A multivariate equivalence test based on Mahalanobis distance with a data-driven margin

Multivariate equivalence testing is needed in a variety of scenarios for drug development. For example, drug products obtained from natural sources may contain many components for which the individual effects and/or their interactions on clinical efficacy and safety cannot be completely characterized. Such lack of sufficient characterization poses a challenge for both generic drug developers to demonstrate and regulatory authorities to determine the sameness of a proposed generic product to its reference product. Another case is to ensure batch-to-batch consistency of naturally derived products containing a vast number of components, such as botanical products. The equivalence or sameness between products containing many components that cannot be individually evaluated needs to be studied in a holistic manner. Multivariate equivalence test based on Mahalanobis distance may be suitable to evaluate many variables holistically. Existing studies based on such method assumed either a predetermined constant margin, for which a consensus is difficult to achieve, or a margin derived from the data, where, however, the randomness is ignored during the testing. In this study, we propose a multivariate equivalence test based on Mahalanobis distance with a data-drive margin with the randomness in the margin considered. Several possible implementations are compared with existing approaches via extensive simulation studies.