A Bayesian semiparametric temporally-stratified proportional hazards model with spatial frailties

Abstract

Incorporating temporal and spatial variation could potentially enhance information gathered from survival data. This paper proposes a Bayesian semi-parametric model for capturing spatio-temporal heterogeneity within the propor-tional hazards framework. The spatial correlation is introduced in the form of county-level frailties. The temporal effect is introduced by considering the strati-fication of the proportional hazards model, where the time-dependent hazards are indirectly modeled using a probability model for related probability distributions. With this aim, an autoregressive dependent tailfree process is introduced. The full Kullback-Leibler support of the proposed process is provided. The approach is illustrated using simulated data and data from the Surveillance Epidemiology and End Results database of the National Cancer Institute on patients in Iowa diagnosed with breast cancer. © 2012 International Society for Bayesian Analysis.