Semiparametric Bayesian joint modeling of clustered binary and continuous outcomes with informative cluster size in developmental toxicity assessment

Many authors have shown that joint modeling outcomes can effectively improve statistical power in studies involving clustered data. For instance, in developmental toxicity studies, fetal weight and malformation have been jointly analyzed to obtain more efficient inferences. Unfortunately, in these studies, the number of subjects is often correlated with the outcome values, which can result in biased estimates if the relationship is not accounted for. Most methods for joint modeling data with informative cluster size assume standard parametric response distributions. However, in developmental toxicity studies, it is possible that response distributions vary in location and shape with dose, which may not be easily captured by parametric models. Motivated by applications in developmental toxicity, we propose a semiparametric Bayesian joint model for clustered binary and continuous responses with informative cluster size. In our model, a nested kernel stick‐breaking process prior is assigned to the distribution of a random effect shared across outcomes, which allows simultaneous grouping of clusters and subjects within clusters, and flexible changes in distribution shape with dose shared across outcomes. We account for informative cluster size by modeling the number of subjects in each cluster using a Poisson regression model with a cluster‐specific random effect that is shared with the outcome variables. The Poisson assumption is relaxed by assigning a Dirichlet process prior to the unknown distribution of the cluster‐specific random effect. We apply our method to data from a developmental toxicity study of diethylhexyl phthalate.