Learning Who to Treat When Treatment is Missing

In many real-world applications, such as healthcare and social services, researchers must allocate limited treatments based on observational data. A major challenge is that treatment assignments are often missing for a subset of the population. While existing policy learning methods typically assume complete data, this paper addresses the problem of learning optimal treatment policies when treatment indicators are missing, either due to administrative gaps or data integration challenges.

The authors extend efficient influence function (IF) methods—commonly used for average treatment effect (ATE) estimation—to policy value and conditional average treatment effect (CATE) estimation. They compare two primary identification strategies: one based on the Missing Completely Conditionally at Random (MCCAR) assumption, which uses only complete cases, and one based on the broader Missing at Random (MAR) assumption, which leverages partially observed units by reweighting outcomes. They prove that the MAR-based estimator is not only valid under both assumptions but also asymptotically more efficient than the MCCAR-based estimator.

The study establishes that the MAR estimator is the preferred choice for policy learning. Through asymptotic efficiency analysis, the authors show that the MAR estimator achieves higher efficiency than the complete-case MCCAR estimator. Furthermore, they implement these findings using a DR-Learner framework, which allows for flexible, doubly robust estimation of treatment policies. Empirical experiments on synthetic and semi-synthetic datasets confirm that when the missingness mechanism is correctly specified, these estimators achieve near-oracle performance. Conversely, the authors warn that misspecification of the missingness mechanism leads to persistent bias that cannot be mitigated by increasing sample size.