Doubly Robust Weighted Regression for Causal Inference under Confounder Missingness
Missingness in confounders is common in observational studies and presents substantial challenges for causal effect estimation by weakening identification and increasing sensitivity to model misspecification. Within the missing-indicator framework, existing approaches typically rely on a single working model and achieve consistency only when that model is correctly specified and are therefore singly robust. In this article, we develop a doubly robust missing indicator weighted ordinary least squares (MI-WOLS) estimator with partially observed confounders. The proposed method integrates propensity score-based weighting into outcome regression under missing-indicator data representation, yielding a class of balancing weights that account for both confounders and their missingness indicators. Under the missingness-strongly-ignorable treatment allocation assumption and assuming either a Conditionally Independent Treatment or Conditionally Independent Outcome structure, the MI-WOLS estimator is consistent when at least the treatment or the outcome model is correctly specified. Simulation studies support the theoretical robustness of the MI-WOLS estimator, demonstrating negligible bias, accurate sandwich-based variance estimation, and near-nominal coverage probability across a wide range of data-generating scenarios. An illustrative application using simulated data designed to reflect a real-world kidney function study further demonstrates the interpretability and practical feasibility of the method, offering a flexible, doubly robust alternative to existing singly robust estimators.