发表机构
Novartis Pharma AG; Otto von Guericke University Magdeburg（诺华制药; 奥托·冯·格里克马格德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文重新审视 CMH 检验，证明其统计量可视为 AIPW 估计的标准化形式，厘清与 Wald 型检验的关系，并指出在等分配下对弱原假设渐近保守。
AI 中文摘要
本文针对临床试验中因果推断方法日益普及的背景，重新审视了 Cochran-Mantel-Haenszel (CMH) 检验。研究表明，CMH 检验统计量可被解释为因果平均处理效应的增强逆概率加权 (AIPW) 估计的标准化版本。因此，其解释并不局限于分层逻辑回归模型中常见比值比的检验。本文随后讨论了该估计量的条件方差与无条件方差，以及方差估计及其对检验的影响。研究结果厘清了经典条件 CMH 检验与 Wald 型 AIPW 检验之间的关系，并表明在治疗分配比例相等的情况下，CMH 检验对于零平均处理效应的弱原假设是渐近保守的。本文在分层随机试验中，针对二元终点和各层间共同的治疗分配比例，证明 CMH 统计量的分子与总体平均因果风险差的增强逆概率加权估计量成正比。这为 CMH 检验提供了一种不依赖于通常用于推导其的常见比值比模型的解释。随后，我们比较了该估计量的条件方差与无条件方差概念，并讨论了它们对检验的影响。研究结果厘清了经典条件 CMH 检验与 Wald 型 AIPW 检验之间的关系，并表明在治疗分配比例相等的情况下，CMH 检验对于零平均处理效应的弱原假设是渐近保守的。
英文摘要
This note revisits the Cochran-Mantel-Haenszel (CMH) test in light of the increasing use of causal inference methods in clinical trials. It shows that the CMH test statistic can be interpreted as a standardized version of the augmented inverse probability weighted (AIPW) estimate of the causal average treatment effect. Consequently, it is not restricted to an interpretation as a test of the common-odds ratio in a stratified logistic regression model. The note then discusses conditional and unconditional variances for this estimator as well as variance estimation and its implications for testing. The results clarify the relationship between the classical conditional CMH test and Wald-type AIPW tests, and show that, under equal treatment allocation, the CMH test is asymptotically conservative for the weak null hypothesis of zero average treatment effect. %This note revisits the Cochran--Mantel--Haenszel (CMH) test in light of the increasing use of causal inference methods in clinical trials. For stratified randomized trials with binary endpoints and a common treatment allocation fraction across strata, we show that the numerator of the CMH statistic is proportional to an augmented inverse probability weighted estimator of the population-average causal risk difference. This provides an interpretation of the CMH test that does not depend on the common-odds-ratio model often used to motivate it. We then compare conditional and unconditional variance concepts for this estimator and discuss their implications for testing. The results clarify the relationship between the classical conditional CMH test and Wald-type AIPW tests, and show that, under equal treatment allocation, the CMH test is asymptotically conservative for the weak null hypothesis of zero average treatment effect.
Comments15 pages
