Statistical Modeling of Within-Laboratory Precision Using a Hierarchical Bayesian Approach.

Background: Reproducibility has been well studied in the field of food analysis; the RSD is said to follow a Horwitz curve with certain exceptions. However, little systematic research has been done on predicting repeatability or intermediate precision.

Objective: We developed a regression method to estimate within-laboratory SDs using hierarchical Bayesian modeling and analyzing duplicate measurement data obtained from actual laboratory tests.

Methods: The Hamiltonian Monte Carlo method was employed and implemented using R with Stan. The basic structure of the statistical model was assumed to be a Chi-squared distribution, the fixed effect of the predictor was assumed to be a nonlinear function with a constant term and a concentration-dependent term, and the random effects were assumed to follow a lognormal distribution as a hierarchical prior.

Results: By analyzing over 300 instances, we obtained regression results that fit well with the assumed model, except for moisture, which was a method-defined analyte. The developed method applies to a wide variety of analytes measured using general principles, including spectroscopy, GC, and HPLC. Although the estimated precisions were within the Horwitz ratio criteria for repeatability, some cases using high-sensitivity detectors, such as mass spectrometers, showed SDs below that range.

Conclusion: We propose utilizing the within-laboratory precision predicted by the model established in this study for internal QC and measurement uncertainty estimation without considering sample matrices.

Highlights: Performing statistical modeling on data from double analysis, which is conducted as a part of internal QCs, will simplify the estimation of the precision that fits each analytical system in a laboratory.