Testing for Equivalence: An Intersection-Union Permutation Solution

The notion of testing for equivalence of two treatments is widely used in clinical trials, pharmaceutical experiments, bioequivalence, and quality control. It is essentially approached within the intersection-union (IU) principle. According to this principle, the null hypothesis is stated as the set of effects lying outside a suitably established interval and the alternative as the set of effects lying inside that interval. The solutions provided in the literature are mostly based on likelihood techniques, which in turn are rather difficult to handle, except for cases lying within the regular exponential family and the invariance principle. The main goal of the present article is to go beyond most of the limitations of likelihood-based methods, that is, to work in a nonparametric setting within the permutation frame. To obtain practical solutions, a new IU permutation test is presented and discussed. A simple simulation study for evaluating its main properties, and three application examples are also presented.