# Presentation: 090743

## Dose- Response Modeling

- Jeff Gift1 and R. Woodrow Setzer1; Contributors: Kenneth G. Brown2; Gary Foureman1, John Fox3; Yiliang Zhu4
- 1U.S. Environmental Protection Agency, Office of Research and Development, Research Triangle Park, NC
- 2KBinc., Chapel Hill, NC; 3U.S. Environmental Protection Agency, Office of Research and Development, Washington, DC; 4University of South Florida

- What can be done to support Agency risk assessors in their efforts to model and characterize dose-response data for the purposes of Agency risk assessments?

**Research Goals**

**Current Methods/Approaches In Use**

**Impact and Outcomes**

**Software Development**

**Future Directions**

**Science Question**

- To answer this question the various study designs, chemical modes of action and dose-response shapes an assessor may encounter need to be considered. Ongoing dose-response modeling research and support activity within the Agency can be divided into five areas: (1) **accounting for various** **study designs** risk assessors will encounter, (2) **accounting for a chemical’s** **mode of action** (MOA) and the various dose-response shapes an assessor will encounter, (3) **interpreting model results**, (4) **developing user-friendly model interfaces**, and (5) **providing guidance and training** on the application of models and the linkage of dose-response modeling to risk assessment.

- Benchmark dose (BMD) is an approach to dose-response assessment first introduced by Crump (Crump, 1984) as an alternative to the NOAEL (no observed adverse effect level) for use as a point of departure to calculate an allowable daily intake (ADI) or reference dose or concentration (RfD, RfC). In BMD analysis, dose-response modeling of appropriate data sets is used to interpolate an estimate of the dose that would be expected to yield a prespecified response (the benchmark response, BMR), and a confidence interval for that dose.  Typically, the lower end of a one-sided 95% confidence interval for the BMD is used (see Figure 1). The Agency has developed models for its benchmark dose software (BMDS) that account for standard study designs involving dichotomous (e.g., tumor), continuous (e.g., organ weight) and nested (e.g., effect in pups following parental exposures) dose-response data (USEPA, 2000).
- The Agency has also developed categorical regression (CatReg) software to evaluate dose-responses for chemicals that elicit effects that can be evaluated over time and/or categorically graded by severity (see Figure 2). The primary advantage of CatReg over the BMD and other dose-response modeling approaches is its ability to incorporate data from multiple studies, and address exposure duration as well as exposure level, all simultaneously.  A recent paper by Brown and Strickland (2003) demonstrates how CatReg can be used in this manner to bring more data to bear on determining a benchmark dose.  They evaluated several studies of a specific endpoint data (mortality) in a single species (rats) for hydrogen sulfide, with options currently available on CatReg.  This approach illustrates CatReg’s ability to evaluate the potential for combining data from different studies, a CatReg capability  that is expected to grow in popularity as the Agency refines its guidance for the application of categorical regression to dose-response.

- The Agency is charged by Congress with developing health benchmarks that protect the public from potentially harmful chemical exposures. Benchmark dose methods are currently used or considered in all Agency  IRIS and most other program office risk assessments.  Over the past few years, the Agency has made BMDS easier to use by improving its user interface and modeling capabilities to keep up with the state-of-the-science in this important and growing risk assessment field (Filipsson et al., 2003).  At the same time, the customer base for BMDS has expanded to over 2,000 registered users in areas of industry, academia and government from over 80 countries.   The Agency plans to maintain and improve dose-response modeling software such as BMDS and CatReg so that they continue to provide a valuable resources to Agency program office, regional, State and international risk assessors.

- ORD laboratories and centers are working together to develop new models that will be able to assess studies which measure responses (e.g., neurotoxicology batteries) over time (Zhu et al. (a), 2004). Dose-response modeling of longitudinal data needs to account for the control population’s time-trajectory and capture dose-effects in a critical time window as exposure effects may be reversible (see Figure 4). Further, BMD calculation should also reflect the time-course of toxic effects (Zhu et al. (b), 2004).  Other models are planned which will allow for the analysis of dose-response for effects measured over time during subchronic or chronic exposure studies, and for more flexible models for continuous and quantal data. Future plans include the development of EPA BMDS models that will allow for a consistent Agency approach to the assessment of chemicals that induce early mortality and early tumor responses. The first planned enhancement will be a multistage Weibull model for times-to-event that accounts for censored observations, having a user interface, risk estimates and confidence intervals that are consistent with the current BMDS software and Agency recommendations.
- Some fundamental aspects of dose-response, such as population variability, remain to be addressed.  The slope of the lines in Figure 5 demonstrate the degree of variability in dose-response that may exist between a test animal population and a human population, either general or sensitive, with the more shallow slope indicating more variability (adapted from Evans et al., 2001).  There are also outstanding statistical issues related to the calculation and use of BMD.  Research sponsored by an NCER has explored confidence interval calculation and sensitivity of the calculated interval to mis-specifying the model.  Ongoing research in ORD is directed towards understanding the consequences of and adjusting for the fact that we do not know the true dose-response functions when we estimate BMDs using dose-response modeling. This results in uncertainty that increases as we require inferences for responses that are far removed from the data. A helpful tool being considered for addition to BMDS is graphical representation of the set of model functions that correspond to the values in the confidence interval for the BMD.  This gives a visual indication of the models that are consistent with the data in a defined statistical sense (see Figure 6).
- The Agency is currently revising BMDS and CatReg and associated training materials in response to comments and suggestions made by Agency and outside experts at the Dose-Response Modeling Workshop held July 30-31, 2002. Suggestions made at the workshop related to both existing and future software and training needs in the area of dose-response modeling.  In order to keep pace with EPA guidance and the state-of-the-art in chemical risk assessment, ORD plans to continue to improve these important Agency tools and expand upon the existing training resources.

**References**

- Brown and Strickland, 2003.  Regulatory Toxicology and Pharmacology 37:305–317
- Crump KS, 1984.  Fundam Appl Toxicol. 4(5):854-71.Evans JS, et al. 2001.  Risk Anal. 21(4):697-717.
- Filipsson, AF, et al., 2003. Critical Reviews in Toxicology, 33(5):505–542.
- Setzer, 2004
- USEPA, 2000 Benchmark dose technical support document [external review draft]. Risk Assessment Forum, Washington, DC; EPA/630/R-00/001.
- USEPA, 2001.  Help Manual for Benchmark Dose Software Version 1.3. EPA 600/R-00/014F
- Zhu et al. (a), 2004. Regulatory Toxicology and Pharmacology, in press.
- Zhu et al. (b), 2004. Regulatory Toxicology and Pharmacology, under review.

**A.  Are my data worth modeling?**

**C.  Does my model fit the data?**

**B.  Is my model appropriate for my data?**

**D.  Have I considered all available model options?**

**D.2.  Are BMDL estimates within a 3-fold range?**

**Can I edit my data (e.g. drop high dose)?**

**Try another model?**

**Use the lowest BMDL**

**D.3. Are** AIC values different from one another?

- Yes

- Yes

- Yes

- Yes

- Yes

- No

- No

- No

- No

- No

- No

**START**

- Yes

- No

**STOP**

**Use BMDL from model that results in the lowest AIC**

- Yes

**Use avg. or geom. mean of BMDLs**

- No

**E.  Choose a BMR**

***Benchmark***
*** ******Dose****** ***

**Training Courses/Guidance**

- Ultimately, Agency risk assessors need guidance and training in the use of these models, and the interpretation of their results (see Figure 3).  To this end, a web-based, online training program was developed by ORD.  The online training course for BMDS reviews the benchmark dose methodology, consistent with the most recent draft of our BMD technical guidance document (USEPA, 2000), and the application of BMDS to the various types of data sets that risk assessors may encounter (USEPA, 2002).

***CatReg***

***Model***
*** ******Selection***

- BMR

- BMDL

***Figure 1***

***Figure 5***

***Figure 2***

***Figure 3***

***Figure 4***

***Figure 6***

***Plots ***
*** ******Showing ***
*** ******Model ***
*** ******Flexibility***

***Population Variability***
***In Dose-Response***

***Longitudinal ***
***Data Dose-***
***Response***

**Future Methods/Approaches Under Consideration**

- Change in hindlimb grip strength of rats after a single dose exposure to TET (top row). Each panel consists of 10 spaghetti lines, one for each rat that was measured at 0, 2, 24, and 168 hours. Data were fit by a toxico-diffusion model with adjustment for individual variation (bottom row).

- 3D spline plot of relationship between ln(time), dose and grip strength.