Equivalence tests for interchangeability based on two one-sided probabilities

A test treatment is considered to be interchangeable with its reference treatment if they are equivalent and expected to produce the same clinical result in any given patient. To assess interchangeability, FDA Draft Guidance (1999) and Guidance for Industry (2001, 2003) recommend using individual bioequivalence (IBE) and population bioequivalence (PBE) procedures. Chow (1999) and Chow and Liu (1999) gave a discussion on the limitation of the aggregate criteria of the IBE and PBE proposed therein. They mentioned that it is not clear whether IBE or PBE can imply average bioequivalence. Alternative approaches have been proposed to address the weakness of IBE and PBE. Dong et al. (2014) discuss the tolerance interval method and an approximate test for interchangeability defined by a two-sided probability. These tests may not be able to test for the two one-sided tests (TOST) with asymmetric margins around the true mean difference. In addition, the tests of two-sided probability provide no direction when failing the equivalence in interchangeability. Thus, we reexamine the statistical properties of the two one-sided tolerance interval approaches proposed by Tsong and Shen (2007, 2008). In this project, we extend their approach for parallel arms trials and paired/crossover data without the assumption of equal sample sizes and variances. We also develop the exact power function and assess the type I error rate of our proposed approach. In addition, we study the sample size determination based on the interchangeability testing utilizing the tolerance interval method.