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 from a single model; however, several challenges remain regarding implementing these methods for general analyses before model averaging becomes ready for risk assessment practice. Questions remain on the number and type of the models considered, what to do when one or more considered models degenerate to another model being considered, and if model averaging is comparable to other methods that account for model uncertainty (e.g., nonparametric dose-response modeling). For benchmark dose estimation, there is little guidance of Bayesian methods that allow inclusion of prior information for both the models and the parameters of the constituent models, which would make full use of the Bayesian paradigm. This manuscript introduces an approach that addresses these issues while providing a Bayesian model averaging framework; furthermore, in contrast to posterior-sampling methods that draw samples from the posterior distribution, we approximate the posterior density using maximum a-posteriori estimation. This approximation allows for accurate estimation while maintaining the speed of maximum likelihood estimation, which is crucial in many applications such as processing massive high throughput datasets. For the purpose of developing a software tool available to the general risk assessment community, we develop a novel model averaging approach, apply this method to real data, and compare it to other approaches through simulation study under a large variety of true underlying dose-response curves, some of which avoid parametric model specification as they are generated from monotone stochastic processes. Through the simulation study, the method is shown to be superior to a number of published software tools that represent competing proposed and traditional methods for the dose-response analysis of dichotomous data.