Semiparametric Bayesian joint models of multivariate longitudinal and survival data

Joint models for longitudinal and survival data are often used to investigate the association between longitudinal data and survival data in many studies. A common assumption for joint models is that random effects are distributed as a fully parametric distribution such as multivariate normal distribution. The fully parametric distribution assumption of random effects is relaxed by specifying a centered Dirichlet Process Mixture Model (CDPMM) for a general distribution of random effects because of some good properties of CDPMM such as inducing zero mean and continuous probability distribution of random effects. A computationally feasible Bayesian case-deletion diagnostic based on the ϕ-divergence is proposed to identify the potential influential cases in the joint models. Several simulation studies and a real example are used to illustrate our proposed methodologies.