Statistical inference for the probability of necessity for causal attribution
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因果归因中必要性概率的统计推断
- 研究问题
- 判断已发生结果是否由先前处理导致时，如何对通常只能部分识别的必要性概率进行有效推断，并处理其上下界的非光滑性？
- 方法与思路
- 作者引入 margin 条件使界限具有路径可微性，建立半参数效率理论，构造上下界的渐近有效估计量及必要性概率的置信区间。
- 材料陈述的贡献
- 摘要称方法面向必要性概率未必点识别的一般情形，提供界限估计和区间推断，并可利用观测协变量缩短最终置信区间。
- 阅读关注点
- 应核对必要性概率及其界限的定义、margin 条件的实质、有效影响函数推导，以及区间如何同时处理界限估计误差和部分识别。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未明确完整识别假设、margin 条件形式或区间缩短幅度，不能推断个体因果确定性。
原文摘要
To answer questions of "causes of effects", the probability of necessity was previously introduced for assessing whether an observed outcome was caused by an earlier treatment. However, statistical inference for the probability of necessity is understudied due to several difficulties, which hinder its application in practice. The evaluation of the probability of necessity involves the joint distribution of potential outcomes, and thus it is generally not point identified and one can at best obtain lower and upper bounds even in randomized experiments, unless fairly stringent monotonicity assumptions on potential outcomes are made. Moreover, these bounds are non-smooth functionals of the observed data distribution and standard estimation and inference methods cannot be directly applied. In this paper, we investigate the statistical inference for the probability of necessity in general situations where it may not be point identified. We introduce a mild margin condition to tackle the non-smoothness, under which the bounds become pathwise differentiable. We establish the semiparametric efficiency theory and propose novel asymptotically efficient estimators of the lower and upper bounds, and further construct confidence intervals for the probability of necessity based on the proposed bound estimators. The resultant confidence intervals can effectively utilize the observed covariates to reduce lengths. The proposed approach has potential application in biomedical, epidemiological, and legal studies where understanding causal attribution beyond traditional causal effects is essential.