Sample size estimation for the ratio of count outcomes in a cluster randomized trial using GEE

Count outcomes often occur in cluster randomized trials. Particularly in the context of epidemiology, the ratio of incidence rates has been used to assess the effectiveness of an intervention. In practice, cluster sizes typically vary across clusters, and sample size estimation based on a constant cluster size assumption may lead to underpowered studies. To address this issue, we propose a sample size method based on the generalized estimating equation (GEE) approach to test the ratio of two incidence rates. A closed-form sample size formula is presented, which is flexible to account for unbalanced randomization and randomly varying cluster sizes. Simulations were performed to assess its performance. In cluster randomized trials of vaccine efficacy, the ratio of disease incidence rates has been frequently used to demonstrate that the vaccine reduces the occurrence of a disease compared to placebo or active control. An application example to the design of a vaccine efficacy cluster randomized trial is presented.