Sample size determination in superiority clinical trials with multiple co-primary correlated endpoints

In pharmaceutical drug development, for regulatory purposes, there are increasing discussions on the establishment of statistically significant results demonstrating the efficacy of a new treatment on multiple co-primary endpoints. At the design stage with multiple co-primary endpoints, it is critical to determine the appropriate sample size for indicating statistical significance for all co-primary endpoints with preserving the intended power set, since the type II error increases as the number of co-primary endpoints increases. We provide fundamental formulae for power and sample size calculation with multiple co-primary endpoints and illustrate the aspect of the provided methods through numerical tables and examples.