Bayesian model averaging: improved variable selection for matched case-control studies

The problem of variable selection for risk factor modeling is an ongoing challenge in statistical practice. Classical methods that select one subset of exploratory risk factors dominate the medical research field. However, this approach has been criticized for not taking into account the uncertainty of the model selection process itself. This limitation can be addressed by a Bayesian model averaging approach: instead of focusing on a single model and a few factors, Bayesian model averaging considers all the models with non-negligible probabilities to make inference.

This paper reports on a simulation study designed to emulate a matched case-control study and compares classical versus Bayesian model averaging selection methods. We used Matthews's correlation coefficient to measure the quality of binary classifications. Both classical and Bayesian model averaging were also applied and compared for the analysis of a matched case-control study of patients with methicillin-resistant Staphylococcus aureus infections after hospital discharge 2011-2013.

Bayesian model averaging outperformed the classical approach with much lower false positive rates and higher Matthew's correlation scores. Bayesian model averaging also produced more reliable and robust effect estimates.

Bayesian model averaging is a conceptually simple, unified approach that produces robust results. It can be used to replace controversial P-values for case-control study in medical research.