Multivariate Adjustments for Average Equivalence Testing

Multivariate (average) equivalence testing is used when we need to show that two conditions are equivalent across several outcomes at the same time. The standard multivariate Two One-Sided Tests (TOST) procedure checks each outcome separately, using marginal confidence intervals to decide whether all effects fall within predefined equivalence limits. While intuitive, this approach becomes overly conservative as the number of outcomes grows or when variances differ across outcomes, often leading to major losses in statistical power. We introduce the multivariate $\alpha$ -TOST, a finite-sample correction that adjusts the significance level while accounting for the dependence between outcomes. This produces a test that rigorously controls type-I error and is uniformly more powerful than the conventional multivariate TOST. We derive an efficient iterative algorithm to compute the corrected level $\alpha^*$ , evaluate the method through asymptotic theory and extensive simulations, and demonstrate its practical benefits in a bioequivalence case study on ticlopidine hydrochloride.