Optimal Treatment Rules under Missing Predictive Covariates: A Covariate-Balancing Doubly Robust Approach

In precision medicine, one of the most important problems is estimating the optimal individualized treatment rules (ITR), which typically involves recommending treatment decisions based on fully observed individual characteristics of patients to maximize overall clinical benefit. In practice, however, there may be missing covariates that are not necessarily confounders, and it remains uncertain whether these missing covariates should be included for learning optimal ITRs. In this paper, we propose a covariate-balancing doubly robust estimator for constructing optimal ITRs, which is particularly suitable for situations with additional predictive covariates. The proposed method is based on two main steps: First, the propensity scores are estimated by solving the covariate-balancing equation. Second, an objective function is minimized to estimate the outcome model, with the function defined by the asymptotic variance under the correctly specified propensity score. The method has three significant advantages: (i) It is doubly robust, ensuring consistency when either the propensity score or outcome model is correctly specified. (ii) It minimizes variance within the class of augmented inverse probability weighted estimators. (iii) When applied to partially observed covariates related to the outcome, the method may further improve estimation efficiency. We demonstrate the proposed method through extensive numerical simulations and two real-world datasets.