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Objective Bayesian model selection for Cox regression.

Leonhard Held1, Isaac Gravestock1, Daniel Sabanés Bové2

  • 1Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Hirschegraben 84, 8001, Zurich, Switzerland.

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|September 2, 2016
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Summary
This summary is machine-generated.

Bayesian methods, including test-based Bayes factors, are extended to Cox proportional hazards models for survival data. This approach aids in clinical prediction and model selection, outperforming alternatives in validation studies.

Keywords:
Bayes factorCox modelclinical predictiong-priormodel selection

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Area of Science:

  • Biostatistics
  • Statistical modeling
  • Survival analysis

Background:

  • Objective Bayesian model selection is established for linear and generalized linear models using g-prior and test-based Bayes factors.
  • The application of these Bayesian methods to survival data, specifically the Cox proportional hazards model, has been limited.

Purpose of the Study:

  • To extend test-based Bayes factors methodology to the Cox proportional hazards model for objective Bayesian model selection.
  • To develop Bayesian approaches for clinical prediction of survival and variable selection in survival data analysis.

Main Methods:

  • Application of test-based Bayes factors to Cox proportional hazards models.
  • Calculation of maximum a posteriori and median probability models for single model selection.
  • Shrinkage of model-specific log hazard ratio estimates for clinical prediction, using Breslow estimate for cumulative baseline hazard.
  • Bayesian model averaging and Bayesian variable selection for optimal conditional prediction via landmarking.

Main Results:

  • Demonstrated successful application of test-based Bayes factors to Cox proportional hazards models.
  • Developed and illustrated methods for clinical prediction and model selection using Bayesian approaches.
  • Cross-validation showed competitive predictive performance compared to established methods (Harrell's c-Index, calibration slope, integrated Brier score).

Conclusions:

  • Test-based Bayes factors provide a viable objective Bayesian approach for model selection in Cox proportional hazards models.
  • The proposed Bayesian methods enhance clinical prediction of survival and facilitate robust variable selection.
  • The methodology offers a powerful alternative for analyzing complex survival data in biomedical research.