On familywise type I error control for multiplicity in equivalence trials with three or more treatments

For the all pairwise comparisons for equivalence of k (k≥2) treatments Lauzon and Caffo proposed simply to divide the type I error level α by k-1 to achieve a Bonferroni-based familywise error control when declaring pairs of two treatments equivalent. This rule is shown to be too liberal for k≥4. It works for k=3 yet for reasons not considered by Lauzon and Caffo. Based on the two one-sided testing procedures and using the closure test principle we develop valid alternatives based on Bonferroni's inequality. The set H of intersection hypotheses reveals a rich structure, leading to the possibility to present H as a directed acyclic graph (DAG). This in turn allows using some graph theoretical theorems and eases proving properties of the resulting multiple testing problems.