Easy multiplicity control in equivalence testing using two one-sided tests

The use of equivalence testing in scientific research is increasing beyond its traditional role in the drug approval process. Largely due to its ease of use and recommendations from the U.S. Food and Drug Administration guidance, the most common statistical method for testing equivalence is the two onesided tests (TOST) procedure. Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. Here we give a condition that bounds the familywise error rate (FWER) using TOST and leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of κ independent groups are being evaluated for equivalence, then simply scaling the nominal type I error rate down by (κ - 1) is sufficient to maintain the FWER at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a nondrug development setting is given.