A1425
Title: Partial optimality and applicability for multivariate equivalence testing
Authors: Luca Insolia - University of Geneva (Switzerland) [presenting]
Yanyuan Ma - Pennsylvania State University (United States)
Younes Boulaguiem - University of Geneva (Switzerland)
Stephane Guerrier - University of Geneva (Switzerland)
Abstract: Average equivalence testing aims at assessing whether an effect of interest, such as the difference in means between Two experimental outcomes, lies within a predetermined region of practical equivalence. While univariate Tests for normal means are widely used in modern applications, multivariate settings remain challenging, especially when experimental constraints limit the available sample sizes or introduce substantial noise. Established approaches, such as the Two One-Sided Tests (TOST), cannot adequately capture the complex multivariate nature of such data and lead to test procedures with limited power. To mitigate the conservativeness of TOST, a corrected TOST framework is developed by simultaneously adjusting its significance level and equivalence margins to ensure control of the test size and increase its power. It is demonstrated that, in large samples, this approach leads to an optimal correction for the univariate TOST procedure, and a further small-sample refinement is developed to control its performance. In multivariate settings, where an optimal correction does not exist, the proposal constrains marginal test sizes, leading to more balanced rejection regions, while maintaining overall size control and maximizing power in important cases. Extensive simulation studies empirically demonstrate the superior performance of the proposed framework and illustrate its practical relevance with a case study in the pharmaceutical sciences.
