Estimation and Testing of Wilcoxon–Mann–Whitney Effects in Factorial Clustered Data Designs

Abstract

Clustered data arise frequently in many practical applications whenever units are repeatedly observed under a certain condition. One typical example for clustered data are animal experiments, where several animals share the same cage and should not be assumed to be completely independent. Standard methods for the analysis of such data are Linear Mixed Models and Generalized Estimating Equations—however, checking their assumptions is not easy, especially in scenarios with small sample sizes, highly skewed, count, and ordinal or binary data. In such situations, Wilcoxon–Mann–Whitney type effects are suitable alternatives to mean-based or other distributional approaches. Hence, no specific data distribution, symmetric or asymmetric, is required. Within this work, we will present different estimation techniques of such effects in clustered factorial designs and discuss quadratic- and multiple contrast type-testing procedures for hypotheses formulated in terms of Wilcoxon–Mann–Whitney effects. Additionally, the framework allows for the occurrence of missing data: estimation and testing hypotheses are based on all-available data instead of complete-cases. An extensive simulation study investigates the precision of the estimators and the behavior of the test procedures in terms of their type-I error control. One real world dataset exemplifies the applicability of the newly proposed procedures.