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Objective Bayesian model selection for Cox regression


Held, Leonhard; Gravestock, Isaac; Sabanés Bové, Daniel (2016). Objective Bayesian model selection for Cox regression. Statistics in Medicine, 35(29):5376-5390.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:20 December 2016
Deposited On:29 Nov 2016 13:31
Last Modified:11 Dec 2016 06:12
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0277-6715
Publisher DOI:https://doi.org/10.1002/sim.7089
PubMed ID:27580645

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