Statistical evaluation of similarity factor f₂ as a criterion for assessment of similarity between dissolution profiles

This paper addresses statistical issues of similarity factor f₂ as a criterion for assessment of similarity between two in vitro dissolution profiles as proposed in 'Guidance on Immediate Release Solid Oral Dosage Forms; Scale-up and Postapproval Changes: Chemistry, Manufacturing, and Controls; In Vitro Dissolution Testing; In Vivo Bioequivalence Documentation' (SUPAC), issued by the United States Food and Drug Administration on November 30, 1995. These issues include the invariant property of f₂ with respect to the location change and the consequence of failure to take into account shape of the curve and unequal spacing between sampling time points. The similarity factor f₂ is a sample statistic which cannot be used to formulate a statistical hypothesis for assessment of dissolution similarity. It is, therefore, impossible to evaluate false positive and false negative rates of decisions for approval of drug products based on f₂. Implementation of f₂ to assess dissolution similarity is, in fact, a one-sided problem rather than an interval criterion suggested by the SUPAC. Complexity of the form in the distribution of f₂ even under a very strict assumption prevents one from finding its expected variance and hence, confidence interval for the mean. The large-sample distribution of f₂ by the usual delta method fails to provide an adequate approximation to the empirical distribution obtained by simulation. In addition, simulation results also indicate that the similarity factor is too liberal in concluding similarity between dissolution profiles.