Testing for equivalence and non-inferiority: IU and UI tests within a permutation approach

In many research areas such as clinical trials, bioequivalence or pharmaceutical experiments, there is often the need to deal with the problem of testing the equivalence of two treatments. There are mainly two approaches with which to address the problem, the choice of which depends on the priority of the researcher who perform the analysis. The intersection-union principle (IU principle) considers as null hypothesis that the effect of a new treatment lies outside a given interval around that of the comparative treatment, and as alternative hypothesis that this effect lies within that interval. Alternatively, the union-intersection principle (UI principle) considers as null hypothesis that the effect of a new treatment lies within a given interval around that of the comparative treatment, and as alternative hypothesis that this effect lies outside that interval. Thus, given a fixed , the researcher has to decide if it is preferable to retain with a probability converging to one an equivalence between treatments (leading to the IU approach), or a non-equivalence between treatments (leading to the UI approach). In the literature, the IU approach seems to be the only one followed, apparently without real motivations. The goal of this paper is at first to present two practical solutions for the two approaches, working in a nonparametric setting within the permutation framework. Two algorithms respectively for IU and UI test are presented. A comparison between the behavior of the two solutions is also discussed using a simulation study.