Prior Distibutions Ans Bayesian Computation for Proportional Hazards Models

In this paper, we propose a class of informative prior distributions for Cox’s proportional hazards model. A novel construction of the prior is developed based on the notion of the availability of historical data. In many situations, especially in clinical trials, the investigator has historical data from past studies which are similar to the current study. We take a semi-parametric approach in that a non-parametric prior is specified for the hazard rate and a fully parametric prior is specified for the regression coefficients. The prior specifications focus on the observables in that the elicitation is based on a prior prediction y0 for the response vector and a quantity a0 quantifying the uncertainty in y0. Then, y0 and a0 are used to specify a prior for the regression coefficients in a semi-automatic fashion. One of the main applications of our proposed priors is for model selection. Efficient computational methods are proposed for sampling from the posterior distribution and computing posterior model probabilities. A real data set is used to demonstrate our methodology.