Practical recommendations on double score matching for estimating causal effects

Unlike in randomized clinical trials (RCTs), confounding control is critical for estimating the causal effects from observational studies due to the lack of treatment randomization. Under the unconfoundedness assumption, matching methods are popular because they can be used to emulate an RCT that is hidden in the observational study. To ensure the key assumption hold, the effort is often made to collect a large number of possible confounders, rendering dimension reduction imperative in matching. Three matching schemes based on the propensity score (PSM), prognostic score (PGM), and double score (DSM, ie, the collection of the first two scores) have been proposed in the literature. However, a comprehensive comparison is lacking among the three matching schemes and has not made inroads into the best practices including variable selection, choice of caliper, and replacement. In this article, we explore the statistical and numerical properties of PSM, PGM, and DSM via extensive simulations. Our study supports that DSM performs favorably with, if not better than, the two single score matching in terms of bias and variance. In particular, DSM is doubly robust in the sense that the matching estimator is consistent requiring either the propensity score model or the prognostic score model is correctly specified. Variable selection on the propensity score model and matching with replacement is suggested for DSM, and we illustrate the recommendations with comprehensive simulation studies. An R package is available at https://github.com/Yunshu7/dsmatch.