Multiple testing to establish superiority/equivalence of a new treatment compared with k standard treatments

In this paper we develop multiple hypotheses testing procedures to compare a new treatment with a set of standard treatments in a clinical trial. The aim is to classify the new treatment with respect to each of the standards, by specifying those to which the new treatment is superior, those to which the new treatment is equivalent and those to which one can establish neither superiority nor equivalence. We propose several stepwise procedures and compare them with respect to their familywise error rates and power. The step-down methods SD1 and SD2 test for superiority first, followed by tests for equivalence for those comparisons where we cannot establish superiority. The step-up methods SU1 and SU2 test for equivalence first, followed by tests for superiority for those comparisons where we can establish at least equivalence. The methods SD3 and SU3 apply the tests for superiority and equivalence in pairs. All the methods require that we specify a threshold value δ > 0 in advance for defining equivalence. In applications where it is not possible to specify a value δ, we can use the method SD1 by testing for superiority first, followed by one-sided confidence limits on the efficacy differences for those comparisons where we cannot establish superiority.