LARGE-SAMPLE BAYESIAN-INFERENCE ON THE PARAMETERS OF THE PROPORTIONALHAZARD MODELS

This paper considers large sample Bayesian analysis of the proportiona l hazards model when interest is in inference on the parameters and es timation of the log relative risk for specified covariate vectors rath er than on prediction of the survival function. We use a normal prior distribution for the parameters and make inferences based on the deriv ed posterior distribution. The suggested approach is much simpler than alternative Bayesian analyses previously suggested for the proportion al hazards models. Using simulated data we compare estimates obtained from the Bayesian analysis with those obtained from the full proportio nal hazards model and the reduced model after backwards elimination. W e show that under a wider range of assumptions, the Bayesian analysis provides reduced estimation errors and improved rejection of noise var iables. Finally, we illustrate the methodology using data from a large study of prognostic markers in breast cancer. (C) 1997 by John Wiley & Sons, Ltd.