Revisiting the relationship between reproducibility and concentration: a new, data-driven statistical model

Background The Horwitz equation has long been used to model the relationship between reproducibility relative standard deviation (RSDR) and analyte concentration. However, modern chromatographic and spectroscopic methods routinely achieve substantially better reproducibility than predicted, particularly for homogeneous nutritional matrices. A new data-driven model is needed to characterize current analytical performance. Objective To develop and evaluate a new statistical model describing the relationship between reproducibility standard deviation (sR) and analyte concentration (C), using data from 961 analyte–matrix combinations across 62 analytes. Methods Previously published multi-laboratory study data were reanalyzed by regressing log-transformed reproducibility standard deviation against log-transformed concentration, with both expressed as mass fractions. Ordinary least squares regression was performed following an approach analogous to that used previously for dietary fiber data. Results A strong linear relationship was observed between log(sR) and log(C) (R2 = 0.98) across concentrations spanning 3.7E-10 to 2.0E-2. Deviations from the model were largely attributable to specific analytical methods or analyte characteristics—particularly AOAC methods 2014.08, 2011.14, and 2015.06. The model indicates that RSDR increases very gradually with decreasing concentration, well below values predicted by the Horwitz equation except at very high concentrations. Conclusion Reproducibility precision for modern analytical techniques applied to homogeneous nutritional matrices can be effectively modeled by a simple linear relationship between log(sR) and log(C). This empirical model captures current analytical performance trends but is not intended as a method performance criterion. Highlights The new regression model describes a linear relationship between log(sR) and log(C) across 961 data points, spanning eight orders of magnitude. RSDR increases far more gradually with decreasing concentration than predicted by the Horwitz model. Deviations are primarily linked to specific methods and analytes.