Study design for a three-arm equivalence clinical trial with binomially distributed outcomes

Equivalence in a clinical trial may be assessed through a three-arm trial (test drug, reference drug, and placebo). A three-arm equivalence trial consists of three hypothesis tests in practice, with two hypothesis tests demonstrating the superiority of the test and reference drugs against placebo, and the other one demonstrating the equivalence of the test and reference drugs. When designing a three-arm equivalence clinical trial, the practitioner should minimize the chances that a test drug will be found to be equivalent to the reference drug but non-superior to the placebo. One way to minimize these chances at the design stage, for a three-arm equivalence trial with a binary primary outcome, is to test the equivalence through hypotheses based upon the ratio of the differences of the proportions. In this article, we derived the test statistics and the power functions based on maximum likelihood estimate (MLE) and restricted MLE for the proposed hypotheses. The required sample size for achieving the desired power at the given significance level can be obtained by solving the power function. We illustrated the proposed design through an example and investigated the required sample sizes for various conditions.