Augmented match weighted estimators: new methods for estimating average treatment effects under extreme propensity scores

Propensity score matching (PSM) and augmented inverse propensity weighting (AIPW) are used in observational studies to estimate causal effects. The AIPW estimator is doubly robust and locally efficient but can be unstable when the propensity scores are close to zero or one. PSM circumvents the instability of propensity score weighting but it hinges on the correctness of the propensity score model and cannot attain the semiparametric efficiency bound. The fixed number of matches, K, renders PSM nonsmooth and thus invalidates standard bootstrap inference. This article presents novel augmented match weighted (AMW) estimators that combine the advantages of matching and weighting estimators. AMW adheres to the form of AIPW for its double robustness and local efficiency but it mitigates the instability. We replace inverse propensity weights with matching weights resulting from PSM with unfixed K. Meanwhile, we propose a new cross-validation procedure to select K that minimizes the mean squared error anchored around an unbiased estimator of the causal estimand. We derive the limiting distribution showing AMW estimators enjoy the double robustness property and can achieve the semiparametric efficiency bound if both nuisance models are correct. As a byproduct of unfixed K which smooths AMW estimators, nonparametric bootstrap can be adopted for variance estimation. Furthermore, simulation and real-data applications support that the AMW estimators are stable and their variances can be obtained by nonparametric bootstrap. Our method is particularly recommended when the propensity score distribution is extreme. In such settings, the AMW estimator is more efficient and robust than PSM, more stable than AIPW, and is accompanied by a valid variance estimation procedure.