Sample size calculation in three-arm equivalence trials including a placebo for binary clinical endpoints

When assessing the equivalence between a generic drug (T) and its innovator drug (R) based on clinical endpoints, three-arm equivalence trials that include a placebo (P) are recommended by regulatory agencies whenever ethically justifiable. In such trials, equivalence of T and R is established only if the equivalence test (T vs. R) and both superiority tests (T vs. P and R vs. P) are simultaneously satisfied. Existing sample size calculation methods have typically considered only the equivalence test and one of the superiority tests (T vs. P), overlooking the other superiority test (R vs. P). We propose two methods for sample size calculation in three-arm equivalence trials with binary endpoints. These methods simultaneously account for the equivalence test based on the ratio of two rates and both superiority tests. Additionally, a grid search approach is proposed to determine the optimal allocation ratio for the sample sizes among the three arms.