Multivariate Assessment for Bioequivalence Based on the Correlation of Random Effect

Abstract

Background and Objective

Bioequivalence tests are fundamental step in assessing the equivalence in bioavailability between a test and reference product. In practice, two separate linear mixed models (LMMs) with random subject effects, which have an area under the concentration-time curve (AUC) and the peak concentration (C_max) as the responses, have become the gold standard for evaluating bioequivalence. Recently, Lee et al developed a multivariate hierarchical generalized linear model (HGLM) for several responses that modeled correlations among multivariate responses via correlated random effects. The objective of this study was to apply this multivariate analysis to the bioequivalence test in practice and to compare the performance of multivariate HGLM and separate LMMs.

Methods

Three pharmacokinetic datasets, fixed-dose combination (naproxen and esomeprazole), tramadol and fimasartan data were analyzed. We compared the 90% confidence interval (CI) for the geometric mean ratio (GMR) of a test product to a reference product using the multivariate HGLM and two conventional separate LMMs.

Results

We found that the 90% CIs for the GMRs of both AUC and C_max from the multivariate HGLM were narrower than those from the separate LMMs: (0.843, 1.152) vs (0.825, 1.177) for C_max of esomeprazole in fixed-dose combination data; (0.805, 0.931) vs (0.797, 0.941) for C_max in tramadol data; (0.801, 1.501) vs (0.762, 1.578) for C_max and (1.163, 1.332) vs (1.009, 1.341) for AUC in fimasartan data, consistent with the random subject effects from two separate LMMs being highly correlated in the three datasets (correlation coefficient r = 0.883; r = 0.966; r = 0.832).

Conclusion

This multivariate HGLM had good performance in the bioequivalence test with multiple endpoints. This method would provide a more reasonable option to reduce the 90% CI by adding correlation parameters and thus an advantage especially in evaluating the bioequivalence of highly variable drugs with broad 90% CIs.

Keywords:

• bioequivalence test
• correlated multiple responses
• multivariate random effects model
• H-likelihood
• multivariate HGLM

Acknowledgments

A portion of this work was published for the degree of Doctor of Philosophy in February 2020. (Hyungmi An. H-likelihood approach for clinical pharmacology data). This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2020R1F1A1072586) and by Gachon University Gil Medical Center (Grant number: FRD2019-11).

Data Sharing Statement

The datasets generated during the current study are available from the corresponding author on reasonable request.

Compliance with Ethics Guidelines

Ethical review and approval were waived for this study, due to anonymized names of the patients.

Author Contributions

All named authors meet the International Committee of Medical Journal Editors (ICMJE) criteria for authorship for this article, take responsibility for the integrity of the work as a whole. All authors contributed to data analysis, drafting or revising the article, have agreed on the journal to which the article will be submitted, gave final approval of the version to be published, and agree to be accountable for all aspects of the work.

Disclosure

The authors have no conflicts of interest to disclose.

Additional information

Funding

The author received no specific funding for this work.