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

Clinical trials often employ two or more primary efficacy endpoints. One of the major problems in such trials is how to determine a sample size suitable for multiple co-primary correlated endpoints. We provide fundamental formulae for the calculation of power and sample size in order to achieve statistical significance for all the multiple primary endpoints given as binary variables. On the basis of three association measures among primary endpoints, we discuss five methods of power and sample size calculation: the asymptotic normal method with and without continuity correction, the arcsine method with and without continuity correction, and Fisher's exact method. For all five methods, the achieved sample size decreases as the value of association measure increases when the effect sizes among endpoints are approximately equal. In particular, a high positive association has a greater effect on the decrease in the sample size. On the other hand, such a relationship is not very strong when the effect sizes are different.