control mean 

3 

4 Confidence level = 0.95 

5 

6 BMD = 6.26103 

7 

8 BMDL = 2.57465 

9 

10 

11 H.3.3.8. Figure for Unrestricted Model: Power, Constant Variance, Power Unrestricted 

 1

 1.5

 2

 2.5

 3

 0 20 40 60 80 100

Mean Response

dose

Power Model with 0.95 Confidence Level

13:44 11/23 2009

BMDL BMD

 

Power

12 

 13 

 14 

15 H.3.3.9. Output File for Unrestricted Model: Power, Constant Variance, Power Unrestricted 16 

17 

18 ==================================================================== 

19 Power Model. (Version: 2.15; Date: 04/07/2008) 

20 Input Data File: C:\USEPA\BMDS21\Nov23\Pwr_CV_Unrest_BMR1_TBARs_Liver.(d) 

21 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov23\Pwr_CV_Unrest_BMR1_TBARs_Liver.plt 

22 Mon Nov 23 13:44:49 2009 

23 ==================================================================== 

24 

25 TBARs, liver only (Table 2) 

26 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

27 

28 The form of the response function is: 

29 

30 Y[dose] = control + slope * dose^power 

31 

32 

33 Dependent variable = Mean 

34 Independent variable = Dose 

35 rho is set to 0 

36 The power is not restricted 

37 A constant variance model is fit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-162 —DO NOT CITE OR QUOTE 

1 

2 Total number of dose groups = 6 

3 Total number of records with missing values = 0 

4 Maximum number of iterations = 250 

5 Relative Function Convergence has been set to: 1e-008 

6 Parameter Convergence has been set to: 1e-008 

7 

8 

9 

10 Default Initial Parameter Values 

11 alpha = 0.178788 

12 rho = 0 Specified 

13 control = 1.469 

14 slope = 0.0756538 

15 power = 0.652114 

16 

17 

18 Asymptotic Correlation Matrix of Parameter Estimates 

19 

20 ( *** The model parameter(s) -rho 

21 have been estimated at a boundary point, or have been specified by the user, 

22 and do not appear in the correlation matrix ) 

23 

24 alpha control slope power 

25 

26 alpha 1 1.1e-008 -1.1e-009 -1.5e-008 

27 

28 control 1.1e-008 1 -0.75 0.47 

29 

30 slope -1.1e-009 -0.75 1 -0.91 

31 

32 power -1.5e-008 0.47 -0.91 1 

33 

34 

35 

36 Parameter Estimates 

37 

38 95.0% Wald Confidence Interval 

39 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

40 alpha 0.194232 0.0457809 0.104503 0.283961 

41 control 1.42104 0.171077 1.08573 1.75634 

42 slope 0.333105 0.166768 0.00624603 0.659963 

43 power 0.262735 0.0983956 0.0698836 0.455587 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 6 1.47 1.42 0.291 0.441 0.267 

53 3 6 1.55 1.87 0.539 0.441 -1.76 

54 10 6 2.15 2.03 0.363 0.441 0.661 

55 22 6 2.28 2.17 0.247 0.441 0.603 

56 46 6 2.62 2.33 0.517 0.441 1.6 

57 100 6 2.29 2.54 0.487 0.441 -1.37 

58 

59 

60 

61 Model Descriptions for likelihoods calculated 

62 

63 

64 Model A1: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 

67 Model A2: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma(i)^2 

69 

70 Model A3: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-163 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma^2 

2 Model A3 uses any fixed variance parameters that 

3 were specified by the user 

4 

5 Model R: Yi = Mu + e(i) 

6 Var{e(i)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) # Param's AIC 

12 A1 16.269770 7 -18.539539 

13 A2 19.127827 12 -14.255654 

14 A3 16.269770 7 -18.539539 

15 fitted 11.496634 4 -14.993268 

16 R 2.442940 2 -0.885880 

17 

18 

19 Explanation of Tests 

20 

21 Test 1: Do responses and/or variances differ among Dose levels? 

22 (A2 vs. R) 

23 Test 2: Are Variances Homogeneous? (A1 vs A2) 

24 Test 3: Are variances adequately modeled? (A2 vs. A3) 

25 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

26 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

27 

28 Tests of Interest 

29 

30 Test -2*log(Likelihood Ratio) Test df p-value 

31 

32 Test 1 33.3698 10 0.000236 

33 Test 2 5.71611 5 0.3348 

34 Test 3 5.71611 5 0.3348 

35 Test 4 9.54627 3 0.02284 

36 

37 The p-value for Test 1 is less than .05. There appears to be a 

38 difference between response and/or variances among the dose levels 

39 It seems appropriate to model the data 

40 

41 The p-value for Test 2 is greater than .1. A homogeneous variance 

42 model appears to be appropriate here 

43 

44 

45 The p-value for Test 3 is greater than .1. The modeled variance appears 

46 to be appropriate here 

47 

48 The p-value for Test 4 is less than .1. You may want to try a different 

49 model 

50 

51 

52 Benchmark Dose Computation 

53 

54 Specified effect = 1 

55 

56 Risk Type = Estimated standard deviations from the control mean 

57 

58 Confidence level = 0.95 

59 

60 BMD = 2.90232 

61 

62 

63 BMDL = 0.0614971 

64 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-164 —DO NOT CITE OR QUOTE 

1 H.3.4. Kitchin et al. (1979): BaP Hydrolase Activity 

2 H.3.4.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 9 <0.0001 247.00 <0.0001 452.67 2.6E+03 1.2E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 9 <0.0001 247.00 <0.0001 452.67 2.6E+03 1.2E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 8 <0.0001 18.96 0.02 226.60 1.8E+00 1.4E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) c 7 <0.0001 16.75 0.02 226.40 3.4E+00 1.6E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 7 <0.0001 16.75 0.02 226.40 3.4E+00 1.6E+00 nonconstant variance, 

power unrestricted 

Hill 7 <.0001 296.88 <.0001 506.53 error error nonconstant variance, n 

restricted >1 

Hill d 7 <.0001 296.88 <.0001 506.53 error error nonconstant variance, n 

unrestricted 

linear 9 <.0001 94.11 <.0001 299.75 2.8E+00 2.0E+00 nonconstant variance 

polynomial 9 <.0001 -197.64 <.0001 8.00 error error nonconstant variance 

power 9 <.0001 94.11 <.0001 299.75 2.8E+00 2.0E+00 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 8 <.0001 63.59 <.0001 271.23 3.0E-01 1.3E-01 nonconstant variance, 

power unrestricted 

exponential (M2) 9 <0.0001 129.40 <0.0001 451.61 3.6E+03 3.1E+03 constant variance, 

power restricted ≥1 

exponential (M3) 9 <0.0001 129.40 <0.0001 451.61 3.6E+03 3.1E+03 constant variance, 

power restricted ≥1 

exponential (M4) 8 <0.0001 6.93 0.54 331.19 2.7E+01 2.1E+01 constant variance, 

power restricted ≥1 

exponential (M5) 8 <0.0001 6.93 0.54 331.19 2.7E+01 2.1E+01 constant variance, 

power restricted ≥1 

exponential (M5) 8 <0.0001 6.93 0.54 331.19 2.7E+01 2.1E+01 constant variance, 

power unrestricted 

Hill 7 <.0001 67.64 <.0001 393.90 5.7E+02 5.2E+00 constant variance, n 

restricted >1 

Hill 7 <.0001 2.70 0.91 328.96 2.0E+01 1.1E+01 constant variance, n 

unrestricted 

linear 9 <.0001 120.31 <.0001 442.57 1.9E+03 1.4E+03 constant variance 

polynomial 9 <.0001 120.31 <.0001 442.57 1.9E+03 1.4E+03 constant variance 

power 9 <.0001 120.31 <.0001 442.57 1.9E+03 1.4E+03 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-165 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 8 <.0001 51.05 <.0001 375.31 1.2E+00 2.5E-01 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.4.2. Figure for Selected Model: Exponential (M5), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

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 100

 150

 200

 250

 0 1000 2000 3000 4000 5000 6000 7000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:26 11/20 2009

BMDBMDL

 

Exponential

5 

 6 

 7 

8 H.3.4.3. Output File for Selected Model: Exponential (M5), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_BaP_hydro_act.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 14:26:45 2009 

17 ==================================================================== 

18 

19 Kitchin 1979, Tbl3, BaP hydrolase activity 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-166 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 11 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 5 

33 -------- -------- 

34 lnalpha -3.27793 

35 rho 1.92227 

36 a 4.655 

37 b 0.000532066 

38 c 42.6316 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 5 

46 -------- ------- 

47 lnalpha -2.6425 

48 rho 1.93734 

49 a 5.43493 

50 b 0.00574894 

51 c 31.1998 

52 d 1.21529 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 9 4.9 1.11 

60 0.2 4 4.9 1.18 

61 0.667 4 6.7 1.4 

62 1.33 4 7.2 1.8 

63 6.67 4 8.3 0.26 

64 20 4 14 5 

65 66.7 4 59 6.8 

66 200 4 96 46 

67 667 4 155 16.4 

68 1670 4 182 26 

69 6670 4 189 26 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-167 —DO NOT CITE OR QUOTE 

1 

2 Estimated Values of Interest 

3 

4 Dose Est Mean Est Std Scaled Residual 

5 ------ ---------- --------- ---------------- 

6 0 5.435 1.375 -1.167 

7 0.2 5.479 1.386 -0.8354 

8 0.667 5.625 1.422 1.513 

9 1.33 5.874 1.483 1.789 

10 6.67 8.524 2.127 -0.211 

11 20 16.86 4.118 -1.391 

12 66.7 49.42 11.67 1.642 

13 200 119.4 27.42 -1.705 

14 667 168.6 38.31 -0.7095 

15 1670 169.6 38.52 0.6454 

16 6670 169.6 38.52 1.009 

17 

18 

19 

20 Other models for which likelihoods are calculated: 

21 

22 Model A1: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma^2 

24 

25 Model A2: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = Sigma(i)^2 

27 

28 Model A3: Yij = Mu(i) + e(ij) 

29 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

30 

31 Model R: Yij = Mu + e(i) 

32 Var{e(ij)} = Sigma^2 

33 

34 

35 Likelihoods of Interest 

36 

37 Model Log(likelihood) DF AIC 

38 ------- ----------------- ---- ------------ 

39 A1 -158.1306 12 340.2613 

40 A2 -84.80028 22 213.6006 

41 A3 -98.82189 13 223.6438 

42 R -234.6252 2 473.2504 

43 5 -107.1994 6 226.3987 

44 

45 

46 Additive constant for all log-likelihoods = -45.03. This constant added to the 

47 above values gives the log-likelihood including the term that does not 

48 depend on the model parameters. 

49 

50 

51 Explanation of Tests 

52 

53 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

54 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

55 Test 3: Are variances adequately modeled? (A2 vs. A3) 

56 

57 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

58 

59 

60 Tests of Interest 

61 

62 Test -2*log(Likelihood Ratio) D. F. p-value 

63 -------- ------------------------ ------ -------------- 

64 Test 1 299.6 20 < 0.0001 

65 Test 2 146.7 10 < 0.0001 

66 Test 3 28.04 9 0.0009381 

67 Test 7a 16.75 7 0.01905 

68 

69 

70 The p-value for Test 1 is less than .05. There appears to be a 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-168 —DO NOT CITE OR QUOTE 

1 difference between response and/or variances among the dose 

2 levels, it seems appropriate to model the data. 

3 

4 The p-value for Test 2 is less than .1. A non-homogeneous 

5 variance model appears to be appropriate. 

6 

7 The p-value for Test 3 is less than .1. You may want to 

8 consider a different variance model. 

9 

10 The p-value for Test 7a is less than .1. Model 5 may not adequately 

11 describe the data; you may want to consider another model. 

12 

13 

14 Benchmark Dose Computations: 

15 

16 Specified Effect = 1.000000 

17 

18 Risk Type = Estimated standard deviations from control 

19 

20 Confidence Level = 0.950000 

21 

22 BMD = 3.41185 

23 

24 BMDL = 1.60436 

25 

26 

27 H.3.4.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

28 Unrestricted

 0

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 0 1000 2000 3000 4000 5000 6000 7000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:27 11/20 2009

BMDBMDL

 

Exponential

29 

 30 

 31 

32 H.3.4.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

33 Power Unrestricted 

34 

35 

36 ==================================================================== 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-169 —DO NOT CITE OR QUOTE 

1 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

2 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_BaP_hydro_act.(d) 

3 Gnuplot Plotting File: 

4 Fri Nov 20 14:27:02 2009 

5 ==================================================================== 

6 

7 Kitchin 1979, Tbl3, BaP hydrolase activity 

8 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

9 

10 The form of the response function by Model: 

11 Model 2: Y[dose] = a * exp{sign * b * dose} 

12 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

13 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

14 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

15 

16 Note: Y[dose] is the median response for exposure = dose; 

17 sign = +1 for increasing trend in data; 

18 sign = -1 for decreasing trend. 

19 

20 Model 2 is nested within Models 3 and 4. 

21 Model 3 is nested within Model 5. 

22 Model 4 is nested within Model 5. 

23 

24 

25 Dependent variable = Mean 

26 Independent variable = Dose 

27 Data are assumed to be distributed: normally 

28 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

29 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

30 

31 Total number of dose groups = 11 

32 Total number of records with missing values = 0 

33 Maximum number of iterations = 250 

34 Relative Function Convergence has been set to: 1e-008 

35 Parameter Convergence has been set to: 1e-008 

36 

37 MLE solution provided: Exact 

38 

39 

40 Initial Parameter Values 

41 

42 Variable Model 5 

43 -------- -------- 

44 lnalpha -3.27793 

45 rho 1.92227 

46 a 4.655 

47 b 0.000532066 

48 c 42.6316 

49 d 1 

50 

51 

52 

53 Parameter Estimates 

54 

55 Variable Model 5 

56 -------- ------- 

57 lnalpha -2.6425 

58 rho 1.93734 

59 a 5.43493 

60 b 0.00574894 

61 c 31.1998 

62 d 1.21529 

63 

64 

65 Table of Stats From Input Data 

66 

67 Dose N Obs Mean Obs Std Dev 

68 ----- --- ---------- ------------- 

69 0 9 4.9 1.11 

70 0.2 4 4.9 1.18 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-170 —DO NOT CITE OR QUOTE 

1 0.667 4 6.7 1.4 

2 1.33 4 7.2 1.8 

3 6.67 4 8.3 0.26 

4 20 4 14 5 

5 66.7 4 59 6.8 

6 200 4 96 46 

7 667 4 155 16.4 

8 1670 4 182 26 

9 6670 4 189 26 

10 

11 

12 Estimated Values of Interest 

13 

14 Dose Est Mean Est Std Scaled Residual 

15 ------ ---------- --------- ---------------- 

16 0 5.435 1.375 -1.167 

17 0.2 5.479 1.386 -0.8354 

18 0.667 5.625 1.422 1.513 

19 1.33 5.874 1.483 1.789 

20 6.67 8.524 2.127 -0.211 

21 20 16.86 4.118 -1.391 

22 66.7 49.42 11.67 1.642 

23 200 119.4 27.42 -1.705 

24 667 168.6 38.31 -0.7095 

25 1670 169.6 38.52 0.6454 

26 6670 169.6 38.52 1.009 

27 

28 

29 

30 Other models for which likelihoods are calculated: 

31 

32 Model A1: Yij = Mu(i) + e(ij) 

33 Var{e(ij)} = Sigma^2 

34 

35 Model A2: Yij = Mu(i) + e(ij) 

36 Var{e(ij)} = Sigma(i)^2 

37 

38 Model A3: Yij = Mu(i) + e(ij) 

39 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

40 

41 Model R: Yij = Mu + e(i) 

42 Var{e(ij)} = Sigma^2 

43 

44 

45 Likelihoods of Interest 

46 

47 Model Log(likelihood) DF AIC 

48 ------- ----------------- ---- ------------ 

49 A1 -158.1306 12 340.2613 

50 A2 -84.80028 22 213.6006 

51 A3 -98.82189 13 223.6438 

52 R -234.6252 2 473.2504 

53 5 -107.1994 6 226.3987 

54 

55 

56 Additive constant for all log-likelihoods = -45.03. This constant added to the 

57 above values gives the log-likelihood including the term that does not 

58 depend on the model parameters. 

59 

60 

61 Explanation of Tests 

62 

63 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

64 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

65 Test 3: Are variances adequately modeled? (A2 vs. A3) 

66 

67 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

68 

69 

70 Tests of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-171 —DO NOT CITE OR QUOTE 

1 

2 Test -2*log(Likelihood Ratio) D. F. p-value 

3 -------- ------------------------ ------ -------------- 

4 Test 1 299.6 20 < 0.0001 

5 Test 2 146.7 10 < 0.0001 

6 Test 3 28.04 9 0.0009381 

7 Test 7a 16.75 7 0.01905 

8 

9 

10 The p-value for Test 1 is less than .05. There appears to be a 

11 difference between response and/or variances among the dose 

12 levels, it seems appropriate to model the data. 

13 

14 The p-value for Test 2 is less than .1. A non-homogeneous 

15 variance model appears to be appropriate. 

16 

17 The p-value for Test 3 is less than .1. You may want to 

18 consider a different variance model. 

19 

20 The p-value for Test 7a is less than .1. Model 5 may not adequately 

21 describe the data; you may want to consider another model. 

22 

23 

24 Benchmark Dose Computations: 

25 

26 Specified Effect = 1.000000 

27 

28 Risk Type = Estimated standard deviations from control 

29 

30 Confidence Level = 0.950000 

31 

32 BMD = 3.41185 

33 

34 BMDL = 1.60436 

35 

36 

37 

38 H.3.4.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

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 200

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 0 1000 2000 3000 4000 5000 6000 7000

Mean Response

dose

Hill Model

14:27 11/20 2009

BMD

Hill

39 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-172 —DO NOT CITE OR QUOTE 

 1 

2 H.3.4.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 3 

4 

5 ==================================================================== 

6 Hill Model. (Version: 2.14; Date: 06/26/2008) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_BaP_hydro_act.(d) 

8 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_BaP_hydro_act.plt 

9 Fri Nov 20 14:27:04 2009 

10 ==================================================================== 

11 

12 Kitchin 1979, Tbl3, BaP hydrolase activity 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function is: 

16 

17 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

18 

19 

20 Dependent variable = Mean 

21 Independent variable = Dose 

22 Power parameter is not restricted 

23 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

24 

25 Total number of dose groups = 11 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 

32 

33 Default Initial Parameter Values 

34 lalpha = 5.70855 

35 rho = 0 

36 intercept = 4.9 

37 v = 184.1 

38 n = 18 

39 k = 1126.48 

40 

41 

42 Asymptotic Correlation Matrix of Parameter Estimates 

43 

44 lalpha rho intercept v n k 

45 

46 lalpha NA NA NA NA NA NA 

47 

48 rho NA NA NA NA NA NA 

49 

50 intercept NA NA 1 -0.012 NA NA 

51 

52 v NA NA -0.012 1 NA NA 

53 

54 n NA NA NA NA NA NA 

55 

56 k NA NA NA NA NA NA 

57 

58 

59 NA - This parameter's variance has been estimated as zero or less. 

60 THE MODEL HAS PROBABLY NOT CONVERGED!!! 

61 

62 

63 

64 Parameter Estimates 

65 

66 95.0% Wald Confidence Interval 

67 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

68 lalpha 8.0472 NA NA NA 

69 rho -0.0780259 NA NA NA 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-173 —DO NOT CITE OR QUOTE 

1 intercept -1.52215e-006 NA NA NA 

2 v 185.167 NA NA NA 

3 n 17.9979 NA NA NA 

4 k 117036 NA NA NA 

5 

6 At least some variance estimates are negative. 

7 THIS USUALLY MEANS THE MODEL HAS NOT CONVERGED! 

8 Try again from another starting point. 

9 

10 

11 

12 Table of Data and Estimated Values of Interest 

13 

14 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

15 ------ --- -------- -------- ----------- ----------- ---------- 

16 

17 0 9 4.9 -1.52e-006 1.11 94.3 0.156 

18 0.2 4 4.9 -1.52e-006 1.18 94.3 0.104 

19 0.667 4 6.7 -1.52e-006 1.4 94.3 0.142 

20 1.33 4 7.2 -1.52e-006 1.8 94.3 0.153 

21 6.67 4 8.3 -1.52e-006 0.26 94.3 0.176 

22 20 4 14 -1.52e-006 5 94.3 0.297 

23 66.7 4 59 -1.52e-006 6.8 94.3 1.25 

24 200 4 96 -1.52e-006 46 94.3 2.04 

25 667 4 155 -1.52e-006 16.4 94.3 3.29 

26 1670 4 182 -1.52e-006 26 94.3 3.86 

27 6670 4 189 -1.52e-006 26 94.3 4.01 

28 

29 

30 

31 Model Descriptions for likelihoods calculated 

32 

33 

34 Model A1: Yij = Mu(i) + e(ij) 

35 Var{e(ij)} = Sigma^2 

36 

37 Model A2: Yij = Mu(i) + e(ij) 

38 Var{e(ij)} = Sigma(i)^2 

39 

40 Model A3: Yij = Mu(i) + e(ij) 

41 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

42 Model A3 uses any fixed variance parameters that 

43 were specified by the user 

44 

45 Model R: Yi = Mu + e(i) 

46 Var{e(i)} = Sigma^2 

47 

48 

49 Likelihoods of Interest 

50 

51 Model Log(likelihood) # Param's AIC 

52 A1 -158.130647 12 340.261294 

53 A2 -84.800279 22 213.600558 

54 A3 -98.821893 13 223.643786 

55 fitted -247.263464 6 506.526928 

56 R -234.625213 2 473.250426 

57 

58 

59 Explanation of Tests 

60 

61 Test 1: Do responses and/or variances differ among Dose levels? 

62 (A2 vs. R) 

63 Test 2: Are Variances Homogeneous? (A1 vs A2) 

64 Test 3: Are variances adequately modeled? (A2 vs. A3) 

65 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

66 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

67 

68 Tests of Interest 

69 

70 Test -2*log(Likelihood Ratio) Test df p-value 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-174 —DO NOT CITE OR QUOTE 

1 

2 Test 1 299.65 20 <.0001 

3 Test 2 146.661 10 <.0001 

4 Test 3 28.0432 9 0.0009381 

5 Test 4 296.883 7 <.0001 

6 

7 The p-value for Test 1 is less than .05. There appears to be a 

8 difference between response and/or variances among the dose levels 

9 It seems appropriate to model the data 

10 

11 The p-value for Test 2 is less than .1. A non-homogeneous variance 

12 model appears to be appropriate 

13 

14 The p-value for Test 3 is less than .1. You may want to consider a 

15 different variance model 

16 

17 The p-value for Test 4 is less than .1. You may want to try a different 

18 model 

19 

20 

21 Benchmark Dose Computation 

22 

23 Specified effect = 1 

24 

25 Risk Type = Estimated standard deviations from the control mean 

26 

27 Confidence level = 0.95 

28 

29 BMD = 1.#QNAN 

30 

31 

32 BMDL computation failed. 

33 

34 

35 

36 H.3.4.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

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 200

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 0 1000 2000 3000 4000 5000 6000 7000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:27 11/20 2009

BMDBMDL

 

Power

37 

 38 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-175 —DO NOT CITE OR QUOTE 

1 H.3.4.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

2 Unrestricted

3 

4 

5 ==================================================================== 

6 Power Model. (Version: 2.15; Date: 04/07/2008) 

7 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_BaP_hydro_act.(d) 

8 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_BaP_hydro_act.plt 

9 Fri Nov 20 14:27:04 2009 

10 ==================================================================== 

11 

12 Kitchin 1979, Tbl3, BaP hydrolase activity 

13 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

14 

15 The form of the response function is: 

16 

17 Y[dose] = control + slope * dose^power 

18 

19 

20 Dependent variable = Mean 

21 Independent variable = Dose 

22 The power is not restricted 

23 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

24 

25 Total number of dose groups = 11 

26 Total number of records with missing values = 0 

27 Maximum number of iterations = 250 

28 Relative Function Convergence has been set to: 1e-008 

29 Parameter Convergence has been set to: 1e-008 

30 

31 

32 

33 Default Initial Parameter Values 

34 lalpha = 5.70855 

35 rho = 0 

36 control = 4.9 

37 slope = 0.984853 

38 power = 0.59404 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 lalpha rho control slope power 

44 

45 lalpha 1 -0.9 -0.45 0.26 -0.23 

46 

47 rho -0.9 1 0.35 -0.24 0.12 

48 

49 control -0.45 0.35 1 -0.45 0.42 

50 

51 slope 0.26 -0.24 -0.45 1 -0.92 

52 

53 power -0.23 0.12 0.42 -0.92 1 

54 

55 

56 

57 Parameter Estimates 

58 

59 95.0% Wald Confidence Interval 

60 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

61 lalpha -3.42083 0.570828 -4.53963 -2.30202 

62 rho 2.42943 0.164289 2.10743 2.75143 

63 control 4.52619 0.315826 3.90719 5.1452 

64 slope 2.4104 0.540821 1.35041 3.47039 

65 power 0.619986 0.0482232 0.525471 0.714502 

66 

67 

68 

69 Table of Data and Estimated Values of Interest 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-176 —DO NOT CITE OR QUOTE 

1 

2 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

3 ------ --- -------- -------- ----------- ----------- ---------- 

4 

5 0 9 4.9 4.53 1.11 1.13 0.991 

6 0.2 4 4.9 5.41 1.18 1.41 -0.732 

7 0.667 4 6.7 6.4 1.4 1.72 0.346 

8 1.33 4 7.2 7.4 1.8 2.06 -0.197 

9 6.67 4 8.3 12.3 0.26 3.83 -2.11 

10 20 4 14 20 5 6.87 -1.74 

11 66.7 4 59 37.1 6.8 14.6 3 

12 200 4 96 68.9 46 30.9 1.75 

13 667 4 155 140 16.4 73.4 0.399 

14 1670 4 182 244 26 144 -0.868 

15 6670 4 189 571 26 403 -1.89 

16 

17 

18 

19 Model Descriptions for likelihoods calculated 

20 

21 

22 Model A1: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma^2 

24 

25 Model A2: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = Sigma(i)^2 

27 

28 Model A3: Yij = Mu(i) + e(ij) 

29 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

30 Model A3 uses any fixed variance parameters that 

31 were specified by the user 

32 

33 Model R: Yi = Mu + e(i) 

34 Var{e(i)} = Sigma^2 

35 

36 

37 Likelihoods of Interest 

38 

39 Model Log(likelihood) # Param's AIC 

40 A1 -158.130647 12 340.261294 

41 A2 -84.800279 22 213.600558 

42 A3 -98.821893 13 223.643786 

43 fitted -130.616947 5 271.233893 

44 R -234.625213 2 473.250426 

45 

46 

47 Explanation of Tests 

48 

49 Test 1: Do responses and/or variances differ among Dose levels? 

50 (A2 vs. R) 

51 Test 2: Are Variances Homogeneous? (A1 vs A2) 

52 Test 3: Are variances adequately modeled? (A2 vs. A3) 

53 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

54 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

55 

56 Tests of Interest 

57 

58 Test -2*log(Likelihood Ratio) Test df p-value 

59 

60 Test 1 299.65 20 <.0001 

61 Test 2 146.661 10 <.0001 

62 Test 3 28.0432 9 0.0009381 

63 Test 4 63.5901 8 <.0001 

64 

65 The p-value for Test 1 is less than .05. There appears to be a 

66 difference between response and/or variances among the dose levels 

67 It seems appropriate to model the data 

68 

69 The p-value for Test 2 is less than .1. A non-homogeneous variance 

70 model appears to be appropriate 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-177 —DO NOT CITE OR QUOTE 

1 

2 The p-value for Test 3 is less than .1. You may want to consider a 

3 different variance model 

4 

5 The p-value for Test 4 is less than .1. You may want to try a different 

6 model 

7 

8 

9 Benchmark Dose Computation 

10 

11 Specified effect = 1 

12 

13 Risk Type = Estimated standard deviations from the control mean 

14 

15 Confidence level = 0.95 

16 

17 BMD = 0.29535 

18 

19 

20 BMDL = 0.12727 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 H.3.5. National Toxicology Program. (2006): EROD Liver Week 53 

33 H.3.5.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 121.00 <0.0001 210.78 5.7E+01 4.0E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 121.00 <0.0001 210.78 5.7E+01 4.0E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 7.05 0.07 98.86 2.7E-01 1.9E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 6.44 0.04 100.25 3.4E-01 2.0E-01 nonconstant variance, 

power restricted ≥1 

Hill c 2 <.0001 3.05 0.22 96.86 5.4E-01 3.3E-01 nonconstant variance, 

n restricted >1 

Hill d 2 <.0001 3.05 0.22 96.86 5.4E-01 3.3E-01 nonconstant variance, n 

unrestricted 

linear 4 <.0001 113.79 <.0001 203.61 2.9E+01 1.1E+01 nonconstant variance 

polynomial 4 <.0001 113.79 <.0001 203.61 2.9E+01 1.1E+01 nonconstant variance 

power 4 <.0001 113.79 <.0001 203.61 2.9E+01 1.1E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

exponential (M2) 4 <0.0001 85.26 <0.0001 209.43 5.0E+01 4.1E+01 constant variance, power 

restricted ≥1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-178 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M3) 4 <0.0001 85.26 <0.0001 209.43 5.0E+01 4.1E+01 constant variance, power 

restricted ≥1 

exponential (M4) 3 <0.0001 4.50 0.21 130.67 1.5E+00 1.2E+00 constant variance, power 

restricted ≥1 

exponential (M5) 3 <0.0001 4.50 0.21 130.67 1.5E+00 1.2E+00 constant variance, power 

restricted ≥1 

Hill 2 <.0001 2.30 0.32 130.48 1.7E+00 9.3E-01 constant variance, n 

restricted >1 

Hill 2 <.0001 2.30 0.32 130.48 1.7E+00 9.3E-01 constant variance, n 

unrestricted 

linear 4 <.0001 77.49 <.0001 201.66 3.2E+01 2.5E+01 constant variance 

polynomial 4 <.0001 77.49 <.0001 201.66 3.2E+01 2.5E+01 constant variance 

power 4 <.0001 77.49 <.0001 201.66 3.2E+01 2.5E+01 constant variance, power 

restricted ≥1, bound hit 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.5.2. Figure for Selected Model: Hill, Nonconstant Variance, n Restricted >1 

 5

 10

 15

 20

 25

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

16:50 11/20 2009

BMDLBMD

 

Hill

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-179 —DO NOT CITE OR QUOTE 

1 H.3.5.3. Output File for Selected Model: Hill, Nonconstant Variance, n Restricted >1 2 

3 

4 ==================================================================== 

5 Hill Model. (Version: 2.14; Date: 06/26/2008) 

6 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_BMR1_Tbl12_wk53_EROD_liv.(d) 

7 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_BMR1_Tbl12_wk53_EROD_liv.plt 

8 Fri Nov 20 16:50:09 2009 

9 ==================================================================== 

10 

11 0 

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

13 

14 The form of the response function is: 

15 

16 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

17 

18 

19 Dependent variable = Mean 

20 Independent variable = Dose 

21 Power parameter restricted to be greater than 1 

22 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

23 

24 Total number of dose groups = 6 

25 Total number of records with missing values = 0 

26 Maximum number of iterations = 250 

27 Relative Function Convergence has been set to: 1e-008 

28 Parameter Convergence has been set to: 1e-008 

29 

30 

31 

32 Default Initial Parameter Values 

33 lalpha = 1.59547 

34 rho = 0 

35 intercept = 3.614 

36 v = 17.599 

37 n = 1.38584 

38 k = 12.1933 

39 

40 

41 Asymptotic Correlation Matrix of Parameter Estimates 

42 

43 lalpha rho intercept v n k 

44 

45 lalpha 1 -0.96 -0.16 0.086 -0.057 0.041 

46 

47 rho -0.96 1 0.14 -0.11 0.06 -0.045 

48 

49 intercept -0.16 0.14 1 -0.18 0.13 0.069 

50 

51 v 0.086 -0.11 -0.18 1 -0.72 0.84 

52 

53 n -0.057 0.06 0.13 -0.72 1 -0.79 

54 

55 k 0.041 -0.045 0.069 0.84 -0.79 1 

56 

57 

58 

59 Parameter Estimates 

60 

61 95.0% Wald Confidence Interval 

62 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

63 lalpha -4.86544 0.741662 -6.31907 -3.4118 

64 rho 2.26969 0.287261 1.70667 2.83271 

65 intercept 3.62908 0.133826 3.36679 3.89138 

66 v 17.9785 0.989021 16.0401 19.917 

67 n 1.43249 0.162632 1.11374 1.75124 

68 k 7.81956 1.00384 5.85206 9.78706 

69 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-180 —DO NOT CITE OR QUOTE 

1 

2 

3 Table of Data and Estimated Values of Interest 

4 

5 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

6 ------ --- -------- -------- ----------- ----------- ---------- 

7 

8 0 8 3.61 3.63 0.486 0.379 -0.113 

9 3 8 7.27 7.27 0.557 0.833 0.0201 

10 10 8 14.8 14.2 1.61 1.78 0.912 

11 22 8 17.3 18.3 1.59 2.37 -1.19 

12 46 8 20.6 20.3 3.05 2.67 0.306 

13 100 8 21.2 21.2 3.82 2.8 0.061 

14 

15 

16 

17 Model Descriptions for likelihoods calculated 

18 

19 

20 Model A1: Yij = Mu(i) + e(ij) 

21 Var{e(ij)} = Sigma^2 

22 

23 Model A2: Yij = Mu(i) + e(ij) 

24 Var{e(ij)} = Sigma(i)^2 

25 

26 Model A3: Yij = Mu(i) + e(ij) 

27 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

28 Model A3 uses any fixed variance parameters that 

29 were specified by the user 

30 

31 Model R: Yi = Mu + e(i) 

32 Var{e(i)} = Sigma^2 

33 

34 

35 Likelihoods of Interest 

36 

37 Model Log(likelihood) # Param's AIC 

38 A1 -59.086537 7 132.173073 

39 A2 -37.515858 12 99.031716 

40 A3 -40.906180 8 97.812359 

41 fitted -42.430348 6 96.860697 

42 R -116.710291 2 237.420582 

43 

44 

45 Explanation of Tests 

46 

47 Test 1: Do responses and/or variances differ among Dose levels? 

48 (A2 vs. R) 

49 Test 2: Are Variances Homogeneous? (A1 vs A2) 

50 Test 3: Are variances adequately modeled? (A2 vs. A3) 

51 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

52 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

53 

54 Tests of Interest 

55 

56 Test -2*log(Likelihood Ratio) Test df p-value 

57 

58 Test 1 158.389 10 <.0001 

59 Test 2 43.1414 5 <.0001 

60 Test 3 6.78064 4 0.1479 

61 Test 4 3.04834 2 0.2178 

62 

63 The p-value for Test 1 is less than .05. There appears to be a 

64 difference between response and/or variances among the dose levels 

65 It seems appropriate to model the data 

66 

67 The p-value for Test 2 is less than .1. A non-homogeneous variance 

68 model appears to be appropriate 

69 

70 The p-value for Test 3 is greater than .1. The modeled variance appears 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-181 —DO NOT CITE OR QUOTE 

1 to be appropriate here 

2 

3 The p-value for Test 4 is greater than .1. The model chosen seems 

4 to adequately describe the data 

5 

6 

7 Benchmark Dose Computation 

8 

9 Specified effect = 1 

10 

11 Risk Type = Estimated standard deviations from the control mean 

12 

13 Confidence level = 0.95 

14 

15 BMD = 0.536614 

16 

17 BMDL = 0.328003 

18 

19 

20 H.3.5.4. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 5

 10

 15

 20

 25

 0 20 40 60 80 100

Mean Response

dose

Hill Model with 0.95 Confidence Level

16:50 11/20 2009

BMDLBMD

 

Hill

21 

 22 

 23 

24 H.3.5.5. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 25 

26 

27 ==================================================================== 

28 Hill Model. (Version: 2.14; Date: 06/26/2008) 

29 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_Tbl12_wk53_EROD_liv.(d) 

30 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_Tbl12_wk53_EROD_liv.plt 

31 Fri Nov 20 16:50:14 2009 

32 ==================================================================== 

33 

34 0 

35 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

36 

37 The form of the response function is: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-182 —DO NOT CITE OR QUOTE 

1 

2 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

3 

4 

5 Dependent variable = Mean 

6 Independent variable = Dose 

7 Power parameter is not restricted 

8 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

9 

10 Total number of dose groups = 6 

11 Total number of records with missing values = 0 

12 Maximum number of iterations = 250 

13 Relative Function Convergence has been set to: 1e-008 

14 Parameter Convergence has been set to: 1e-008 

15 

16 

17 

18 Default Initial Parameter Values 

19 lalpha = 1.59547 

20 rho = 0 

21 intercept = 3.614 

22 v = 17.599 

23 n = 1.38584 

24 k = 12.1933 

25 

26 

27 Asymptotic Correlation Matrix of Parameter Estimates 

28 

29 lalpha rho intercept v n k 

30 

31 lalpha 1 -0.96 -0.16 0.086 -0.057 0.041 

32 

33 rho -0.96 1 0.14 -0.11 0.06 -0.045 

34 

35 intercept -0.16 0.14 1 -0.18 0.13 0.069 

36 

37 v 0.086 -0.11 -0.18 1 -0.72 0.84 

38 

39 n -0.057 0.06 0.13 -0.72 1 -0.79 

40 

41 k 0.041 -0.045 0.069 0.84 -0.79 1 

42 

43 

44 

45 Parameter Estimates 

46 

47 95.0% Wald Confidence Interval 

48 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

49 lalpha -4.86544 0.741662 -6.31907 -3.4118 

50 rho 2.26969 0.287261 1.70667 2.83271 

51 intercept 3.62908 0.133826 3.36679 3.89138 

52 v 17.9785 0.989021 16.0401 19.917 

53 n 1.43249 0.162632 1.11374 1.75124 

54 k 7.81956 1.00384 5.85206 9.78706 

55 

56 

57 

58 Table of Data and Estimated Values of Interest 

59 

60 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

61 ------ --- -------- -------- ----------- ----------- ---------- 

62 

63 0 8 3.61 3.63 0.486 0.379 -0.113 

64 3 8 7.27 7.27 0.557 0.833 0.0201 

65 10 8 14.8 14.2 1.61 1.78 0.912 

66 22 8 17.3 18.3 1.59 2.37 -1.19 

67 46 8 20.6 20.3 3.05 2.67 0.306 

68 100 8 21.2 21.2 3.82 2.8 0.061 

69 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-183 —DO NOT CITE OR QUOTE 

1 

2 Model Descriptions for likelihoods calculated 

3 

4 

5 Model A1: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma^2 

7 

8 Model A2: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = Sigma(i)^2 

10 

11 Model A3: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

13 Model A3 uses any fixed variance parameters that 

14 were specified by the user 

15 

16 Model R: Yi = Mu + e(i) 

17 Var{e(i)} = Sigma^2 

18 

19 

20 Likelihoods of Interest 

21 

22 Model Log(likelihood) # Param's AIC 

23 A1 -59.086537 7 132.173073 

24 A2 -37.515858 12 99.031716 

25 A3 -40.906180 8 97.812359 

26 fitted -42.430348 6 96.860697 

27 R -116.710291 2 237.420582 

28 

29 

30 Explanation of Tests 

31 

32 Test 1: Do responses and/or variances differ among Dose levels? 

33 (A2 vs. R) 

34 Test 2: Are Variances Homogeneous? (A1 vs A2) 

35 Test 3: Are variances adequately modeled? (A2 vs. A3) 

36 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

37 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

38 

39 Tests of Interest 

40 

41 Test -2*log(Likelihood Ratio) Test df p-value 

42 

43 Test 1 158.389 10 <.0001 

44 Test 2 43.1414 5 <.0001 

45 Test 3 6.78064 4 0.1479 

46 Test 4 3.04834 2 0.2178 

47 

48 The p-value for Test 1 is less than .05. There appears to be a 

49 difference between response and/or variances among the dose levels 

50 It seems appropriate to model the data 

51 

52 The p-value for Test 2 is less than .1. A non-homogeneous variance 

53 model appears to be appropriate 

54 

55 The p-value for Test 3 is greater than .1. The modeled variance appears 

56 to be appropriate here 

57 

58 The p-value for Test 4 is greater than .1. The model chosen seems 

59 to adequately describe the data 

60 

61 

62 Benchmark Dose Computation 

63 

64 Specified effect = 1 

65 

66 Risk Type = Estimated standard deviations from the control mean 

67 

68 Confidence level = 0.95 

69 

70 BMD = 0.536614 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-184 —DO NOT CITE OR QUOTE 

1 

2 BMDL = 0.328003 

3 

4 

5 H.3.6. National Toxicology Program. (2006): Lung EROD Week 31 

6 H.3.6.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 129.30 <0.0001 396.45 8.9E+01 6.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 129.30 <0.0001 396.45 8.9E+01 6.2E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 20.80 0.00 289.99 1.0E-01 6.9E-02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 20.80 0.00 289.99 1.0E-01 6.9E-02 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 <0.0001 20.80 0.00 289.99 1.0E-01 6.9E-02 nonconstant variance, 

power unrestricted 

Hill 3 <.0001 78.84 <.0001 348.02 9.6E+00 error nonconstant variance, n 

restricted >1, bound hit 

Hill d 3 <.0001 78.84 <.0001 348.02 9.6E+00 error nonconstant variance, n 

unrestricted 

linear 4 <.0001 125.96 <.0001 393.15 6.3E+01 3.1E+01 nonconstant variance 

polynomial 4 <.0001 128.35 <.0001 395.53 1.0E+02 2.3E+01 nonconstant variance 

power 4 <.0001 125.96 <.0001 393.15 6.3E+01 3.1E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 22.50 <.0001 291.68 1.9E-06 1.9E-06 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 87.28 <0.0001 397.44 6.6E+01 5.3E+01 constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 87.28 <0.0001 397.44 6.6E+01 5.3E+01 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 15.56 0.00 327.72 1.7E+00 1.2E+00 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 15.56 0.00 327.72 1.7E+00 1.2E+00 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 15.56 0.00 327.72 1.7E+00 1.2E+00 constant variance, 

power unrestricted 

Hill 2 <.0001 34.01 <.0001 348.17 2.8E+00 2.4E-01 constant variance, n 

restricted >1 

Hill 2 <.0001 34.01 <.0001 348.17 2.8E+00 5.0E-05 constant variance, n 

unrestricted 

linear 4 <.0001 81.72 <.0001 391.88 4.6E+01 3.5E+01 constant variance 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-185 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

polynomial 4 <.0001 81.72 <.0001 391.88 4.6E+01 3.5E+01 constant variance 

power 4 <.0001 81.72 <.0001 391.88 4.6E+01 3.5E+01 

constant variance, 

power restricted ≥1, 

bound hit 

power 3 <.0001 22.22 <.0001 334.38 1.0E-02 6.9E-04 constant variance, 

power unrestricted 

a

Values < 0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be 

selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.6.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 10

 20

 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:28 11/20 2009

BMDBMDL

 

Exponential

5 

 6 

 7 

8 H.3.6.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_Lung_EROD_wk31.(d) 

15 Gnuplot Plotting File: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-186 —DO NOT CITE OR QUOTE 

1 Fri Nov 20 14:28:10 2009 

2 ==================================================================== 

3 

4 Tbl 12, Week 31, Lung Microsomes EROD 

5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

6 

7 The form of the response function by Model: 

8 Model 2: Y[dose] = a * exp{sign * b * dose} 

9 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

10 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

11 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

12 

13 Note: Y[dose] is the median response for exposure = dose; 

14 sign = +1 for increasing trend in data; 

15 sign = -1 for decreasing trend. 

16 

17 Model 2 is nested within Models 3 and 4. 

18 Model 3 is nested within Model 5. 

19 Model 4 is nested within Model 5. 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 Data are assumed to be distributed: normally 

25 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 MLE solution provided: Exact 

35 

36 

37 Initial Parameter Values 

38 

39 Variable Model 4 

40 -------- -------- 

41 lnalpha -1.42653 

42 rho 1.46168 

43 a 1.96745 

44 b 0.034997 

45 c 26.7857 

46 d 1 

47 

48 

49 

50 Parameter Estimates 

51 

52 Variable Model 4 

53 -------- ------- 

54 lnalpha -1.46439 

55 rho 1.61106 

56 a 2.12443 

57 b 0.19145 

58 c 22.311 

59 d 1 

60 

61 

62 Table of Stats From Input Data 

63 

64 Dose N Obs Mean Obs Std Dev 

65 ----- --- ---------- ------------- 

66 0 10 2.071 0.9708 

67 3 10 25.34 2.549 

68 10 10 30.39 5.831 

69 22 10 50.19 8.68 

70 46 10 49.07 13.91 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-187 —DO NOT CITE OR QUOTE 

1 100 10 48.42 8.933 

2 

3 

4 Estimated Values of Interest 

5 

6 Dose Est Mean Est Std Scaled Residual 

7 ------ ---------- --------- ---------------- 

8 0 2.124 0.8823 -0.1915 

9 3 21.91 5.779 1.88 

10 10 40.72 9.524 -3.432 

11 22 46.73 10.64 1.029 

12 46 47.39 10.76 0.4921 

13 100 47.4 10.76 0.3006 

14 

15 

16 

17 Other models for which likelihoods are calculated: 

18 

19 Model A1: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = Sigma^2 

21 

22 Model A2: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma(i)^2 

24 

25 Model A3: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

27 

28 Model R: Yij = Mu + e(i) 

29 Var{e(ij)} = Sigma^2 

30 

31 

32 Likelihoods of Interest 

33 

34 Model Log(likelihood) DF AIC 

35 ------- ----------------- ---- ------------ 

36 A1 -152.0793 7 318.1586 

37 A2 -123.367 12 270.734 

38 A3 -129.5911 8 275.1823 

39 R -206.5175 2 417.0349 

40 4 -139.9927 5 289.9853 

41 

42 

43 Additive constant for all log-likelihoods = -55.14. This constant added to the 

44 above values gives the log-likelihood including the term that does not 

45 depend on the model parameters. 

46 

47 

48 Explanation of Tests 

49 

50 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

51 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

52 Test 3: Are variances adequately modeled? (A2 vs. A3) 

53 

54 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

55 

56 

57 Tests of Interest 

58 

59 Test -2*log(Likelihood Ratio) D. F. p-value 

60 -------- ------------------------ ------ -------------- 

61 Test 1 166.3 10 < 0.0001 

62 Test 2 57.42 5 < 0.0001 

63 Test 3 12.45 4 0.01431 

64 Test 6a 20.8 3 0.0001157 

65 

66 

67 The p-value for Test 1 is less than .05. There appears to be a 

68 difference between response and/or variances among the dose 

69 levels, it seems appropriate to model the data. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-188 —DO NOT CITE OR QUOTE 

1 The p-value for Test 2 is less than .1. A non-homogeneous 

2 variance model appears to be appropriate. 

3 

4 The p-value for Test 3 is less than .1. You may want to 

5 consider a different variance model. 

6 

7 The p-value for Test 6a is less than .1. Model 4 may not adequately 

8 describe the data; you may want to consider another model. 

9 

10 

11 Benchmark Dose Computations: 

12 

13 Specified Effect = 1.000000 

14 

15 Risk Type = Estimated standard deviations from control 

16 

17 Confidence Level = 0.950000 

18 

19 BMD = 0.102798 

20 

21 BMDL = 0.069311 

22 

23 

24 H.3.6.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

25 Unrestricted

 0

 10

 20

 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:28 11/20 2009

BMDBMDL

 

Exponential

26 

 27 

 28 

29 H.3.6.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

30 Power Unrestricted 

31 

32 

33 ==================================================================== 

34 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

35 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_Lung_EROD_wk31.(d) 

36 Gnuplot Plotting File: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-189 —DO NOT CITE OR QUOTE 

1 Fri Nov 20 14:28:17 2009 

2 ==================================================================== 

3 

4 Tbl 12, Week 31, Lung Microsomes EROD 

5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

6 

7 The form of the response function by Model: 

8 Model 2: Y[dose] = a * exp{sign * b * dose} 

9 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

10 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

11 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

12 

13 Note: Y[dose] is the median response for exposure = dose; 

14 sign = +1 for increasing trend in data; 

15 sign = -1 for decreasing trend. 

16 

17 Model 2 is nested within Models 3 and 4. 

18 Model 3 is nested within Model 5. 

19 Model 4 is nested within Model 5. 

20 

21 

22 Dependent variable = Mean 

23 Independent variable = Dose 

24 Data are assumed to be distributed: normally 

25 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

26 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

27 

28 Total number of dose groups = 6 

29 Total number of records with missing values = 0 

30 Maximum number of iterations = 250 

31 Relative Function Convergence has been set to: 1e-008 

32 Parameter Convergence has been set to: 1e-008 

33 

34 MLE solution provided: Exact 

35 

36 

37 Initial Parameter Values 

38 

39 Variable Model 5 

40 -------- -------- 

41 lnalpha -1.42653 

42 rho 1.46168 

43 a 1.96745 

44 b 0.034997 

45 c 26.7857 

46 d 1 

47 

48 

49 

50 Parameter Estimates 

51 

52 Variable Model 5 

53 -------- ------- 

54 lnalpha -1.46439 

55 rho 1.61106 

56 a 2.12443 

57 b 0.19145 

58 c 22.311 

59 d 1 

60 

61 

62 Table of Stats From Input Data 

63 

64 Dose N Obs Mean Obs Std Dev 

65 ----- --- ---------- ------------- 

66 0 10 2.071 0.9708 

67 3 10 25.34 2.549 

68 10 10 30.39 5.831 

69 22 10 50.19 8.68 

70 46 10 49.07 13.91 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-190 —DO NOT CITE OR QUOTE 

1 100 10 48.42 8.933 

2 

3 

4 Estimated Values of Interest 

5 

6 Dose Est Mean Est Std Scaled Residual 

7 ------ ---------- --------- ---------------- 

8 0 2.124 0.8823 -0.1915 

9 3 21.91 5.779 1.88 

10 10 40.72 9.524 -3.432 

11 22 46.73 10.64 1.029 

12 46 47.39 10.76 0.4921 

13 100 47.4 10.76 0.3006 

14 

15 

16 

17 Other models for which likelihoods are calculated: 

18 

19 Model A1: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = Sigma^2 

21 

22 Model A2: Yij = Mu(i) + e(ij) 

23 Var{e(ij)} = Sigma(i)^2 

24 

25 Model A3: Yij = Mu(i) + e(ij) 

26 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

27 

28 Model R: Yij = Mu + e(i) 

29 Var{e(ij)} = Sigma^2 

30 

31 

32 Likelihoods of Interest 

33 

34 Model Log(likelihood) DF AIC 

35 ------- ----------------- ---- ------------ 

36 A1 -152.0793 7 318.1586 

37 A2 -123.367 12 270.734 

38 A3 -129.5911 8 275.1823 

39 R -206.5175 2 417.0349 

40 5 -139.9927 5 289.9853 

41 

42 

43 Additive constant for all log-likelihoods = -55.14. This constant added to the 

44 above values gives the log-likelihood including the term that does not 

45 depend on the model parameters. 

46 

47 

48 Explanation of Tests 

49 

50 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

51 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

52 Test 3: Are variances adequately modeled? (A2 vs. A3) 

53 

54 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

55 

56 

57 Tests of Interest 

58 

59 Test -2*log(Likelihood Ratio) D. F. p-value 

60 -------- ------------------------ ------ -------------- 

61 Test 1 166.3 10 < 0.0001 

62 Test 2 57.42 5 < 0.0001 

63 Test 3 12.45 4 0.01431 

64 Test 7a 20.8 3 0.0001157 

65 

66 

67 The p-value for Test 1 is less than .05. There appears to be a 

68 difference between response and/or variances among the dose 

69 levels, it seems appropriate to model the data. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-191 —DO NOT CITE OR QUOTE 

1 The p-value for Test 2 is less than .1. A non-homogeneous 

2 variance model appears to be appropriate. 

3 

4 The p-value for Test 3 is less than .1. You may want to 

5 consider a different variance model. 

6 

7 The p-value for Test 7a is less than .1. Model 5 may not adequately 

8 describe the data; you may want to consider another model. 

9 

10 

11 Benchmark Dose Computations: 

12 

13 Specified Effect = 1.000000 

14 

15 Risk Type = Estimated standard deviations from control 

16 

17 Confidence Level = 0.950000 

18 

19 BMD = 0.102798 

20 

21 BMDL = 0.0693109 

22 

23 

24 H.3.6.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 10

 20

 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Hill Model

14:28 11/20 2009

BMD

Hill

25 

 26 

 27 

28 H.3.6.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 29 

30 

31 ==================================================================== 

32 Hill Model. (Version: 2.14; Date: 06/26/2008) 

33 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_Lung_EROD_wk31.(d) 

34 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_Lung_EROD_wk31.plt 

35 Fri Nov 20 14:28:19 2009 

36 ==================================================================== 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-192 —DO NOT CITE OR QUOTE 

1 Tbl 12, Week 31, Lung Microsomes EROD 

2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

3 

4 The form of the response function is: 

5 

6 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

7 

8 

9 Dependent variable = Mean 

10 Independent variable = Dose 

11 Power parameter is not restricted 

12 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

13 

14 Total number of dose groups = 6 

15 Total number of records with missing values = 0 

16 Maximum number of iterations = 250 

17 Relative Function Convergence has been set to: 1e-008 

18 Parameter Convergence has been set to: 1e-008 

19 

20 

21 

22 Default Initial Parameter Values 

23 lalpha = 4.17467 

24 rho = 0 

25 intercept = 2.071 

26 v = 48.119 

27 n = 18 

28 k = 15.9059 

29 

30 

31 Asymptotic Correlation Matrix of Parameter Estimates 

32 

33 ( *** The model parameter(s) -n 

34 have been estimated at a boundary point, or have been specified by the user, 

35 and do not appear in the correlation matrix ) 

36 

37 lalpha rho intercept v k 

38 

39 lalpha 1 -0.98 0.04 -0.054 -0.092 

40 

41 rho -0.98 1 -0.027 0.046 0.096 

42 

43 intercept 0.04 -0.027 1 -0.82 0.36 

44 

45 v -0.054 0.046 -0.82 1 -0.16 

46 

47 k -0.092 0.096 0.36 -0.16 1 

48 

49 

50 

51 Parameter Estimates 

52 

53 95.0% Wald Confidence Interval 

54 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

55 lalpha 5.40756 1.03169 3.38548 7.42964 

56 rho -0.228427 0.299513 -0.815462 0.358608 

57 intercept 13.5736 2.48089 8.71112 18.436 

58 v 35.6207 3.03486 29.6725 41.5689 

59 n 18 NA 

60 k 10.0457 0.22238 9.60987 10.4816 

61 

62 NA - Indicates that this parameter has hit a bound 

63 implied by some inequality constraint and thus 

64 has no standard error. 

65 

66 

67 Table of Data and Estimated Values of Interest 

68 

69 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

70 ------ --- -------- -------- ----------- ----------- ---------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-193 —DO NOT CITE OR QUOTE 

1 

2 0 10 2.07 13.6 0.971 11.1 -3.28 

3 3 10 25.3 13.6 2.55 11.1 3.36 

4 10 10 30.4 30.7 5.83 10.1 -0.0833 

5 22 10 50.2 49.2 8.68 9.57 0.329 

6 46 10 49.1 49.2 13.9 9.57 -0.0424 

7 100 10 48.4 49.2 8.93 9.57 -0.255 

8 

9 

10 Model Descriptions for likelihoods calculated 

11 

12 

13 Model A1: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma^2 

15 

16 Model A2: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma(i)^2 

18 

19 Model A3: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

21 Model A3 uses any fixed variance parameters that 

22 were specified by the user 

23 

24 Model R: Yi = Mu + e(i) 

25 Var{e(i)} = Sigma^2 

26 

27 

28 Likelihoods of Interest 

29 

30 Model Log(likelihood) # Param's AIC 

31 A1 -152.079318 7 318.158637 

32 A2 -123.366985 12 270.733969 

33 A3 -129.591134 8 275.182269 

34 fitted -169.011448 5 348.022896 

35 R -206.517459 2 417.034919 

36 

37 

38 Explanation of Tests 

39 

40 Test 1: Do responses and/or variances differ among Dose levels? 

41 (A2 vs. R) 

42 Test 2: Are Variances Homogeneous? (A1 vs A2) 

43 Test 3: Are variances adequately modeled? (A2 vs. A3) 

44 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

45 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

46 

47 Tests of Interest 

48 

49 Test -2*log(Likelihood Ratio) Test df p-value 

50 

51 Test 1 166.301 10 <.0001 

52 Test 2 57.4247 5 <.0001 

53 Test 3 12.4483 4 0.01431 

54 Test 4 78.8406 3 <.0001 

55 

56 The p-value for Test 1 is less than .05. There appears to be a 

57 difference between response and/or variances among the dose levels 

58 It seems appropriate to model the data 

59 

60 The p-value for Test 2 is less than .1. A non-homogeneous variance 

61 model appears to be appropriate 

62 

63 The p-value for Test 3 is less than .1. You may want to consider a 

64 different variance model 

65 

66 The p-value for Test 4 is less than .1. You may want to try a different 

67 model 

68 

69 

70 Benchmark Dose Computation 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-194 —DO NOT CITE OR QUOTE 

1 

2 Specified effect = 1 

3 

4 Risk Type = Estimated standard deviations from the control mean 

5 

6 Confidence level = 0.95 

7 

8 BMD = 9.61218 

9 

10 

11 BMDL computation failed. 

12 

13 

14 H.3.6.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 10

 20

 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Power Model with 0.95 Confidence Level

14:28 11/20 2009

BMDBMDL

 

Power

15 

 16 

 17 

18 H.3.6.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

19 Unrestricted

20 

21 

22 ==================================================================== 

23 Power Model. (Version: 2.15; Date: 04/07/2008) 

24 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_Lung_EROD_wk31.(d) 

25 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_Lung_EROD_wk31.plt 

26 Fri Nov 20 14:28:19 2009 

27 ==================================================================== 

28 

29 Tbl 12, Week 31, Lung Microsomes EROD 

30 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

31 

32 The form of the response function is: 

33 

34 Y[dose] = control + slope * dose^power 

35 

36 

37 Dependent variable = Mean 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-195 —DO NOT CITE OR QUOTE 

1 Independent variable = Dose 

2 The power is not restricted 

3 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

4 

5 Total number of dose groups = 6 

6 Total number of records with missing values = 0 

7 Maximum number of iterations = 250 

8 Relative Function Convergence has been set to: 1e-008 

9 Parameter Convergence has been set to: 1e-008 

10 

11 

12 

13 Default Initial Parameter Values 

14 lalpha = 4.17467 

15 rho = 0 

16 control = 2.071 

17 slope = 18.9386 

18 power = 0.224076 

19 

20 

21 Asymptotic Correlation Matrix of Parameter Estimates 

22 

23 lalpha rho control slope power 

24 

25 lalpha 1 -0.94 -0.42 0.15 -0.13 

26 

27 rho -0.94 1 0.38 -0.19 0.14 

28 

29 control -0.42 0.38 1 -0.15 0.093 

30 

31 slope 0.15 -0.19 -0.15 1 -0.94 

32 

33 power -0.13 0.14 0.093 -0.94 1 

34 

35 

36 

37 Parameter Estimates 

38 

39 95.0% Wald Confidence Interval 

40 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

41 lalpha -1.53358 0.571219 -2.65315 -0.414007 

42 rho 1.6412 0.166321 1.31521 1.96718 

43 control 2.10983 0.270093 1.58046 2.6392 

44 slope 18.5389 2.01491 14.5897 22.488 

45 power 0.233238 0.0324661 0.169605 0.29687 

46 

47 

48 

49 Table of Data and Estimated Values of Interest 

50 

51 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

52 ------ --- -------- -------- ----------- ----------- ---------- 

53 

54 0 10 2.07 2.11 0.971 0.857 -0.143 

55 3 10 25.3 26.1 2.55 6.74 -0.338 

56 10 10 30.4 33.8 5.83 8.35 -1.3 

57 22 10 50.2 40.2 8.68 9.63 3.27 

58 46 10 49.1 47.4 13.9 11 0.481 

59 100 10 48.4 56.4 8.93 12.7 -1.98 

60 

61 

62 

63 Model Descriptions for likelihoods calculated 

64 

65 

66 Model A1: Yij = Mu(i) + e(ij) 

67 Var{e(ij)} = Sigma^2 

68 

69 Model A2: Yij = Mu(i) + e(ij) 

70 Var{e(ij)} = Sigma(i)^2 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-196 —DO NOT CITE OR QUOTE 

1 

2 Model A3: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

4 Model A3 uses any fixed variance parameters that 

5 were specified by the user 

6 

7 Model R: Yi = Mu + e(i) 

8 Var{e(i)} = Sigma^2 

9 

10 

11 Likelihoods of Interest 

12 

13 Model Log(likelihood) # Param's AIC 

14 A1 -152.079318 7 318.158637 

15 A2 -123.366985 12 270.733969 

16 A3 -129.591134 8 275.182269 

17 fitted -140.838955 5 291.677909 

18 R -206.517459 2 417.034919 

19 

20 

21 Explanation of Tests 

22 

23 Test 1: Do responses and/or variances differ among Dose levels? 

24 (A2 vs. R) 

25 Test 2: Are Variances Homogeneous? (A1 vs A2) 

26 Test 3: Are variances adequately modeled? (A2 vs. A3) 

27 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

28 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

29 

30 Tests of Interest 

31 

32 Test -2*log(Likelihood Ratio) Test df p-value 

33 

34 Test 1 166.301 10 <.0001 

35 Test 2 57.4247 5 <.0001 

36 Test 3 12.4483 4 0.01431 

37 Test 4 22.4956 3 <.0001 

38 

39 The p-value for Test 1 is less than .05. There appears to be a 

40 difference between response and/or variances among the dose levels 

41 It seems appropriate to model the data 

42 

43 The p-value for Test 2 is less than .1. A non-homogeneous variance 

44 model appears to be appropriate 

45 

46 The p-value for Test 3 is less than .1. You may want to consider a 

47 different variance model 

48 

49 The p-value for Test 4 is less than .1. You may want to try a different 

50 model 

51 

52 

53 Benchmark Dose Computation 

54 

55 Specified effect = 1 

56 

57 Risk Type = Estimated standard deviations from the control mean 

58 

59 Confidence level = 0.95 

60 

61 BMD = 1.88864e-006 

62 

63 

64 BMDL = 1.88864e-006 

65 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-197 —DO NOT CITE OR QUOTE 

1 H.3.7. National Toxicology Program. (2006): Lung EROD Week 53 

2 H.3.7.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 66.01 <0.0001 316.32 1.3E+02 8.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 66.01 <0.0001 316.32 1.3E+02 8.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 2.82 0.42 255.12 1.2E-01 7.5E-02 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 16.10 0.00 270.40 2.6E-01 1.5E-04 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 2 <0.0001 16.10 0.00 270.40 2.6E-01 1.5E-04 nonconstant variance, 

power unrestricted 

Hill 2 <.0001 81.88 <.0001 336.18 3.0E+02 error nonconstant variance, n 

restricted >1 

Hill d 2 <.0001 81.88 <.0001 336.18 3.0E+02 error nonconstant variance, n 

unrestricted 

linear 4 <.0001 65.65 <.0001 315.96 1.2E+02 6.3E+01 nonconstant variance 

polynomial 4 <.0001 65.65 <.0001 315.96 1.2E+02 6.3E+01 nonconstant variance 

power 4 <.0001 65.65 <.0001 315.96 1.2E+02 6.3E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 8.50 0.04 260.80 3.8E-10 3.8E-10 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 43.26 <0.0001 319.80 8.0E+01 6.0E+01 constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 43.26 <0.0001 319.80 8.0E+01 6.0E+01 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 3.04 0.39 281.57 9.2E-01 5.5E-01 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 2.71 0.26 283.24 2.2E+00 5.7E-01 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 2.71 0.26 283.24 2.2E+00 5.7E-01 constant variance, 

power unrestricted 

Hill 2 <.0001 2.71 0.26 283.24 2.7E+00 3.2E-01 constant variance, n 

restricted >1 

Hill 2 <.0001 2.71 0.26 283.24 2.7E+00 1.2E-02 constant variance, n 

unrestricted 

linear 4 <.0001 41.45 <.0001 317.99 6.5E+01 4.4E+01 constant variance 

polynomial 4 <.0001 41.45 <.0001 317.99 6.5E+01 4.4E+01 constant variance 

power 4 <.0001 41.45 <.0001 317.99 6.5E+01 4.4E+01 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-198 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 3 <.0001 5.93 0.11 284.47 5.3E-04 5.3E-04 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.7.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 10

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 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:29 11/20 2009

BMDLBMD

 

Exponential

5 

 6 

 7 

8 H.3.7.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_Lung_EROD_wk53.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 14:29:03 2009 

17 ==================================================================== 

18 

19 Tbl 12, Week 53, Lung Microsomes EROD 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-199 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 6 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 4 

33 -------- -------- 

34 lnalpha -0.80064 

35 rho 1.47683 

36 a 2.86045 

37 b 0.0390303 

38 c 16.0581 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 4 

46 -------- ------- 

47 lnalpha -1.07501 

48 rho 1.68859 

49 a 3.011 

50 b 3.22004 

51 c 12.8877 

52 d 18 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 8 3.011 1.584 

60 3 8 27.15 5.269 

61 10 8 42.85 11.15 

62 22 8 36.57 12.99 

63 46 8 43.75 18.55 

64 100 8 43.71 6.322 

65 

66 

67 Estimated Values of Interest 

68 

69 Dose Est Mean Est Std Scaled Residual 

70 ------ ---------- --------- ---------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-200 —DO NOT CITE OR QUOTE 

1 0 3.068 1.404 -0.1156 

2 3 26.26 8.088 0.3111 

3 10 40.44 11.5 0.5912 

4 22 42.43 11.96 -1.386 

5 46 42.49 11.98 0.2969 

6 100 42.49 11.98 0.2891 

7 

8 

9 

10 Other models for which likelihoods are calculated: 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

20 

21 Model R: Yij = Mu + e(i) 

22 Var{e(ij)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) DF AIC 

28 ------- ----------------- ---- ------------ 

29 A1 -135.2677 7 284.5353 

30 A2 -115.6885 12 255.3771 

31 A3 -121.1517 8 258.3034 

32 R -162.0902 2 328.1805 

33 4 -122.5608 5 255.1215 

34 

35 

36 Additive constant for all log-likelihoods = -44.11. This constant added to the 

37 above values gives the log-likelihood including the term that does not 

38 depend on the model parameters. 

39 

40 

41 Explanation of Tests 

42 

43 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

44 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

45 Test 3: Are variances adequately modeled? (A2 vs. A3) 

46 

47 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

48 

49 

50 Tests of Interest 

51 

52 Test -2*log(Likelihood Ratio) D. F. p-value 

53 -------- ------------------------ ------ -------------- 

54 Test 1 92.8 10 < 0.0001 

55 Test 2 39.16 5 < 0.0001 

56 Test 3 10.93 4 0.0274 

57 Test 6a 2.818 3 0.4205 

58 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose 

62 levels, it seems appropriate to model the data. 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous 

65 variance model appears to be appropriate. 

66 

67 The p-value for Test 3 is less than .1. You may want to 

68 consider a different variance model. 

69 

70 The p-value for Test 6a is greater than .1. Model 4 seems 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-201 —DO NOT CITE OR QUOTE 

1 to adequately describe the data. 

2 

3 

4 Benchmark Dose Computations: 

5 

6 Specified Effect = 1.000000 

7 

8 Risk Type = Estimated standard deviations from control 

9 

10 Confidence Level = 0.950000 

11 

12 BMD = 0.122595 

13 

14 BMDL = 0.0752795 

15 

16 

17 

18 H.3.7.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

19 Unrestricted

 0

 10

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 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:29 11/20 2009

BMDLBMD

 

Exponential

20 

 21 

 22 

23 H.3.7.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

24 Power Unrestricted 

25 

26 

27 ==================================================================== 

28 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

29 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_Lung_EROD_wk53.(d) 

30 Gnuplot Plotting File: 

31 Fri Nov 20 14:29:09 2009 

32 ==================================================================== 

33 

34 Tbl 12, Week 53, Lung Microsomes EROD 

35 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

36 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-202 —DO NOT CITE OR QUOTE 

1 The form of the response function by Model: 

2 Model 2: Y[dose] = a * exp{sign * b * dose} 

3 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

4 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

5 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

6 

7 Note: Y[dose] is the median response for exposure = dose; 

8 sign = +1 for increasing trend in data; 

9 sign = -1 for decreasing trend. 

10 

11 Model 2 is nested within Models 3 and 4. 

12 Model 3 is nested within Model 5. 

13 Model 4 is nested within Model 5. 

14 

15 

16 Dependent variable = Mean 

17 Independent variable = Dose 

18 Data are assumed to be distributed: normally 

19 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

20 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

21 

22 Total number of dose groups = 6 

23 Total number of records with missing values = 0 

24 Maximum number of iterations = 250 

25 Relative Function Convergence has been set to: 1e-008 

26 Parameter Convergence has been set to: 1e-008 

27 

28 MLE solution provided: Exact 

29 

30 

31 Initial Parameter Values 

32 

33 Variable Model 5 

34 -------- -------- 

35 lnalpha -0.80064 

36 rho 1.47683 

37 a 2.86045 

38 b 0.0390303 

39 c 16.0581 

40 d 1 

41 

42 

43 

44 Parameter Estimates 

45 

46 Variable Model 5 

47 -------- ------- 

48 lnalpha -1.07501 

49 rho 1.68859 

50 a 3.011 

51 b 3.22004 

52 c 12.8877 

53 d 18 

54 

55 

56 Table of Stats From Input Data 

57 

58 Dose N Obs Mean Obs Std Dev 

59 ----- --- ---------- ------------- 

60 0 8 3.011 1.584 

61 3 8 27.15 5.269 

62 10 8 42.85 11.15 

63 22 8 36.57 12.99 

64 46 8 43.75 18.55 

65 100 8 43.71 6.322 

66 

67 

68 Estimated Values of Interest 

69 

70 Dose Est Mean Est Std Scaled Residual 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-203 —DO NOT CITE OR QUOTE 

1 ------ ---------- --------- ---------------- 

2 0 3.011 1.482 -4.539e-008 

3 3 38.8 12.82 -2.571 

4 10 38.8 12.82 0.8915 

5 22 38.8 12.82 -0.4931 

6 46 38.8 12.82 1.09 

7 100 38.8 12.82 1.082 

8 

9 

10 

11 Other models for which likelihoods are calculated: 

12 

13 Model A1: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma^2 

15 

16 Model A2: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = Sigma(i)^2 

18 

19 Model A3: Yij = Mu(i) + e(ij) 

20 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

21 

22 Model R: Yij = Mu + e(i) 

23 Var{e(ij)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) DF AIC 

29 ------- ----------------- ---- ------------ 

30 A1 -135.2677 7 284.5353 

31 A2 -115.6885 12 255.3771 

32 A3 -121.1517 8 258.3034 

33 R -162.0902 2 328.1805 

34 5 -129.2006 6 270.4011 

35 

36 

37 Additive constant for all log-likelihoods = -44.11. This constant added to the 

38 above values gives the log-likelihood including the term that does not 

39 depend on the model parameters. 

40 

41 

42 Explanation of Tests 

43 

44 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

45 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

46 Test 3: Are variances adequately modeled? (A2 vs. A3) 

47 

48 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

49 

50 

51 Tests of Interest 

52 

53 Test -2*log(Likelihood Ratio) D. F. p-value 

54 -------- ------------------------ ------ -------------- 

55 Test 1 92.8 10 < 0.0001 

56 Test 2 39.16 5 < 0.0001 

57 Test 3 10.93 4 0.0274 

58 Test 7a 16.1 2 0.0003195 

59 

60 

61 The p-value for Test 1 is less than .05. There appears to be a 

62 difference between response and/or variances among the dose 

63 levels, it seems appropriate to model the data. 

64 

65 The p-value for Test 2 is less than .1. A non-homogeneous 

66 variance model appears to be appropriate. 

67 

68 The p-value for Test 3 is less than .1. You may want to 

69 consider a different variance model. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-204 —DO NOT CITE OR QUOTE 

1 The p-value for Test 7a is less than .1. Model 5 may not adequately 

2 describe the data; you may want to consider another model. 

3 

4 

5 Benchmark Dose Computations: 

6 

7 Specified Effect = 1.000000 

8 

9 Risk Type = Estimated standard deviations from control 

10 

11 Confidence Level = 0.950000 

12 

13 BMD = 0.260501 

14 

15 BMDL = 0.000148718 

16 

17 

18 H.3.7.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 10

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 30

 40

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 60

 0 20 40 60 80 100

Mean Response

dose

Hill Model

14:29 11/20 2009

Hill

19 

 20 

 21 

22 H.3.7.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 23 

24 

25 ==================================================================== 

26 Hill Model. (Version: 2.14; Date: 06/26/2008) 

27 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_Lung_EROD_wk53.(d) 

28 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_Lung_EROD_wk53.plt 

29 Fri Nov 20 14:29:11 2009 

30 ==================================================================== 

31 

32 Tbl 12, Week 53, Lung Microsomes EROD 

33 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

34 

35 The form of the response function is: 

36 

37 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-205 —DO NOT CITE OR QUOTE 

1 

2 

3 Dependent variable = Mean 

4 Independent variable = Dose 

5 Power parameter is not restricted 

6 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

7 

8 Total number of dose groups = 6 

9 Total number of records with missing values = 0 

10 Maximum number of iterations = 250 

11 Relative Function Convergence has been set to: 1e-008 

12 Parameter Convergence has been set to: 1e-008 

13 

14 

15 

16 Default Initial Parameter Values 

17 lalpha = 4.76968 

18 rho = 0 

19 intercept = 3.011 

20 v = 40.735 

21 n = 1.63324 

22 k = 3.46862 

23 

24 

25 Asymptotic Correlation Matrix of Parameter Estimates 

26 

27 lalpha rho intercept v n k 

28 

29 lalpha 1 -1 0.00098 -0.015 NA NA 

30 

31 rho -1 1 -0.00098 0.015 NA NA 

32 

33 intercept 0.00098 -0.00098 1 -1.5e-005 NA NA 

34 

35 v -0.015 0.015 -1.5e-005 1 NA NA 

36 

37 n NA NA NA NA NA NA 

38 

39 k NA NA NA NA NA NA 

40 

41 

42 NA - This parameter's variance has been estimated as zero or less. 

43 THE MODEL HAS PROBABLY NOT CONVERGED!!! 

44 

45 

46 

47 Parameter Estimates 

48 

49 95.0% Wald Confidence Interval 

50 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

51 lalpha 16.2956 NA NA NA 

52 rho -3.01917 NA NA NA 

53 intercept 32.8392 NA NA NA 

54 v 81.7793 NA NA NA 

55 n 17.5977 NA NA NA 

56 k 324.491 NA NA NA 

57 

58 At least some variance estimates are negative. 

59 THIS USUALLY MEANS THE MODEL HAS NOT CONVERGED! 

60 Try again from another starting point. 

61 

62 

63 

64 Table of Data and Estimated Values of Interest 

65 

66 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

67 ------ --- -------- -------- ----------- ----------- ---------- 

68 

69 0 8 3.01 32.8 1.58 17.8 -4.75 

70 3 8 27.1 32.8 5.27 17.8 -0.906 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-206 —DO NOT CITE OR QUOTE 

1 10 8 42.8 32.8 11.2 17.8 1.59 

2 22 8 36.6 32.8 13 17.8 0.594 

3 46 8 43.7 32.8 18.5 17.8 1.74 

4 100 8 43.7 32.8 6.32 17.8 1.73 

5 

6 

7 

8 Model Descriptions for likelihoods calculated 

9 

10 

11 Model A1: Yij = Mu(i) + e(ij) 

12 Var{e(ij)} = Sigma^2 

13 

14 Model A2: Yij = Mu(i) + e(ij) 

15 Var{e(ij)} = Sigma(i)^2 

16 

17 Model A3: Yij = Mu(i) + e(ij) 

18 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

19 Model A3 uses any fixed variance parameters that 

20 were specified by the user 

21 

22 Model R: Yi = Mu + e(i) 

23 Var{e(i)} = Sigma^2 

24 

25 

26 Likelihoods of Interest 

27 

28 Model Log(likelihood) # Param's AIC 

29 A1 -135.267662 7 284.535325 

30 A2 -115.688533 12 255.377067 

31 A3 -121.151707 8 258.303413 

32 fitted -162.090242 6 336.180484 

33 R -162.090242 2 328.180484 

34 

35 

36 Explanation of Tests 

37 

38 Test 1: Do responses and/or variances differ among Dose levels? 

39 (A2 vs. R) 

40 Test 2: Are Variances Homogeneous? (A1 vs A2) 

41 Test 3: Are variances adequately modeled? (A2 vs. A3) 

42 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

43 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

44 

45 Tests of Interest 

46 

47 Test -2*log(Likelihood Ratio) Test df p-value 

48 

49 Test 1 92.8034 10 <.0001 

50 Test 2 39.1583 5 <.0001 

51 Test 3 10.9263 4 0.0274 

52 Test 4 81.8771 2 <.0001 

53 

54 The p-value for Test 1 is less than .05. There appears to be a 

55 difference between response and/or variances among the dose levels 

56 It seems appropriate to model the data 

57 

58 The p-value for Test 2 is less than .1. A non-homogeneous variance 

59 model appears to be appropriate 

60 

61 The p-value for Test 3 is less than .1. You may want to consider a 

62 different variance model 

63 

64 The p-value for Test 4 is less than .1. You may want to try a different 

65 model 

66 

67 

68 Benchmark Dose Computation 

69 

70 Specified effect = 1 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-207 —DO NOT CITE OR QUOTE 

1 

2 Risk Type = Estimated standard deviations from the control mean 

3 

4 Confidence level = 0.95 

5 

6 BMD = 301.687 

7 

8 

9 BMDL computation failed. 

10 

11 

12 H.3.7.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 10

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 30

 40

 50

 60

 0 20 40 60 80 100

Mean Response

dose

Power Model with 0.95 Confidence Level

14:29 11/20 2009

BMDBMDL

 

Power

13 

 14 

 15 

16 H.3.7.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

17 Unrestricted

18 

19 

20 ==================================================================== 

21 Power Model. (Version: 2.15; Date: 04/07/2008) 

22 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_Lung_EROD_wk53.(d) 

23 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_Lung_EROD_wk53.plt 

24 Fri Nov 20 14:29:12 2009 

25 ==================================================================== 

26 

27 Tbl 12, Week 53, Lung Microsomes EROD 

28 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

29 

30 The form of the response function is: 

31 

32 Y[dose] = control + slope * dose^power 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 The power is not restricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-208 —DO NOT CITE OR QUOTE 

1 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

2 

3 Total number of dose groups = 6 

4 Total number of records with missing values = 0 

5 Maximum number of iterations = 250 

6 Relative Function Convergence has been set to: 1e-008 

7 Parameter Convergence has been set to: 1e-008 

8 

9 

10 

11 Default Initial Parameter Values 

12 lalpha = 4.76968 

13 rho = 0 

14 control = 3.011 

15 slope = 23.6162 

16 power = 0.133025 

17 

18 

19 Asymptotic Correlation Matrix of Parameter Estimates 

20 

21 lalpha rho control slope power 

22 

23 lalpha 1 -0.96 -0.48 0.11 -0.048 

24 

25 rho -0.96 1 0.45 -0.14 0.053 

26 

27 control -0.48 0.45 1 -0.14 0.05 

28 

29 slope 0.11 -0.14 -0.14 1 -0.93 

30 

31 power -0.048 0.053 0.05 -0.93 1 

32 

33 

34 

35 Parameter Estimates 

36 

37 95.0% Wald Confidence Interval 

38 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

39 lalpha -1.03233 0.815925 -2.63152 0.566849 

40 rho 1.63033 0.23978 1.16037 2.10029 

41 control 3.01788 0.518168 2.00229 4.03347 

42 slope 24.0756 3.58644 17.0463 31.1049 

43 power 0.128899 0.0448635 0.040968 0.21683 

44 

45 

46 

47 Table of Data and Estimated Values of Interest 

48 

49 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

50 ------ --- -------- -------- ----------- ----------- ---------- 

51 

52 0 8 3.01 3.02 1.58 1.47 -0.0133 

53 3 8 27.1 30.8 5.27 9.74 -1.05 

54 10 8 42.8 35.4 11.2 10.9 1.92 

55 22 8 36.6 38.9 13 11.8 -0.554 

56 46 8 43.7 42.5 18.5 12.7 0.288 

57 100 8 43.7 46.6 6.32 13.7 -0.599 

58 

59 

60 

61 Model Descriptions for likelihoods calculated 

62 

63 

64 Model A1: Yij = Mu(i) + e(ij) 

65 Var{e(ij)} = Sigma^2 

66 

67 Model A2: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma(i)^2 

69 

70 Model A3: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-209 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

2 Model A3 uses any fixed variance parameters that 

3 were specified by the user 

4 

5 Model R: Yi = Mu + e(i) 

6 Var{e(i)} = Sigma^2 

7 

8 

9 Likelihoods of Interest 

10 

11 Model Log(likelihood) # Param's AIC 

12 A1 -135.267662 7 284.535325 

13 A2 -115.688533 12 255.377067 

14 A3 -121.151707 8 258.303413 

15 fitted -125.400472 5 260.800944 

16 R -162.090242 2 328.180484 

17 

18 

19 Explanation of Tests 

20 

21 Test 1: Do responses and/or variances differ among Dose levels? 

22 (A2 vs. R) 

23 Test 2: Are Variances Homogeneous? (A1 vs A2) 

24 Test 3: Are variances adequately modeled? (A2 vs. A3) 

25 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

26 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

27 

28 Tests of Interest 

29 

30 Test -2*log(Likelihood Ratio) Test df p-value 

31 

32 Test 1 92.8034 10 <.0001 

33 Test 2 39.1583 5 <.0001 

34 Test 3 10.9263 4 0.0274 

35 Test 4 8.49753 3 0.03677 

36 

37 The p-value for Test 1 is less than .05. There appears to be a 

38 difference between response and/or variances among the dose levels 

39 It seems appropriate to model the data 

40 

41 The p-value for Test 2 is less than .1. A non-homogeneous variance 

42 model appears to be appropriate 

43 

44 The p-value for Test 3 is less than .1. You may want to consider a 

45 different variance model 

46 

47 The p-value for Test 4 is less than .1. You may want to try a different 

48 model 

49 

50 

51 Benchmark Dose Computation 

52 

53 Specified effect = 1 

54 

55 Risk Type = Estimated standard deviations from the control mean 

56 

57 Confidence level = 0.95 

58 

59 BMD = 3.76923e-010 

60 

61 

62 BMDL = 3.76923e-010 

63 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-210 —DO NOT CITE OR QUOTE 

1 H.3.8. National Toxicology Program. (2006): Tbl11 Index Week 31 

2 H.3.8.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) c 4 <0.0001 21.34 0.00 47.30 3.3E+01 2.6E+01 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 21.34 0.00 47.30 3.3E+01 2.6E+01 nonconstant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 25.36 <0.0001 53.32 1.7E+01 1.1E+01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 21.10 <0.0001 51.06 4.6E+01 2.9E+01 nonconstant variance, 

power restricted ≥1 

Hill 3 <.0001 21.10 0.00 49.06 4.6E+01 error nonconstant variance, n 

restricted >1, bound hit 

linear 4 <.0001 25.36 <.0001 51.32 1.7E+01 1.1E+01 nonconstant variance 

polynomial 3 <.0001 21.87 <.0001 49.83 3.9E+01 1.7E+01 nonconstant variance 

power 3 <.0001 21.87 <.0001 49.83 4.5E+01 2.4E+01 nonconstant variance, 

power restricted ≥1 

exponential (M2) 4 <0.0001 1.02 0.91 101.49 6.4E+01 5.7E+01 constant variance, 

power restricted ≥1 

exponential (M3) 3 <0.0001 1.00 0.80 103.47 6.7E+01 5.7E+01 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 3.38 0.34 105.85 4.4E+01 3.3E+01 constant variance, 

power restricted ≥1 

exponential (M5) 2 <0.0001 1.10 0.58 105.57 6.6E+01 3.9E+01 constant variance, 

power restricted ≥1 

Hill 2 <.0001 1.10 0.58 105.57 6.6E+01 3.9E+01 constant variance, n 

restricted >1 

linear 4 <.0001 3.38 0.50 103.85 4.4E+01 3.3E+01 constant variance 

polynomial 3 <.0001 1.08 0.78 103.55 6.4E+01 3.9E+01 constant variance 

power 3 <.0001 1.10 0.78 103.57 6.6E+01 3.9E+01 constant variance, 

power restricted ≥1 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 

4 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-211 —DO NOT CITE OR QUOTE 

1 H.3.8.2. Figure for Selected Model: Exponential (M2), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 1

 2

 3

 4

 5

 6

 0 20 40 60 80 100

Mean Response

dose

Exponential_beta Model 2 with 0.95 Confidence Level

16:50 11/20 2009

BMDL BMD

 

Exponential

3 

 4 

 5 

6 H.3.8.3. Output File for Selected Model: Exponential (M2), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_Tbl11_31wk.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 16:50:52 2009 

15 ==================================================================== 

16 

17 Tbl 11, 31wk, Hep Cell Proliferation Labeling Index 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-212 —DO NOT CITE OR QUOTE 

1 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

2 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

3 

4 Total number of dose groups = 6 

5 Total number of records with missing values = 0 

6 Maximum number of iterations = 250 

7 Relative Function Convergence has been set to: 1e-008 

8 Parameter Convergence has been set to: 1e-008 

9 

10 MLE solution provided: Exact 

11 

12 

13 Initial Parameter Values 

14 

15 Variable Model 2 

16 -------- -------- 

17 lnalpha -0.674004 

18 rho 2.29189 

19 a 0.31065 

20 b 0.024912 

21 c 12.9995 

22 d 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 Variable Model 2 

29 -------- ------- 

30 lnalpha -0.495833 

31 rho 1.97486 

32 a 0.740304 

33 b 0.0199927 

34 c 5.16751 

35 d 18 

36 

37 

38 Table of Stats From Input Data 

39 

40 Dose N Obs Mean Obs Std Dev 

41 ----- --- ---------- ------------- 

42 0 9 0.327 0.189 

43 3 10 0.852 0.6514 

44 10 10 0.956 0.7368 

45 22 10 0.792 0.4617 

46 46 10 1.333 1.123 

47 100 10 3.846 3.08 

48 

49 

50 Estimated Values of Interest 

51 

52 Dose Est Mean Est Std Scaled Residual 

53 ------ ---------- --------- ---------------- 

54 0 0.6166 0.4987 -1.742 

55 3 0.651 0.5251 1.21 

56 10 0.7391 0.5925 1.158 

57 22 0.9186 0.7287 -0.5493 

58 46 1.419 1.102 -0.2466 

59 100 3.775 2.796 0.08069 

60 

61 

62 

63 Other models for which likelihoods are calculated: 

64 

65 Model A1: Yij = Mu(i) + e(ij) 

66 Var{e(ij)} = Sigma^2 

67 

68 Model A2: Yij = Mu(i) + e(ij) 

69 Var{e(ij)} = Sigma(i)^2 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-213 —DO NOT CITE OR QUOTE 

1 Model A3: Yij = Mu(i) + e(ij) 

2 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

3 

4 Model R: Yij = Mu + e(i) 

5 Var{e(ij)} = Sigma^2 

6 

7 

8 Likelihoods of Interest 

9 

10 Model Log(likelihood) DF AIC 

11 ------- ----------------- ---- ------------ 

12 A1 -47.23498 7 108.47 

13 A2 -8.679256 12 41.35851 

14 A3 -8.980651 8 33.9613 

15 R -63.44829 2 130.8966 

16 2 -19.6508 4 47.30161 

17 

18 

19 Additive constant for all log-likelihoods = -54.22. This constant added to the 

20 above values gives the log-likelihood including the term that does not 

21 depend on the model parameters. 

22 

23 

24 Explanation of Tests 

25 

26 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

27 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

28 Test 3: Are variances adequately modeled? (A2 vs. A3) 

29 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

30 

31 

32 Tests of Interest 

33 

34 Test -2*log(Likelihood Ratio) D. F. p-value 

35 -------- ------------------------ ------ -------------- 

36 Test 1 109.5 10 < 0.0001 

37 Test 2 77.11 5 < 0.0001 

38 Test 3 0.6028 4 0.9628 

39 Test 4 21.34 4 0.0002711 

40 

41 

42 The p-value for Test 1 is less than .05. There appears to be a 

43 difference between response and/or variances among the dose 

44 levels, it seems appropriate to model the data. 

45 

46 The p-value for Test 2 is less than .1. A non-homogeneous 

47 variance model appears to be appropriate. 

48 

49 The p-value for Test 3 is greater than .1. The modeled 

50 variance appears to be appropriate here. 

51 

52 The p-value for Test 4 is less than .1. Model 2 may not adequately 

53 describe the data; you may want to consider another model. 

54 

55 

56 Benchmark Dose Computations: 

57 

58 Specified Effect = 1.000000 

59 

60 Risk Type = Estimated standard deviations from control 

61 

62 Confidence Level = 0.950000 

63 

64 BMD = 32.7092 

65 

66 BMDL = 26.1405 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-214 —DO NOT CITE OR QUOTE 

1 H.3.9. Van Birgelen et al. (1995b): T4 UGT 

2 H.3.9.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 4 <0.0001 35.16 <0.0001 38.57 5.0E+02 3.5E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 35.16 <0.0001 38.57 5.0E+02 3.5E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 3 <0.0001 1.01 0.80 6.42 1.2E+01 6.2E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 1.01 0.80 6.42 1.2E+01 6.2E+00 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 3 <0.0001 1.01 0.80 6.42 1.2E+01 6.2E+00 nonconstant variance, 

power unrestricted 

Hill 2 <.0001 1.12 0.57 8.52 1.3E+01 6.1E+00 nonconstant variance, n 

restricted >1 

Hill d 2 <.0001 1.12 0.57 8.52 1.3E+01 3.7E+00 nonconstant variance, n 

unrestricted 

linear 4 <.0001 23.17 0.00 26.57 1.7E+02 9.4E+01 nonconstant variance 

polynomial 4 <.0001 23.17 0.00 26.57 1.7E+02 9.4E+01 nonconstant variance 

power 4 <.0001 23.17 0.00 26.57 1.7E+02 9.4E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 3 <.0001 5.05 0.17 10.45 4.0E+00 4.8E-01 nonconstant variance, 

power unrestricted 

exponential (M2) 4 <0.0001 14.22 0.01 39.63 6.1E+02 5.2E+02 constant variance, 

power restricted ≥1 

exponential (M3) 4 <0.0001 14.22 0.01 39.63 6.1E+02 5.2E+02 constant variance, 

power restricted ≥1 

exponential (M4) 3 <0.0001 0.16 0.98 27.56 8.8E+01 3.6E+01 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 0.16 0.98 27.56 8.8E+01 3.6E+01 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 0.16 0.98 27.56 8.8E+01 3.6E+01 constant variance, 

power unrestricted 

Hill 2 <.0001 0.10 0.95 29.51 7.1E+01 2.7E+01 constant variance, n 

restricted >1 

Hill 2 <.0001 0.10 0.95 29.51 7.1E+01 1.9E+01 constant variance, n 

unrestricted 

linear 4 <.0001 9.68 0.05 35.08 4.0E+02 3.0E+02 constant variance 

polynomial 4 <.0001 9.68 0.05 35.08 4.0E+02 3.0E+02 constant variance 

power 4 <.0001 9.68 0.05 35.08 4.0E+02 3.0E+02 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-215 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 3 <.0001 2.09 0.55 29.49 5.7E+01 9.9E+00 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.9.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:33 11/20 2009

BMDL BMD

 

Exponential

5 

 6 

 7 

8 H.3.9.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_T4_UGT.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 14:33:47 2009 

17 ==================================================================== 

18 

19 Tbl2, T4 UGT 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-216 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 6 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 4 

33 -------- -------- 

34 lnalpha -0.937573 

35 rho 1.54913 

36 a 0.3135 

37 b 0.00297568 

38 c 8.67464 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 4 

46 -------- ------- 

47 lnalpha -0.937201 

48 rho 1.6967 

49 a 0.294922 

50 b 0.0100397 

51 c 7.64822 

52 d 1 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 8 0.33 0.198 

60 14 8 0.6 0.4243 

61 26 8 0.64 0.4525 

62 47 8 0.87 0.9051 

63 320 8 2.08 1.329 

64 1024 8 2.59 0.8768 

65 

66 

67 Estimated Values of Interest 

68 

69 Dose Est Mean Est Std Scaled Residual 

70 ------ ---------- --------- ---------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-217 —DO NOT CITE OR QUOTE 

1 0 0.2949 0.2221 0.4466 

2 14 0.552 0.3781 0.3589 

3 26 0.7454 0.4878 -0.6111 

4 47 1.032 0.6431 -0.7146 

5 320 2.177 1.211 -0.2259 

6 1024 2.256 1.248 0.758 

7 

8 

9 

10 Other models for which likelihoods are calculated: 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

20 

21 Model R: Yij = Mu + e(i) 

22 Var{e(ij)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) DF AIC 

28 ------- ----------------- ---- ------------ 

29 A1 -9.701316 7 33.40263 

30 A2 4.934967 12 14.13007 

31 A3 2.296438 8 11.40712 

32 R -29.51921 2 63.03841 

33 4 1.790563 5 6.418874 

34 

35 

36 Additive constant for all log-likelihoods = -44.11. This constant added to the 

37 above values gives the log-likelihood including the term that does not 

38 depend on the model parameters. 

39 

40 

41 Explanation of Tests 

42 

43 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

44 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

45 Test 3: Are variances adequately modeled? (A2 vs. A3) 

46 

47 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

48 

49 

50 Tests of Interest 

51 

52 Test -2*log(Likelihood Ratio) D. F. p-value 

53 -------- ------------------------ ------ -------------- 

54 Test 1 68.91 10 < 0.0001 

55 Test 2 29.27 5 < 0.0001 

56 Test 3 5.277 4 0.26 

57 Test 6a 1.012 3 0.7984 

58 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose 

62 levels, it seems appropriate to model the data. 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous 

65 variance model appears to be appropriate. 

66 

67 The p-value for Test 3 is greater than .1. The modeled 

68 variance appears to be appropriate here. 

69 

70 The p-value for Test 6a is greater than .1. Model 4 seems 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-218 —DO NOT CITE OR QUOTE 

1 to adequately describe the data. 

2 

3 

4 Benchmark Dose Computations: 

5 

6 Specified Effect = 1.000000 

7 

8 Risk Type = Estimated standard deviations from control 

9 

10 Confidence Level = 0.950000 

11 

12 BMD = 11.9766 

13 

14 BMDL = 6.23544 

15 

16 

17 H.3.9.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

18 Unrestricted

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:33 11/20 2009

BMDL BMD

 

Exponential

19 

 20 

 21 

22 H.3.9.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

23 Power Unrestricted 

24 

25 

26 ==================================================================== 

27 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

28 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_T4_UGT.(d) 

29 Gnuplot Plotting File: 

30 Fri Nov 20 14:33:53 2009 

31 ==================================================================== 

32 

33 Tbl2, T4 UGT 

34 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

35 

36 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-219 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 6 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 5 

33 -------- -------- 

34 lnalpha -0.937573 

35 rho 1.54913 

36 a 0.3135 

37 b 0.00297568 

38 c 8.67464 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 5 

46 -------- ------- 

47 lnalpha -0.937201 

48 rho 1.6967 

49 a 0.294922 

50 b 0.0100397 

51 c 7.64822 

52 d 1 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 8 0.33 0.198 

60 14 8 0.6 0.4243 

61 26 8 0.64 0.4525 

62 47 8 0.87 0.9051 

63 320 8 2.08 1.329 

64 1024 8 2.59 0.8768 

65 

66 

67 Estimated Values of Interest 

68 

69 Dose Est Mean Est Std Scaled Residual 

70 ------ ---------- --------- ---------------- 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-220 —DO NOT CITE OR QUOTE 

1 0 0.2949 0.2221 0.4466 

2 14 0.552 0.3781 0.3589 

3 26 0.7454 0.4878 -0.6111 

4 47 1.032 0.6431 -0.7146 

5 320 2.177 1.211 -0.2259 

6 1024 2.256 1.248 0.758 

7 

8 

9 

10 Other models for which likelihoods are calculated: 

11 

12 Model A1: Yij = Mu(i) + e(ij) 

13 Var{e(ij)} = Sigma^2 

14 

15 Model A2: Yij = Mu(i) + e(ij) 

16 Var{e(ij)} = Sigma(i)^2 

17 

18 Model A3: Yij = Mu(i) + e(ij) 

19 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

20 

21 Model R: Yij = Mu + e(i) 

22 Var{e(ij)} = Sigma^2 

23 

24 

25 Likelihoods of Interest 

26 

27 Model Log(likelihood) DF AIC 

28 ------- ----------------- ---- ------------ 

29 A1 -9.701316 7 33.40263 

30 A2 4.934967 12 14.13007 

31 A3 2.296438 8 11.40712 

32 R -29.51921 2 63.03841 

33 5 1.790563 5 6.418874 

34 

35 

36 Additive constant for all log-likelihoods = -44.11. This constant added to the 

37 above values gives the log-likelihood including the term that does not 

38 depend on the model parameters. 

39 

40 

41 Explanation of Tests 

42 

43 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

44 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

45 Test 3: Are variances adequately modeled? (A2 vs. A3) 

46 

47 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

48 

49 

50 Tests of Interest 

51 

52 Test -2*log(Likelihood Ratio) D. F. p-value 

53 -------- ------------------------ ------ -------------- 

54 Test 1 68.91 10 < 0.0001 

55 Test 2 29.27 5 < 0.0001 

56 Test 3 5.277 4 0.26 

57 Test 7a 1.012 3 0.7984 

58 

59 

60 The p-value for Test 1 is less than .05. There appears to be a 

61 difference between response and/or variances among the dose 

62 levels, it seems appropriate to model the data. 

63 

64 The p-value for Test 2 is less than .1. A non-homogeneous 

65 variance model appears to be appropriate. 

66 

67 The p-value for Test 3 is greater than .1. The modeled 

68 variance appears to be appropriate here. 

69 

70 The p-value for Test 7a is greater than .1. Model 5 seems 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-221 —DO NOT CITE OR QUOTE 

1 to adequately describe the data. 

2 

3 

4 Benchmark Dose Computations: 

5 

6 Specified Effect = 1.000000 

7 

8 Risk Type = Estimated standard deviations from control 

9 

10 Confidence Level = 0.950000 

11 

12 BMD = 11.9766 

13 

14 BMDL = 6.23544 

15 

16 

17 H.3.9.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 200 400 600 800 1000

Mean Response

dose

Hill Model with 0.95 Confidence Level

14:33 11/20 2009

BMDL BMD

 

Hill

18 

 19 

 20 

21 H.3.9.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 22 

23 

24 ==================================================================== 

25 Hill Model. (Version: 2.14; Date: 06/26/2008) 

26 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_T4_UGT.(d) 

27 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_T4_UGT.plt 

28 Fri Nov 20 14:33:54 2009 

29 ==================================================================== 

30 

31 Tbl2, T4 UGT 

32 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

33 

34 The form of the response function is: 

35 

36 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

37 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-222 —DO NOT CITE OR QUOTE 

1 

2 Dependent variable = Mean 

3 Independent variable = Dose 

4 Power parameter is not restricted 

5 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

6 

7 Total number of dose groups = 6 

8 Total number of records with missing values = 0 

9 Maximum number of iterations = 250 

10 Relative Function Convergence has been set to: 1e-008 

11 Parameter Convergence has been set to: 1e-008 

12 

13 

14 

15 Default Initial Parameter Values 

16 lalpha = -0.462247 

17 rho = 0 

18 intercept = 0.33 

19 v = 2.26 

20 n = 0.430022 

21 k = 459.884 

22 

23 

24 Asymptotic Correlation Matrix of Parameter Estimates 

25 

26 lalpha rho intercept v n k 

27 

28 lalpha 1 0.036 -0.26 -0.16 -0.017 0.037 

29 

30 rho 0.036 1 0.48 -0.46 0.02 -0.2 

31 

32 intercept -0.26 0.48 1 -0.37 0.26 -0.15 

33 

34 v -0.16 -0.46 -0.37 1 -0.64 0.81 

35 

36 n -0.017 0.02 0.26 -0.64 1 -0.85 

37 

38 k 0.037 -0.2 -0.15 0.81 -0.85 1 

39 

40 

41 

42 Parameter Estimates 

43 

44 95.0% Wald Confidence Interval 

45 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

46 lalpha -0.935113 0.256585 -1.43801 -0.432217 

47 rho 1.68648 0.441197 0.821746 2.55121 

48 intercept 0.295265 0.0703668 0.157348 0.433181 

49 v 2.14661 0.547941 1.07267 3.22056 

50 n 1.16336 0.46393 0.25407 2.07264 

51 k 80.2777 52.4068 -22.4378 182.993 

52 

53 

54 

55 Table of Data and Estimated Values of Interest 

56 

57 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

58 ------ --- -------- -------- ----------- ----------- ---------- 

59 

60 0 8 0.33 0.295 0.198 0.224 0.439 

61 14 8 0.6 0.544 0.424 0.375 0.422 

62 26 8 0.64 0.751 0.453 0.492 -0.637 

63 47 8 0.87 1.04 0.905 0.65 -0.76 

64 320 8 2.08 2.08 1.33 1.16 -0.00947 

65 1024 8 2.59 2.34 0.877 1.28 0.56 

66 

67 

68 

69 Model Descriptions for likelihoods calculated 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-223 —DO NOT CITE OR QUOTE 

1 

2 Model A1: Yij = Mu(i) + e(ij) 

3 Var{e(ij)} = Sigma^2 

4 

5 Model A2: Yij = Mu(i) + e(ij) 

6 Var{e(ij)} = Sigma(i)^2 

7 

8 Model A3: Yij = Mu(i) + e(ij) 

9 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

10 Model A3 uses any fixed variance parameters that 

11 were specified by the user 

12 

13 Model R: Yi = Mu + e(i) 

14 Var{e(i)} = Sigma^2 

15 

16 

17 Likelihoods of Interest 

18 

19 Model Log(likelihood) # Param's AIC 

20 A1 -9.701316 7 33.402631 

21 A2 4.934967 12 14.130066 

22 A3 2.296438 8 11.407124 

23 fitted 1.738274 6 8.523453 

24 R -29.519205 2 63.038411 

25 

26 

27 Explanation of Tests 

28 

29 Test 1: Do responses and/or variances differ among Dose levels? 

30 (A2 vs. R) 

31 Test 2: Are Variances Homogeneous? (A1 vs A2) 

32 Test 3: Are variances adequately modeled? (A2 vs. A3) 

33 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

34 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

35 

36 Tests of Interest 

37 

38 Test -2*log(Likelihood Ratio) Test df p-value 

39 

40 Test 1 68.9083 10 <.0001 

41 Test 2 29.2726 5 <.0001 

42 Test 3 5.27706 4 0.26 

43 Test 4 1.11633 2 0.5723 

44 

45 The p-value for Test 1 is less than .05. There appears to be a 

46 difference between response and/or variances among the dose levels 

47 It seems appropriate to model the data 

48 

49 The p-value for Test 2 is less than .1. A non-homogeneous variance 

50 model appears to be appropriate 

51 

52 The p-value for Test 3 is greater than .1. The modeled variance appears 

53 to be appropriate here 

54 

55 The p-value for Test 4 is greater than .1. The model chosen seems 

56 to adequately describe the data 

57 

58 

59 Benchmark Dose Computation 

60 

61 Specified effect = 1 

62 

63 Risk Type = Estimated standard deviations from the control mean 

64 

65 Confidence level = 0.95 

66 

67 BMD = 12.6477 

68 

69 BMDL = 3.73502 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-224 —DO NOT CITE OR QUOTE 

1 H.3.9.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

 0

 0.5

 1

 1.5

 2

 2.5

 3

 3.5

 0 200 400 600 800 1000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:33 11/20 2009

BMDLBMD

 

Power

2 

 3 

 4 

5 H.3.9.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_T4_UGT.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_T4_UGT.plt 

13 Fri Nov 20 14:33:55 2009 

14 ==================================================================== 

15 

16 Tbl2, T4 UGT 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 6 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-225 —DO NOT CITE OR QUOTE 

1 lalpha = -0.462247 

2 rho = 0 

3 control = 0.33 

4 slope = 0.0542809 

5 power = 0.537973 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho control slope power 

11 

12 lalpha 1 0.032 -0.26 -0.19 0.071 

13 

14 rho 0.032 1 0.57 0.021 -0.19 

15 

16 control -0.26 0.57 1 -0.23 0.077 

17 

18 slope -0.19 0.021 -0.23 1 -0.94 

19 

20 power 0.071 -0.19 0.077 -0.94 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 lalpha -0.85465 0.259915 -1.36407 -0.345225 

29 rho 1.67517 0.448857 0.795428 2.55492 

30 control 0.275898 0.0675474 0.143507 0.408288 

31 slope 0.12137 0.0517127 0.0200146 0.222725 

32 power 0.43322 0.0764873 0.283308 0.583132 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 8 0.33 0.276 0.198 0.222 0.69 

42 14 8 0.6 0.657 0.424 0.459 -0.349 

43 26 8 0.64 0.774 0.453 0.526 -0.719 

44 47 8 0.87 0.919 0.905 0.608 -0.229 

45 320 8 2.08 1.75 1.33 1.04 0.886 

46 1024 8 2.59 2.72 0.877 1.51 -0.245 

47 

48 

49 

50 Model Descriptions for likelihoods calculated 

51 

52 

53 Model A1: Yij = Mu(i) + e(ij) 

54 Var{e(ij)} = Sigma^2 

55 

56 Model A2: Yij = Mu(i) + e(ij) 

57 Var{e(ij)} = Sigma(i)^2 

58 

59 Model A3: Yij = Mu(i) + e(ij) 

60 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

61 Model A3 uses any fixed variance parameters that 

62 were specified by the user 

63 

64 Model R: Yi = Mu + e(i) 

65 Var{e(i)} = Sigma^2 

66 

67 

68 Likelihoods of Interest 

69 

70 Model Log(likelihood) # Param's AIC 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-226 —DO NOT CITE OR QUOTE 

1 A1 -9.701316 7 33.402631 

2 A2 4.934967 12 14.130066 

3 A3 2.296438 8 11.407124 

4 fitted -0.226526 5 10.453053 

5 R -29.519205 2 63.038411 

6 

7 

8 Explanation of Tests 

9 

10 Test 1: Do responses and/or variances differ among Dose levels? 

11 (A2 vs. R) 

12 Test 2: Are Variances Homogeneous? (A1 vs A2) 

13 Test 3: Are variances adequately modeled? (A2 vs. A3) 

14 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

15 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

16 

17 Tests of Interest 

18 

19 Test -2*log(Likelihood Ratio) Test df p-value 

20 

21 Test 1 68.9083 10 <.0001 

22 Test 2 29.2726 5 <.0001 

23 Test 3 5.27706 4 0.26 

24 Test 4 5.04593 3 0.1685 

25 

26 The p-value for Test 1 is less than .05. There appears to be a 

27 difference between response and/or variances among the dose levels 

28 It seems appropriate to model the data 

29 

30 The p-value for Test 2 is less than .1. A non-homogeneous variance 

31 model appears to be appropriate 

32 

33 The p-value for Test 3 is greater than .1. The modeled variance appears 

34 to be appropriate here 

35 

36 The p-value for Test 4 is greater than .1. The model chosen seems 

37 to adequately describe the data 

38 

39 

40 Benchmark Dose Computation 

41 

42 Specified effect = 1 

43 

44 Risk Type = Estimated standard deviations from the control mean 

45 

46 Confidence level = 0.95 

47 

48 BMD = 4.02257 

49 

50 

51 BMDL = 0.480637 

52 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-227 —DO NOT CITE OR QUOTE 

1 H.3.10. Van Birgelen et al. (1995b): UGT 1A1 

2 H.3.10.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 3 0.00 29.54 <0.0001 167.34 7.4E+02 2.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M3) 3 0.00 29.54 <0.0001 167.34 7.4E+02 2.1E+02 nonconstant variance, 

power restricted ≥1 

exponential (M4) c 2 0.00 1.28 0.53 141.08 1.6E+00 8.5E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 1.28 0.53 141.08 1.6E+00 8.5E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) d 2 0.00 1.28 0.53 141.08 1.6E+00 8.5E-01 nonconstant variance, 

power unrestricted 

Hill 1 0.00 1.31 0.25 143.11 1.8E+00 error nonconstant variance, n 

restricted >1 

Hill d 1 0.00 1.31 0.25 143.11 1.8E+00 error nonconstant variance, n 

unrestricted 

linear 3 0.00 27.83 <.0001 165.63 2.1E+02 5.8E+01 nonconstant variance 

polynomial 3 0.00 30.93 <.0001 168.73 1.8E+03 2.9E+01 nonconstant variance 

power 3 0.00 27.83 <.0001 165.63 2.1E+02 5.8E+01 

nonconstant variance, 

power restricted ≥1, 

bound hit 

power d 2 0.00 5.39 0.07 145.19 3.4E-03 3.4E-03 nonconstant variance, 

power unrestricted 

exponential (M2) 3 0.00 22.45 <0.0001 165.95 1.3E+03 6.4E+02 constant variance, 

power restricted ≥1 

exponential (M3) 3 0.00 22.45 <0.0001 165.95 1.3E+03 6.4E+02 constant variance, 

power restricted ≥1 

exponential (M4) 2 0.00 7.89 0.02 153.38 1.1E+01 4.7E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 7.89 0.02 153.38 1.1E+01 4.7E+00 constant variance, 

power restricted ≥1 

exponential (M5) 2 0.00 7.89 0.02 153.38 1.1E+01 4.7E+00 constant variance, 

power unrestricted 

Hill 1 0.00 8.15 0.00 155.65 1.3E+01 3.0E+00 constant variance, n 

restricted >1 

Hill 1 0.00 8.15 0.00 155.65 1.3E+01 1.9E+00 constant variance, n 

unrestricted 

linear 3 0.00 22.15 <.0001 165.65 1.1E+03 4.9E+02 constant variance 

polynomial 3 0.00 22.15 <.0001 165.65 1.1E+03 4.9E+02 constant variance 

power 3 0.00 22.15 <.0001 165.65 1.1E+03 4.9E+02 

constant variance, 

power restricted ≥1, 

bound hit 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-228 —DO NOT CITE OR QUOTE 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

power 2 0.00 12.90 0.00 158.40 1.6E-01 5.2E-06 constant variance, 

power unrestricted 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

d

Alternate model also presented in this appendix 

1 

2 

3 H.3.10.2. Figure for Selected Model: Exponential (M4), Nonconstant Variance, Power 

4 Restricted ≥1 

-100

 0

 100

 200

 300

 400

 500

 600

 700

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 4 with 0.95 Confidence Level

14:34 11/20 2009

BMDLBMD

 

Exponential

5 

 6 

 7 

8 H.3.10.3. Output File for Selected Model: Exponential (M4), Nonconstant Variance, Power 

9 Restricted ≥1 

10 

11 

12 ==================================================================== 

13 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

14 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_UGT_1A1.(d) 

15 Gnuplot Plotting File: 

16 Fri Nov 20 14:34:36 2009 

17 ==================================================================== 

18 

19 Tbl2, UGT_1A1 

20 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

21 

22 The form of the response function by Model: 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-229 —DO NOT CITE OR QUOTE 

1 Model 2: Y[dose] = a * exp{sign * b * dose} 

2 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

3 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

4 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

5 

6 Note: Y[dose] is the median response for exposure = dose; 

7 sign = +1 for increasing trend in data; 

8 sign = -1 for decreasing trend. 

9 

10 Model 2 is nested within Models 3 and 4. 

11 Model 3 is nested within Model 5. 

12 Model 4 is nested within Model 5. 

13 

14 

15 Dependent variable = Mean 

16 Independent variable = Dose 

17 Data are assumed to be distributed: normally 

18 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

19 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

20 

21 Total number of dose groups = 5 

22 Total number of records with missing values = 0 

23 Maximum number of iterations = 250 

24 Relative Function Convergence has been set to: 1e-008 

25 Parameter Convergence has been set to: 1e-008 

26 

27 MLE solution provided: Exact 

28 

29 

30 Initial Parameter Values 

31 

32 Variable Model 4 

33 -------- -------- 

34 lnalpha -1.53604 

35 rho 1.59958 

36 a 95.95 

37 b 0.00148532 

38 c 4.94633 

39 d 1 

40 

41 

42 

43 Parameter Estimates 

44 

45 Variable Model 4 

46 -------- ------- 

47 lnalpha -10.1636 

48 rho 3.25851 

49 a 101.863 

50 b 0.0256373 

51 c 3.78343 

52 d 1 

53 

54 

55 Table of Stats From Input Data 

56 

57 Dose N Obs Mean Obs Std Dev 

58 ----- --- ---------- ------------- 

59 0 3 101 15.59 

60 14 3 194 36.37 

61 47 3 304 17.32 

62 320 3 452 48.5 

63 1024 3 296 149 

64 

65 

66 Estimated Values of Interest 

67 

68 Dose Est Mean Est Std Scaled Residual 

69 ------ ---------- --------- ---------------- 

70 0 101.9 11.6 -0.1288 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-230 —DO NOT CITE OR QUOTE 

1 14 187.4 31.32 0.3668 

2 47 300.4 67.58 0.09183 

3 320 385.3 101.4 1.139 

4 1024 385.4 101.4 -1.527 

5 

6 

7 

8 Other models for which likelihoods are calculated: 

9 

10 Model A1: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma^2 

12 

13 Model A2: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = Sigma(i)^2 

15 

16 Model A3: Yij = Mu(i) + e(ij) 

17 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

18 

19 Model R: Yij = Mu + e(i) 

20 Var{e(ij)} = Sigma^2 

21 

22 

23 Likelihoods of Interest 

24 

25 Model Log(likelihood) DF AIC 

26 ------- ----------------- ---- ------------ 

27 A1 -68.74833 6 149.4967 

28 A2 -58.69126 10 137.3825 

29 A3 -64.89907 7 143.7981 

30 R -80.72265 2 165.4453 

31 4 -65.54073 5 141.0815 

32 

33 

34 Additive constant for all log-likelihoods = -13.78. This constant added to the 

35 above values gives the log-likelihood including the term that does not 

36 depend on the model parameters. 

37 

38 

39 Explanation of Tests 

40 

41 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

42 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

43 Test 3: Are variances adequately modeled? (A2 vs. A3) 

44 

45 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

46 

47 

48 Tests of Interest 

49 

50 Test -2*log(Likelihood Ratio) D. F. p-value 

51 -------- ------------------------ ------ -------------- 

52 Test 1 44.06 8 < 0.0001 

53 Test 2 20.11 4 0.0004741 

54 Test 3 12.42 3 0.006087 

55 Test 6a 1.283 2 0.5264 

56 

57 

58 The p-value for Test 1 is less than .05. There appears to be a 

59 difference between response and/or variances among the dose 

60 levels, it seems appropriate to model the data. 

61 

62 The p-value for Test 2 is less than .1. A non-homogeneous 

63 variance model appears to be appropriate. 

64 

65 The p-value for Test 3 is less than .1. You may want to 

66 consider a different variance model. 

67 

68 The p-value for Test 6a is greater than .1. Model 4 seems 

69 to adequately describe the data. 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-231 —DO NOT CITE OR QUOTE 

1 

2 Benchmark Dose Computations: 

3 

4 Specified Effect = 1.000000 

5 

6 Risk Type = Estimated standard deviations from control 

7 

8 Confidence Level = 0.950000 

9 

10 BMD = 1.62983 

11 

12 BMDL = 0.853335 

13 

14 

15 H.3.10.4. Figure for Unrestricted Model: Exponential (M5), Nonconstant Variance, Power 

16 Unrestricted

-100

 0

 100

 200

 300

 400

 500

 600

 700

 0 200 400 600 800 1000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

14:34 11/20 2009

BMDLBMD

 

Exponential

17 

 18 

 19 

20 H.3.10.5. Output File for Unrestricted Model: Exponential (M5), Nonconstant Variance, 

21 Power Unrestricted 

22 

23 

24 ==================================================================== 

25 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

26 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_Unrest_BMR1_UGT_1A1.(d) 

27 Gnuplot Plotting File: 

28 Fri Nov 20 14:34:44 2009 

29 ==================================================================== 

30 

31 Tbl2, UGT_1A1 

32 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

33 

34 The form of the response function by Model: 

35 Model 2: Y[dose] = a * exp{sign * b * dose} 

36 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

37 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-232 —DO NOT CITE OR QUOTE 

1 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

2 

3 Note: Y[dose] is the median response for exposure = dose; 

4 sign = +1 for increasing trend in data; 

5 sign = -1 for decreasing trend. 

6 

7 Model 2 is nested within Models 3 and 4. 

8 Model 3 is nested within Model 5. 

9 Model 4 is nested within Model 5. 

10 

11 

12 Dependent variable = Mean 

13 Independent variable = Dose 

14 Data are assumed to be distributed: normally 

15 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

16 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

17 

18 Total number of dose groups = 5 

19 Total number of records with missing values = 0 

20 Maximum number of iterations = 250 

21 Relative Function Convergence has been set to: 1e-008 

22 Parameter Convergence has been set to: 1e-008 

23 

24 MLE solution provided: Exact 

25 

26 

27 Initial Parameter Values 

28 

29 Variable Model 5 

30 -------- -------- 

31 lnalpha -1.53604 

32 rho 1.59958 

33 a 95.95 

34 b 0.00148532 

35 c 4.94633 

36 d 1 

37 

38 

39 

40 Parameter Estimates 

41 

42 Variable Model 5 

43 -------- ------- 

44 lnalpha -10.1636 

45 rho 3.25851 

46 a 101.863 

47 b 0.0256373 

48 c 3.78343 

49 d 1 

50 

51 

52 Table of Stats From Input Data 

53 

54 Dose N Obs Mean Obs Std Dev 

55 ----- --- ---------- ------------- 

56 0 3 101 15.59 

57 14 3 194 36.37 

58 47 3 304 17.32 

59 320 3 452 48.5 

60 1024 3 296 149 

61 

62 

63 Estimated Values of Interest 

64 

65 Dose Est Mean Est Std Scaled Residual 

66 ------ ---------- --------- ---------------- 

67 0 101.9 11.6 -0.1288 

68 14 187.4 31.32 0.3668 

69 47 300.4 67.58 0.09183 

70 320 385.3 101.4 1.139 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-233 —DO NOT CITE OR QUOTE 

1 1024 385.4 101.4 -1.527 

2 

3 

4 

5 Other models for which likelihoods are calculated: 

6 

7 Model A1: Yij = Mu(i) + e(ij) 

8 Var{e(ij)} = Sigma^2 

9 

10 Model A2: Yij = Mu(i) + e(ij) 

11 Var{e(ij)} = Sigma(i)^2 

12 

13 Model A3: Yij = Mu(i) + e(ij) 

14 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

15 

16 Model R: Yij = Mu + e(i) 

17 Var{e(ij)} = Sigma^2 

18 

19 

20 Likelihoods of Interest 

21 

22 Model Log(likelihood) DF AIC 

23 ------- ----------------- ---- ------------ 

24 A1 -68.74833 6 149.4967 

25 A2 -58.69126 10 137.3825 

26 A3 -64.89907 7 143.7981 

27 R -80.72265 2 165.4453 

28 5 -65.54073 5 141.0815 

29 

30 

31 Additive constant for all log-likelihoods = -13.78. This constant added to the 

32 above values gives the log-likelihood including the term that does not 

33 depend on the model parameters. 

34 

35 

36 Explanation of Tests 

37 

38 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

39 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

40 Test 3: Are variances adequately modeled? (A2 vs. A3) 

41 

42 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

43 

44 

45 Tests of Interest 

46 

47 Test -2*log(Likelihood Ratio) D. F. p-value 

48 -------- ------------------------ ------ -------------- 

49 Test 1 44.06 8 < 0.0001 

50 Test 2 20.11 4 0.0004741 

51 Test 3 12.42 3 0.006087 

52 Test 7a 1.283 2 0.5264 

53 

54 

55 The p-value for Test 1 is less than .05. There appears to be a 

56 difference between response and/or variances among the dose 

57 levels, it seems appropriate to model the data. 

58 

59 The p-value for Test 2 is less than .1. A non-homogeneous 

60 variance model appears to be appropriate. 

61 

62 The p-value for Test 3 is less than .1. You may want to 

63 consider a different variance model. 

64 

65 The p-value for Test 7a is greater than .1. Model 5 seems 

66 to adequately describe the data. 

67 

68 

69 Benchmark Dose Computations: 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-234 —DO NOT CITE OR QUOTE 

1 Specified Effect = 1.000000 

2 

3 Risk Type = Estimated standard deviations from control 

4 

5 Confidence Level = 0.950000 

6 

7 BMD = 1.62983 

8 

9 BMDL = 0.853335 

10 

11 

12 

13 H.3.10.6. Figure for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 

-100

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 100

 200

 300

 400

 500

 600

 700

 0 200 400 600 800 1000

Mean Response

dose

Hill Model

14:34 11/20 2009

BMD

Hill

14 

 15 

 16 

17 H.3.10.7. Output File for Unrestricted Model: Hill, Nonconstant Variance, n Unrestricted 18 

19 

20 ==================================================================== 

21 Hill Model. (Version: 2.14; Date: 06/26/2008) 

22 Input Data File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_UGT_1A1.(d) 

23 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Hill_Unrest_BMR1_UGT_1A1.plt 

24 Fri Nov 20 14:34:45 2009 

25 ==================================================================== 

26 

27 Tbl2, UGT_1A1 

28 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

29 

30 The form of the response function is: 

31 

32 Y[dose] = intercept + v*dose^n/(k^n + dose^n) 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Power parameter is not restricted 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-235 —DO NOT CITE OR QUOTE 

1 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) 

2 

3 Total number of dose groups = 5 

4 Total number of records with missing values = 0 

5 Maximum number of iterations = 250 

6 Relative Function Convergence has been set to: 1e-008 

7 Parameter Convergence has been set to: 1e-008 

8 

9 

10 

11 Default Initial Parameter Values 

12 lalpha = 8.57191 

13 rho = 0 

14 intercept = 101 

15 v = 351 

16 n = 0.273231 

17 k = 55.25 

18 

19 

20 Asymptotic Correlation Matrix of Parameter Estimates 

21 

22 lalpha rho intercept v n k 

23 

24 lalpha 1 -0.99 -0.19 0.12 0.12 -0.017 

25 

26 rho -0.99 1 0.18 -0.16 -0.12 0.0049 

27 

28 intercept -0.19 0.18 1 -0.11 0.031 0.096 

29 

30 v 0.12 -0.16 -0.11 1 -0.61 0.82 

31 

32 n 0.12 -0.12 0.031 -0.61 1 -0.76 

33 

34 k -0.017 0.0049 0.096 0.82 -0.76 1 

35 

36 

37 

38 Parameter Estimates 

39 

40 95.0% Wald Confidence Interval 

41 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

42 lalpha -10.516 3.69809 -17.7641 -3.26786 

43 rho 3.32204 0.675078 1.99891 4.64517 

44 intercept 101.644 6.48157 88.9405 114.348 

45 v 298.646 56.3141 188.273 409.02 

46 n 1.1568 0.50134 0.17419 2.13941 

47 k 29.0772 13.7717 2.08512 56.0693 

48 

49 

50 

51 Table of Data and Estimated Values of Interest 

52 

53 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

54 ------ --- -------- -------- ----------- ----------- ---------- 

55 

56 0 3 101 102 15.6 11.2 -0.0994 

57 14 3 194 191 36.4 32.1 0.143 

58 47 3 304 291 17.3 64.6 0.338 

59 320 3 452 383 48.5 102 1.18 

60 1024 3 296 396 149 107 -1.61 

61 

62 

63 

64 Model Descriptions for likelihoods calculated 

65 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-236 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

5 Model A3 uses any fixed variance parameters that 

6 were specified by the user 

7 

8 Model R: Yi = Mu + e(i) 

9 Var{e(i)} = Sigma^2 

10 

11 

12 Likelihoods of Interest 

13 

14 Model Log(likelihood) # Param's AIC 

15 A1 -68.748326 6 149.496653 

16 A2 -58.691256 10 137.382511 

17 A3 -64.899072 7 143.798144 

18 fitted -65.554216 6 143.108432 

19 R -80.722651 2 165.445302 

20 

21 

22 Explanation of Tests 

23 

24 Test 1: Do responses and/or variances differ among Dose levels? 

25 (A2 vs. R) 

26 Test 2: Are Variances Homogeneous? (A1 vs A2) 

27 Test 3: Are variances adequately modeled? (A2 vs. A3) 

28 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

29 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

30 

31 Tests of Interest 

32 

33 Test -2*log(Likelihood Ratio) Test df p-value 

34 

35 Test 1 44.0628 8 <.0001 

36 Test 2 20.1141 4 0.0004741 

37 Test 3 12.4156 3 0.006087 

38 Test 4 1.31029 1 0.2523 

39 

40 The p-value for Test 1 is less than .05. There appears to be a 

41 difference between response and/or variances among the dose levels 

42 It seems appropriate to model the data 

43 

44 The p-value for Test 2 is less than .1. A non-homogeneous variance 

45 model appears to be appropriate 

46 

47 The p-value for Test 3 is less than .1. You may want to consider a 

48 different variance model 

49 

50 The p-value for Test 4 is greater than .1. The model chosen seems 

51 to adequately describe the data 

52 

53 

54 Benchmark Dose Computation 

55 

56 Specified effect = 1 

57 

58 Risk Type = Estimated standard deviations from the control mean 

59 

60 Confidence level = 0.95 

61 

62 BMD = 1.76282 

63 

64 

65 BMDL computation failed. 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-237 —DO NOT CITE OR QUOTE 

1 H.3.10.8. Figure for Unrestricted Model: Power, Nonconstant Variance, Power Unrestricted 

-100

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 0 200 400 600 800 1000

Mean Response

dose

Power Model with 0.95 Confidence Level

14:34 11/20 2009

BMDBMDL

 

Power

2 

 3 

 4 

5 H.3.10.9. Output File for Unrestricted Model: Power, Nonconstant Variance, Power 

6 Unrestricted

7 

8 

9 ==================================================================== 

10 Power Model. (Version: 2.15; Date: 04/07/2008) 

11 Input Data File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_UGT_1A1.(d) 

12 Gnuplot Plotting File: C:\USEPA\BMDS21\Nov20\Pwr_Unrest_BMR1_UGT_1A1.plt 

13 Fri Nov 20 14:34:47 2009 

14 ==================================================================== 

15 

16 Tbl2, UGT_1A1 

17 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

18 

19 The form of the response function is: 

20 

21 Y[dose] = control + slope * dose^power 

22 

23 

24 Dependent variable = Mean 

25 Independent variable = Dose 

26 The power is not restricted 

27 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

28 

29 Total number of dose groups = 5 

30 Total number of records with missing values = 0 

31 Maximum number of iterations = 250 

32 Relative Function Convergence has been set to: 1e-008 

33 Parameter Convergence has been set to: 1e-008 

34 

35 

36 

37 Default Initial Parameter Values 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-238 —DO NOT CITE OR QUOTE 

1 lalpha = 8.57191 

2 rho = 0 

3 control = 101 

4 slope = 75.1984 

5 power = 0.19277 

6 

7 

8 Asymptotic Correlation Matrix of Parameter Estimates 

9 

10 lalpha rho control slope power 

11 

12 lalpha 1 -0.99 -0.22 0.054 0.018 

13 

14 rho -0.99 1 0.2 -0.038 -0.052 

15 

16 control -0.22 0.2 1 -0.2 0.11 

17 

18 slope 0.054 -0.038 -0.2 1 -0.95 

19 

20 power 0.018 -0.052 0.11 -0.95 1 

21 

22 

23 

24 Parameter Estimates 

25 

26 95.0% Wald Confidence Interval 

27 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit 

28 lalpha -11.5264 3.45692 -18.3019 -4.75098 

29 rho 3.53579 0.629031 2.30291 4.76867 

30 control 101.425 6.34917 88.981 113.869 

31 slope 53.9904 20.7283 13.3638 94.617 

32 power 0.279427 0.0834726 0.115823 0.44303 

33 

34 

35 

36 Table of Data and Estimated Values of Interest 

37 

38 Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res. 

39 ------ --- -------- -------- ----------- ----------- ---------- 

40 

41 0 3 101 101 15.6 11.1 -0.0666 

42 14 3 194 214 36.4 41.5 -0.847 

43 47 3 304 260 17.3 58.3 1.31 

44 320 3 452 372 48.5 110 1.26 

45 1024 3 296 476 149 170 -1.83 

46 

47 

48 

49 Model Descriptions for likelihoods calculated 

50 

51 

52 Model A1: Yij = Mu(i) + e(ij) 

53 Var{e(ij)} = Sigma^2 

54 

55 Model A2: Yij = Mu(i) + e(ij) 

56 Var{e(ij)} = Sigma(i)^2 

57 

58 Model A3: Yij = Mu(i) + e(ij) 

59 Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) 

60 Model A3 uses any fixed variance parameters that 

61 were specified by the user 

62 

63 Model R: Yi = Mu + e(i) 

64 Var{e(i)} = Sigma^2 

65 

66 

67 Likelihoods of Interest 

68 

69 Model Log(likelihood) # Param's AIC 

70 A1 -68.748326 6 149.496653 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-239 —DO NOT CITE OR QUOTE 

1 A2 -58.691256 10 137.382511 

2 A3 -64.899072 7 143.798144 

3 fitted -67.596085 5 145.192170 

4 R -80.722651 2 165.445302 

5 

6 

7 Explanation of Tests 

8 

9 Test 1: Do responses and/or variances differ among Dose levels? 

10 (A2 vs. R) 

11 Test 2: Are Variances Homogeneous? (A1 vs A2) 

12 Test 3: Are variances adequately modeled? (A2 vs. A3) 

13 Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) 

14 (Note: When rho=0 the results of Test 3 and Test 2 will be the same.) 

15 

16 Tests of Interest 

17 

18 Test -2*log(Likelihood Ratio) Test df p-value 

19 

20 Test 1 44.0628 8 <.0001 

21 Test 2 20.1141 4 0.0004741 

22 Test 3 12.4156 3 0.006087 

23 Test 4 5.39403 2 0.06741 

24 

25 The p-value for Test 1 is less than .05. There appears to be a 

26 difference between response and/or variances among the dose levels 

27 It seems appropriate to model the data 

28 

29 The p-value for Test 2 is less than .1. A non-homogeneous variance 

30 model appears to be appropriate 

31 

32 The p-value for Test 3 is less than .1. You may want to consider a 

33 different variance model 

34 

35 The p-value for Test 4 is less than .1. You may want to try a different 

36 model 

37 

38 

39 Benchmark Dose Computation 

40 

41 Specified effect = 1 

42 

43 Risk Type = Estimated standard deviations from the control mean 

44 

45 Confidence level = 0.95 

46 

47 BMD = 0.00343319 

48 

49 

50 BMDL = 0.00343312 

51 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-240 —DO NOT CITE OR QUOTE 

1 H.3.11. Vanden Heuvel et al. (1994): Hepatic CYP1A1 mRNA Expression 

2 H.3.11.1. Summary Table of BMDS Modeling Results 

Model 

Degrees 

of 

Freedom 

Variance 

p-Value a χ 2 Test 

Statistic 

χ 2 pValue b AIC 

BMD 

(ng/kgday) 

BMDL 

(ng/kgday) Model Notes 

exponential (M2) 5 <0.0001 568.80 <0.0001 1164.38 4.7E+03 1.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M3) 5 <0.0001 568.80 <0.0001 1164.38 4.7E+03 1.7E+03 nonconstant variance, 

power restricted ≥1 

exponential (M4) 4 <0.0001 63.39 <0.0001 661.01 4.5E-01 2.6E-01 nonconstant variance, 

power restricted ≥1 

exponential (M5) c 3 <0.0001 35.71 <0.0001 635.33 1.5E+01 1.0E+01 nonconstant variance, 

power restricted ≥1 

Hill 3 <.0001 33.98 <.0001 633.59 1.9E+01 error nonconstant variance, n 

restricted >1 

linear 5 <.0001 71.94 <.0001 667.55 5.0E-01 3.1E-01 nonconstant variance 

polynomial 5 <.0001 137.66 <.0001 733.28 5.4E+03 1.7E+01 nonconstant variance 

power 4 <.0001 71.83 <.0001 669.44 5.6E-01 3.2E-01 nonconstant variance, 

power restricted ≥1 

exponential (M2) 5 <0.0001 27.93 <0.0001 1178.88 5.9E+03 5.1E+03 constant variance, 

power restricted ≥1 

exponential (M3) 5 <0.0001 27.93 <0.0001 1178.88 5.9E+03 5.1E+03 constant variance, 

power restricted ≥1 

exponential (M4) 4 <0.0001 0.34 0.99 1153.28 4.0E+02 2.8E+02 constant variance, 

power restricted ≥1 

exponential (M5) 3 <0.0001 0.00 1.00 1154.95 5.7E+02 2.9E+02 constant variance, 

power restricted ≥1 

Hill 3 <.0001 0.00 1.00 1154.95 5.3E+02 2.1E+02 constant variance, n 

restricted >1 

linear 5 <.0001 21.45 0.00 1172.40 2.8E+03 2.2E+03 constant variance 

polynomial 5 <.0001 22.53 0.00 1173.48 3.1E+03 2.1E+03 constant variance 

power 5 <.0001 21.45 0.00 1172.40 2.8E+03 2.2E+03 

constant variance, 

power restricted ≥1, 

bound hit 

a

Values <0.1 means nonconstant variance model should be selected; Values ≥0.1 means a constant variance model should be selected 

b

Values <0.1 fail to meet BMDS goodness-of-fit criteria 

c

Best-fitting model as assessed by lowest-AIC criterion, bolded, presented in this appendix 

3 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-241 —DO NOT CITE OR QUOTE 

1 H.3.11.2. Figure for Selected Model: Exponential (M5), Nonconstant Variance, Power 

2 Restricted ≥1 

 0

 10000

 20000

 30000

 40000

 50000

 60000

 70000

 0 2000 4000 6000 8000 10000

Mean Response

dose

Exponential_beta Model 5 with 0.95 Confidence Level

16:52 11/20 2009

BMDLBMD

 

Exponential

3 

 4 

 5 

6 H.3.11.3. Output File for Selected Model: Exponential (M5), Nonconstant Variance, Power 

7 Restricted ≥1 

8 

9 

10 ==================================================================== 

11 Exponential Model. (Version: 1.5; Date: 4/23/2009) 

12 Input Data File: C:\USEPA\BMDS21\Nov20\Exp_BMR1_hepatic_CYP1A1_mRNA_expression.(d) 

13 Gnuplot Plotting File: 

14 Fri Nov 20 16:52:21 2009 

15 ==================================================================== 

16 

17 [insert study notes] 

18 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

19 

20 The form of the response function by Model: 

21 Model 2: Y[dose] = a * exp{sign * b * dose} 

22 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

23 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

24 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

25 

26 Note: Y[dose] is the median response for exposure = dose; 

27 sign = +1 for increasing trend in data; 

28 sign = -1 for decreasing trend. 

29 

30 Model 2 is nested within Models 3 and 4. 

31 Model 3 is nested within Model 5. 

32 Model 4 is nested within Model 5. 

33 

34 

35 Dependent variable = Mean 

36 Independent variable = Dose 

37 Data are assumed to be distributed: normally 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-242 —DO NOT CITE OR QUOTE 

1 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

2 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

3 

4 Total number of dose groups = 7 

5 Total number of records with missing values = 0 

6 Maximum number of iterations = 250 

7 Relative Function Convergence has been set to: 1e-008 

8 Parameter Convergence has been set to: 1e-008 

9 

10 MLE solution provided: Exact 

11 

12 

13 Initial Parameter Values 

14 

15 Variable Model 5 

16 -------- -------- 

17 lnalpha -0.89532 

18 rho 2.01401 

19 a 5.13 

20 b 0.000307638 

21 c 7511.7 

22 d 1 

23 

24 

25 

26 Parameter Estimates 

27 

28 Variable Model 5 

29 -------- ------- 

30 lnalpha 0.176234 

31 rho 1.90467 

32 a 9.74751 

33 b 0.00106447 

34 c 3247.52 

35 d 1.96414 

36 

37 

38 Table of Stats From Input Data 

39 

40 Dose N Obs Mean Obs Std Dev 

41 ----- --- ---------- ------------- 

42 0 13 5.4 3.606 

43 0.1 5 7.2 5.59 

44 1 12 14.8 14.9 

45 10 7 12.8 4.498 

46 100 7 536 320.1 

47 1000 11 1.8e+004 1.522e+004 

48 1e+004 5 3.67e+004 2.214e+004 

49 

50 

51 Estimated Values of Interest 

52 

53 Dose Est Mean Est Std Scaled Residual 

54 ------ ---------- --------- ---------------- 

55 0 9.748 9.551 -1.641 

56 0.1 9.748 9.551 -0.5965 

57 1 9.793 9.593 1.808 

58 10 13.97 13.45 -0.2296 

59 100 395.9 325.2 1.14 

60 1000 2.144e+004 1.456e+004 -0.7835 

61 1e+004 3.166e+004 2.11e+004 0.5347 

62 

63 

64 

65 Other models for which likelihoods are calculated: 

66 

67 Model A1: Yij = Mu(i) + e(ij) 

68 Var{e(ij)} = Sigma^2 

69 

70 Model A2: Yij = Mu(i) + e(ij) 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-243 —DO NOT CITE OR QUOTE 

1 Var{e(ij)} = Sigma(i)^2 

2 

3 Model A3: Yij = Mu(i) + e(ij) 

4 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

5 

6 Model R: Yij = Mu + e(i) 

7 Var{e(ij)} = Sigma^2 

8 

9 

10 Likelihoods of Interest 

11 

12 Model Log(likelihood) DF AIC 

13 ------- ----------------- ---- ------------ 

14 A1 -572.4744 8 1160.949 

15 A2 -290.7965 14 609.5929 

16 A3 -293.806 9 605.6119 

17 R -603.6646 2 1211.329 

18 5 -311.6633 6 635.3266 

19 

20 

21 Additive constant for all log-likelihoods = -55.14. This constant added to the 

22 above values gives the log-likelihood including the term that does not 

23 depend on the model parameters. 

24 

25 

26 Explanation of Tests 

27 

28 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

29 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

30 Test 3: Are variances adequately modeled? (A2 vs. A3) 

31 

32 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

33 

34 

35 Tests of Interest 

36 

37 Test -2*log(Likelihood Ratio) D. F. p-value 

38 -------- ------------------------ ------ -------------- 

39 Test 1 625.7 12 < 0.0001 

40 Test 2 563.4 6 < 0.0001 

41 Test 3 6.019 5 0.3044 

42 Test 7a 35.71 3 < 0.0001 

43 

44 

45 The p-value for Test 1 is less than .05. There appears to be a 

46 difference between response and/or variances among the dose 

47 levels, it seems appropriate to model the data. 

48 

49 The p-value for Test 2 is less than .1. A non-homogeneous 

50 variance model appears to be appropriate. 

51 

52 The p-value for Test 3 is greater than .1. The modeled 

53 variance appears to be appropriate here. 

54 

55 The p-value for Test 7a is less than .1. Model 5 may not adequately 

56 describe the data; you may want to consider another model. 

57 

58 

59 Benchmark Dose Computations: 

60 

61 Specified Effect = 1.000000 

62 

63 Risk Type = Estimated standard deviations from control 

64 

65 Confidence Level = 0.950000 

66 

67 BMD = 15.1574 

68 

69 BMDL = 10.4625 

70 
This document is a draft for review purposes only and does not constitute Agency policy. 

1/15/10 DRAFT H-244 —DO NOT CITE OR QUOTE 

1 H.4. REFERENCES 

2 Hassoun, EA; Li, F; Abushaban, A; et al. (2000) The relative abilities of TCDD and its congeners to induce 

3 oxidative stress in the hepatic and brain tissues of rats after subchronic exposure. Toxicology 145:103−113. 

4 NTP (National Toxicology Program). (2006) Studies of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in female 

5 Harlan Sprague-Dawley rats (gavage studies) Tech. Rep. Ser. No. 521. U.S. Department of Health and Human 

6 Services, Public Health Service, Research Triangle Park, NC. 

7 Van Birgelen et al. 1995a and 1995b – I assume below is one of them? 

8 Van Birgelen, AP; Van der Kolk, J; Fase, KM; et al. (1995) Subchronic dose-response study of 2,3,7,8-

9 tetrachlorodibenzo-p-dioxin in female Sprague-Dawley rats. Toxicol Appl Pharmacol 132:1-13.

10 van den Heuvel, JP; Clark, GC; Kohn, MC; et al. (1994) Dioxin-responsive genes: examination of dose-response 

11 relationships using quantitative reverse transcriptase-polymerase chain reaction. Cancer Res 54:62–68.