Wilcoxon-Mann-Whitney Effects for Clustered Data: Informative Cluster Size

Abstract

In recent research, there has been a growing interest in understanding the impact of informative cluster size (ICS) on statistical inference for clustered data. In the non-parametric context, the problem for testing equality of distribution functions has been the main consideration. We are aiming to develop inferential procedures for the Wilcoxon-Mann-Whitney effect, also known as the non-parametric relative effect, involving two or more groups. Computationally, results from both simulated and real-world data have shown promising results that our proposed tests effectively account for ICS and they particularly outperform other methods in the literature designed for ignorable cluster sizes. The applications of our methods are illustrated using data from a longitudinal study of alcohol use and a periodontal study