Bayesian Analysis of Proportional Hazards Models Built from Monotone Functions

A Bayesian approach is taken for fitting the usual proportional hazards model in the case where the baseline hazard, the covariate link, and the covariATE coefficients are all unknown.

Abstract

We consider the usual proportional hazards model in the case where the baseline hazard, the covariate link, and the covariate coefficients are all unknown. Both the baseline hazard and the covariate link are monotone functions and thus are characterized using a dense class of such functions which arises, upon transformation, as a mixture of Beta distribution functions. We take a Bayesian approach for fitting such a model. Since interest focuses more upon the likelihood, we consider vague prior specifications including Jeffreys's prior. Computations are carried out using sampling-based methods. Model criticism is also discussed. Finally, a data set studying survival of a sample of lung cancer patients is analyzed.