Robust estimation of optimal dynamic treatment regimes with nonignorable missing covariates

Estimating optimal dynamic treatment regimes (DTRs) from observational data is often complicated by nonignorable missing covariates arising from informative monitoring in clinical practice. A recent weighted Q-learning approach addresses such nonignorable missingness but relies on parametric Q-function models. In multistage settings, misspecification of Q-function models can propagate backwards through pseudo-outcomes and accumulate bias, both directly through Q-function estimation and indirectly through biased estimation of missingness propensities, raising robustness concerns. Motivated by these limitations, we develop robust direct-search estimators of optimal single-stage and multistage treatment rules with nonignorable missing covariates. For single-stage rules, under a future-independent missingness assumption, we construct robust estimators of treatment regime values using covariate balancing weights, augmented with nonparametrically estimated Q-functions. For DTRs, we extend the augmented value estimator by incorporating pseudo-outcomes with inverse missingness propensity weighting, where missingness propensities are modeled semiparametrically using nonresponse instrumental variables. Simulation studies demonstrate that the proposed estimators are more robust to model misspecification and contamination by invalid instrumental variables than weighted Q-learning. An application to electronic medical record data illustrates improved estimation of early fluid resuscitation strategies for sepsis patients when nonignorable missing hemodynamic variables are utilized.