In applications that involve clustered data, such as longitudinal studies and developmental toxicity experiments, the number of subunits within a cluster is often correlated with outcomes measured on the individual subunits. Analyses that ignore this dependency can produce biased inferences. This article proposes a Bayesian framework for jointly modeling cluster size and multiple categorical and continuous outcomes measured on each subunit. We use a continuation ratio probit model for the cluster size and underlying normal regression models for each of the subunit-specific outcomes. Dependency between cluster size and the different outcomes is accommodated through a latent variable structure. The form of the model facilitates posterior computation via a simple and computationally e±cient Gibbs sampler. The approach is illustrated through application to developmental toxicity data, and applications to joint modeling of longitudinal and event time data are discussed.

Keywords: Continuation ratio; Developmental toxicity; Factor analysis; Informative cluster size; Litter size; Multiple outcomes; Probit model; Random length data

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