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The AAPS Journal

, Volume 17, Issue 2, pp 370–379 | Cite as

Application of the Modified Chi-Square Ratio Statistic in a Stepwise Procedure for Cascade Impactor Equivalence Testing

  • Benjamin Weber
  • Sau L. LeeEmail author
  • Renishkumar Delvadia
  • Robert Lionberger
  • Bing V. Li
  • Yi Tsong
  • Guenther Hochhaus
Research Article Theme: Current Scientific and Regulatory Approaches for Development of Orally Inhaled and Nasal Drug Products
Part of the following topical collections:
  1. Theme: Current Scientific and Regulatory Approaches for Development of Orally Inhaled and Nasal Drug Products

Abstract

Equivalence testing of aerodynamic particle size distribution (APSD) through multi-stage cascade impactors (CIs) is important for establishing bioequivalence of orally inhaled drug products. Recent work demonstrated that the median of the modified chi-square ratio statistic (MmCSRS) is a promising metric for APSD equivalence testing of test (T) and reference (R) products as it can be applied to a reduced number of CI sites that are more relevant for lung deposition. This metric is also less sensitive to the increased variability often observed for low-deposition sites. A method to establish critical values for the MmCSRS is described here. This method considers the variability of the R product by employing a reference variance scaling approach that allows definition of critical values as a function of the observed variability of the R product. A stepwise CI equivalence test is proposed that integrates the MmCSRS as a method for comparing the relative shapes of CI profiles and incorporates statistical tests for assessing equivalence of single actuation content and impactor sized mass. This stepwise CI equivalence test was applied to 55 published CI profile scenarios, which were classified as equivalent or inequivalent by members of the Product Quality Research Institute working group (PQRI WG). The results of the stepwise CI equivalence test using a 25% difference in MmCSRS as an acceptance criterion provided the best matching with those of the PQRI WG as decisions of both methods agreed in 75% of the 55 CI profile scenarios.

KEY Words

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

Supplementary material

12248_2014_9698_MOESM1_ESM.png (422 kb)
Figure S1 PQRI scenarios 1–4. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 421 kb)
12248_2014_9698_MOESM2_ESM.png (411 kb)
Figure S2 PQRI scenarios 5–8. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 411 kb)
12248_2014_9698_MOESM3_ESM.png (427 kb)
Figure S3 PQRI scenarios 9–12. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 427 kb)
12248_2014_9698_MOESM4_ESM.png (421 kb)
Figure S4 PQRI scenarios 13–16. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 420 kb)
12248_2014_9698_MOESM5_ESM.png (422 kb)
Figure S5 PQRI scenarios 17–20. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 421 kb) (PNG 421 kb)
12248_2014_9698_MOESM6_ESM.png (419 kb)
Figure S6 PQRI scenarios 21–24. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 419 kb)
12248_2014_9698_MOESM7_ESM.png (425 kb)
Figure S7 PQRI scenarios 25–28. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 425 kb)
12248_2014_9698_MOESM8_ESM.png (432 kb)
Figure S8 PQRI scenarios 29–32. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 431 kb)
12248_2014_9698_MOESM9_ESM.png (429 kb)
Figure S9 PQRI scenarios 33–36. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 428 kb)
12248_2014_9698_MOESM10_ESM.png (430 kb)
Figure S10 PQRI scenarios 37–40. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 429 kb)
12248_2014_9698_MOESM11_ESM.png (410 kb)
Figure S11 PQRI scenarios 41–44. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 410 kb)
12248_2014_9698_MOESM12_ESM.png (415 kb)
Figure S12 PQRI scenarios 45–48. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 414 kb)
12248_2014_9698_MOESM13_ESM.png (369 kb)
Figure S13 PQRI scenarios 49–51. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 369 kb)
12248_2014_9698_MOESM14_ESM.png (442 kb)
Figure S14 PQRI scenarios 52–55. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Eight ISM sites. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 441 kb)
12248_2014_9698_MOESM15_ESM.png (433 kb)
Figure S15 PQRI scenarios 52–55. Mean profiles on ISM sites after normalization on ISM and T/R ISM ratio. Seven ISM sites. Red: T product, Blue: R product. Original data is available elsewhere (6, 7) (PNG 433 kb)

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Copyright information

© American Association of Pharmaceutical Scientists 2014

Authors and Affiliations

  • Benjamin Weber
    • 1
  • Sau L. Lee
    • 2
    Email author
  • Renishkumar Delvadia
    • 3
  • Robert Lionberger
    • 3
  • Bing V. Li
    • 3
  • Yi Tsong
    • 4
  • Guenther Hochhaus
    • 1
  1. 1.Department of Pharmaceutics, College of Pharmacy, Center of Pharmacometrics and Systems PharmacologyUniversity of FloridaGainesvilleUSA
  2. 2.Office of Pharmaceutical ScienceCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringUSA
  3. 3.Office of Generic DrugsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringUSA
  4. 4.Division of Biometrics VI, Office of BiostatisticsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringUSA

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