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

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, alpha (1), alpha (2), beta and gamma 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 CV 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 five-dimensional to the four-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.