Robust Testing of Paired Outcomes Incorporating Covariate Effects in Clustered Data with Informative Cluster Size

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on the outcomes. However, when potentially important covariate data is available in observational studies, ignoring these covariate effects on the outcomes can result in a flawed inference. In this article, using rank based weighted estimating equations, we propose a robust procedure for covariate effect adjusted comparison of paired outcomes in a clustered data that can also address the issue of informative cluster size. Through simulated scenarios and real-life neuroimaging data, we demonstrate the importance of considering covariate effects during paired testing and robust performances of our proposed method in covariate adjusted paired comparisons in complex clustered data settings.