Bayesian semiparametric modeling of survival data based on mixtures of B-spline distributions

Abstract

The nonparametric part of a semiparametric regression model usually involves prior specification for an infinite-dimensional parameter F. This paper introduces a class of finite mixture models based on B-spline distributions as an approximation to priors on the set of cumulative distribution functions. This class includes the mixture of beta distributions of Diaconis and Ylvisaker (1985) and the mixtures of triangular distributions of Perron and Mengersen (2001) as special cases. We describe how this approach can be used to model the baseline hazards in a Bayesian stratified proportional hazards model. A numerical illustration is given using survival data from a multicenter clinical AIDS trial, thus generalizing the approach by Carlin and Hodges (1999). Using conditional predictive ordinates and the deviance information criterion, we compare the fit of hierarchical proportional hazards regression models based on mixtures of B-spline distributions of various degrees.