提出通用样本量分析方法，精准估算因果概率估计所需数据量。
General sample size analysis for probabilities of causation: a delta method approach
- 基于德尔塔法构建通用样本量框架，适用于多种因果概率场景。
- 仿真验证表明该方法能稳定实现目标误差范围内的因果概率边界估计。
- 适合关注因果推断置信度与实验设计的科研人员参考使用。
因果概率（PoCs），如必要性与充分性概率（PNS），是决策的重要工具，但通常无法精确识别。现有研究利用实验与观察数据结合推导这些量的边界，但对样本量分析——即达到预定误差范围所需的实验与观察样本数量——研究极为有限。本文提出一种基于德尔塔法的通用样本量分析框架，适用于目标边界可表示为实验与观察概率线性组合的极值（有限最小或最大）的情形。通过模拟研究，我们证明所提样本量计算能稳定实现这些边界的估计，确保在给定精度下的可靠性。
原文摘要 · Abstract (English)
Probabilities of causation (PoCs), such as the probability of necessity and sufficiency (PNS), are important tools for decision making but are generally not point identifiable. Existing work has derived bounds for these quantities using combinations of experimental and observational data. However, there is very limited research on sample size analysis, namely, how many experimental and observational samples are required to achieve a desired margin of error. In this paper, we propose a general sample size framework based on the delta method. Our approach applies to settings in which the target bounds of PoCs can be expressed as finite minima or maxima of linear combinations of experimental and observational probabilities. Through simulation studies, we demonstrate that the proposed sample size calculations lead to stable estimation of these bounds.
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