Multivariate lifetime data in presence of censoring and covariates: Use of semiparametric models under a Bayesian approach

A generalization of the popular proportional hazards model introduced by Cox (1972) is given by the class of semiparametric or transformation models to be used in the analysis of lifetime data in presence of censored data and covariates. In this study, we consider the use of semiparametric (transformation models) for the situation where there are two or more responses associated to the same individual or unit. We assume a hierarchical Bayesian analysis for semiparametric models considering the complete likelihood function obtained from the transformation models considering the unknown hazard functions as unknown latent variables and Markov Chain Monte Carlo (MCMC) methods to get the posterior summaries of interest. The dependence between multivariate responses for the same individual is captured by the introduction of another latent variable or frailty. Illustrations of the proposed methodology are presented considering two medical multivariate lifetime data sets.