Large sample Bayesian inference on the parameters of the proportional hazard models

This paper considers large sample Bayesian analysis of the proportional hazards model when interest is in inference on the parameters and estimation of the log relative risk for specified covariate vectors rather than on prediction of the survival function. We use a normal prior distribution for the parameters and make inferences based on the derived posterior distribution. The suggested approach is much simpler than alternative Bayesian analyses previously suggested for the proportional hazards models. Using simulated data we compare estimates obtained from the Bayesian analysis with those obtained from the full proportional hazards model and the reduced model after backwards elimination. We show that under a wider range of assumptions, the Bayesian analysis provides reduced estimation errors and improved rejection of noise variables. Finally, we illustrate the methodology using data from a large study of prognostic markers in breast cancer.