Validation of a Method for the Determination of Artificial Sweeteners and Caffeine in Soft Drinks: The Impact of Regression Function Selection on Quantification Limits Considering Trueness and Precision

Background: Method quantification limits are typically determined by measuring variability at blank level only, without accounting for the uncertainties associated with the parameters of the calibration function applied. Methods: A method for the determination of artificial sweeteners and caffeine in soft drinks was validated. The effect of chosen regression function on quantification limits was assessed, considering both trueness and precision. Results: The validated method exhibited heteroscedasticity for all analytes, which is common in experimental methods. A linear response was observed within the working range for sweeteners, while a quadratic regression was required for caffeine. Due to the heteroscedasticity nature of the responses, weighted regressions were necessary to obtain the lowest method quantification limits, allowing for accurate (i.e., unbiased and precise) estimates at the lower end of the calibration range. Under weighted conditions, the regression equations obtained, with an upper range set at 600 mg·L⁻¹, were as follows: y = 3.9 + 58.9x for acesulfame K; y = 0.8 + 185.1x for saccharin; y = 3.5 + 43.3x for aspartame, and y = −7 + 159x − 0.242x² for caffeine. The method quantification limits determined using weighted regressions were 2 mg·L⁻¹ for each analyte, whereas these limits increased to 20 mg·L⁻¹ when non-weighted regressions were applied. Conclusions: The choice of regression function for transforming instrumental signals into analyte concentrations significantly affects the determination of quantification limits, owing to the inherent heteroscedasticity of analytical and bioanalytical calibrations. Weighted regressions are essential for producing accurate estimates at lower concentration levels. Applying weighted regression in the context of heteroscedastic calibrations can lead to quantification limits that are more than 10 times lower than unweighted approaches.

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