[Proof of equivalence as a new issue in confirmatory statistics]

A correct confirmatory analysis of studies aiming at demonstration of equivalence requires the use of a class of testing procedures that is still widely unknown among non-specialists and not even mentioned in traditional textbooks on Applied Statistics. The naive approach to equivalence testing, i.e. performing an ordinary two-sided test and inferring equivalence from the absence of a significant difference, is unacceptable since it entails an uncontrolled increase of the risk of false positive conclusions. A technically simple approach to avoiding such fallacies is based on the principle of confidence interval inclusion. However, the latter suffers from the disadvantage of yielding testing procedures that tend to exhibit comparatively poor power properties. For the sake of keeping the numbers of patients or subjects to be recruited for the respective trials as low as possible, application of optimum testing procedures, also for equivalence assessment, has much to recommend it. The rationale of such an optimum test for equivalence is described in some detail for four standard settings frequently encountered in clinical research.