Bayesian adaptive B-spline estimation in proportional hazards frailty models

Abstract

Frailty models derived from the proportional hazards regression model are frequently used to analyze clustered right-censored survival data. We propose a semiparametric Bayesian methodology for this purpose, modeling both the unknown baseline hazard and density of the random effects using mixtures of B-splines. The posterior distributions for all regression coefficients and spline parameters are obtained using Markov Chain Monte Carlo (MCMC). The methodology permits the use of weighted mixtures of parametric and nonparametric components in modeling the hazard function and frailty distribution; in addition, the spline knots may also be selected adaptively using reversible-jump MCMC. Simulations indicate that the method produces smooth and accurate posterior hazard and frailty density estimates. The Bayesian approach not only produces point estimators that outperform existing approaches in certain circumstances, but also offers a wealth of information about the parameters of interest in the form of MCMC samples from the joint posterior probability distribution. We illustrate the adaptability of the method with data from a study of congestive heart failure.