Multiplicity adjustments in testing for bioequivalence

Abstract

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.

Simultaneous confidence regions for multivariate bioequivalence

“…In this paper, we go beyond such univariate considerations and discuss how bioequivalence can and should be demonstrated for two or more PK parameters simultaneously. The TOST procedure itself is easy to extend by applying the intersection‐union principle, and other multivariate equivalence tests are available as well,() but there have been controversies about how to construct a simultaneous confidence region around the vector of estimated PK measures. A number of ideas have been put forward in the past two decades: Various authors suggested methods tailored to (bio‐)equivalence problems,() but also approaches that were not specifically designed for application in pharmaceutical statistics() may prove useful.…”

Adaptive Seamless Design for Establishing Pharmacokinetic and Efficacy Equivalence in Developing Biosimilars

“…As a further and practical consideration, a multiple testing issue for multiple PK endpoints would be needed in addition to the fixed sequence testing procedure considered between PK and efficacy endpoints because two PK endpoints, that is, AUC and Cmax, are often evaluated in practice in the PK trial. 49 In addition, several types of AUC are often set as primary endpoints. For instance, AUCs from time zero to predicted infinity and from time zero to the last measurable concentration were assessed in addition to Cmax as primary endpoints in the PK study within the development of the biosimilar adalimumab.…”

Statistical strategies for multiple testing in the safety evaluation of a genetically modified crop

“…In other words, testing such an expanded family of hypotheses is as good as testing the family with individual hypotheses only. It is worthwhile to mention that similar UI formulation of composite hypotheses is becoming increasingly common in multi-endpoint bioequivalence and non-inferiority studies of drugs (Quan et al 2001; Logan & Tamhane 2008; Hasler & Hothorn 2013; Hua et al 2015). This stems from the need for inference on individual endpoints.…”