Use of the Wilcoxon Rank Sum Statistic for Clustered Data: The Case of Subunit Specific Covariates

• Activity Number: 182
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): Bernard Rosner*+ and Mei-Ling Lee
• Affiliation(s): Harvard Medical School and Harvard University
• Keywords: nonparametric statistics ; clustered data ; ophthalmologic data

Abstract

The Wilcoxon rank sum test is widely used for two-group comparisons for non-normal data. An assumption of this test is independence of sampling units both between and within groups. In ophthalmology, data are often collected on two eyes of an individual which are highly correlated. If the underlying distribution is non-normal, then it is desirable to use the Wilcoxon rank sum test to perform two group comparisons. However, a modification to the usual Wilcoxon rank sum variance formula must be made to account for the clustering. Another issue is that in ophthalmological clinical trials, randomization is usually performed at the subject level, the unit of analysis is the eye. However, in observational studies, binary eye-specific covariates may be present (scored as exposed or unexposed) and one wishes to compare non-normally distributed outcomes between exposed and unexposed eyes, using the Wilcoxon rank sum test while accounting for the clustering. In this talk, we present a correlated variance formula for the Wilcoxon rank sum statistic in this situation and apply it to compare visual field in retinitis pigmentosa patients between eyes with vs. without cataract.