Learning Who to Treat When Treatment is Missing
This work provides practitioners with theoretically grounded tools for robust policy learning under missing treatment data, addressing a common real-world problem.
The paper extends efficient estimators from ATE estimation to policy value and CATE estimation under MAR and MCCAR missing treatment data, proving that the MAR estimator is more efficient than the MCCAR estimator when MCCAR holds. Experiments show that correctly specifying the missingness mechanism is crucial, with their estimators achieving near-oracle performance when assumptions are satisfied.
Policy learning methods are increasingly used to inform treatment allocation under budget constraints. Most proposed methods assume complete treatment data, yet applications frequently suffer from missingness that can bias estimates and lead to suboptimal policies. We address this gap by extending efficient estimators for average treatment effect (ATE) estimation to policy value and conditional average treatment effect (CATE) estimation under missing at random (MAR) and missing completely conditionally at random (MCCAR) treatment data. Through asymptotic efficiency analysis, we prove that the MAR estimator, which leverages partially-observed units, is both valid and more efficient than the MCCAR estimator when MCCAR assumptions hold. This result provides formal justification for preferring MAR-based estimation in policy learning under both missing data settings. Our comprehensive experiments using synthetic and semi-synthetic datasets confirm that correctly specifying the missingness mechanism is crucial: misspecified estimators remain biased regardless of sample size, while our estimators achieve near-oracle performance when assumptions are satisfied. Our work provides practitioners with theoretically grounded, empirically validated tools for robust policy learning in the presence of missing treatment data.