Augmented match weighted estimators for average treatment effects

Propensity score matching (PSM) and augmented inverse propensity weighting (AIPW) are widely used in observational studies to estimate causal effects. The two approaches present complementary features. The AIPW estimator is doubly robust and locally efficient but can be unstable when the propensity scores are close to zero or one due to weighting by the inverse of the propensity score. On the other hand, 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. Besides, the fixed number of matches, K, renders PSM nonsmooth and thus invalidates standard nonparametric 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 due to weighting. 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. Besides, we derive the limiting distribution for the AMW estimators showing that they 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 the AMW estimators, nonparametric bootstrap can be adopted for variance estimation and inference. Furthermore, simulation studies and real data applications support that the AMW estimators are stable with extreme propensity scores and their variances can be obtained by naive bootstrap.