An empirical comparison of tree-based methods for propensity score estimation

To illustrate the use of ensemble tree-based methods (random forest classification [RFC] and bagging) for propensity score estimation and to compare these methods with logistic regression, in the context of evaluating the effect of physical and occupational therapy on preschool motor ability among very low birth weight (VLBW) children.

We used secondary data from the Early Childhood Longitudinal Study Birth Cohort (ECLS-B) between 2001 and 2006.

We estimated the predicted probability of treatment using tree-based methods and logistic regression (LR). We then modeled the exposure-outcome relation using weighted LR models while considering covariate balance and precision for each propensity score estimation method.

Among approximately 500 VLBW children, therapy receipt was associated with moderately improved preschool motor ability. Overall, ensemble methods produced the best covariate balance (Mean Squared Difference: 0.03-0.07) and the most precise effect estimates compared to LR (Mean Squared Difference: 0.11). The overall magnitude of the effect estimates was similar between RFC and LR estimation methods.

Propensity score estimation using RFC and bagging produced better covariate balance with increased precision compared to LR. Ensemble methods are a useful alterative to logistic regression to control confounding in observational studies.