Understanding treatment heterogeneity is crucial for reliable decision-making in treatment evaluation and selection. While the conditional average treatment effect (CATE) is commonly used to capture treatment heterogeneity induced by covariates and design individualized treatment policies, it remains an averaging metric within subpopulations. This limitation prevents it from unveiling individual-level risks, potentially leading to misleading results. This article addresses this gap by examining individual risk for binary outcomes, specifically focusing on the fraction negatively affected (FNA) conditional on covariates -- a metric assessing the percentage of individuals experiencing worse outcomes with treatment compared to control. Under the strong ignorability assumption, FNA is unidentifiable, and we find that previous bounds are wide and practically unattainable except in certain degenerate cases. By introducing a plausible positive correlation assumption for the potential outcomes, we obtain significantly improved bounds compared to previous studies. We show that even with a positive and statistically significant CATE, the lower bound on FNA can be positive, i.e., in the best-case scenario many units will be harmed if receiving treatment. 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 present a practical and tractable method for selecting the range of correlation coefficients. Furthermore, we propose flexible estimators for refined FNA bounds and prove their consistency and asymptotic normality.

翻译：理解治疗异质性对于治疗评估和选择中的可靠决策至关重要。虽然条件平均处理效应（CATE）常被用于捕捉由协变量引发的治疗异质性并设计个体化治疗方案，但它仍是亚组内的平均度量指标。这一局限性使其无法揭示个体层面的风险，可能产生误导性结论。本文通过考察二元结局的个体风险来填补这一空白，重点研究了条件于协变量的负向影响比例（FNA）——该指标评估相较于对照组，治疗组中出现更差结局的个体占比。在强可忽略性假设下，FNA不可识别，且我们发现除某些退化情形外，现有边界过于宽泛且难以实际应用。通过引入潜在结果的正相关合理假设，我们获得了相较以往研究显著优化的边界。研究表明，即使CATE为正且具有统计显著性，FNA的下界仍可能为正，即在最优情形下，若接受治疗，许多个体仍会受到伤害。我们以皮尔逊相关系数作为敏感度参数，建立了FNA的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，并提出了一种实用且易行的相关系数取值范围选取方法。此外，我们提出了用于优化FNA边界的灵活估计量，并证明了其一致性与渐近正态性。