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Analytical Quality by Design Approach to a Green Chromatographic Method for Simultaneous Estimation of a Fixed-Dose Combination: Method Greenness Assessment Using AGREE and Blue Applicability Grade Index

Abstract

Background. Empagliflozin and linagliptin are co-formulated as a fixed-dose combination, and many liquid chromatographic assays have been published for it. Few were developed under the enhanced approach of ICH Q14, and none has been judged against both greenness and practicality metrics. Objective. To apply an Analytical Quality by Design (AQbD) workflow in silico to the simultaneous chromatographic assay of empagliflozin and linagliptin, benchmark published methods with the Analytical GREEnness metric (AGREE) and the Blue Applicability Grade Index (BAGI), and define a greenness design space for a replacement method. Methods. Ten peer-reviewed methods were coded under uniform rules and scored with a re-implementation of AGREE that reproduced the published case studies, and with BAGI. Retention factors were estimated from reported column geometry. A failure mode and effects analysis ranked method parameters, AGREE was mapped over flow rate and run time under a retention constraint, and robustness to coding assumptions was tested by Monte Carlo simulation (5000 draws). Results. AGREE scores of published methods ranged from 0.39 to 0.50 (median 0.45) and BAGI from 80 to 82.5, with no rank correlation between the two (Spearman rho 0.18, p = 0.621). Only one of nine evaluable methods gave an estimated retention factor of at least 2 for the first-eluting drug; six gave values below 0.5. Mobile-phase pH (risk priority number 60) and organic modifier (40) were the dominant risks. An ethanol-phosphate design on a 100 x 2.1 mm column reached AGREE 0.59 and BAGI 82.5 with 1.2 mL of mobile phase per run; both ethanol designs exceeded every published method in 92.9% of simulations. Conclusion. Greenness of this assay is governed by column volume, sample-preparation solvent and modifier toxicity, not by flow rate. The proposed operating region is a testable hypothesis that now requires laboratory verification and ICH Q2(R2) validation.

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