Model selection in Medical Research: A simulation study comparing Bayesian Model Averaging and Stepwise Regression

Automatic variable selection methods are usually discouraged in medical research although we believe they might be valuable for studies where subject matter knowledge is limited. Bayesian model averaging may be useful for model selection but only limited attempts to compare it to stepwise regression have been published. We therefore performed a simulation study to compare stepwise regression with Bayesian model averaging.

We simulated data corresponding to five different data generating processes and thirty different values of the effect size (the parameter estimate divided by its standard error). Each data generating process contained twenty explanatory variables in total and had between zero and two true predictors. Three data generating processes were built of uncorrelated predictor variables while two had a mixture of correlated and uncorrelated variables. We fitted linear regression models to the simulated data. We used Bayesian model averaging and stepwise regression respectively as model selection procedures and compared the estimated selection probabilities.

The estimated probability of not selecting a redundant variable was between 0.99 and 1 for Bayesian model averaging while approximately 0.95 for stepwise regression when the redundant variable was not correlated with a true predictor. These probabilities did not depend on the effect size of the true predictor. In the case of correlation between a redundant variable and a true predictor, the probability of not selecting a redundant variable was 0.95 to 1 for Bayesian model averaging while for stepwise regression it was between 0.7 and 0.9, depending on the effect size of the true predictor. The probability of selecting a true predictor increased as the effect size of the true predictor increased and leveled out at between 0.9 and 1 for stepwise regression, while it leveled out at 1 for Bayesian model averaging.

Our simulation study showed that under the given conditions, Bayesian model averaging had a higher probability of not selecting a redundant variable than stepwise regression and had a similar probability of selecting a true predictor. Medical researchers building regression models with limited subject matter knowledge could thus benefit from using Bayesian model averaging.