Weighted simulations redefining quadratic calibration: democratisation of analytical uncertainty evaluation

Instrumental methods of analysis are often calibrated across broad analyte level ranges. Nevertheless, instrumental responses over such extended ranges are frequently nonlinear and heteroscedastic. Accurately assessing these responses, particularly the uncertainty associated with quantifications derived from calibration curves under these conditions, is challenging. Although simpler models may appear attractive, they require more assumptions that can be difficult to verify, even when suitable software is available, which considerably limits their widespread application. This study presents a weighted simulation method that enables reliable and straightforward weighted regression of quadratic relationships between instrumental responses and calibrator concentrations, while also supporting the evaluation of uncertainty from quantifications obtained in such regressions. The proposed tool requires only that the instrumental response follows a quadratic function and that uncertainty in calibrator values is negligible. The algorithm's simplicity is achieved by replicating simulation lines in proportion to the inverse of the signal variance. The method was successfully tested using artificially generated instrumental responses exhibiting a quadratic dependence on analyte concentration and heteroscedastic variance. The approach produced accurate regression coefficients and analyte concentration estimates for unknown samples with low associated uncertainty. Furthermore, the method is potentially applicable to other types of regression and has been implemented in a user-friendly MS Excel spreadsheet. This work aims to democratise access to accurate weighted quadratic regression and uncertainty evaluation for quantifications based on such calibrations, thereby contributing to the improvement of measurement quality in chemistry performed in conformity assessment and research and development.