title: 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.
authors: Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Hirschegraben 84, 8001, Zurich, Switzerland.
authors: Leonhard
authors: L
authors: Held
authors: Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Hirschegraben 84, 8001, Zurich, Switzerland.
authors: Isaac
authors: I
authors: Gravestock
authors: F. Hoffmann-La Roche Ltd, 4070, Basel, Switzerland.
authors: Daniel
authors: D
authors: Sabanés Bové
mesh_terms: D001499:Bayes Theorem; D015331:Cohort Studies; D006801:Humans; D016014:Linear Models; D016016:Proportional Hazards Models; D012107:Research Design
keywords: Bayes factor; Cox model; clinical prediction; g-prior; model selection