Objective Bayesian model selection for Cox regression

Abstract

There is now a large literature on objective Bayesian model selection in the linear model based on the g‐prior. The methodology has been recently extended to generalized linear models using test‐based Bayes factors. In this paper, we show that test‐based Bayes factors can also be applied to the Cox proportional hazards model. If the goal is to select a single model, then both the maximum a posteriori and the median probability model can be calculated. For clinical prediction of survival, we shrink the model‐specific log hazard ratio estimates with subsequent calculation of the Breslow estimate of the cumulative baseline hazard function. A Bayesian model average can also be employed. We illustrate the proposed methodology with the analysis of survival data on primary biliary cirrhosis patients and the development of a clinical prediction model for future cardiovascular events based on data from the Second Manifestations of ARTerial disease (SMART) cohort study. Cross‐validation is applied to compare the predictive performance with alternative model selection approaches based on Harrell's c‐Index, the calibration slope and the integrated Brier score. Finally, a novel application of Bayesian variable selection to optimal conditional prediction via landmarking is described. Copyright © 2016 John Wiley & Sons, Ltd.