  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.
