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

Area of Science:

• Statistics
• Biostatistics
• Clinical Trials

Background:

• The Mann-Whitney U-test is widely used for comparing two independent samples when normality is not assumed.
• Existing methods are limited when dealing with clustered or replicate data within groups.

Purpose of the Study:

• To develop and validate a generalized Mann-Whitney U-test for clustered data.
• To enable robust comparison of central tendency measures between groups with non-normal, clustered observations.

Main Methods:

• A generalized Mann-Whitney U-statistic (Wc) is computed using all pairwise replicate comparisons.
• A modified standard deviation (sigma c) accounts for intra-cluster correlation.
• An explicit variance formula incorporating four clustering parameters is derived.

Main Results:

• The proposed test statistic (zc) approximates a standard normal distribution under the null hypothesis.
• A simulation study validated the test's statistical properties.
• The method was successfully applied to compare visual field data in retinitis pigmentosa patients.

Conclusions:

• The generalized Mann-Whitney U-test provides a valid statistical approach for analyzing clustered data.
• This method enhances the analysis of non-normal data in clinical trials and other research areas.
• It offers a reliable alternative for comparing groups when data exhibits clustering effects.