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The AAPS Journal

, Volume 15, Issue 1, pp 1–9 | Cite as

A Stability Analysis of a Modified Version of the Chi-Square Ratio Statistic: Implications for Equivalence Testing of Aerodynamic Particle Size Distribution

  • Benjamin Weber
  • Guenther Hochhaus
  • Wallace Adams
  • Robert Lionberger
  • Bing Li
  • Yi Tsong
  • Sau L. LeeEmail author
Research Article

Abstract

Demonstration of equivalence in aerodynamic particle size distribution (APSD; e.g., by comparing cascade impactor (CI) profiles) constitutes one of key in vitro tests for supporting bioequivalence between test (T) and reference (R) orally inhaled drug products (OIDPs). A chi-square ratio statistic (CSRS) was previously proposed for equivalence testing of CI profiles. However, it was reported that the CSRS could not consistently discriminate between equivalent and inequivalent CI profiles. The objective of the overall project was to develop a robust and sensitive methodology for assessing equivalence of APSD profiles of T and R OIDPs. We propose here a modified version of the CSRS (mCSRS) and evaluated systematically its behavior when T and R CI profiles were identical. Different scenarios comprising CI profiles with different number of deposition sites and shapes were generated by Monte-Carlo simulation. For each scenario, the mCSRS was applied to 20,000 independent sets of 30 T and 30 R CI profiles that were identical. Different metrics (including mean and median) of the distribution of 900 mCSRSs (30 T × 30 R) were then evaluated for their suitability as a test statistic (i.e., independent of the number of sites and shape of the CI profile) for APSD equivalence testing. The median of the distribution of 900 mCSRSs (MmCSRS) was one regardless of the number of sites and shape of the CI profile. Hence, the MmCSRS is a robust metric for CI profile equivalence testing when T and R CI profiles are identical and potentially useful for APSD equivalence testing.

KEY WORDS

aerodynamic particle size distribution bioequivalence cascade impactor chi-square ratio statistic orally inhaled drug products 

Supplementary material

12248_2012_9410_Fig4_ESM.jpg (554 kb)
Electronic supplementary material

Representative CI profile plots (rank-ordered, see “Methods” sectopm) of “beta scenarios” 1–8 for eight deposition sites (JPEG 554 kb)

12248_2012_9410_MOESM1_ESM.tif (714 kb)
High-resolution image (TIFF 714 kb)

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Copyright information

© American Association of Pharmaceutical Scientists 2012

Authors and Affiliations

  • Benjamin Weber
    • 1
  • Guenther Hochhaus
    • 1
  • Wallace Adams
    • 2
  • Robert Lionberger
    • 2
  • Bing Li
    • 2
  • Yi Tsong
    • 3
  • Sau L. Lee
    • 2
    • 4
    Email author
  1. 1.Department of Pharmaceutics, College of Pharmacy, Center of Pharmacometrics and Systems PharmacologyUniversity of FloridaGainesvilleUSA
  2. 2.Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug AdministrationRockvilleUSA
  3. 3.Division of Biometrics VI, Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringUSA
  4. 4.RockvilleUSA

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