Intra-cluster correlation selection for cluster randomized trials.

In this paper, we give focus to cluster randomized trials, also known as group randomized trials, which randomize clusters, or groups, of subjects to different trial arms, such as intervention or control. Outcomes from subjects within the same cluster tend to exhibit an exchangeable correlation measured by the intra-cluster correlation coefficient (ICC). Our primary interest is to test if the intervention has an impact on the marginal mean of an outcome. Using recently developed methods, we propose how to select a working ICC structure with the goal of choosing the structure that results in the smallest standard errors for regression parameter estimates and thus the greatest power for this test. Specifically, we utilize small-sample corrections for the estimation of the covariance matrix of regression parameter estimates. This matrix is incorporated within correlation selection criteria proposed in the generalized estimating equations literature to choose one of multiple working ICC structures under consideration. We demonstrate the potential power and utility of this approach when used in cluster randomized trial settings via a simulation study and application example, and we discuss practical considerations for its use in practice.