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Dynamic treatment regimes (DTRs) formalize medical decision-making as asequence of rules for different stages, mapping patient-level information torecommended treatments. In practice, estimating an optimal DTR usingobservational data from electronic medical record (EMR) databases can becomplicated by covariates that are missing not at random (MNAR) due toinformative monitoring of patients. Since complete case analysis can result inconsistent estimation of outcome model parameters under the assumption ofoutcome-independent missingness, Q-learning is a natural approach toaccommodating MNAR covariates. However, the backward induction algorithm usedin Q-learning can introduce challenges, as MNAR covariates at later stages canresult in MNAR pseudo-outcomes at earlier stages, leading to suboptimal DTRs,even if the longitudinal outcome variables are fully observed. To address thisunique missing data problem in DTR settings, we propose two weighted Q-learningapproaches where inverse probability weights for missingness of thepseudo-outcomes are obtained through estimating equations with validnonresponse instrumental variables or sensitivity analysis. Asymptoticproperties of the weighted Q-learning estimators are derived and thefinite-sample performance of the proposed methods is evaluated and comparedwith alternative methods through extensive simulation studies. Using EMR datafrom the Medical Information Mart for Intensive Care database, we apply theproposed methods to investigate the optimal fluid strategy for sepsis patientsin intensive care units.

Weighted Q-learning for optimal dynamic treatment regimes with MNAR coavriates