A note about the R Coefficient, the intraclass correlation coefficient and their association with outcome prevalence

Background In cluster randomized trials, the intraclass correlation coefficient (ICC) is classically used to measure clustering. When the outcome is binary, the ICC is known to be associated with the prevalence of the outcome [1] . This association challenges its interpretation. To overcome this situation, Crespi et al. [2] extended a coefficient named R, initially proposed by Rosner [3] for ophthalmologic data, to cluster randomized trials. Crespi et al. asserted that R is less influenced by the outcome prevalence than is the ICC. The aim of this study was to evaluate the association between both R and the ICC and the outcome prevalence. Methods Considering the particular case of 2 individuals per cluster, we developed a simplified expression of both R and the ICC, and demonstrated that the ICC but not R is symmetrical around the 0.5 prevalence value. We also conducted a simulation study to explore the case of both fixed and variable cluster sizes greater than 2. Results This simulation study confirmed that the ICC increases until the 0.5 prevalence value and then decreases until the 1 prevalence value. The simulation study also demonstrated that R decreases when the prevalence increases from 0 to 1. Conclusion As for the ICC, R depends on the outcome prevalence. Consequently, R is not an appropriate coefficient if one wants an index independent of the outcome prevalence.