Sharp Bounds for Treatment Effect Generalization under Outcome Distribution Shift

Amir Asiaee, Samhita Pal, Cole Beck, Jared Davis Huling

Keywords: Generalizability; Transportability; Sensitivity analysis; Partial identification; Randomized trials; Treatment effect heterogeneity

TL;DR: We derive sharp, closed-form bounds on treatment effects when generalizing from a trial to a target population under bounded outcome distribution shift, with an O(n log n) greedy algorithm that just sorts outcomes and redistributes probability mass.

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.

Submission Number: 94