Optimal Design and Analysis for Equivalence Tests in Randomized Controlled Trials

Testing the equivalence rather than the difference of two-group means might be of interest. Researchers may verify randomization validity by testing the equivalence of baseline means in randomized controlled trials and the equivalence of post-treatment outcomes when they expect equal means, while other dimensions (e.g., costs) differ. However, the analytical and design strategies for equivalence tests are limited. For example, the analytical and design methods usually do not include covariate adjustments, and the power formula development has not used the correct product function. The present study develops and validates the statistical power formula for randomized controlled trials to detect statistical equivalence with and without covariate adjustment. It further presents an optimal design framework for identifying the sample allocation that maximizes statistical power under a fixed budget. The proposed methods have been implemented in the R package anomo . Illustration examples are also provided.