A comparison of Bayesian and frequentist variable selection methods for estimating average treatment effects in logistic regression

In many manuscripts, researchers use multivariable logistic regression to adjust for potential confounding variables when estimating a direct relationship of a treatment or exposure on a binary outcome. After choosing how variables are entered into that model, researchers can calculate an estimated average treatment effect (ATE), or the estimated change in the outcome probability with and without an exposure present. Which potential confounding variables should be included in that logistic regression model is often a concern, which is sometimes determined from variable selection methods. We explore how forward, backward, and stepwise confounding variable selection estimate the ATE compared to spike-and-slab Bayesian variable selection across 1,000 randomly generated scenarios and various sample sizes. Our large simulation study allow us to make pseudo-theoretical conclusions about which methods perform best for different sample sizes, rarities of coutcomes, and number of confounders. An R package is also described to implement variable selection on the confounding variables only and provide estimates of the ATE. Overall, results suggest that Bayesian variable selection is more appealing in smaller sample sizes than frequentist variable selection methods in terms of estimating the ATE. Differences are minimal in larger sample sizes.