The AAPS Journal

, 20:62 | Cite as

Equivalence Testing of Complex Particle Size Distribution Profiles Based on Earth Mover’s Distance

  • Meng Hu
  • Xiaohui Jiang
  • Mohammad Absar
  • Stephanie Choi
  • Darby Kozak
  • Meiyu Shen
  • Yu-Ting Weng
  • Liang Zhao
  • Robert Lionberger
Research Article


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.


earth 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).


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Copyright information

© American Association of Pharmaceutical Scientists 2018

Authors and Affiliations

  • Meng Hu
    • 1
  • Xiaohui Jiang
    • 1
  • Mohammad Absar
    • 1
  • Stephanie Choi
    • 1
  • Darby Kozak
    • 1
  • Meiyu Shen
    • 2
  • Yu-Ting Weng
    • 2
  • Liang Zhao
    • 1
  • Robert Lionberger
    • 1
  1. 1.Office of Research and Standards, Office of Generic DrugsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringUSA
  2. 2.Office of Biostatistics, Office of Translational SciencesCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringUSA

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