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Cascade Impactor Equivalence Testing: Comparison of the Performance of the Modified Chi-Square Ratio Statistic (mCSRS) with the Original CSRS and EMA’s Average Bioequivalence Approach


The performances of three statistical approaches for assessing in vitro equivalence was evaluated with a set of 55 scenarios of realistic test (T) and reference (R) cascade impactor (CI) profiles (originally employed by the Product Quality Research Institute to evaluate the chi-square ratio statistic: CSRS) by comparing the outcomes against experts’ opinion (surrogate for the truth). The three methods were (A) a stepwise aerodynamic particle size distribution (APSD) equivalence test integrating population bioequivalence (PBE) testing of impactor-sized mass (ISM) with the CSRS (PBE-CSRS approach), previously suggested by the USFDA; (B) the combination of PBE testing of single actuation content and ISM with the newly suggested modified CSRS (PBE-mCSRS approach), a method employing reference variance scaling; and (C) EMA’s average bioequivalence (ABE approach). Based on Monte-Carlo simulations, both PBE-CSRS and ABE approaches resulted in high misclassification rates, the former with highest false-pass rate and the latter with highest false-fail rate at both ≥ 50% and ≥ 80% classification threshold values (the % of simulations or experts necessary to judge a given scenario as equivalent). Based on DeLong’s tests, the PBE-mCSRS approach showed significantly better overall agreement with experts’ opinion compared to the other approaches. Comparison of CSRS with mCSRS (both without PBE) suggested that the more discriminatory characteristics of the mCSRS method is based on the integration of variance scaling into the mCSRS method. Contrary to the ABE approach, the application of PBE-mCSRS approach for assessing APSD profiles of three dry powder inhaler (DPI) formulations supported the pharmacokinetic bioequivalence assessment of these formulations.

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We would like to thank Dr. Benjamin Weber and Dr. Renishkumar Delvadia for their help with computations in this project.

Views expressed in this publication do not necessarily reflect the official policies of the Department of Health and Human Services, nor does any mention of trade names, commercial practices, or organization imply endorsement by the US Government.


The International Pharmaceutical Aerosol Consortium-Regulatory Science (IPAC-RS) funded part of this project. In addition, the Office of Generic Drugs (OGD) at FDA sponsored the in vitro CI profile testing and clinical PK study of experimental DPI formulations through GDUFA-funded contracts HHSF223201110117A, HHSF223201610099C, and HHSF223201300479A.

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Correspondence to Günther Hochhaus.

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Kurumaddali, A., Christopher, D., Sandell, D. et al. Cascade Impactor Equivalence Testing: Comparison of the Performance of the Modified Chi-Square Ratio Statistic (mCSRS) with the Original CSRS and EMA’s Average Bioequivalence Approach. AAPS PharmSciTech 20, 249 (2019).

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  • aerodynamic particle size distribution
  • bioequivalence
  • cascade impactor
  • modified chi-square ratio statistic (mCSRS)
  • receiver operating characteristic curves (ROC)