2026/04/22 by Md. Shaddam Hossain Bagmar, Hua Shen
#stat.ME
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.