On the relative efficiency of the intent-to-treat Wilcoxon–Mann–Whitney test in the presence of noncompliance
研究了随机实验中存在不可忽略不依从时，意向治疗Wilcoxon-Mann-Whitney检验的渐近性质，推导了其与t检验的Pitman效率，发现当依从者更可能出现在结果分布高密度区域时该检验更优，并给出了效率的上下界，帮助研究者选择更有效的检验和计算样本量。
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.