We develop a new rank-based approach for univariate two-sample testing in the presence of missing data which makes no assumptions about the missingness mechanism. This approach is a theoretical extension of the Wilcoxon-Mann-Whitney test that controls the Type I error by providing exact bounds for the test statistic after accounting for the number of missing values. Greater statistical power is shown when the method is extended to account for a bounded domain. Furthermore, exact bounds are provided on the proportions of data that can be missing in the two samples while yielding a significant result. Simulations demonstrate that our method has good power, typically for cases of $10\%$ to $20\%$ missing data, while standard imputation approaches fail to control the Type I error. We illustrate our method on complex clinical trial data in which patients' withdrawal from the trial lead to missing values.

翻译：我们提出了一种新的基于秩的方法，用于处理存在缺失数据的单变量两样本检验问题。该方法无需对缺失机制做任何假设，是Wilcoxon-Mann-Whitney检验的理论扩展——通过计入缺失值数量后给出检验统计量的精确界，从而控制第一类错误率。当将该方法扩展至有界域时，显示出更高的统计功效。此外，我们提供了两个样本中可缺失数据比例的精确界，使得在该比例下仍能获得显著结果。模拟实验表明，在缺失数据比例为10%至20%的典型场景下，本方法具有良好的检验功效，而标准插补方法则无法控制第一类错误率。我们通过一项复杂的临床试验数据验证了该方法——该数据中患者退出试验导致产生缺失值。