Mao Lu
Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison, Madison, Wisconsin 53726, U.S.A.
Biometrika. 2021 Oct 25;109(3):873-880. doi: 10.1093/biomet/asab053. eCollection 2022 Sep.
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 and [Formula: see text] tests 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 and [Formula: see text] distributions. 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.
建立了一个通用框架，用于研究随机试验中存在不可忽略的不依从性时意向性治疗的Wilcoxon-Mann-Whitney检验的渐近性质。在位置转移备择假设下，推导了意向性治疗的Wilcoxon-Mann-Whitney检验和[公式：见原文]检验的皮特曼效率。结果表明，如果依从者更有可能出现在结果分布的高密度区域，或者等价地，如果不依从者倾向于分布在尾部，则前者更优。通过逻辑扩展，两种检验的相对效率被最有利和最不利的情况严格界定，在这两种情况下，依从者分别被隔离在密度最低和最高的区域。对于高斯、拉普拉斯、逻辑斯蒂和[公式：见原文]分布等常见位置族，可以根据依从率解析地得出这些界限。这些结果可以帮助实证研究人员为现有数据选择更有效的检验方法，并在预期存在不依从性的情况下为未来试验计算样本量。非加性备择假设和其他检验的结果也遵循类似的思路。
