Bayesian Frailty Models for Multi-State Survival Data

Abstract

Multi-state models can be viewed as generalizations of both the standard and competing risks models for survival data. Models for multi-state data have been the theme of many recent published works. Motivated by bone marrow transplant data, we develop a Bayesian model using the gap times between two successive events in a path of events experienced by a subject. Path specific frailties are introduced to capture the dependence among the gap times sharing the same path with two or more states. In this study, we focus on a single terminal event. Under improper prior distributions for the parameters, we establish propriety of the posterior distribution. An efficient Gibbs sampling algorithm is developed for sampling from the posterior distribution. A bone marrow transplant data set is analyzed in details to demonstrate the proposed methodology.