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.

翻译：倾向得分匹配（PSM）和增强逆概率加权（AIPW）广泛应用于观察性研究中的因果效应估计。这两种方法具有互补特性。AIPW估计量具有双重鲁棒性和局部有效性，但当倾向得分接近0或1时，由于使用倾向得分的逆进行加权，可能导致估计不稳定。另一方面，PSM避免了倾向得分加权的不稳定性，但其有效性依赖于倾向得分模型的正确性，且无法达到半参数效率界。此外，固定匹配数K使得PSM非平滑，从而无法使用标准的非参数自举推断。本文提出了一种新型增强匹配加权（AMW）估计量，结合了匹配和加权估计量的优势。AMW沿用AIPW的结构以保持双重鲁棒性和局部有效性，同时缓解了加权导致的不稳定性。我们将逆倾向权重替换为基于非固定K的PSM生成的匹配权重。同时，我们提出了一种新的交叉验证过程来选择K，该过程以因果估计量的无偏估计为基准，最小化均方误差。此外，我们推导了AMW估计量的极限分布，证明其具有双重鲁棒性，且当两个扰动模型均正确时能够达到半参数效率界。作为非固定K（平滑AMW估计量）的副产品，可采用非参数自举进行方差估计和推断。仿真研究和实际数据应用进一步表明，AMW估计量在极端倾向得分下仍保持稳定性，且其方差可通过朴素自举方法获得。