EFSPI CMCSNE SIG position on the 'Expected f2'

Abstract

The method called 'expected $f_2$' ($\hat{f}_{2,\exp}$), as proposed by Noce et al. (2020) and Xu et al. (2021), has been adopted in two health authority guidelines for dissolution profile comparison when variability precludes the use of the conventional similarity factor $\hat{f}_2$. This position paper, developed by a working group of the European Federation of Statisticians in the Pharmaceutical Industry CMC Statistical Network Europe Special Interest Group (EFSPI CMCSNE SIG), presents a critical evaluation of this method. Fundamental concerns are identified. First, the formula for $\hat{f}_{2,\exp}$ has no traceable origin in the references cited by its proponents. Noce et al. (2020) and Xu et al. (2021) attribute $\hat{f}_{2,\exp}$ to Shah et al. (1998) and Ma et al. (1999, 2000), but neither mentions nor suggests it. Second, no mathematical justification has been provided for the formula. Where Shah et al. (1998) subtract a variance term to reduce the upward bias of $\hat{f}_2$, the $\hat{f}_{2,\exp}$ formula adds this term, thereby increasing rather than correcting the bias. This has also been noted by FDA statisticians Liu et al. (2024). Third, the method exhibits poor statistical properties: for highly variable profiles, the variance term dominates the statistic, resulting in low power even as the true difference between profiles approaches zero. The method can reject equivalence when profiles are identical. Fourth, the formula as published by Noce et al. (2020) contains a notation ambiguity that renders the intended grouping of terms unclear. This ambiguity has propagated into regulatory guidance. A survey of working group members, designed to elicit arguments both for and against the method, found no scientifically meaningful advantage. The EFSPI CMCSNE SIG concludes that $\hat{f}_{2,\exp}$ should not be recommended for dissolution profile comparison.