In paired design studies, it is common to have multiple measurements taken for the same set of subjects under different conditions. In observational studies, it is many times of interest to conduct pair matching on multiple covariates between a treatment group and a control group, and to test the treatment effect represented by multiple response variables on well pair-matched data. However, there is a lack of an effective test on multivariate paired data. The multivariate paired Hotelling's $T^2$ test can sometimes be used, but its power decreases fast as the dimension increases. Existing methods for assessing the balance of multiple covariates in matched observational studies usually ignore the paired structure and thus they do not perform well under some settings. In this work, we propose a new non-parametric test for paired data, which exhibits a substantial power improvement over existing methods under a wide range of situations. We also derive the asymptotic distribution of the new test and the approximate $p$-value is reasonably accurate under finite samples through simulation studies even when the dimension is larger than the sample size, making the new test an easy-off-the-shelf tool for real applications. The proposed test is illustrated through an analysis of a real data set on the Alzheimer's disease research.
翻译:在配对设计研究中,通常会在不同条件下对同一组主题进行多种测量。在观察研究中,对一个治疗组和一个控制组之间的多个共变体进行配对配对,并测试配对数据中多重反应变量所代表的治疗效果,对配对数据进行配对数据。然而,对多种变式配对数据缺乏有效的测试。多变量对对口酒店的测试有时可以使用,但随着尺寸的增加,其功率会迅速下降。对匹配的观测研究中多种共变体的平衡进行评估的现有方法通常忽略配对结构,因此在某些环境下效果不佳。在这项工作中,我们提议对配对数据进行新的非参数测试,显示在广泛情况下现有方法的功率有很大改善。我们还通过模拟研究得出新测试的无症状分布,而大约1美元的价值在定数样本中是相当准确的,即使其尺寸大于样本尺寸,使新测试成为真实应用的易变现数据分析工具。拟议通过真实的测试模型,将一个真实数据显示一个测试工具。