Extending the Mann-WhitneyWilcoxon Rank Sum Test for Multiple Treatment Groups and Longitudinal Study Data - Abstract
Popular models for longitudinal data analysis with continuous outcomes such as linear mixed-effects model and weighted generalized estimating equations lack robustness in the presence of outliers. For example, in a study to evaluate the efficacy of a sexual risk-reduction intervention for sexually active teenage girls in low-income urban settings, some adolescent girls reported very large numbers such as 450 and even 1,000,000 for their unprotected vaginal sex over a three-month period. Although answers like this are clearly not legitimate values of the outcome, they do indicate the extremely high level of sexual activity among these girls and thus should not be completely ignored. However, the mean-based GLMM and WGEE are not capable of dealing with this type of “ outliers”, due to the sensitivity of the sample mean to values of extremely large magnitude. Rank based methods such as the popular Mann-Whitney-Wilcoxon (MWW) rank sum test are more effective alternatives to address such outliers. Unfortunately, available methods for inference are limited to cross-sectional data and cannot be applied to longitudinal studies, especially in the presence of missing data.
In this paper, we propose to extend the MWW test for comparing multiple groups within a longitudinal data setting, by utilizing the function response models. Inference is based on a class of U-statistics weighted generalized estimating equations, which provides consistent estimates, with asymptotic normal distributions, not only for complete data but also for missing data under MAR, the most popular missing mechanism in real studies. The approach is illustrated with data from both real and simulated studies.