Department of Pharmacokinetics, Towa Pharmaceutical Europe, S.L., Polgono Industrial de Martorelles, Barcelona, 08107, Spain; Department of Pharmacy and Pharmaceutical Technology and Parasitology, University of Valencia, Valencia, Spain.
Department of Pharmacy and Pharmaceutical Technology and Parasitology, University of Valencia, Valencia, Spain; Interuniversity Research Institute for Molecular Recognition and Technological Development, Polytechnic University of Valencia-University of Valencia, Valencia, Spain.
Comput Methods Programs Biomed. 2021 Nov;212:106449. doi: 10.1016/j.cmpb.2021.106449. Epub 2021 Oct 2.
The most widely used method to compare dissolution profiles is the similarity factor f. When this method is not applicable, the confidence interval of f using bootstrap methodology has been recommended instead. As neither details of the estimator nor the types of confidence intervals are described in the guidelines, the suitability of five estimators and fourteen types of confidence intervals were investigated in this study by simulation.
One million individual dissolution profiles were simulated for the reference and test populations with predefined target population f values, where random samples of different sizes were drawn without replacement. From each pair of random samples, five f estimators were calculated, and fourteen types of confidence intervals were obtained using 5000 bootstrap samples. The whole process was repeated 10000 times and the percentage of the similarity conclusions was measured. In addition, the uncertainty associated with the current practice of using f^ point estimate alone for the statistical inference was evaluated.
When combined with different types of confidence intervals, the estimated f (f^), the bias-corrected f (f^), and the variance- and bias-corrected f (f^) are not suitable estimators due to higher-than-acceptable type I errors. The estimator f^, calculated based on the mathematical expectation of f^, and f^, the variance-corrected f^, showed acceptable type I errors when combined with any of the ten percentile intervals. However, they have the drawback of low power, which might be addressed by increasing the sample size. To properly control the type I error, samples with at least 12 units should be used.
The best combinations of estimator and type of confidence interval are f^ and f^ combined with any of the ten types of percentile intervals. When the sample f value is close to 50, the use of the confidence interval of f is recommended even when the variability of the dissolution profiles is low and the prerequisites defined in the regulatory guidelines for using the conventional f method are fulfilled in order to control the type I error rate.
最常用的溶出曲线比较方法是相似因子 f。当该方法不适用时，建议使用 bootstrap 方法的 f 置信区间代替。由于指南中没有描述估计量的细节和置信区间的类型，因此本研究通过模拟考察了五种估计量和十四种置信区间的适用性。
对于参考人群和测试人群，根据预设的目标人群 f 值模拟了 100 万份个体溶出曲线，其中无替换随机抽取不同大小的样本。从每对随机样本中计算了五个 f 估计量，并使用 5000 个 bootstrap 样本获得了 14 种置信区间。整个过程重复了 10000 次，并测量了相似结论的百分比。此外，还评估了当前仅使用 f^点估计值进行统计推断的不确定性。
当与不同类型的置信区间结合使用时，估计的 f（f^）、校正后的 f（f^）和校正后的方差和偏倚的 f（f^）由于高于可接受的 I 型错误而不是合适的估计量。基于 f^的数学期望计算的估计量 f^和校正后的方差 f^，与任何一种十分位数区间结合使用时，I 型错误都可接受。然而，它们的缺点是功效低，这可以通过增加样本量来解决。为了正确控制 I 型错误，应使用至少 12 个单位的样本。
最佳的估计量和置信区间类型组合是 f^和 f^与任何一种十分位数区间类型结合使用。当样本 f 值接近 50 时，即使在溶出曲线变异性低且满足监管指南中使用常规 f 方法的前提条件下，也建议使用 f 的置信区间，以控制 I 型错误率。
