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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.
Luo et al. (Thu,) studied this question.