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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 4680642, 6 pages
Research Article

A Bioequivalence Test by the Direct Comparison of Concentration-versus-Time Curves Using Local Polynomial Smoothers

1Division of Clinical Research, First Hospital of Jilin University, 71 Xinmin Street, Changchun, Jilin 130021, China
2Center for Clinical and Translational Science, The Rockefeller University, 1230 York Avenue, New York, NY 10065, USA
3School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun, Jilin 130012, China
4Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, 1518 Clifton Road NE, Atlanta, GA 30322, USA
5Laboratory of Molecular Neurooncology, The Rockefeller University, 1230 York Avenue, New York, NY 10065, USA
6Division of Rheumatology, Hospital for Special Surgery, 535 East 70th Street, New York, NY 10021, USA
7Clinical Pharmacology Center, Research Institute of Translational Medicine, First Hospital of Jilin University, Dongminzhu Street, Changchun 130021, China
8College of Life Science, Jilin University, 2699 Qianjin Street, Changchun 130012, China
9Center for Biostatistics, Department of Population, Health Science and Policy, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA
10Department of Genetics and Genomics Science, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA

Received 23 June 2016; Revised 29 August 2016; Accepted 7 September 2016

Academic Editor: Andrzej Kloczkowski

Copyright © 2016 Suyan Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to test if two chemically or pharmaceutically equivalent products have the same efficacy and/or toxicity, a bioequivalence (BE) study is conducted. The 80%/125% rule is the most commonly used criteria for BE and states that BE cannot be claimed unless the 90% CIs for the ratio of selected pharmacokinetics (PK) parameters of the tested to the reference drug are within 0.8 to 1.25. Considering that estimates of these PK parameters are derived from the concentration-versus-time curves, a direct comparison between these curves motivates an alternative and more flexible approach to test BE. Here, we propose to frame the BE test in terms of an equivalence of concentration-versus-time curves which are constructed using local polynomial smoother (LPS). A metric is presented to quantify the distance between the curves and its 90% CIs are calculated via bootstrapping. Then, we applied the proposed procedures to data from an animal study and found that BE between a generic drug and its brand name cannot be concluded, which was consistent with the results by applying the 80%/125% rule. However, the proposed procedure has the advantage of testing only on a single metric, instead of all PK parameters.