Use of mixed models in the analysis of homogeneity studies for proficiency testing

Abstract

Proficiency testing has proven to be an extremely powerful tool to evaluate the quality of measurements. This paper evaluates the advantages of using linear mixed models over traditional random-effects models in the analysis of homogeneity studies in proficiency testing and describes their application with a study case of elements measurement in drinking water (proficiency testing DMQ-001-2018 by LCM). Both models were adjusted and evaluated for calcium (Ca) and magnesium (Mg) measurement data using R software. A trend by measurement was evidenced for Mg (p = 0.0005) but not for Ca (p = 0.4265). An analysis of uncertainty components due to lack of homogeneity between units (u_hom) and repeatability (u_r) showed the similarity in the components obtained for the models in the case without trends (linear mixed model: u_hom = 0.4536 mg/L and u_r = 0.4643 mg/L, random-effects model: u_hom = 0.4705 mg/L and u_r = 0.4494 mg/L). However, significant differences were observed in the case with trends (linear mixed model: u_hom = 3.0468 ∙ 10^-6 mg/L and u_r = 0.0842 mg/L, random-effects model: u_hom = undefined and u_r = 0.2343 mg/L). Great advantages were evidenced for the mixed linear model compared to the traditional model, highlighting the possibility of eliminating mathematical undefinitions in the estimation of u_hom and the mitigation of possible overestimations of u_r. Finally, an R-code is provided to process data from homogeneity studies based on the fit of a linear mixed model.