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

The Mann-Whitney U-test is ubiquitous in statistical practice for the comparison of measures of location for two samples where the assumption of normality is questionable. Frequently, one has replicate data for each individual in a group and would like to compare measures of central tendency between groups without assuming normality. For this purpose, we present a generalization of the Mann-Whitney U-test for clustered data. The test is performed by computing zc = (Wc - mu c)/sigma c, approximately N(0, 1) under H0, where Wc, mu c are the observed and expected Mann-Whitney U-statistic based on a comparison of all pairs of replicates in the two groups and sigma c is the standard deviation of Wc that is modified to account for clustering effects within a cluster. We obtain an explicit variance formula that is a function of four clustering parameters. We validate the properties of the test procedure in a simulation study. We illustrate the methods with an example comparing the baseline Humphrey visual field between two treatment groups in a randomized clinical trial of patients with retinitis pigmentosa (RP).