Effect of imbalance and intracluster correlation coefficient in cluster randomized trials with binary outcomes

Cluster randomization trials are increasingly popular among healthcare researchers. Intact groups (called 'clusters') of subjects are randomized to receive different interventions, and all subjects within a cluster receive the same intervention. In cluster randomized trials, a cluster is the unit of randomization, and a subject is the unit of analysis. Variation in cluster sizes can affect the sample size estimate or the power of the study. [Guittet, L., Ravaud, P., Giraudeau, B., 2006. Planning a cluster randomized trial with unequal cluster sizes: Practical issues involving continuous outcomes. BMC Medical Research Methodology 6 (17), 1-15] investigated the impact of an imbalance in cluster size on the power of trials with continuous outcomes through simulations. In this paper, we examine the impact of cluster size variation and intracluster correlation on the power of the study for binary outcomes through simulations. Because the sample size formula for cluster randomization trials is based on a large sample approximation, we evaluate the performance of the sample size formula with small sample sizes through simulation. Simulation study findings show that the sample size formula (m_p) accounting for unequal cluster sizes yields empirical powers closer to the nominal power than the sample size formula (m_a) for the average cluster size method. The differences in sample size estimates and empirical powers between m_a and m_p get smaller as the imbalance in cluster sizes gets smaller.