The multivariate coefficient of variation for comparing serum protein electrophoresis techniques in external quality assessment schemes

Abstract

External Quality Assessment (EQA) schemes are national or transnational programmes designed to control the analytical performance of clinical laboratories and to maintain inter-laboratory variability within acceptable limits. In such EQA programmes, participants are usually grouped by the type of assay technique/equipment they use. The coefficient of variation (CV) is a simple tool for comparing the inter-laboratory reproducibility of such techniques: the lower the CV, the better the analytical performance.Serum protein electrophoresis, a laboratory test profile consisting of five fractions (albumin, α 1 , α 2 , β and γ globulins) summing up to 100% of total proteins, can also be assayed in different ways depending on the media or the analytical principle. We propose a multivariate coefficient of variation for comparing the performance of electrophoretic techniques in EQA, thus extending the univariate CV concept. First, the compositional nature of electrophoretic data requires a one-to-one transformation from the 5-dimensional to the 4-dimensional space.Next, robust estimations of the mean and the covariance matrix are needed to avoid the effect of outliers. The new approach is illustrated on electrophoretic datasets from the French and Belgian national EQA programmes.

Demystifying EQA statistics and reports

“…This distance, the so-called Mahalanobis distance, is obtained by robust estimates of multivariate centre and variability ( 50 ). Performance characterisation of analytical methods for profile data is also possible by means of a multivariate CV, which encompasses the variability estimates of the different parameters that the profile is made of ( 51 ). …”

Robust asymptotic tests for the equality of multivariate coefficients of variation

“…Finally, through a real dataset, we illustrate how this paper meets a real practical need, raised by Zhang et al (2010) in the context of EQA schemes, for non-arbitrary statistical testing procedures to compare several multivariate coefficients of variation.…”

“…For instance, Zhang et al (2010), noting that EQA datasets often entail outliers or blunders, advocate the use of robust MCVs to compare serum protein electrophoresis techniques. A measure of electrophoretic profile consists in 5 fractions, summing up to 100%, corresponding to the proportion of albumin and α 1 , α 2 , β and gamma-globulins in the blood.…”

“…In practice, using the plug-in principle, µ and Σ can be replaced by any pair of location and covariance estimators. As in the univariate case, the use of robust estimators is preferable in the presence of outliers, as already mentioned in Zhang et al (2010) and Aerts et al (2015). The properties of these coefficients have so far been little studied and no testing procedure for comparing K p-variate MCVs, either based on classical estimators or on robust ones, has been proposed in the literature.…”

“…However, until now, no statistical test was available in the literature in order to highlight significant differences between the techniques. The data set used herein, obtained from Zhang et al (2010), focuses on four techniques using distinct support medium, staining color or analytical principle. These techniques will be denoted simply as CH, EH, JW and GB (the full names are reported in Table 6).…”