Bayesian analysis of multivariate mortality data with large families

This paper presents a Bayesian method for the analysis of toxicological multivariate mortality data when the discrete mortality rate for each family of subjects at a given time depends on familial random effects and the toxicity level experienced by the family. Our aim is to model and analyse one set of such multivariate mortality data with large family sizes: the potassium thiocyanate (KSCN) tainted fish tank data of O'Hara Hines. The model used is based on a discretized hazard with additional time‐varying familial random effects. A similar previous study (using sodium thiocyanate (NaSCN)) is used to construct a prior for the parameters in the current study. A simulation‐based approach is used to compute posterior estimates of the model parameters and mortality rates and several other quantities of interest. Recent tools in Bayesian model diagnostics and variable subset selection have been incorporated to verify important modelling assumptions regarding the effects of time and heterogeneity among the families on the mortality rate. Further, Bayesian methods using predictive distributions are used for comparing several plausible models.