Comparison of free software platforms for the calculation of the 90% confidence interval of f2 similarity factor by bootstrap analysis

https://doi.org/10.1016/j.ejps.2020.105259Get rights and content

Highlights

  • E-f2 provides the most conservative unbiased estimation of f2.

  • 90% CI estimation based on the percentile bootstrap method might be adequate.

  • 500 bootstrap replicates could be sufficient for 90% CI estimation.

  • DDsolver should not be used for dissolution comparison in high variability conditions.

Abstract

Introduction

The calculation of the 90% confidence interval of f2 based on the bootstrap methodology has been proposed and accepted by the main regulatory authorities when the dissolution data shows excessive variability. Different free software platforms allow the calculation of the 90% CI of f2 by means of bootstrapping. Their use in regulatory submissions is growing, but divergent results have been observed between the available software platforms. Therefore, the objective of this work is to analyze the characteristics of these software platforms and evaluate their results.

Methods and materials

Highly variable in vitro dissolution data from two products were selected. Three different similarity factors, f2, E(f2) and bc-f2, and their corresponding 90% confidence intervals were calculated with three free software platforms, Pheq_bootstrap, Bootf2bca and DDSolver, and computed by four different approaches, normal approximation, bootstrap-t-CI, percentile CI, and bias corrected and accelerated CI.

Results

All three platforms report the same f2 value, 49.66 upon comparison of products 1 and 3 and 54.87 for products 2 and 3 (no truncation rule). Bootf2bca and Pheq_bootstrap provided the same f2 and E(f2) also under other truncation rules (EMA or FDA), which are not implemented in DDSolver. Pheq_bootstrap allowed the calculation of bc-f2. The conclusion of similarity is based on a bootstrap percentile CI of E(f2) and f2 in Pheq_bootstrap and DDSolver, respectively. Bootf2bca provides all four 90% CI.

Discussion

Bootf2bca or Pheq_bootstrap should be considered for the estimation of the 90% CI of the f2 similarity factor when dissolution profiles show high variability.

Introduction

Dissolution profile comparison is an essential tool for drug development and regulatory approval. Its use has been recognized by the main regulatory authorities (FDA and EMA) as a surrogate for bioequivalence in the case of minor variations of drug products (EMA, 2010; FDA, 2014), biowaivers based on the Biopharmaceutics Classification System (EMA, 2010; FDA, 2015), biowaivers for additional strengths (EMA, 2010; FDA, 2014), and as part of the evidence demonstrating therapeutic equivalence for certain dosage forms (EMA, 2018a; FDA, 1997, 2012).

The regulatory guidelines (EMA, 2010; FDA, 2017) describe different methodologies for the comparison of in vitro dissolution profiles, depending on the variability observed in the dissolution data. When a low coefficient of variation (CV) is observed in the amounts dissolved at the different sampling times (low variability: <20% up to 10 min and <10% in the rest of sampling times (EMA, 2010; FDA, 2017)), the dissolution profile comparison is generally based on the similarity factor (f2) equation, which assumes the mean dissolution profile of each product is an appropriate surrogate of the dissolution performance. The use of f2 has been extended worldwide due to its easy implementation. The f2 equation is based on the Euclidean distance, where similarity between test and reference products is concluded when f2 ≥50. This cut-off value of 50 has been defined since it is the value that corresponds to a difference of 10% between the average amounts dissolved at all sampling times.

On the contrary, dissolution comparison under high variability conditions has remained confusing until recently. Over the last few years, there have been a large number of publications where different methodologies were evaluated for the comparison of highly variable dissolution profiles (Cardot et al., 2017; Gomez-Mantilla et al., 2013; Mangas-Sanjuan et al., 2016; Martinez and Zhao, 2018; Ocaña et al., 2009; Paixao et al., 2017; Yoshida et al., 2017). Currently, the 90% confidence interval (CI) of f2 based on the bootstrap methodology has been proposed and accepted by the main regulatory authorities as a possible methodology for dissolution comparison under high variability conditions (Davit et al., 2013), or even as the preferred approach (EMA, 2018b). The value of f2 takes into account not only the differences in the dissolution of both products/formulations, but also its variance, which is negligible when low variability conditions are present. However, when two highly variable drug products/formulations are compared, the estimated value of f2 is clearly affected when the variance of both drug products/formulations is not considered. Some modifications of f2 have been proposed (Liu et al., 1997; Shah et al., 1998), but they have not been explored sufficiently and have no recognition by regulatory authorities.

Different free software platforms allow the calculation of the 90% CI of f2 by means of bootstrapping for the comparison of highly variable dissolution profiles, although none of them seems to have been adequately validated. Their use in regulatory submissions is growing, but divergent results have been observed between them. Therefore, the objective of this work is to analyze the characteristics of these software platforms and evaluate the results.

Section snippets

Experimental dataset

In order to investigate and compare the characteristics of the software platforms and their outputs, the calculation of the 90% CI of the f2 similarity factor was performed for the datasets displayed in Table 1. In vitro dissolution data were obtained from two modified-release products. Product 1 (30 mg) and product 2 (60 mg) were classified as test products (e.g. variation and additional strength, respectively), whereas product 3 (30 mg) was considered as reference. A sample of 12 tablets was

Experimental dataset

Fig. 1 shows the mean dissolution profiles of product 1, 2, and 3. Mean dissolved values of product 3 (reference) are always lower than those of product 1 (test), showing a slower dissolution rate. Compared to product 2, product 3 dissolves faster up to 145 min (25 min after the change of buffer to pH 6.8), but then, product 2 (test) shows a faster dissolution. Individual experimental values of each drug product are summarized in Table 1. The CV within each product exceeds the 20% at sampling

Discussion

DDsolver should not be used for the comparison of dissolution profiles with high variability because E(f2) and bc-f2 cannot be calculated with this software platform and the available 90% CI of f2 is biased due to high variability. Another major limitation of DDSolver is that this platform does not truncate the data sets to ensure that only one sampling point includes more than 85% dissolved for the first product to reach that value (EMA rule) or for both test and reference product (FDA rule).

Acknowledgments

None.

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