Understanding treatment effect heterogeneity is crucial for reliable decision-making in treatment evaluation and selection. The conditional average treatment effect (CATE) is widely used to capture treatment effect heterogeneity induced by observed covariates and to design individualized treatment policies. However, it is an average metric within subpopulations, which prevents it from revealing individual-level risks, potentially leading to misleading results. This article fills this gap by examining individual risk for binary outcomes, specifically focusing on the fraction negatively affected (FNA), a metric that quantifies the percentage of individuals experiencing worse outcomes under treatment compared with control. Even under the strong ignorability assumption, FNA is still unidentifiable, and the existing Frechet-Hoeffding bounds are usually too wide and attainable only under extreme data-generating processes. By invoking mild conditions on the value range of the Pearson correlation coefficient between potential outcomes, we obtain improved bounds compared with previous studies. We show that paradoxically, even with a positive CATE, the lower bound on FNA can be positive, i.e., in the best-case scenario many units will be harmed if they receive treatment. Additionally, we establish a nonparametric sensitivity analysis framework for FNA using the Pearson correlation coefficient as the sensitivity parameter, thereby exploring the relationships among the correlation coefficient, FNA, and CATE. We also propose a method for selecting the range of correlation coefficients. Furthermore, we propose nonparametric estimators for the refined FNA bounds and prove their consistency and asymptotic normality.

翻译：理解处理效应异质性对于治疗评估与选择中的可靠决策至关重要。条件平均处理效应（CATE）被广泛用于捕捉由观测协变量引起的处理效应异质性，并设计个体化治疗策略。然而，它是一种亚群内的平均度量，这使其无法揭示个体层面的风险，可能导致误导性结果。本文通过考察二元结果的个体风险来填补这一空白，特别聚焦于负面受影响比例（FNA）这一度量，它量化了在接受治疗时相比对照情况下结果更差的个体百分比。即使在强可忽略性假设下，FNA仍然不可识别，且现有的Fréchet-Hoeffding界通常过宽，并仅在极端的数据生成过程下可达。通过对潜在结果间皮尔逊相关系数的取值范围施加温和条件，我们获得了相较于先前研究改进的界。我们证明，矛盾的是，即使在CATE为正的情况下，FNA的下界也可能为正，即在最佳情形下，许多个体若接受治疗仍将受到损害。此外，我们利用皮尔逊相关系数作为敏感性参数，为FNA建立了一个非参数敏感性分析框架，从而探索相关系数、FNA与CATE之间的关系。我们还提出了一种选择相关系数取值范围的方法。进一步地，我们针对精化后的FNA界提出了非参数估计量，并证明了它们的一致性和渐近正态性。