Primary Submission Category: Heterogeneous Treatment Effects
Causal inference with constraints on the probability of intervention
Authors: Alexander Levis, Eli Ben-Michael, Edward Kennedy,
Presenting Author: Alexander Levis*
Treatment rules or policies are mappings from individual patient characteristics to tailored treatment assignments. Optimal policies that maximize mean outcomes have been well characterized in unconstrained settings, in cases where one treatment level is limited in supply, and under cost constraints when treatment cost is random. In this work, we describe a novel resource-limited setting, important for applications in health policy, in which treatment options are freely accessible but the ability to intervene on a portion of a target population is constrained, e.g., if the population is large, and follow-up and encouragement of treatment uptake is labor-intensive. We derive formulas for optimal treatment rules in such settings, and for any given budget, quantify the loss compared to the optimal unconstrained rule. We then propose efficient and robust influence function-based estimators of the mean outcome under the optimal constrained rule, and other related quantities that are of independent interest beyond this resource-limited setting. Finally, we demonstrate our framework in simulations and in a longitudinal observational study.