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

Dateng Li, Jing Cao, Song Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1064-1074
Number of pages11
Issue number4
StatePublished - Dec 2020


  • binary
  • cluster randomized trials
  • multiple co-primary endpoints
  • power analysis
  • sample size

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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