Bayesian variable selection method for censored survival data

A Bayesian variable selection method for censored data is proposed in this paper. Based on the sufficiency and asymptotic normality of the maximum par tial likelihood estimator, we approximate the posterior distribution of the parameters in a proportional hazards model. We consider a parsimonious mod el as the full model with some covariates unobserved and replaced by their conditional expected values. A loss function based on the posterior expecte d estimation error of the log-risk for the proportional hazards model is us ed to select a parsimonious model. We derive computational expressions for this loss function for both continuous and binary covariates. This approach provides an extension of Lindley's (1968, Journal of the Royal Statistical Society, Series B 30, 31-66) variable selection criterion for the linear c ase. Data from a randomized clinical trial of patients with primary biliary cirrhosis of the liver (PBC) (Fleming and Harrington, 1991, Counting Proce sses and Survival Analysis) is used to illustrate the proposed method and a simulation study compares it with the backward elimination procedure.