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

Abstract

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.

A hybrid stochastic/fixed-sectional method for solving the population balance equation

“…It does not require the same discretization of the compared distributions. EMD has previously been used for Particle Size Distributions and compared with other distance measures (Hu et al, 2018). The EMD is normalised by the standard deviation of the exact distribution.…”

Regulating Generic Ophthalmologic Drug Bioequivalence—Envisioning Accessibility for Patients

“…In addition, under GDUFA, a portion of these user fees fund FDA-directed research to provide new tools and address knowledge gaps to evaluate generic drug therapeutic equivalence. 6,7 Examples of recent GDUFA-funded projects that have focused on ophthalmic drug products include assessing how manufacturing processes can affect the critical quality attributes (CQAs) of complex dosage forms and developing new analytical and statistical methods for characterizing ocular drug product CQAs, [8][9][10] developing new in vitro release testing (IVRT) methods, 11 ocular drug modeling and simulation, [12][13][14] and very importantly, developing in vitro-in vivo correlations (IVIVCs), 15 with a target of providing justification for in vitroweighted approaches to bioequivalence determinations.…”

A new Wasserstein distance- and cumulative sum-dependent health indicator and its application in prediction of remaining useful life of bearing

“…To date, the WD has been widely applied in the color-based image retrieval [26], shape matching [27] and machine learning [28]. For two vibration signals of bearings X= x 1 , x 2 , … x n and Y= y 1 , y 2 , … y n , the WD can be obtained as follows [29][30][31]:…”