针对二元结局配对研究的随机化推断

中文摘要 AI 辅助

针对具有二元结局的配对研究，我们提出了一种基于精确随机化的平均处理效应（ATE）置信集，该方法既不要求单调性，也无需配对内抛硬币之外的任何分布假设。其核心是对归因效应的最坏情况分配给出解析解：两个二项式对称性引理将最难拒绝的模式识别为单一边界角，因此检验原假设无需整数规划和数值搜索。通过二分法逆变换该检验，可在O(log S)次二项式尾部计算中得到归因效应的预测集；Rigdon和Hudgens（2015）的Bonferroni命题以相同计算成本生成ATE置信集。该同一角无需额外机制即可扩展至Rosenbaum的Γ模型下配对观察研究的敏感性分析。设计敏感性的简单公式阐明了观察研究何时有望提供效应证据。

英文摘要

We give an exact randomization-based confidence set for the average treatment effect (ATE) in matched-pair studies with a binary outcome, requiring neither monotonicity nor any distributional assumption beyond the within-pair coin flip. At its core is an analytic solution to the worst-case allocation of attributable effects: two binomial-symmetry lemmas identify the pattern hardest to reject as a single boundary corner, so testing null hypotheses needs no integer program and no numerical search. Inverting the test via binary search yields a prediction set for the attributable effect in O(log S) Binomial tail calculations; the Bonferroni proposition of Rigdon and Hudgens (2015) produces the ATE confidence set at the same computational cost. The same corner extends without further machinery to a sensitivity analysis for matched observational studies under Rosenbaum's $Γ$-model. A simple formula for the design sensitivity illuminates when an observational study can hope to provide evidence for an effect.

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