Risk Assessment for Toxicity Experiments with Joint Discrete-continuous Outcomes: a Bayesian Nonparametric Approach

We present a Bayesian nonparametric mixture modeling approach to inference and risk assessment for developmental toxicity studies. The primary objective of these studies is to determine the relationship between the level of exposure to a toxic chemical and the probability of a physiological or biochemical response. We consider the general data setting involving clustered categorical responses on the number of prenatal deaths, the number of live pups, and the number of live malformed pups from each laboratory animal, as well as continuous outcomes (e.g., body weight) on each of the live pups. We utilize mixture modeling to provide flexibility in the functional form of both the multivariate response distribution and the various dose-response curves of interest. The nonparametric mixture model is built from a dependent Dirichlet process prior, where the dependence of the mixing distribution is governed by the dose level. Particular emphasis is placed on the structure of the mixture kernel and the formulation of the nonparametric prior. The modeling framework enables general inference for the implied dose-response relationships and for dose-dependent correlations between the different endpoints, features which provide practical advances relative to traditional parametric models for developmental toxicology. The methodology is illustrated with data from a toxicity experiment that investigated the toxic effects of diethylene glycol dimethyl ether, an organic solvent.