Equivalence Testing of Complex Particle Size Distribution Profiles Based on Earth Mover’s Distance
- 67 Downloads
Particle size distribution (PSD) is an important property of particulates in drug products. In the evaluation of generic drug products formulated as suspensions, emulsions, and liposomes, the PSD comparisons between a test product and the branded product can provide useful information regarding in vitro and in vivo performance. Historically, the FDA has recommended the population bioequivalence (PBE) statistical approach to compare the PSD descriptors D50 and SPAN from test and reference products to support product equivalence. In this study, the earth mover’s distance (EMD) is proposed as a new metric for comparing PSD particularly when the PSD profile exhibits complex distribution (e.g., multiple peaks) that is not accurately described by the D50 and SPAN descriptor. EMD is a statistical metric that measures the discrepancy (distance) between size distribution profiles without a prior assumption of the distribution. PBE is then adopted to perform statistical test to establish equivalence based on the calculated EMD distances. Simulations show that proposed EMD-based approach is effective in comparing test and reference profiles for equivalence testing and is superior compared to commonly used distance measures, e.g., Euclidean and Kolmogorov–Smirnov distances. The proposed approach was demonstrated by evaluating equivalence of cyclosporine ophthalmic emulsion PSDs that were manufactured under different conditions. Our results show that proposed approach can effectively pass an equivalent product (e.g., reference product against itself) and reject an inequivalent product (e.g., reference product against negative control), thus suggesting its usefulness in supporting bioequivalence determination of a test product to the reference product which both possess multimodal PSDs.
KEY WORDSearth mover’s distance equivalence test particle size distribution profile comparison
The authors wish to thank Dr. Xiaoming Xu for the assistance with laboratory work. Dr. Yi Tsong and Dr. Sarah Dutcher are acknowledged for their valuable inputs in this project.
Compliance with Ethical Standards
The views expressed in this article are those of the authors and not necessarily those of the Food and Drug Administration (FDA).
- 1.2016 Generic Drug Savings & Access in the United States Report. Available at http://www.gphaonline.org/media/generic-drug-savings-2016/index.html.
- 2.Code of Federal Regulations 21CFR320.1. Available at http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRSearch.cfm?fr=320.1.
- 3.Product-Specific Recommendations for Generic Drug Development. Available at http://www.fda.gov/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/ucm075207.htm.
- 4.Guidance for Industry: Bioavailability and bioequivalence studies for nasal aerosols and nasal sprays for local action. Available at http://www.fda.gov/downloads/drugs/guidancecomplianceregulatoryinformation/guidances/ucm070111.pdf.
- 6.Lu Y, Chow SC, Zhu S. In vivo and in vitro bioequivalence testing. J Bioequiv Availab. 2014;6(2):067–74.Google Scholar
- 8.A guidebook to particle size analysis (HORIBA Scientific). Available at https://www.horiba.com/fileadmin/uploads/Scientific/Documents/PSA/PSA_Guidebook.pdf.
- 14.Guidance for Industry - Statistical Approaches to Establishing Bioequivalence. 2001. Available at http://www.fda.gov/downloads/Drugs/.../Guidances/ucm070244.pdf.
- 16.Gonzalez RC, Woods RE. Digital image processing. 3rd ed. Upper Saddle River: Prentice Hall; 2008.Google Scholar
- 21.Product-specific guidance for Budesonide Suspension/Inhalation. 2012. Available at http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM319977.pdf.
- 22.Product-specific guidance for Cyclosporine Emulsion; ophthalmic. 2016. Available at http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM358114.pdf.
- 23.Drug general information for Restasis. Available at https://www.drugs.com/restasis.html.
- 25.Levina E, Bickel P. The earth mover’s distance is the mallows distance: some insights from statistics. Proc IEEE Int Conf Comput Vis. 2001;2:251–6.Google Scholar