Quantifying individual risk for binary outcomes

• 成果类型: Article; Early Access
• 署名作者: Wu, Peng; Ding, Peng; Geng, Zhi; Liu, Yue
• 署名单位: Beijing Technology & Business University; University of California System; University of California Berkeley; Renmin University of China; Renmin University of China
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag071
• 发表日期: 2026-05-19
• 关键词: Causal Inference; fraction negatively affected; partial identification; sensitivity analysis; ACTIVATED PROTEIN-C; TREATMENT HARM RATE; Causal Inference; propensity score; Heterogeneity; selection

摘要

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 Fr & eacute;chet-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 Fr & eacute;chet-Hoeffding bounds. 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.