A stability analysis of a modified version of the chi-square ratio statistic: implications for equivalence testing of aerodynamic particle size distribution.

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.