Rosner Bernard, Glynn Robert J, Lee Mei-Ling Ting
Channing Laboratory, Harvard Medical School, 181 Longwood Avenue, Boston, Massachusetts, USA.
Biometrics. 2003 Dec;59(4):1089-98. doi: 10.1111/j.0006-341x.2003.00125.x.
The Wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance. An assumption of the ordinary rank sum test is that individual sampling units are independent. In many ophthalmologic clinical trials, the Early Treatment for Diabetic Retinopathy Scale (ETDRS) is a principal endpoint used for measuring the level of diabetic retinopathy. This is an ordinal scale, and it is natural to consider the Wilcoxon rank sum test for the comparison of the level of diabetic retinopathy between treatment groups. However, under this design, unlike the usual Wilcoxon rank sum test, the subject is the unit of randomization, but the eye is the unit of analysis. Furthermore, a person will tend to have different, but correlated, ETDRS scores for fellow eyes. Thus, we propose a correction to the variance of the Wilcoxon rank sum statistic that accounts for clustering effects and that can be used for both balanced (same number of subunits per cluster) or unbalanced (different number of subunits per cluster) data, both in the presence or absence of ties, with p-value adjusted accordingly. In this article, we present large-sample theory and simulation results for this test procedure and apply it to diabetic retinopathy data from type I diabetics in the Sorbinil Retinopathy Trial.
当基础分布远离正态分布或事先未知时，威尔科克森秩和检验在统计实践中经常用于位置度量的比较。普通秩和检验的一个假设是各个抽样单元是独立的。在许多眼科临床试验中，糖尿病视网膜病变早期治疗量表（ETDRS）是用于测量糖尿病视网膜病变程度的主要终点。这是一个有序量表，考虑使用威尔科克森秩和检验来比较治疗组之间糖尿病视网膜病变的程度是很自然的。然而，在这种设计下，与通常的威尔科克森秩和检验不同，受试者是随机化的单位，但眼睛是分析的单位。此外，一个人两只眼睛的ETDRS分数往往不同但相关。因此，我们提出对威尔科克森秩和统计量的方差进行校正，以考虑聚类效应，并且该校正可用于平衡（每个聚类中亚单元数量相同）或不平衡（每个聚类中亚单元数量不同）的数据，无论是否存在平局情况，p值都会相应调整。在本文中，我们给出了该检验程序的大样本理论和模拟结果，并将其应用于索比尼尔视网膜病变试验中I型糖尿病患者的糖尿病视网膜病变数据。
