Power analysis for cluster randomized trials with multiple binary co-primary endpoints

Cluster randomized trials (CRTs) are widely used in different areas of medicine and public health. Recently, with increasing complexity of medical therapies and technological advances in monitoring multiple outcomes, many clinical trials attempt to evaluate multiple co-primary endpoints. In this study, we present a power analysis method for CRTs with (Formula presented.) binary co-primary endpoints. It is developed based on the GEE (generalized estimating equation) approach, and three types of correlations are considered: inter-subject correlation within each endpoint, intra-subject correlation across endpoints, and inter-subject correlation across endpoints. A closed-form joint distribution of the K test statistics is derived, which facilitates the evaluation of power and type I error for arbitrarily constructed hypotheses. We further present a theorem that characterizes the relationship between various correlations and testing power. We assess the performance of the proposed power analysis method based on extensive simulation studies. An application example to a real clinical trial is presented.