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

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.

SUBMITTER: Weber B

PROVIDER: S-EPMC3535092 | biostudies-literature |

REPOSITORIES: biostudies-literature

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A sensitivity analysis of the modified chi-square ratio statistic for equivalence testing of aerodynamic particle size distribution.

Project description: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.

| S-EPMC3675742 | biostudies-literature

Application of the modified chi-square ratio statistic in a stepwise procedure for cascade impactor equivalence testing.

Project description: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.

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Equivalence of binormal likelihood-ratio and bi-chi-squared ROC curve models.

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