Estimation of uncertainty from duplicate measurements: new quantification procedure in the case of concentration-dependent precision

Abstract

In many analytical measurements, the analyte concentration in test samples can vary considerably. In such cases, the standard deviation (SD) quantifying measurement imprecision should be expressed as a function of the concentration, c: \({s}_{c}=\sqrt{{\mathrm{s}}_{0}^{2}+{ s}_{r}^{2}{c}^{2}}\), where s₀ represents a non-zero SD at zero concentration and s_r represents a near-constant relative SD at very high concentrations. In the case of SD repeatability, these parameters can be estimated from the differences of duplicated results measured on routine test samples. Datasets with a high number of duplicate results can be obtained within internal quality control. Most procedures recommended for this estimation are based on statistically demanding weighted regression.

This article proposes a statistically less demanding procedure. The s₀ and s_r parameters are estimated from selected subsets of absolute and relative differences of duplicates measured at low to medium concentrations and high to medium concentrations, respectively. The estimates are obtained by iterative calculations from the root mean square of the differences with a correction for the influence of the second parameter. This procedure was verified on Monte Carlo simulated datasets. The variability of the parameter estimates obtained by this proposed procedure may be similar or slightly worse than that of the estimates obtained by the best regression procedure, but better than the variability of the estimates obtained by other tested regression procedures. However, a selection of the duplicates from an inappropriate concentration range may cause a substantial increase in variability of the estimates obtained.