Should a propensity score model be super? The utility of ensemble procedures for causal adjustment

Abstract

In investigations of the effect of treatment on outcome, the propensity score is a tool to eliminate imbalance in the distribution of confounding variables between treatment groups. Recent work has suggested that Super Learner, an ensemble method, outperforms logistic regression in nonlinear settings; however, experience with real-data analyses tends to show overfitting of the propensity score model using this approach. We investigated a wide range of simulated settings of varying complexities including simulations based on real data to compare the performances of logistic regression, generalized boosted models, and Super Learner in providing balance and for estimating the average treatment effect via propensity score regression, propensity score matching, and inverse probability of treatment weighting. We found that Super Learner and logistic regression are comparable in terms of covariate balance, bias, and mean squared error (MSE); however, Super Learner is computationally very expensive thus leaving no clear advantage to the more complex approach. Propensity scores estimated by generalized boosted models were inferior to the other two estimation approaches. We also found that propensity score regression adjustment was superior to either matching or inverse weighting when the form of the dependence on the treatment on the outcome is correctly specified.

Keywords: Super Learner; average treatment effect; confounding; covariate balance; inverse probability weighting; matching; propensity score.