Document ID: EPA-HQ-OPP-2008-0140-0027
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2008-09-02T04:00Z

UNITED STATES ENVIRONMENTAL PROTECTION AGENCY

WASHINGTON, D.C. 20460      

	OFFICE OF PREVENTION, PESTICIDE

	AND TOXIC SUBSTANCES

	

  SEQ CHAPTER \h \r 1 MEMORANDUM

Date:  August 19, 2008

SUBJECT:	d-Phenothrin (Sumithrin®):  Benchmark Dose Analysis of
Toxicity Endpoint for Incidental Oral Exposure

 

PC Code:  069005	DP Barcode: 326934

Decision No.: 364966	Registration No.: 2596-150, 2596-151

Petition No.:  None	Regulatory Action: Reregistration

Assessment Type: BMD	Reregistration Case No.: 0426

TXR No.:  0052377	CAS No.: 026022-80-2

MRID No.:  47500101	40 CFR: NA

        	

FROM:	Becky Daiss

Biologist

Reregistration Branch 4/HED (7509C)

THROUGH:	Susan Hummel

Branch Senior Scientist

Reregistration Branch 4/HED (7509C)

TO:		Jennifer Howenstine 

Chemical Review Manager

		Reregistration Branch 3

		Special Review and Registration Division (7508C)

		       and

	Ann Sibold 

Review Manager

Insecticide Branch

	Registration Division (7505C)

	This provides a benchmark dose (BMD) analysis of organ weight data from
a d-phenothrin 2-generation rat reproduction study with 2 litters per
generation (MRID 40276404).  The phenothrin registrants submitted a
benchmark dose analysis of the rat reproduction study using EPA’s BMD
software.  HED agrees that a benchmark dose analysis may be
appropriately used to further refine the dose response relationship. 
HED conducted a separate BMD analysis for this study based in part on
the registrant’s submission.  

BMD Analysis

The toxicity endpoint for short- and intermediate-term incidental oral
exposures to d-phenothrin was selected from a 2-generation rat
reproduction study.  The NOAEL is 1000 ppm and the  LOAEL is 3000 ppm 
based on decreased body weight (4-6%) and increased liver weight in F0
and F1 parental animals, and an increase in absolute and relative spleen
weight, and decreased absolute uterine weight in F1 adults and on
decreased body weight gain during lactation of F2b pups, and decreased
litter size of F1b litters at day 1, decreased absolute heart and kidney
weight in F2b males, increased relative liver weight in male and female
F2b pups.  

A BMD is defined as an exposure due to a dose of a substance associated
with a specified low incidence of risk, generally in the range of 1% to
10%, of a health effect; or the dose associated with a specified measure
or change of a biological effect.  This dose is estimated using
statistical methods for fitting curves to experimental data.  

EPA’s Benchmark Dose Software (BMDS version 1.4.1) was used for the
BMD analysis of d-phenothrin organ weight data from the rat reproduction
study.  A benchmark dose (BMD) approach is used to more accurately
estimate a point of departure (POD) for the observed effects.  The BMDS
continuous models were selected to model the data being evaluated based
on the continuous nature of organ and body weight data.  BMDS linear,
polynomial and power models were used to derive the BMD10, the estimated
benchmark doses that results in 10% organ weight change, and the BMDL10,
the lower 95% confidence interval on the BMD10, for the data evaluated. 
The BMDS continuous model default option of relative deviation was used
for the benchmark response (BMR) type, with a corresponding BMR factor
of 0.1 (10%) used as a basis for BMD and BMDL derivation.  The default
benchmark response (BMR) level of 10% is considered reasonable for
determining a point of departure for organ weight effects because organ
weight changes below 10% are ordinarily not associated with adverse
effects.  Since it is particularly important that the data be adequately
modeled for BMD calculation, a p-value of 0.1 was used to assess
goodness of fit.  

Study Used for BMD Analysis						

Tesh, J.; Willoughby, C.; Fowler, J. (1986) Sumithrin: Effects upon
Reproductive Performance of Rats Treated Continuously throughout Two
Successive Generations: (ET-61-0101): Laboratory Project ID:
85/SUM009/331. Unpublished study prepared by Life Science Research. 1449
p.  MRID 40276404

Effects Modeled

F0 Liver Weight Females

F0 Relative Liver Weight Females

F1 Spleen Weight Males

F1 Relative Liver Weight Females

F1 Spleen Weight Females

F1 Relative Spleen Weight Females

F1 Uterus Weight Females

F1 Relative Uterus Weight Females

F2B Heart Weight Males

F2B Kidney Weight Males

F2B Body Weight Males

F2B Brain Weight Males

F2B Relative Liver Weight Males

The doses used for the BMD analysis were based on chemical intake data
(mg/kg/day) provided in the toxicity study.  Chemical intake for the F1
males was based on the lifetime average (arithmetic mean) intake for
each dose level.  Lifetime average doses (including dosing through
gestation and weaning) were used for the F0 and F1 females.  Average
doses from gestation to weaning for the F1 dams that gave birth to and
nursed F2b pups were used to represent dosage for the F2b pups. 
Dose-response model input data sets used in the analysis are attached
(Attachment 1).  

Summary of Results

	Summary results of the BMD analysis are provided in the following
table.  BMDLs are selected based on absolute model fit (goodness of fit
statistics i.e., P-value > 0.10), comparative model fit (Akaike
Information Criteria (AIC)), and visual inspection of modeled data fit. 
Results of the BMDS analysis were generally consistent across models. 
The linear and the power models generally produced the same PODs and fit
statistics.  Based on the AIC comparative goodness of fit measure, the
linear and power models consistently provided slightly better data fit. 
The polynomial model consistently generated lower BMDL10 values.  The
polynomial models also tended to produce exaggerated curves which may
not reflect biologically plausible dose response for the observed
effects.  BMDS dose-response graphs and select model outputs are
attached (Attachments 2 and 3).  

A BMDL10 of 100 mg/kg/day is recommended for use in risk assessment
based on the combined results of the linear, polynomial and power BMDS
models.  This endpoint is considered conservative based on the
methodology used to establish the dose levels used for the BMD analysis.
 

BMDS Modeling Results for d-Phenothrin – Rat Reproduction Study

Effects Modeled	BMDL10  Results by Model (mg/kg/day)

	Linear	Polynomial 2°	Power

F0 Liver Weight Females	169	90*	169

F0 Relative Liver Weight Females	156	90*	156

F1 Relative Liver Weight Females	184	118	184

F1 Spleen Weight Males	84	66*	84

F1 Spleen Weight Females	120	90*	120

F1 Relative Spleen Weight Females	94	90*	96

F1 Uterus Weight Females	103	90*	103

F1 Relative Uterus Weight Females	115	90*	115

F2B Heart Weight Males	136	92*	136

F2B Kidney Weight Males	129	92*	129

F2B Body Weight Males	153	92*	153

F2B Brain Weight Males	165	92*	165

F2B Relative Liver Weight Males	153	103	154

* Modeled BMDL10 is below the empirical NOAEL based on chemical intake
data.  Conservatively assume BMDL10 equals chemical intake NOAEL.  

Attachment

Attachment 1 – BMDS Inputs

Attachment 2 -   BMDS dose-response graphs and model outputs Attachment
1 – BMDS Inputs

Inputs for d-Phenothrin BMD Analysis

F0 Liver Wt Females (Table 43 pg 124)

Dose (ppm)	Dose (mkd) 2	N	Liver Weight (g)	SD

0	0	20	13.6	1.1

300	26.6	20	14.3	1.3

1000	90	20	14.6	2

3000	271	20	15.3	1.6

F0 Relative Liver Wt Females (Table 44 pg 126)	 

Dose (ppm)	Dose (mkd) 2	N	Relative Liver Weight (g)	SD

0	0	20	3.89	0.36

300	26.6	20	3.94	0.27

1000	90	20	4.14	0.43

3000	271	20	4.39	0.36

F1 Relative Liver Wt Females (Table 92 pg 196)

	Dose (ppm)	Dose (mkd) 2	N	Relative Liver Weight (g)	SD

0	0	18	3.57	0.21

300	26.6	17	3.59	0.27

1000	90	20	3.72	0.28

3000	271	20	3.96	0.25

F1 Spleen Wt Males (Table 89 pg 189)

Dose (ppm)	Dose (mkd) 2	N	Spleen Weight (g)	SD

0	0	20	0.87	0.1

300	15.5	20	0.88	0.11

1000	65.6	20	0.87	0.14

3000	198	20	0.9	0.68

F1 Spleen Wt Females (Table 91 pg 195)

Dose (ppm)	Dose (mkd) 2	N	Spleen Weight (g)	SD

0	0	19	0.53	0.06

300	26.6	17	0.55	0.06

1000	90	20	0.57	0.09

3000	271	19	0.61	0.13

F1 Relative Spleen Wt Females (Table 92 pg 197)

	Dose (ppm)	Dose (mkd) 2	N	Relative Spleen Weight (g)	SD

0	0	18	0.148	0.014

300	26.6	17	0.149	0.021

1000	90	20	0.154	0.022

3000	271	19	0.176	0.034

F1 Uterus Wt Females (Table 91 pg 195)	 	 

Dose (ppm)	Dose (mkd) 2	N	Uterus Weight (g)	SD

0	0	19	0.72	0.18

300	26.6	17	0.68	0.26

1000	90	20	0.6	0.11

3000	271	20	0.6	0.13

F1 Relative Uterus Wt Females (Table 92 pg 197)

	Dose (ppm)	Dose (mkd) 2	N	Relative Uterus Weight (g)	SD

0	0	18	0.203	0.049

300	26.6	17	0.186	0.074

1000	90	20	0.162	0.03

3000	271	20	0.173	0.039

F2B Heart Weight Males (Table 85 pg 178)

Dose (ppm)	Dose (mkd) 2	N	Heart Weight (g)	SD

0	0	10	0.5	0.06

300	26.4	10	0.479	0.034

1000	92	10	0.456	0.031

3000	285	10	0.417	0.044

F2B Kidney Weight Males (Table 85 pg 178)

	Dose (ppm)	Dose (mkd) 2	N	Kidney Weight (g)	SD

0	0	10	1.13	0.14

300	26.4	10	1.05	0.06

1000	92	10	1.01	0.08

3000	285	10	0.93	0.15

F2B Body Weight Males (Table 85 pg 178)

Dose (ppm)	Dose (mkd) 2	N	Body Weight (g)	SD

0	0	9	85.5	10.3

300	26.4	10	82.5	5.8

1000	92	10	79.2	4

3000	285	10	73.9	11.1

F2B Relative Brain Weight Males (Table 86 pg 181)

	Dose (ppm)	Dose (mkd) 2	N	Brain Weight (g)	SD

0	0	9	1.858	0.157

300	26.4	10	1.908	0.125

1000	92	10	1.957	0.131

3000	285	10	2.083	0.224

F2B Relative Liver Weight Males (Table 86 pg 182)

	Dose (ppm)	Dose (mkd) 2	N	Relative Liver Weight (g)	SD

0	0	9	5.08	0.4

300	26.4	10	4.98	0.39

1000	92	10	5.22	0.39

3000	285	10	5.67	0.36

F2B Relative Liver Weight Females (Table 88 pg 186)

	Dose (ppm)	Dose (mkd) 2	N	Relative Liver Weight (g)	SD

0	0	10	5.26	0.24

300	26.4	10	5.01	0.23

1000	92	10	5.23	0.33

3000	285	10	5.86	0.33

1 Dose based on actual chemical intake data

Attachment 2  - BMDS Outputs

F0 Liver Weight Females

Model	BMD10	BMDL10	P-Value	AIC

Linear	258	169	0.41	152

Polynomial 2°	157	63	0.39	154

Power	258	169	0.41	152

F0 Relative Liver Weight Females 

Model	BMD10	BMDL10	P-Value	AIC

Linear	212	156	0.66	-81

Polynomial 2°	155	76	0.73	-80

Power	212	156	0.66	-81



F1 Relative Liver Weight Females 

Model	BMD10	BMDL10	P-Value	AIC

Linear	243	184	0.89	-128

Polynomial 2°	232	118	0.71	-126

Power	243	184	0.89	-128

F1 Spleen Weight Males 

Model	BMD10	BMDL10	P-Value	AIC

Linear	639	84	0.99	-84

Polynomial 2°	317	24	0.91	-82

Power	218	84	0.91	-82





F1 Relative Spleen Weight Females 

Model	BMD10	BMDL10	P-Value	AIC

Linear	136	94	0.88	-475

Polynomial 2°	174	65	0.95	-472

Power	171	96	0.99	-474



F1 Uterus Weight Females 

Model	BMD10	BMDL10	P-Value	AIC

Linear	179	103	0.25	-184

Polynomial 2°	46	26	0.93	-184

Power	179	103	0.25	-184

 





F2B Heart Weight Males 

Model	BMD10	BMDL10	P-Value	AIC

Linear	183	136	0.54	-207

Polynomial 2°	111	58	0.68	-206

Power	183	136	0.54	-207



F2B Kidney Weight Males 

Model	BMD10	BMDL10	P-Value	AIC

Linear	182	129	0.32	-130

Polynomial 2°	90	47	0.34	-129

Power	182	129	0.32	-130



F2B Body Weight Males 

Model	BMD10	BMDL10	P-Value	AIC

Linear	226	153	0.72	206

Polynomial 2°	145	61	0.76	207

Power	119	80	0.72	206





Statistically Significant results but Poor BMDS Model Fit p < 0.1 

F2B Relative Liver Wt Females 

Model	BMD10	BMDL10	P-Value	AIC

Linear	157	123	0.52	-41

Polynomial	185	83	0.29	-39

Power	188	125	0.31	-39

Spleen Wt Males

==================================================================== 

   	  Polynomial Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt

 							Wed Aug 06 08:01:17 2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

   The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =     0.126025

                            rho =            0   Specified

                         beta_0 =     0.870503

                         beta_1 =  0.000136116

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1

     alpha            1     3.2e-009    -4.1e-009

    beta_0     3.2e-009            1        -0.67

    beta_1    -4.1e-009        -0.67            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha         0.119761        0.0189359           0.0826476   
        0.156875

         beta_0         0.870503        0.0519428            0.768697   
        0.972308

         beta_1      0.000136116      0.000496681        -0.000837362   
      0.00110959

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0    20       0.87        0.871          0.1        0.346      
-0.00649

 15.5    20       0.88        0.873         0.11        0.346        
0.0955

 65.6    20       0.87        0.879         0.14        0.346        
-0.122

  198    20        0.9        0.897         0.68        0.346        
0.0329

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           44.902731            5     -79.805462

             A2           99.284439            8    -182.568877

             A3           44.902731            5     -79.805462

         fitted           44.890181            3     -83.780363

              R           44.852647            2     -85.705294

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              108.864          6          <.0001

   Test 2              108.763          3          <.0001

   Test 3              108.763          3          <.0001

   Test 4            0.0250993          2          0.9875

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is less than .1.  Consider running a 

non-homogeneous variance model

The p-value for Test 3 is less than .1.  You may want to consider a 

different variance model

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =         639.53

            BMDL =        84.4008

==================================================================== 

   	  Polynomial Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt

 							Wed Aug 06 08:06:22 2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

   The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =     0.126025

                            rho =            0   Specified

                         beta_0 =     0.874783

                         beta_1 = -0.000121189

                         beta_2 = 1.25015e-006

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1       beta_2

     alpha            1     4.4e-010    -6.9e-011    -8.5e-011

    beta_0     4.4e-010            1        -0.69         0.59

    beta_1    -6.9e-011        -0.69            1        -0.98

    beta_2    -8.5e-011         0.59        -0.98            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha         0.119742        0.0189329           0.0826344   
         0.15685

         beta_0         0.874783        0.0643098            0.748738   
         1.00083

         beta_1     -0.000121189       0.00233296         -0.00469371   
      0.00445133

         beta_2     1.25015e-006     1.10752e-005       -2.04568e-005   
    2.29572e-005

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0    20       0.87        0.875          0.1        0.346       
-0.0618

 15.5    20       0.88        0.873         0.11        0.346        
0.0878

 65.6    20       0.87        0.872         0.14        0.346       
-0.0286

  198    20        0.9          0.9         0.68        0.346        
0.0026

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           44.902731            5     -79.805462

             A2           99.284439            8    -182.568877

             A3           44.902731            5     -79.805462

         fitted           44.896552            4     -81.793103

              R           44.852647            2     -85.705294

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              108.864          6          <.0001

   Test 2              108.763          3          <.0001

   Test 3              108.763          3          <.0001

   Test 4            0.0123588          1          0.9115

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is less than .1.  Consider running a 

non-homogeneous variance model

The p-value for Test 3 is less than .1.  You may want to consider a 

different variance model

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =          317.4

            BMDL =        23.7592

==================================================================== 

   	  Power Model. (Version: 2.14;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt

 							Wed Aug 06 08:09:26 2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

   The form of the response function is: 

   Y[dose] = control + slope * dose^power

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   The power is restricted to be greater than or equal to 1

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =     0.126025

                            rho =            0   Specified

                        control =         0.87

                          slope =   0.00306657

                          power =     0.431264

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha      control        slope        power

     alpha            1     3.3e-009    -1.7e-005    -1.7e-005

   control    -7.5e-009            1     -0.00029     8.1e-005

     slope     3.8e-006     -0.00029            1           -1

     power    -3.8e-006     8.1e-005           -1            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha          0.11974        0.0189326           0.0826332   
        0.156848

        control         0.873333         0.044673            0.785776   
        0.960891

          slope     3.78513e-031     3.07838e-027       -6.03314e-027   
     6.0339e-027

          power          12.5608           1537.9            -3001.68   
          3026.8

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0    20       0.87        0.873          0.1        0.346       
-0.0431

 15.5    20       0.88        0.873         0.11        0.346        
0.0862

 65.6    20       0.87        0.873         0.14        0.346       
-0.0431

  198    20        0.9          0.9         0.68        0.346     
8.27e-008

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           44.902731            5     -79.805462

             A2           99.284439            8    -182.568877

             A3           44.902731            5     -79.805462

         fitted           44.897163            4     -81.794326

              R           44.852647            2     -85.705294

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              108.864          6          <.0001

   Test 2              108.763          3          <.0001

   Test 3              108.763          3          <.0001

   Test 4             0.011136          1           0.916

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is less than .1.  Consider running a 

non-homogeneous variance model

The p-value for Test 3 is less than .1.  You may want to consider a 

different variance model

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

               Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD = 217.612       

            BMDL = 84.6088       

F2B Relative Liver Wt Males

==================================================================== 

   	  Linear Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Wed Aug 06 09:49:09
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =      0.14812

                            rho =            0   Specified

                         beta_0 =      5.00476

                         beta_1 =   0.00231011

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1

     alpha            1    -1.7e-010     1.2e-009

    beta_0    -1.7e-010            1        -0.68

    beta_1     1.2e-009        -0.68            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha         0.136086        0.0308175           0.0756853   
        0.196488

         beta_0          5.00118        0.0804478              4.8435   
         5.15885

         beta_1       0.00232607      0.000528502          0.00129023   
      0.00336191

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0     9       5.08            5          0.4        0.369         
0.641

   26    10       4.98         5.06         0.39        0.369          
-0.7

   92    10       5.22         5.22         0.39        0.369        
0.0413

  285    10       5.67         5.66         0.36        0.369        
0.0505

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           19.849949            5     -29.699898

             A2           19.905731            8     -23.811463

             A3           19.849949            5     -29.699898

         fitted           19.392062            3     -32.784124

              R           11.528531            2     -19.057061

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              16.7544          6         0.01023

   Test 2             0.111564          3          0.9904

   Test 3             0.111564          3          0.9904

   Test 4             0.915774          2          0.6326

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =        215.005

            BMDL =        152.815

==================================================================== 

   	  Polynomial Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Wed Aug 06 09:50:51
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =      0.14812

                            rho =            0   Specified

                         beta_0 =      5.02406

                         beta_1 =   0.00153781

                         beta_2 = 2.58955e-006

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1       beta_2

     alpha            1    -2.2e-008     3.6e-008    -3.6e-008

    beta_0    -2.2e-008            1        -0.72         0.63

    beta_1     3.6e-008        -0.72            1        -0.98

    beta_2    -3.6e-008         0.63        -0.98            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha         0.135805        0.0307537           0.0755286   
        0.196081

         beta_0          5.01966         0.103357             4.81709   
         5.22224

         beta_1       0.00161646       0.00255005         -0.00338154   
      0.00661446

         beta_2      2.3668e-006     8.32101e-006       -1.39421e-005   
    1.86757e-005

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0     9       5.08         5.02          0.4        0.369         
0.491

   26    10       4.98         5.06         0.39        0.369        
-0.715

   92    10       5.22         5.19         0.39        0.369         
0.271

  285    10       5.67         5.67         0.36        0.369       
-0.0223

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           19.849949            5     -29.699898

             A2           19.905731            8     -23.811463

             A3           19.849949            5     -29.699898

         fitted           19.432472            4     -30.864944

              R           11.528531            2     -19.057061

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              16.7544          6         0.01023

   Test 2             0.111564          3          0.9904

   Test 3             0.111564          3          0.9904

   Test 4             0.834954          1          0.3608

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =        231.837

            BMDL =        103.096

==================================================================== 

   	  Power Model. (Version: 2.14;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Wed Aug 06 09:52:15
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = control + slope * dose^power

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   The power is restricted to be greater than or equal to 1

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =      0.14812

                            rho =            0   Specified

                        control =         4.98

                          slope =   0.00351618

                          power =     0.933981

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha      control        slope        power

     alpha            1     3.3e-009     1.9e-009    -2.2e-009

   control     3.3e-009            1        -0.65         0.62

     slope     1.9e-009        -0.65            1           -1

     power    -2.2e-009         0.62           -1            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha         0.135522        0.0306898           0.0753715   
        0.195673

        control          5.02588        0.0979186             4.83396   
         5.21779

          slope      0.000579886       0.00235882         -0.00404332   
      0.00520309

          power           1.2419         0.706931           -0.143665   
         2.62745

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0     9       5.08         5.03          0.4        0.368         
0.441

   26    10       4.98         5.06         0.39        0.368        
-0.679

   92    10       5.22         5.19         0.39        0.368         
0.299

  285    10       5.67         5.67         0.36        0.368       
-0.0388

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           19.849949            5     -29.699898

             A2           19.905731            8     -23.811463

             A3           19.849949            5     -29.699898

         fitted           19.473058            4     -30.946115

              R           11.528531            2     -19.057061

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              16.7544          6         0.01023

   Test 2             0.111564          3          0.9904

   Test 3             0.111564          3          0.9904

   Test 4             0.753783          1          0.3853

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

               Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD = 232.078       

            BMDL = 154.244       

Relative Liver Wt Females

==================================================================== 

   	  Linear Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Wed Aug 06 10:44:51
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =     0.082075

                            rho =            0   Specified

                         beta_0 =      5.07781

                         beta_1 =   0.00260235

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1

     alpha            1       9e-011    -9.4e-010

    beta_0       9e-011            1        -0.67

    beta_1    -9.4e-010        -0.67            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha        0.0890665        0.0199159           0.0500321   
        0.128101

         beta_0          5.07781         0.063588             4.95318   
         5.20244

         beta_1       0.00260235      0.000423063          0.00177316   
      0.00343154

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0    10       5.26         5.08         0.24        0.298          
1.93

   26    10       5.01         5.15         0.23        0.298         
-1.44

   92    10       5.23         5.32         0.33        0.298        
-0.924

  285    10       5.86         5.82         0.33        0.298         
0.429

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           32.109647            5     -54.219293

             A2           33.248386            8     -50.496772

             A3           32.109647            5     -54.219293

         fitted           28.367445            3     -50.734889

              R           15.052602            2     -26.105204

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              36.3916          6          <.0001

   Test 2              2.27748          3          0.5168

   Test 3              2.27748          3          0.5168

   Test 4               7.4844          2          0.0237

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is less than .1.  You may want to try a different

model

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =        195.124

            BMDL =        151.164

==================================================================== 

   	  Polynomial Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Wed Aug 06 10:47:56
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =     0.082075

                            rho =            0   Specified

                         beta_0 =      5.16868

                         beta_1 =    -0.001032

                         beta_2 = 1.21861e-005

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1       beta_2

     alpha            1     1.1e-009    -3.9e-011    -5.2e-010

    beta_0     1.1e-009            1        -0.71         0.61

    beta_1    -3.9e-011        -0.71            1        -0.98

    beta_2    -5.2e-010         0.61        -0.98            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha        0.0815686        0.0182393           0.0458202   
        0.117317

         beta_0          5.16868        0.0771258             5.01751   
         5.31984

         beta_1        -0.001032        0.0019381         -0.00483062   
      0.00276662

         beta_2     1.21861e-005     6.35516e-006       -2.69788e-007   
     2.4642e-005

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0    10       5.26         5.17         0.24        0.286          
1.01

   26    10       5.01         5.15         0.23        0.286         
-1.55

   92    10       5.23         5.18         0.33        0.286         
0.588

  285    10       5.86         5.86         0.33        0.286       
-0.0484

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           32.109647            5     -54.219293

             A2           33.248386            8     -50.496772

             A3           32.109647            5     -54.219293

         fitted           30.126221            4     -52.252442

              R           15.052602            2     -26.105204

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              36.3916          6          <.0001

   Test 2              2.27748          3          0.5168

   Test 3              2.27748          3          0.5168

   Test 4              3.96685          1          0.0464

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is less than .1.  You may want to try a different

model

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =        252.599

            BMDL =        192.768

==================================================================== 

   	  Polynomial Model. (Version: 2.12;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Thu Aug 07 10:25:26
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ...

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   Signs of the polynomial coefficients are not restricted

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =      0.14812

                            rho =            0   Specified

                         beta_0 =      5.02417

                         beta_1 =   0.00152596

                         beta_2 = 2.63032e-006

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha       beta_0       beta_1       beta_2

     alpha            1    -2.1e-008     3.4e-008    -3.5e-008

    beta_0    -2.1e-008            1        -0.73         0.63

    beta_1     3.4e-008        -0.73            1        -0.98

    beta_2    -3.5e-008         0.63        -0.98            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha         0.135834        0.0307605           0.0755451   
        0.196124

         beta_0          5.01976          0.10365             4.81661   
         5.22291

         beta_1       0.00160492       0.00255253         -0.00339795   
       0.0066078

         beta_2     2.40664e-006      8.3247e-006       -1.39095e-005   
    1.87228e-005

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0     9       5.08         5.02          0.4        0.369          
0.49

 26.4    10       4.98         5.06         0.39        0.369        
-0.719

   92    10       5.22         5.19         0.39        0.369         
0.276

  285    10       5.67         5.67         0.36        0.369       
-0.0226

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           19.849949            5     -29.699898

             A2           19.905731            8     -23.811463

             A3           19.849949            5     -29.699898

         fitted           19.428201            4     -30.856402

              R           11.528531            2     -19.057061

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              16.7544          6         0.01023

   Test 2             0.111564          3          0.9904

   Test 3             0.111564          3          0.9904

   Test 4             0.843496          1          0.3584

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is greater than .1.  The model chosen seems 

to adequately describe the data

 

             Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD =        232.036

            BMDL =        103.192

==================================================================== 

   	  Power Model. (Version: 2.14;  Date: 02/20/2007) 

  	  Input Data File: C:\BMDS\UNSAVED1.(d)  

  	  Gnuplot Plotting File:  C:\BMDS\UNSAVED1.plt Wed Aug 06 10:48:47
2008

 ==================================================================== 

 BMDS MODEL RUN 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    The form of the response function is: 

   Y[dose] = control + slope * dose^power

   Dependent variable = MEAN

   Independent variable = dose

   rho is set to 0

   The power is restricted to be greater than or equal to 1

   A constant variance model is fit

   Total number of dose groups = 4

   Total number of records with missing values = 0

   Maximum number of iterations = 250

   Relative Function Convergence has been set to: 1e-008

   Parameter Convergence has been set to: 1e-008

                  Default Initial Parameter Values  

                          alpha =     0.082075

                            rho =            0   Specified

                        control =         5.01

                          slope =  0.000988471

                          power =      1.19537

           Asymptotic Correlation Matrix of Parameter Estimates

           ( *** The model parameter(s)  -rho   

                 have been estimated at a boundary point, or have been
specified by the user,

                 and do not appear in the correlation matrix )

                  alpha      control        slope        power

     alpha            1     1.1e-009    -1.9e-009     1.9e-009

   control     1.1e-009            1        -0.55         0.54

     slope    -1.9e-009        -0.55            1           -1

     power     1.9e-009         0.54           -1            1

                                 Parameter Estimates

                                                         95.0% Wald
Confidence Interval

       Variable         Estimate        Std. Err.     Lower Conf. Limit 
 Upper Conf. Limit

          alpha        0.0821321        0.0183653           0.0461368   
        0.118127

        control          5.14238        0.0642091             5.01653   
         5.26823

          slope     5.11233e-006     3.53688e-005       -6.42092e-005   
    7.44339e-005

          power          2.09703          1.21652           -0.287307   
         4.48137

     Table of Data and Estimated Values of Interest

 Dose       N    Obs Mean     Est Mean   Obs Std Dev  Est Std Dev  
Scaled Res.

------     ---   --------     --------   -----------  -----------  
----------

    0    10       5.26         5.14         0.24        0.287           
1.3

   26    10       5.01         5.15         0.23        0.287         
-1.51

   92    10       5.23         5.21         0.33        0.287         
0.226

  285    10       5.86         5.86         0.33        0.287       
-0.0112

 Model Descriptions for likelihoods calculated

 Model A1:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

 Model A2:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma(i)^2

 Model A3:        Yij = Mu(i) + e(ij)

           Var{e(ij)} = Sigma^2

     Model A3 uses any fixed variance parameters that

     were specified by the user

 Model  R:         Yi = Mu + e(i)

            Var{e(i)} = Sigma^2

                       Likelihoods of Interest

            Model      Log(likelihood)   # Param's      AIC

             A1           32.109647            5     -54.219293

             A2           33.248386            8     -50.496772

             A3           32.109647            5     -54.219293

         fitted           29.988517            4     -51.977034

              R           15.052602            2     -26.105204

                   Explanation of Tests  

 Test 1:  Do responses and/or variances differ among Dose levels? 

          (A2 vs. R)

 Test 2:  Are Variances Homogeneous? (A1 vs A2)

 Test 3:  Are variances adequately modeled? (A2 vs. A3)

 Test 4:  Does the Model for the Mean Fit? (A3 vs. fitted)

 (Note:  When rho=0 the results of Test 3 and Test 2 will be the same.)

                     Tests of Interest    

   Test    -2*log(Likelihood Ratio)  Test df        p-value    

   Test 1              36.3916          6          <.0001

   Test 2              2.27748          3          0.5168

   Test 3              2.27748          3          0.5168

   Test 4              4.24226          1         0.03943

The p-value for Test 1 is less than .05.  There appears to be a

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1.  A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1.  The modeled variance appears

 to be appropriate here

The p-value for Test 4 is less than .1.  You may want to try a different

model

 

               Benchmark Dose Computation

Specified effect =           0.1

Risk Type        =     Relative risk 

Confidence level =          0.95

             BMD = 242.961       

            BMDL = 182.751       

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