Primary Submission Category: Sensitivity Analysis
Causal Effects of Modified Treatment Policies under Limited Overlap: A Partial Identification Approach
Authors: Taehyeon Koo, Kara Rudolph, Caleb Miles,
Presenting Author: Taehyeon Koo*
Modified treatment policies (MTPs) define causal effects of interventions on continuous or multivariate treatments by mapping observed exposures to counterfactual values. Identification of MTP effects typically relies on positivity assumptions that are frequently violated in practice, particularly in settings with high-dimensional or highly correlated treatments. We propose a partial identification framework for causal effects of modified treatment policies under limited overlap. Our approach decomposes the target estimand into a point-identified component over regions where overlap holds and a non-identifiable component arising from extrapolation beyond these regions. For the latter, we derive partial identification bounds under the assumption of Lipschitz continuity on the conditional mean of potential outcomes, extending smoothness-based identification methods to multivariate continuous treatments. We show that the length of these bounds is minimized by projecting counterfactual treatment–covariate values onto the overlap region and introduce a regularized projection operator to address the non-regularity induced by hard projections. We develop efficient influence function–based estimators for the resulting bounds, establish their asymptotic normality, and construct valid confidence intervals for partially identified causal effects. Simulation studies demonstrate favorable finite-sample performance, and an application to pesticide data from the CHAMACOS cohort.