Kassandra Fronczyk, Athanasios Kottas
04/29/2010 09:00 AM
Applied Mathematics & Statistics
Developmental toxicity studies investigate birth defects induced by toxic chemicals. The main purpose of these studies is to examine the relationship between the level of exposure to the toxin (dose level) and the probability of malformation. At each experimental dose level, a number of pregnant labratory animals are exposed to the toxin and the number of prenatal deaths, the number of live pups, and the number of live malformed pups from each dam are typically recorded. We present a Bayesian nonparametric approach to modeling and inference for developmental toxicity studies in which the animals are exposed before implantation. Here, the number of observed implants is expected to have a dose-dependent trend due to the interference of the toxin with successful implantations. We introduce a Poisson-Binomial mixture to model both the number of observed implants and the number of malformations. The modeling framework is built upon a dependent Dirichlet process prior where the dependence is governed by the dose level. The model is examined with a simulation study, and further illustrated with a dominant lethal assay data set.
