Use of the Mann-Whitney U-test for clustered data

The Mann-Whitney U-test is ubiquitous in statistical practice for the compa rison of measures of location for two samples where the assumption of norma lity is questionable. Frequently, one has replicate data for each individua l in a group and would like to compare measures of central tendency between groups without assuming normality. For this purpose, we present a generali zation of the Mann-Whitney U-test for clustered data. The test is performed by computing z(c) = (W-c - mu(c))/sigma(c), similar to N(0, 1) under H-0, where W-c, mu(c) are the observed and expected Mann-Whitney U-statistic bas ed on a comparison of all pairs of replicates in the two groups and sigma(c ) is the standard deviation of W-c that is modified to account for clusteri ng effects within a cluster. We obtain an explicit variance formula that is a function of four clustering parameters. We validate the properties of th e test procedure in a simulation study. We illustrate the methods with an e xample comparing the baseline Humphrey visual field between two treatment g roups in a randomized clinical trial of patients with retinitis pigmentosa (RP). (C) 1999 John Wiley & Sons, Ltd.