A Multivariate Equivalence Test Based on Mahalanobis Distance with a Data-Driven Margin

TL;DR

This paper introduces a new multivariate equivalence test using Mahalanobis distance with a data-driven margin that accounts for randomness, improving the assessment of product sameness in complex scenarios like drug development.

Contribution

It proposes a novel multivariate equivalence testing method with a data-driven margin that incorporates randomness, addressing limitations of existing fixed or purely data-derived margins.

Findings

The proposed method outperforms existing approaches in simulations.

It effectively handles high-dimensional data with many variables.

The approach provides a more reliable assessment of equivalence.

Abstract

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.