On the relative efficiency of the intent-to-treat Wilcoxon–Mann–Whitney test in the presence of noncompliance
On the relative efficiency of the intent-to-treat Wilcoxon–Mann–Whitney test in the presence of noncompliance
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关于存在违规情况下意向治疗 Wilcoxon-Manna-Whitney 测试的相对效率
DOI：
10.1093/biomet/asab053
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发表时间：
2021
期刊：
影响因子：
2.7
通讯作者：
Mao, Lu
中科院分区：
文献类型：
--
作者：
Mao, Lu
本文建立了一个一般框架，研究了在不可验证的不依从随机试验中意向治疗Wilcoxon-Mann-Whitney检验的渐近性质。在位置转移的替代方案下，推导出了意向治疗Wilcoxon-Mann-Whitney检验的皮特曼效率。它表明，前者是上级，如果顺从者更有可能被发现在高密度区域的结果分布，或者等价地，如果noncompliers往往驻留在尾部。通过逻辑延伸，这两种测试的相对效率明显受到最不利和最有利情景的限制，在这些情景中，遵守者分别被隔离到密度最低和最高的区域。这样的界限可以推导出分析作为一个函数的遵守率为常见的位置家庭，如高斯，拉普拉斯，逻辑和分布。这些结果可以帮助实证研究者为现有数据选择更有效的检验，并为未来的试验计算样本量，以预测不依从性。非加性替代品和其他测试的结果遵循沿着类似的路线。
A general framework is set up to study the asymptotic properties of the intent-to-treat Wilcoxon–Mann–Whitney test in randomized experiments with nonignorable noncompliance. Under location-shift alternatives, the Pitman efficiencies of the intent-to-treat Wilcoxon–Mann–Whitney andtests are derived. It is shown that the former is superior if the compliers are more likely to be found in high-density regions of the outcome distribution or, equivalently, if the noncompliers tend to reside in the tails. By logical extension, the relative efficiency of the two tests is sharply bounded by least and most favourable scenarios in which the compliers are segregated into regions of lowest and highest density, respectively. Such bounds can be derived analytically as a function of the compliance rate for common location families such as Gaussian, Laplace, logistic anddistributions. These results can help empirical researchers choose the more efficient test for existing data, and calculate sample size for future trials in anticipation of noncompliance. Results for nonadditive alternatives and other tests follow along similar lines.