Finite sample corrections for average equivalence testing

Abstract

Average (bio)equivalence tests are used to assess if a parameter, like the mean difference in treatment response between two conditions for example, lies within a given equivalence interval, hence allowing to conclude that the conditions have "equivalent" means. The two one-sided tests (TOST) procedure, consisting in testing whether the target parameter is respectively significantly greater and lower than some pre-defined lower and upper equivalence limits, is typically used in this context, usually by checking whether the confidence interval for the target parameter lies within these limits. This intuitive and visual procedure is however known to be conservative, especially in the case of highly variable drugs, where it shows a rapid power loss, often reaching zero, hence making it impossible to conclude for equivalence when it is actually true. Here, we propose a finite sample correction of the TOST procedure, the $\alpha$ -TOST, which consists in a correction of the significance level of the TOST allowing to guarantee a test size (or type-I error rate) of $\alpha$ . This new procedure essentially corresponds to a finite sample and variability correction of the TOST procedure. We show that this procedure is uniformly more powerful than the TOST, easy to compute, and that its operating characteristics outperform the ones of its competitors. A case study about econazole nitrate deposition in porcine skin is used to illustrate the benefits of the proposed method and its advantages compared to other available procedures.

Keywords: bioequivalence; interval inclusion principle; scaled average bioequivalence; similarity test; two one-sided test.