Semiparametric Bayesian joint modeling of a binary and continuous outcome with applications in toxicological risk assessment

Many dose-response studies collect data on correlated outcomes. For example, in developmental toxicity studies, uterine weight and presence of malformed pups are measured on the same dam. Joint modeling can result in more efficient inferences than independent models for each outcome. Most methods for joint modeling assume standard parametric response distributions. However, in toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by standard models. To address this issue, we propose a semiparametric Bayesian joint model for a binary and continuous response. In our model, a kernel stick-breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows flexible changes in distribution shape with dose shared across outcomes. The model also includes outcome-specific fixed effects to allow different location effects. In simulation studies, we found that the proposed model provides accurate estimates of toxicological risk when the data do not satisfy assumptions of standard parametric models. We apply our method to data from a developmental toxicity study of ethylene glycol diethyl ether.