Estimating intra-cluster correlation coefficients for planning longitudinal cluster randomized trials: a tutorial

Abstract

It is well-known that designing a cluster randomized trial (CRT) requires an advance estimate of the intra-cluster correlation coefficient (ICC). In the case of longitudinal CRTs, where outcomes are assessed repeatedly in each cluster over time, estimates for more complex correlation structures are required. Three common types of correlation structures for longitudinal CRTs are exchangeable, nested/block exchangeable and exponential decay correlations—the latter two allow the strength of the correlation to weaken over time. Determining sample sizes under these latter two structures requires advance specification of the within-period ICC and cluster autocorrelation coefficient as well as the intra-individual autocorrelation coefficient in the case of a cohort design. How to estimate these coefficients is a common challenge for investigators. When appropriate estimates from previously published longitudinal CRTs are not available, one possibility is to re-analyse data from an available trial dataset or to access observational data to estimate these parameters in advance of a trial. In this tutorial, we demonstrate how to estimate correlation parameters under these correlation structures for continuous and binary outcomes. We first introduce the correlation structures and their underlying model assumptions under a mixed-effects regression framework. With practical advice for implementation, we then demonstrate how the correlation parameters can be estimated using examples and we provide programming code in R, SAS, and Stata. An Rshiny app is available that allows investigators to upload an existing dataset and obtain the estimated correlation parameters. We conclude by identifying some gaps in the literature.

Sample size requirements for testing treatment effect heterogeneity in cluster randomized trials with binary outcomes

“…For example, the logistic linear mixed model could be fitted to estimate regression parameters and variance component parameters based on two‐level data, and standard ICC estimators 24 could be used to obtain the covariate ICC. More recently, Ouyang et al 37 provided a tutorial on how to obtain ICC estimates from published longitudinal CRTs to inform the design of more complex trials, and the general recommendations there should apply to our settings. If routinely collected data or pilot data are unavailable, information from the published literature might be helpful.…”

Sample size determination for external pilot cluster randomised trials with binary feasibility outcomes: a tutorial

“…All are UK- or European-based trials; most include more than 20 clusters/centres, and the total sample size is greater than 500 for the majority. We estimate the correlations on the proportions scale (as is appropriate for binary outcomes) [ 24 , 25 ], using REML and implemented in Stata 17 using mixed (with the exception for two outcomes where mixed failed to converge and we used ANOVA implemented in Stata using loneway ). The upper interquartile range across all available intra-cluster correlation coefficients is 0.11 [ IQR : 0.05 to 0.18].…”