Zhengguo Xu (1, 2), Matilde Merino-Sanjuan (2, 3), Victor Mangas-Sanjuan (2, 3), Alfredo GarcÃa-Arieta (4)
(1) R&D Clinical Development Department, Towa Pharmaceutical Europe, S.L., C./ St. MartÃ, 75–97, 08107 Martorelles, Barcelona, Spain. (2) Department of Pharmacy and Pharmaceutical Technology and Parasitology, University of Valencia, Valencia, Spain. (3) Interuniversity Research Institute for Molecular Recognition and Technological Development, Polytechnic University of Valencia–University of Valencia, Valencia, Spain. (4) División de FarmacologÃa y Evaluación ClÃnica, Departamento de Medicamentos de Uso Humano, Agencia Española de Medicamentos y Productos Sanitarios, Calle Campezo 1, Edificio 8, 28022, Madrid, Spain
Objectives: The importance of dissolution profiles comparison has been widely recognized by the pharmaceutical industry and regulatory authorities due to the significant roles the dissolution tests played in the development of medicinal products [1‒4]. Similarity factor f2 is the recommended method to compare dissolution profiles, but there are restrictions for its use due to various drawbacks associated with this method [5‒10]. Alternative methods such as confidence interval of f2 using bootstrap methodology have been proposed and recommended by several regulatory agencies when the requirements for using f2 are not fulfilled [11‒14]. Different point estimates, types of confidence intervals of f2, and the associated Type I errors and statistical power have been evaluated recently when bootstrap f2 method was employed [14‒16]. However, while the criteria for using conventional f2 are defined in regulatory guidelines, when bootstrap f2 method is applied, no clear criteria, such as the minimum number of time points in the bootstrapped data sets to be included to calculate the f2, has been described in any guidelines. The effects of applying minimum number of time points on the accuracy, precision, type I error, and statistical power, along with effects of variability and sample sizes, have been investigated using simulation in the current study.
Methods: Three-parameter Weibull model was used to simulate population dissolution profiles of the reference (R) and test (T) product. Four scenarios were simulated where the R dissolves more than 85% at 10 minutes (A), 15 minutes (B), 20 minutes (C) and 45 minutes (D). For each scenario, 17 population dissolution profiles of T were simulated that has the predefined target population f2 values of 35, 40, 45, …, 55, 60, 65, 75, and 85. Individual profiles of T and R were simulated with individual model parameters that were obtained based on the population model parameters using the exponential error model. Five variability scenarios (CV of 10%, 20%, 30%, 40%, and 50% at 10 minutes time points) and 8 samples sizes (12, 24, 36, 48, 60, 72, 84, and 120 units) were simulated for each population f2. Comparisons between T and R were made with the same sample sizes and variability scenarios. For each bootstrapped data set, the expected f2 was calculated as recommended by EMA [12]. There were 2720 comparisons in total and for each comparison, 90% percentile confidence interval (CI) was estimated twice, both with (denote as TP3) and without (denote as TP1) applying the restriction of minimum three time points. The whole process was repeated 10,000 times and the percentage of the similarity conclusions was determined to evaluate the type I error and statistical power. Accuracy was assessed by bias and coverage probability, and precision was measured by square root of the mean squared error.
Results: In general, larger sample sizes show better accuracy and precision, and higher statistical power, as expected. Effects of number of time points are similar for scenario B/C/D different for A due to lack of enough time points in the bootstrapped data set in this scenario. For A, in general, the accuracy and precision of TP1 are better than those of TP3. However, when population f2 values are large (e.g., greater than 65) and variability is high (e.g., CV of 40% or 50%), where population f2 values are generally underestimated, TP3 are more accurate and precise than TP1. For B/C/D, both TP1 and TP3 showed that the type I errors were all well controlled, but they all showed low statistical power (power of D is slightly less than C, which in turn is slightly less than B), e.g., for D, when population f2 is greater than 53 at least 48 units are needed to have at least 80% power for low variability scenario (CV is 10%), and when population f2 is greater than 75 with CV of 50%, at least 72 units are necessary to have at least 80% power. In general, TP1 has even lower power for A compared to B/C/D. For scenario A, TP3 showed higher power than TP1, but also much higher type I errors.
Conclusions: When there are insufficient time points, such as for those product with fast dissolution rate, it is recommended to apply minimum number of 3 time points for each bootstrapped data set for the calculation of expected f2 due to the extremely low power observed if such restriction is not applied. When the variability is high, industry is advised to increase sample size to obtain 90% CI of expected f2.
References:
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Reference: PAGE 32 (2024) Abstr 11110 [www.page-meeting.org/?abstract=11110]
Poster: Methodology - Estimation Methods