Mathematical and regulatory limitations of the similarity factor f₂ under incomplete dissolution: analysis of the ICH M13B guideline and applicability of alternative metrics

Introduction. The similarity factor f₂ (Moore & Flanner, 1996) remains the gold standard for assessing dissolution profile equivalence in pharmaceutical development, biowaiver procedures, and the justification of post-approval changes. However, the mathematical framework of this metric was conceived in the late 1990s strictly for routine quality control under complete dissolution conditions (Q > 85 %). The international guideline ICH M13B establishes a threshold rule: dissolution profiles with less than 10 % release are deemed comparable without mathematical evaluation, whereas profiles exceeding 10 % release require calculation of f₂ (or Bootstrap f₂). Under non-sink conditions, typical for Biopharmaceutics Classification System (BCS) Class II and IV active substances in physiological media lacking surfactants, the f₂ metric loses sensitivity to relative kinetic discrepancies.

Aim. To analyze the mathematical limitations of the similarity factor f₂ under incomplete dissolution, to perform a comparative evaluation of f₂, the difference factor f₁, and the Two One-Sided Tests (TOST) procedure, and to provide recommendations for statistical evaluation of comparative in vitro dissolution test (CIDT) data within the framework of EAEU regulations and the ICH M13B guideline.

Materials and methods. Using a critical model CIDT scenario for a poorly soluble compound with mean dissolution profiles of the test product T = (6,0 %; 10,0 %; 13,0 %; 18,0 %); and the reference product R = (11.0 %;18.0 %; 22.0 %; 30.0 %); parallel calculations of f₂ and f₁ were performed in accordance with Annex 5 to the EEC Council Decision No. 85 dated November 3, 2016, along with an equivalence assessment on a relative logarithmic scale (TOST approach).

Results and discussion. For the analyzed dataset, the f₂ metric was 52.49, formally satisfying the similarity criterion (f₂ ≥ 50), despite the reference product releasing 1.7—1.9 times faster and more completely than the test product. Conversely, calculation of the difference factor f₁ yielded 41.98 %, which is nearly three times higher than the regulatory threshold for acceptable difference (f₁ ≤ 15 %). The mean dissolution ratio T/R ranged between 54.55 % and 60.00 %, falling well outside the bioequivalence acceptance interval (80.00—125.00 %). This paradox arises from the absolute dimensionality of the Moore and Flanner metric, which is anchored to a 0—100 % scale and remains indifferent to substantial relative discrepancies at low analyte concentrations.

Conclusion. Relying on f₂ within the range of incomplete dissolution (from 10 % to 30—40 %) introduces substantial regulatory and technical risks of concluding pseudo-equivalence between batches. When conducting CIDT for poorly soluble BCS Class II and IV compounds in physiological media without surfactants, a comprehensive statistical evaluation is required, including mandatory calculation of f₁, application of TOST on a relative scale, and physiologically based pharmacokinetic (PBPK) modeling.

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