Multivariate classical least squares-based model for spectrophotometric determination of celecoxib and Tramadol in their new formulated dosage form

Celecoxib (CLB) and tramadol (TRD) are frequently co-administered in clinical practice due to their complementary mechanisms in managing acute and chronic pain. Their combination has recently been formulated into a fixed-dose oral medication, representing the first FDA-approved multimodal analgesic targeting COX-2 and central opioid receptors simultaneously. However, the strong spectral overlap between CLB and TRD complicates their simultaneous determination using traditional spectrophotometric methods. In this study, a chemometric-assisted spectrophotometric method was developed for the simultaneous quantification of CLB and TRD without prior separation. The classical least squares (CLS) were ultimately selected due to its suitability when pure spectra are available, its robustness with small calibration sets, and its greater interpretability for routine quality control. A five-level, two-factor experimental design produced 25 binary mixtures, split into 13 calibration and 12 validation samples. After spectral preprocessing and removal of non-informative regions, the CLS model was applied to 81 variables across the 210–290 nm range. The model achieved mean recovery values of 99.85% for CLB and 99.99% for TRD in the calibration set, and 101.29% for CLB and 99.52% for TRD in the validation set, demonstrating excellent accuracy and consistency across both datasets. Linearity was established in the range of 6–14 µg/mL for both drugs, with detection limits of 0.55 µg/mL (CLB) and 0.67 µg/mL (TRD). The method showed excellent selectivity in the presence of common co-formulated drugs and was successfully applied to determine both analytes in commercial Seglentis^® tablets. This developed method provides a rapid, accurate, and cost-effective solution for routine quality control of complex pharmaceutical formulations.