Nonparametric Bayesian methods for benchmark dose estimation

Quantitative Risk Assessment: Developing a Bayesian Approach to Dichotomous Dose-Response Uncertainty

Model averaging for dichotomous dose-response estimation is preferred to estimate the benchmark dose (BMD) from a single model, but challenges remain regarding implementing these methods for general analyses before model averaging is feasible to use in many risk assessment applications, and there is little work on Bayesian methods that include informative prior information for both the models and the parameters of the constituent models. This article introduces a novel approach that addresses many of the challenges seen while providing a fully Bayesian framework. Furthermore, in contrast to methods that use Monte Carlo Markov Chain, we approximate the posterior density using maximum a posteriori estimation. The approximation allows for an accurate and reproducible estimate while maintaining the speed of maximum likelihood, which is crucial in many applications such as processing massive high throughput data sets. We assess this method by applying it to empirical laboratory dose-response data and measuring the coverage of confidence limits for the BMD. We compare the coverage of this method to that of other approaches using the same set of models. Through the simulation study, the method is shown to be markedly superior to the traditional approach of selecting a single preferred model (e.g., from the U.S. EPA BMD software) for the analysis of dichotomous data and is comparable or superior to the other approaches.

A Review of Recent Advances in Benchmark Dose Methodology

In this review, recent methodological developments for the benchmark dose (BMD) methodology are summarized. Specifically, we introduce the advances for the main steps in BMD derivation: selecting the procedure for defining a BMD from a predefined benchmark response (BMR), setting a BMR, selecting a dose-response model, and estimating the corresponding BMD lower limit (BMDL). Although the last decade has shown major progress in the development of BMD methodology, there is still room for improvement. Remaining challenges are the implementation of new statistical methods in user-friendly software and the lack of consensus about how to derive the BMDL.

Weight of Evidence for Hazard Identification: A Critical Review of the Literature

BACKGROUND

Transparency when documenting and assessing weight of evidence (WOE) has been an area of increasing focus for national and international health agencies.

OBJECTIVE

The objective of this work was to conduct a critical review of WOE analysis methods as a basis for developing a practical framework for considering and assessing WOE in hazard identification in areas of application at the French Agency for Food, Environmental and Occupational Health and Safety (ANSES).

METHODS

Based on a review of the literature and directed requests to 63 international and national agencies, 116 relevant articles and guidance documents were selected. The WOE approaches were assessed based on three aspects: the extent of their prescriptive nature, their purpose-specific relevance, and their ease of implementation.

RESULTS

Twenty-four approaches meeting the specified criteria were identified from selected reviewed documents. Most approaches satisfied one or two of the assessed considerations, but not all three. The approaches were grouped within a practical framework comprising the following four stages: (1) planning the assessment, including scoping, formulating the question, and developing the assessment method; (2) establishing lines of evidence (LOEs), including identifying and selecting studies, assessing their quality, and integrating with studies of similar type; (3) integrating the LOEs to evaluate WOE; and (4) presenting conclusions.

DISCUSSION

Based on the review, considerations for selecting methods for a wide range of applications are proposed. Priority areas for further development are identified. https://doi.org/10.1289/EHP3067.

Bayesian model-averaged benchmark dose analysis via reparameterized quantal-response models

An important objective in biomedical and environmental risk assessment is estimation of minimum exposure levels that induce a pre-specified adverse response in a target population. The exposure points in such settings are typically referred to as benchmark doses (BMDs). Parametric Bayesian estimation for finding BMDs has grown in popularity, and a large variety of candidate dose-response models is available for applying these methods. Each model can possess potentially different parametric interpretation(s), however. We present reparameterized dose-response models that allow for explicit use of prior information on the target parameter of interest, the BMD. We also enhance our Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce point estimates and (lower) credible bounds, overcoming associated questions of model adequacy when multimodel uncertainty is present. An example from carcinogenicity testing illustrates the calculations.

Historical Context and Recent Advances in Exposure-Response Estimation for Deriving Occupational Exposure Limits

Virtually no occupational exposure standards specify the level of risk for the prescribed exposure, and most occupational exposure limits are not based on quantitative risk assessment (QRA) at all. Wider use of QRA could improve understanding of occupational risks while increasing focus on identifying exposure concentrations conferring acceptably low levels of risk to workers. Exposure-response modeling between a defined hazard and the biological response of interest is necessary to provide a quantitative foundation for risk-based occupational exposure limits; and there has been considerable work devoted to establishing reliable methods quantifying the exposure-response relationship including methods of extrapolation below the observed responses. We review several exposure-response modeling methods available for QRA, and demonstrate their utility with simulated data sets.

Benchmark Dose Analysis via Nonparametric Regression Modeling

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose-response modeling. It is a well-known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low-dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal-response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap-based confidence limits for the BMD. We explore the confidence limits' small-sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.

Semiparametric Bayesian joint modeling of a binary and continuous outcome with applications in toxicological risk assessment

Many dose-response studies collect data on correlated outcomes. For example, in developmental toxicity studies, uterine weight and presence of malformed pups are measured on the same dam. Joint modeling can result in more efficient inferences than independent models for each outcome. Most methods for joint modeling assume standard parametric response distributions. However, in toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by standard models. To address this issue, we propose a semiparametric Bayesian joint model for a binary and continuous response. In our model, a kernel stick-breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows flexible changes in distribution shape with dose shared across outcomes. The model also includes outcome-specific fixed effects to allow different location effects. In simulation studies, we found that the proposed model provides accurate estimates of toxicological risk when the data do not satisfy assumptions of standard parametric models. We apply our method to data from a developmental toxicity study of ethylene glycol diethyl ether.