Bayesian semiparametric analysis of developmental toxicology data

Modeling of developmental toxicity studies often requires simple parametric analyses of the dose-response relationship between exposure and probabilit y of a birth defect but poses challenges because of nonstandard distributio ns of birth defects for a fixed level of exposure. This article is motivate d by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmen tal toxicology studies. It combines parametric dose-response relationships with a flexible nonparametric specification of the distribution of the resp onse, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of t he response adapts nonparametrically to the observations is driven by the d ata, and (3) the marginal posterior distribution of the parameters of inter est is available in closed form. The logistic regression model, as well as many of its extensions such as the beta-binomial model and finite mixture m odels, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersi on diagnostics that can assist model specification, show how to derive post erior distributions of the effective dose parameters and predictive distrib utions of response, and discuss the sensitivity of the results to the choic e of the prior distribution.