Exact test-based approach for equivalence test with parameter margin

The equivalence test has a wide range of applications in pharmaceutical statistics which we need to test for the similarity between two groups. In recent years, the equivalence test has been used in assessing the analytical similarity between a proposed biosimilar product and a reference product. More specifically, the mean values of the two products for a given quality attribute are compared against an equivalence margin in the form of ±f × σ_R, where ± f × σ R is a function of the reference variability. In practice, this margin is unknown and is estimated from the sample as ±f × S_R. If we use this estimated margin with the classic t-test statistic on the equivalence test for the means, both Type I and Type II error rates may inflate. To resolve this issue, we develop an exact-based test method and compare this method with other proposed methods, such as the Wald test, the constrained Wald test, and the Generalized Pivotal Quantity (GPQ) in terms of Type I error rate and power. Application of those methods on data analysis is also provided in this paper. This work focuses on the development and discussion of the general statistical methodology and is not limited to the application of analytical similarity.