Sharp Bounds for Treatment Effect Generalization under Outcome Distribution Shift

TL;DR

This paper introduces a sensitivity analysis framework that provides sharp bounds on treatment effect generalization under outcome distribution shift, relaxing the invariance assumption with a scalable, closed-form algorithm.

Contribution

It develops a novel bounding method for treatment effect generalization that accounts for outcome distribution shifts using a simple likelihood ratio constraint and a closed-form solution.

Findings

Bounds achieve nominal coverage when true outcome shift is within the specified range.

The proposed estimator is computationally efficient, running in O(n log n) time.

Simulations show bounds are tighter than worst-case bounds and remain informative under realistic violations.

Abstract

Generalizing treatment effects from a randomized trial to a target population requires the assumption that potential outcome distributions are invariant across populations after conditioning on observed covariates. This assumption fails when unmeasured effect modifiers are distributed differently between trial participants and the target population. We develop a sensitivity analysis framework that bounds how much conclusions can change when this transportability assumption is violated. Our approach constrains the likelihood ratio between target and trial outcome densities by a scalar parameter $\Lambda \geq 1$, with $\Lambda = 1$ recovering standard transportability. For each $\Lambda$, we derive sharp bounds on the target average treatment effect -- the tightest interval guaranteed to contain the true effect under all data-generating processes compatible with the observed data and the sensitivity model. We show that the optimal likelihood ratios have a simple threshold structure, leading to a closed-form greedy algorithm that requires only sorting trial outcomes and redistributing probability mass. The resulting estimator runs in $O(n \log n)$ time and is consistent under standard regularity conditions. Simulations demonstrate that our bounds achieve nominal coverage when the true outcome shift falls within the specified $\Lambda$, provide substantially tighter intervals than worst-case bounds, and remain informative across a range of realistic violations of transportability.