Rank‐based inference for covariate and group effects in clustered data in presence of informative intra‐cluster group size

There have been numerous attempts to extend the Wilcoxon rank-sum test to clustered data. Recently, one such rank-sum test (Dutta & Datta, 2016, Biometrics 72, 432-440) was developed to compare the group-specific marginal distributions of outcomes in clustered data where the conditional distributions of outcomes depend on the number of observations from that group in a given cluster, a phenomenon referred to as informative intra-cluster group (ICG) size. However, comparison of group-specific marginal distributions may not be sufficient in presence of some potentially useful covariables that are observed in the study. In addition, not accounting for the effect of these covariates can lead to biased and misleading inference for the group comparisons. Thus, the purpose of this article is twofold. First, we develop a method to estimate the covariate effects using rank-based weighted estimating equations that are appropriate when the ICG size is informative. Second, we construct an aligned rank-sum test based on the covariate adjusted outcomes. Asymptotic distributions of the R-estimators and the test statistic are provided. Through simulation studies, we show the importance of selecting proper weights in constructing the estimating equations when informativeness is present through the cluster or ICG sizes. We also demonstrate the superiority and the robustness of our method in comparison to regular parametric linear mixed models in clustered data. We apply our method to analyze different real-life data sets including a data on birthweights of rat pups in different litters and a dental data on tooth attachment loss.