In observational studies, covariates with substantial missing data are often omitted, despite their strong predictive capabilities. These excluded covariates are generally believed not to simultaneously affect both treatment and outcome, indicating that they are not genuine confounders and do not impact the identification of the average treatment effect (ATE). In this paper, we introduce an alternative doubly robust (DR) estimator that fully leverages non-confounding predictive covariates to enhance efficiency, while also allowing missing values in such covariates. Beyond the double robustness property, our proposed estimator is designed to be more efficient than the standard DR estimator. Specifically, when the propensity score model is correctly specified, it achieves the smallest asymptotic variance among the class of DR estimators, and brings additional efficiency gains by further integrating predictive covariates. Simulation studies demonstrate the notable performance of the proposed estimator over current popular methods. An illustrative example is provided to assess the effectiveness of right heart catheterization (RHC) for critically ill patients.

翻译：在观察性研究中，缺失率较高的协变量常被忽略，尽管它们具有很强的预测能力。这些被排除的协变量通常被认为不会同时影响处理变量和结果变量，表明它们并非真正的混淆变量，也不会影响平均处理效应（ATE）的识别。本文提出了一种替代性双重稳健（DR）估计量，该估计量充分利用无混淆预测协变量来提升效率，同时允许这些协变量存在缺失值。除具备双重稳健性外，我们提出的估计量被设计为比标准DR估计量更高效。具体而言，当倾向得分模型正确设定时，该估计量在DR估计量类中达到最小渐近方差，并通过进一步整合预测协变量带来额外的效率提升。模拟研究表明，所提估计量相对于当前流行方法具有显著优势。通过一个实例展示了右心导管插入术（RHC）对危重患者疗效的评估效果。