Identifying and bounding the probability of necessity for causes of effects with ordinal outcomes

• 成果类型: Article
• 署名作者: Zhang, Chao; Geng, Zhi; Li, Wei; Ding, Peng
• 署名单位: Beijing Technology & Business University; Renmin University of China; Renmin University of China; University of California System; University of California Berkeley
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaf049
• 发表日期: 2025
• 关键词: causation

摘要

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment, given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose the novel assumption of a monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.