Learning Who to Treat When Treatment is Missing

2026-07-15

AI Summary

This study addresses the challenge of learning treatment assignment policies under missing data, proposing a robust framework that mitigates bias and suboptimal decisions arising from ignoring the missingness mechanism. The authors extend efficient estimation of the average treatment effect (ATE) to settings with missing-at-random (MAR) and missing completely at random conditional on covariates and treatment (MCCAR) assumptions. Leveraging semiparametric efficiency theory, they develop a doubly robust estimator that jointly models the missingness mechanism and the conditional average treatment effect (CATE), thereby effectively utilizing partially observed samples. A key contribution is the first systematic comparison of estimation efficiency for policy value under MAR versus MCCAR, with theoretical proof that the MAR-based estimator remains more efficient even when MCCAR holds. Experiments demonstrate that the proposed method achieves near-oracle performance when the missingness mechanism is correctly specified, whereas misspecified approaches incur substantial bias.

Abstract

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.

Problem

• policy learning
• missing treatment data
• treatment allocation
• missing at random
• conditional average treatment effect

Innovation

• policy learning
• missing treatment data
• conditional average treatment effect
• asymptotic efficiency
• missing at random