Effects of the Minimum Number of Usable Time Points in Bootstrapped Data Sets on f 2 Confidence Interval Using...

To use the conventional $f_2$ method to compare dissolution profiles, at least 3 time points should be included; however, when the bootstrap $f_2$ method is applied, there are no clear criteria in regulatory guidelines in this regard. The effects of applying the minimum number of time points on the accuracy, precision, type I error (TIE), and statistical power have been investigated in the current study. Four scenarios were simulated where the reference product (R) dissolves at different rates. For each scenario, 17 population dissolution profiles of the test product (T) were simulated with predefined target population $f_2$ values with different variability and samples sizes. For each bootstrapped data set, the expected $f_2$ was calculated twice to obtain the 90% (CI) by applying the requirement of at least 3 time points (TP3) or at least 1 time point (TP1). The whole process was repeated 10000 times to evaluate the statistical properties. Effects on TIE and statistical power of TP1 and TP3 are similar for scenario B to D but different for A due to lack of enough time points in the bootstrapped data set. For A, TP3 shows much higher power than TP1, and TIE can be controlled at an acceptable level. It is recommended to calculate the expected $f_2$ with at least 3 time points for each bootstrapped data set, and there should be enough number of calculable expected $f_2$ from the bootstrapped samples to obtain 90% CI to control TIE. When the variability is high, sample size should be increased to improve statistical power.