Robust estimation of optimal dynamic treatment regimes with nonignorable missing covariates

Abstract: Estimating optimal dynamic treatment regimes (DTRs) using observational data is often challenged by nonignorable missing covariates arsing from informative monitoring of patients in clinical practice. To address nonignorable missingness of pseudo-outcomes induced by nonignorable missing covariates, a weighted Q-learning approach using parametric Q-function models and a semiparametric missingness propensity model has recently been proposed. However, misspecification of parametric Q-functions at later stages of a DTR can propagate estimation errors to earlier stages via the pseudo-outcomes themselves and indirectly through biased estimation of the missingness propensity of the pseudo-outcomes. This robustness concern motivates us to develop a direct-search-based optimal DTR estimator built on a robust and efficient value estimator, where nonparametric methods are employed for treatment propensity and Q-function estimation, and inverse probability weighting is applied using missingness propensity estimated with the aid of nonresponse instrumental variables. Specifically, in our value estimator, we replace weights estimated by prediction models of treatment propensity with stable weights estimated by balancing covariate functions in a reproducing-kernel Hilbert space (RKHS). Augmented by Q-functions estimated by RKHS-based smoothing splines, our value estimator mitigates the misspecification risk of the weighted Q-learning approach while maintaining the efficiency gain from employing pseudo-outcomes in missing data scenarios. The asymptotic properties of the proposed estimator are derived, and simulations demonstrate its superior performance over weighted Q-learning under model misspecification. We apply the proposed methods to investigate the optimal fluid strategy for sepsis patients using data from the MIMIC database.