Testing for Multivariate Equivalence with Random Quadratic Forms

Multivariate equivalence testing becomes necessary whenever the similarity rather than a difference between several treatment groups with multiple endpoints has to be shown. This problem occurs in various applications, including bioequivalence or the comparison of dissolution profiles. Therefore, several tests have been suggested during the last decade for the assessment of multivariate equivalence. Recently Munk & Pflüger (1999) proposed to test ellipsoidal instead of rectangular hypotheses as it is current practice in many applications. In this paper we provide several asymptotic tests for ellipsoidal equivalence which are compared numerically with competitors suggested by Brown, Cassella & Hwang (1995) and Munk & Pflüger (1999). We find that the proposed tests are superior (up to 90%) to both tests with respect to power. In addition, a simulation study reveals the suggested tests as robust against violation of normality. These tests are very simple to apply, because inversion of confidence regions is avoided. Asymptotic formulas for the power function and sample size determination are given. Finally, all procedures are compared in two data examples.