Sharp Bounds for Treatment Effect Generalization under Outcome Distribution Shift

Amir Asiaee, Samhita Pal, Cole Beck, Jared Davis Huling
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:1572-1603, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-asiaee26a, title = {Sharp Bounds for Treatment Effect Generalization under Outcome Distribution Shift}, author = {Asiaee, Amir and Pal, Samhita and Beck, Cole and Huling, Jared Davis}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {1572--1603}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/asiaee26a/asiaee26a.pdf}, url = {https://proceedings.mlr.press/v323/asiaee26a.html}, 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.} }
Endnote
%0 Conference Paper %T Sharp Bounds for Treatment Effect Generalization under Outcome Distribution Shift %A Amir Asiaee %A Samhita Pal %A Cole Beck %A Jared Davis Huling %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-asiaee26a %I PMLR %P 1572--1603 %U https://proceedings.mlr.press/v323/asiaee26a.html %V 323 %X 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.
APA
Asiaee, A., Pal, S., Beck, C. & Huling, J.D.. (2026). Sharp Bounds for Treatment Effect Generalization under Outcome Distribution Shift. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:1572-1603 Available from https://proceedings.mlr.press/v323/asiaee26a.html.

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