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 risk, 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 Fréchet--Hoeffding bounds are often 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 the Fréchet--Hoeffding bounds. 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 individuals 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. Furthermore, we propose nonparametric estimators for the refined FNA bounds and prove their consistency and asymptotic normality. We use simulation to evaluate the performance of the proposed estimators and apply the method to a canonical observational study.

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）广泛用于捕捉由观测协变量诱导的处理效应异质性，并设计个体化治疗策略。然而，CATE作为亚群层面的平均指标，无法揭示个体风险，可能导致误导性结论。本文通过分析二值结局下的个体风险来填补这一空白，重点研究负向影响比例（FNA）这一量化指标，即相较于对照组，治疗组出现更差结局的个体占比。即使在强可忽略性假设下，FNA仍不可识别，而现有的Fr\'echet-Hoeffding界通常过宽且仅在极端数据生成过程下可达。通过引入潜在结果间皮尔逊相关系数取值范围的温和约束，我们获得了较Fr\'echet-Hoeffding界更优的改进界。研究显示，矛盾的是，即使CATE为正，FNA的下界仍可能为正，即在最优情景下，若接受治疗仍有许多个体将受损。此外，我们以皮尔逊相关系数为敏感性参数，建立了FNA的非参数敏感性分析框架。进一步，我们提出改进FNA界的非参数估计量，并证明其一致性与渐近正态性。通过模拟实验评估所提估计量的表现，并将该方法应用于一项经典观察性研究。