This thesis addresses critical challenges in equivalence testing and proposes novel solutions to improve the statistical power and accuracy of current methodologies. In the first chapter, we focus in the univariate setting and develop the α-TOST, a design-agnostic finite sample corrective procedure to the Two One-Sided Tests (TOST) that adjusts the significance level to ensure an accurate type-I error rate while improving statistical power. This procedure is validated through a rigorous theoretical study, extensive simulations and is demonstrated to outperform existing methods. The chapter concludes with a case study illustrating the practical application and advantages of the α-TOST over its competitors.

In the second chapter, the α-TOST is extended to the multivariate setting, introducing new complexities related to the size function and its derivation. We address these challenges by developing a lean and stable algorithm to compute the α-TOST, and provide the theoretical framework and empirical evidence showing its superiority over competing methods in terms of operating characteristics. The chapter concludes with a case study showcasing the method’s applicability and effectiveness in a four-dimensional multivariate bioequivalence setting.

To support practical implementation, the third chapter introduces the cTOST R package, which puts into practice the methods developed in the first two chapters. This chapter offers a hands-on guide for specifying inputs and applying the procedures across common (bio)equivalence trial designs, including parallel-group, paired, and crossover studies. It also shows how to reproduce the results of the case studies presented in the two first chapters, making it easier for researchers to understand and apply the methods in their own work.