A simulation based technique to estimate intracluster correlation for a binary variable

Cluster randomized trials have become the design of choice for evaluating the effect of selected interventions on well-known health indicators such as neonatal mortality rate, episiotomy rate, and postpartum hemorrhage rate in a community setting. Determining the sample size of a cluster randomized trial requires a reliable estimate of cluster size and the intracluster correlation (ICC), because sample size can be substantially impacted by these parameters. During the design phase of a trial, the investigators may have estimates of the valid range of the health indicator which is the primary outcome variable. Furthermore, investigators often have an estimate of the average cluster size or range of cluster sizes that exist among the proposed samples they are planning to include in the trial. We present in this article a simulation technique to estimate the ICC value and its distribution for known binary outcome variables and a varying number of clusters and cluster sizes. We applied this technique to estimate ICC values and confidence intervals for a multi-country trial assessing the effect of neonatal resuscitation to decrease seven-day neonatal mortality, where communities within a country were clusters. This simulation technique can be used to estimate the possible ranges of the ICC values and to help to design an appropriately powered trial.