Estimators and confidence intervals of f₂ using bootstrap methodology for the comparison of dissolution profiles

Background and objectives: The most widely used method to compare dissolution profiles is the similarity factor f₂. When this method is not applicable, the confidence interval of f₂ 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.

Methods: One million individual dissolution profiles were simulated for the reference and test populations with predefined target population f₂ values, where random samples of different sizes were drawn without replacement. From each pair of random samples, five f₂ 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^₂ point estimate alone for the statistical inference was evaluated.

Results: When combined with different types of confidence intervals, the estimated f₂ (f^₂), the bias-corrected f₂ (f^_2,bc), and the variance- and bias-corrected f₂ (f^_2,vcbc) are not suitable estimators due to higher-than-acceptable type I errors. The estimator f^_2,exp, calculated based on the mathematical expectation of f^₂, and f^_2,vcexp, the variance-corrected f^_2,exp, 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.

Conclusion: The best combinations of estimator and type of confidence interval are f^_2,exp and f^_2,vcexp combined with any of the ten types of percentile intervals. When the sample f₂ value is close to 50, the use of the confidence interval of f₂ is recommended even when the variability of the dissolution profiles is low and the prerequisites defined in the regulatory guidelines for using the conventional f₂ method are fulfilled in order to control the type I error rate.