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 $Λ\geq 1$, with $Λ= 1$ recovering standard transportability. For each $Λ$, 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 $Λ$, provide substantially tighter intervals than worst-case bounds, and remain informative across a range of realistic violations of transportability.

翻译：将随机试验中的治疗效果泛化至目标群体，需要假设在给定观测协变量后，潜在结果分布在各群体间保持不变。当未测量的效应修饰因子在试验参与者与目标群体间分布不同时，该假设即失效。我们开发了一个敏感性分析框架，用于界定当此可迁移性假设被违反时，结论可能改变的最大程度。我们的方法通过标量参数 $Λ\geq 1$ 约束目标群体与试验结果密度之间的似然比，其中 $Λ= 1$ 对应标准的可迁移性假设。对于每个 $Λ$，我们推导出目标平均处理效应的锐利界——这是在所有与观测数据及敏感性模型兼容的数据生成过程下，保证包含真实效应的最紧区间。我们证明最优似然比具有简单的阈值结构，从而导出一个仅需对试验结果排序并重新分配概率质量的闭式贪心算法。所得估计器的时间复杂度为 $O(n \log n)$，并在标准正则性条件下具有一致性。仿真结果表明，当真实结果偏移落在指定的 $Λ$ 范围内时，我们的界能达到名义覆盖水平；相比最坏情况界，其提供的区间显著更紧；并且在一系列现实的可迁移性违反情形下仍能提供信息量。