A Semiparametric Bayesian Approach for the Analysis of Competing Risks Data

Abstract

In survival studies, the failure (death) of an individual may be classified into one of k (k > 1) mutually exclusive classes, usually causes of failure. Competing risks models are used to analyze such situations, where the eventual failure (death) of an individual may due to any one of the k possible causes. In the present study, we introduce a semiparametric Bayesian method for the analysis of competing risks data. We assume that each cumulative baseline cause specific hazard rate function has a gamma prior distribution. A marginal likelihood function based on data and the prior parameter values is proposed for the estimation of regression parameters, by considering cumulative baseline cause specific hazard rate functions as a nuisance parameter. We derive posterior distributions of cumulative baseline cause specific hazard rate functions and then propose a Bayes estimator for the same under squared error loss function. A simulation study is carried out to assess the finite sample performance of the proposed method. We illustrate the practical utility of the method using a real lifetime data set.