Prior Elicitation for Semiparametric Bayesian Survival Analysis

Abstract

The quantification of prior information is a very important problem in a Bayesian analysis. In many situations, especially in clinical trials, the investigator has historical data from past studies which are similar to the current study. In this chapter, we discuss a class of informative prior distributions for Cox’s proportional hazards model. A novel construction of the prior is developed for this semiparametric model based on the notion of the availability of historical data. The prior specifications focus on the observables in that the elicitation is based on a prior prediction yo for the response vector and a quantity ao quantifying the uncertainty in yo. Then, yo and ao 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.