An alternative for the robust assessment of the repeatability and reproducibility of analytical measurements using bivariate dispersion.

Assessing repeatability and reproducibility in analytical chemistry is commonly based on parametric dispersion indicators, such as relative standard deviation and standard deviation, calculated for each detected variable using repeated measurements of Quality Control (QC) samples collected throughout the data acquisition sequence. However, their reliability strongly relies on the assumption of normality distribution. Knowing that analytical variability is conditional to many sources, the use of such parametric estimators is not always suitable. There is therefore a need for robust indicators of data quality independent of central values and any parametric assumption. Three specific indicators were developed: (i) intra-group dispersion, based on the mean area of the convex hull of QC samples within an analytical batch; (ii) inter-group dispersion, defined as the gradient of the deviation between analytical batches; and (iii) intra/inter group Dispersion Index. Mathematical properties of these indicators, including positivity, stability, and translation invariance, were then evaluated using synthetic data under normal and non-normal distributions. Finally, the relevance of these indicators and the associated visualization methods were highlighted based on a metabolomics case study involving liquid chromatography coupled to mass spectrometry measurements of the NIST SRM1950 reference material analyzed over more than one year within different projects. The proposed indicators were shown to be translation invariant, positive and stable for multiplication, while first investigations performed on synthetic data revealed a high stability. Moreover, their application to experimental data revealed specific behaviors depending on the characteristics of the signal associated with the different detected analytes, showing their ability to capture the variability observed either in parametric or non-parametric conditions. Moreover, this investigation showed different structures of sensitivity to analytical variability all along the data processing steps. The proposed indicators also allowed a visualization of the analytical drift in two dimensions, to facilitate result interpretation. These indicators open the way to a better and more robust assessment of repeatability and reproducibility but also to improvements of long-term data comparability involving suitability testing.