Multiplicity adjustments in testing for bioequivalence.

Bioequivalence of two drugs is usually demonstrated by rejecting two one-sided null hypotheses using the two one-sided tests for pharmacokinetic parameters: area under the concentration-time curve (AUC) and maximum concentration (Cmax). By virtue of the intersection-union test, there is no need for multiplicity adjustment in testing the two one-sided null hypotheses within each parameter. However, the decision rule for bioequivalence often requires equivalence to be achieved simultaneously on both parameters that contain four one-sided null hypotheses together; without adjusting for multiplicity, the family wise error rate (FWER) could fail to be controlled at the nominal type-I error rate α. The multiplicity issue for bioequivalence in this regard is scarcely discussed in the literature. To address this issue, we propose two approaches including a closed test procedure that controls FWER for the simultaneous AUC and Cmax bioequivalence and requires no adjustment of the type-I error, and an alpha-adaptive sequential testing (AAST) that controls FWER by pre-specifying the significance level on AUC (α1) and obtaining it for Cmax (α2) adaptively after testing of AUC. While both methods control FWER, the closed test requires testing of eight intersection null hypotheses each at α, and AAST is at times accomplished through a slight deduction in α1 and no deduction in α2 relative to α. The latter considers equivalence reached in AUC a higher importance than that in Cmax. Illustrated with published data, the two approaches, although operate differently, can lead to the same substantive conclusion and are better than a traditional method like Bonferroni adjustment.