A Bayesian joint model for continuous and zero-inflated count data in developmental toxicity studies

Abstract

In many applications, we frequently encounter correlated multiple outcomes measured on the same subject. Joint modeling of such multiple outcomes can improve e ffi ciency of inference compared to independent modeling. For instance, in developmental toxicity studies, fetal weight and number of malformed pups are measured on the pregnant dams exposed to di ff erent levels of a toxic substance, in which the association between such outcomes should be taken into account in the model. The number of malformations may possibly have many zeros, which should be analyzed via zero-inflated count models. Motivated by applications in developmental toxicity studies, we propose a Bayesian joint modeling framework for continuous and count outcomes with excess zeros. In our model, zero-inflated Poisson (ZIP) regression model would be used to describe count data, and a subject-specific random e ff ects would account for the correlation across the two outcomes. We implement a Bayesian approach using MCMC procedure with data augmentation method and adaptive rejection sampling. We apply our proposed model to dose-response analysis in a developmental toxicity study to estimate the benchmark dose in a risk assessment.