Missing confounders are common in observational studies and present fundamental challenges for causal effect estimation by weakening identification and increasing sensitivity to model misspecification. Within the missing-indicator framework, existing methods 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 MI-WOLS estimator incorporates the treatment assignment mechanism, commonly known as the propensity score model, into the weighting structure of the outcome regression. Building on the missing-indicator framework, we define propensity score based regression weights that satisfy a covariate-balancing condition in the presence of confounder missingness. 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 to kidney function outcomes further demonstrates the interpretability and practical feasibility of the method, offering a flexible, doubly robust alternative to existing singly robust estimators.

翻译：混杂变量缺失在观察性研究中普遍存在，通过削弱识别能力和增加模型误设敏感性，对因果效应估计构成根本性挑战。在缺失指示变量框架内，现有方法依赖单一工作模型，仅当该模型正确设定时才能达到一致性，因此属于单重稳健。本文针对部分观测混杂变量，开发了一种双重稳健的缺失指示变量加权普通最小二乘（MI-WOLS）估计量。该估计量将通常称为倾向得分模型的处理分配机制纳入结果回归的加权结构中。基于缺失指示变量框架，我们定义了在存在混杂变量缺失时满足协变量平衡条件的基于倾向得分的回归权重。在缺失过程强可忽略处理分配假设下，并假定条件独立处理结构或条件独立结果结构，MI-WOLS估计量在至少处理模型或结果模型之一正确设定时具有一致性。模拟研究支持MI-WOLS估计量的理论稳健性，显示在广泛数据生成场景下偏差可忽略、基于夹心法的方差估计准确、且覆盖概率接近名义水平。对肾功能结局的实证应用进一步展示了该方法的可解释性与实践可行性，为现有单重稳健估计量提供了灵活的双重稳健替代方案。