# A Sensitivity Analysis of the Modified Chi-square Ratio Statistic for Equivalence Testing of Aerodynamic Particle Size Distribution

- 503 Downloads
- 9 Citations

## Abstract

Demonstration of equivalence in aerodynamic particle size distribution (APSD) is one key component for establishing bioequivalence of orally inhaled drug products. We previously proposed a modified version of the Chi-square ratio statistic (mCSRS) for APSD equivalence testing and demonstrated that the median of the distribution of the mCSRS (MmCSRS) is a robust metric when test (T) and reference (R) cascade impactor (CI) profiles are identical. Here, we systematically evaluate the behavior of the MmCSRS when T and R CI profiles differ from each other in their mean deposition and variability on a single and multiple sites. All CI profiles were generated by Monte-Carlo simulations based upon modified actual CI data. Twenty thousand sets of 30 T and 30 R CI profiles were simulated for each scenario, and the behavior of the MmCSRS was correlated to metrics that characterize the difference between T and R product in mean deposition and variability. The two key findings were, first, that the MmCSRS is more sensitive to difference between T and R CI profiles on high deposition sites, and second, that a cut-off value for APSD equivalence testing based on the MmCSRS needs to be scaled on the variability of the R product. The former is considered as beneficial for equivalence testing of CI profiles as it decreases the likelihood of failing identical CI profiles by chance, in part, due to increasing analytical variability associated with lower deposition sites. The latter is expected to be important for consistently being able to discriminate equivalent from inequivalent CI profiles.

## KEY WORDS

aerodynamic particle size distribution bioequivalence cascade impactor modified Chi-square ratio statistic orally inhaled drug products## Supplementary material

## REFERENCES

- 1.Lee SL, Adams WP, Li BV, Conner DP, Chowdhury BA, Yu LX.
*In vitro*considerations to support bioequivalence of locally acting drugs in dry powder inhalers for lung diseases. AAPS J. 2009;11:414–23.PubMedCrossRefGoogle Scholar - 2.Weber B, Hochhaus G, Adams W, Lionberger R, Li B, Tsong Y,
*et al.*A stability analysis of a modified version of the chi-square ratio statistic: implications for equivalence testing of aerodynamic particle size distribution. AAPS J. 2013;15:1–9.Google Scholar - 3.Food and Drug Administration Center for Drug Evaluation and Research (CDER). Guidance for industry - bioavailability and bioequivalence studies for nasal aerosols and nasal sprays for local action (Draft Guidance), June 1999. http://www.fda.gov/ohrms/dockets/ac/00/backgrd/36099b1l.pdf. Accessed 13 June 2012
- 4.Christopher D, Adams W, Amann A, Bertha C, Byron PR, Doub W,
*et al*. Product quality research institute evaluation of cascade impactor profiles of pharmaceutical aerosols, part 3: final report on a statistical procedure for determining equivalence. AAPS PharmSciTech. 2007;8:65–74.CrossRefGoogle Scholar - 5.Christopher D, Adams WP, Lee DS, Morgan B, Pan Z, Singh GJ,
*et al*. Product quality research institute evaluation of cascade impactor profiles of pharmaceutical aerosols: part 2—evaluation of a method for determining equivalence. AAPS PharmSciTech. 2007;8:E39–48.CrossRefGoogle Scholar - 6.Izenman AJ. Modern multivariate statistical techniques—regression, classification, and manifold learning. 1st ed. New York: Springer; 2008. p. 56–61.CrossRefGoogle Scholar
- 7.Christensen R. Plane answers to complex questions. 4th ed. New York: Springer; 2011. p. 5–8.CrossRefGoogle Scholar
- 8.Genz A, Bretz F, Miwa T, Mi X, Leisch F, Scheipl F,
*et al.*Multivariate normal and t distributions. http://cran.r-project.org/web/packages/mvtnorm/mvtnorm.pdf. Accessed 07/02/2012. - 9.Evans C, Cipolla D, Chesworth T, Agurell E, Ahrens R, Conner D,
*et al*. Equivalence considerations for orally inhaled products for local action-ISAM/IPAC-RS European workshop report. J Aerosol Med Pulm Drug Deliv. 2012;25:117–39.PubMedCrossRefGoogle Scholar - 10.European Medicines Agency. Guideline on the requirements for clinical documentation for Orally Inhaled Products (OIP) including the requirements for demonstration of therapeutic equivalence between two inhaled products for use in the treatment of Asthma and Chronic Obstructive Pulmonary Disease (COPD) in adults and for use in the treatment of Asthma in children and adolescents. http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500003504.pdf. Accessed 13 June 2012.