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Statistical analysis of serum protein electrophoresis results in External Quality Assessment schemes

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Abstract

The goal of External Quality Assessment (EQA) schemes is to ensure that results obtained on a particular specimen in a given clinical laboratory are compatible with those obtained by other laboratories on the same specimen. Serum protein electrophoresis is a laboratory test consisting of five fractions (albumin, α1, α2, β and γ globulins), which sum up to 100% of total proteins. So far, in EQA schemes the five fractions have been analyzed separately as for ordinary tests like glucose or cholesterol. This approach does not consider the fractions as a whole and the linear relationship between them. A statistical approach has been developed to analyze EQA electrophoresis results from a global standpoint by using robust multivariate method to eliminate the effect of outlying profiles. As illustrated on electrophoretic data from the Belgian EQA scheme, the novel approach improves the detection of poor performing laboratories. The method will be implemented in the Belgian EQA scheme on a routine basis.

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Acknowledgments

This study was supported by a research grant from the Scientific Institute of Public Health—Louis Pasteur (Federal Public Service of Social Security, Public Health and Environment), Brussels, Belgium.

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Correspondence to Adelin Albert.

Appendices

Appendix 1

Table 5 displays the dataset that was used to illustrate the new methodology.

Table 5 List of electrophoresis results supplied by 64 laboratories using Sebia’s Hydrasis Electrophoresis System (Belgian EQA scheme)

Appendix 2

Calculation of the mean, variance and covariances of the fraction omitted from the electrophoretic profile.

Let M i be the mean of x i and S ij the covariance between x i and x j (i, = 1,...,4).

From the formula x 5 = 100−(x 1 + x 2 + x 3 + x 4), it can be shown that:

$$ {\text{Mean}}(x_{5} ) = 100 - {\left( {M_{1} + M_{2} + M_{3} + M_{4} } \right)} $$
$$ {\text{Var}}(x_{5} ) = S_{{55}} = {\left( {S_{{11}} + S_{{22}} + S_{{33}} + S_{{44}} } \right)} + 2{\left( {S_{{12}} + S_{{13}} + S_{{14}} + S_{{23}} + S_{{24}} + S_{{34}} } \right)} $$
$$ {\text{Cov}}(x_{i} ,x_{5} ) = - {\left( {S_{{i1}} + S_{{i2}} + S_{{i3}} + S_{{i4}} } \right)}\quad {\left( {i = 1, \ldots ,4} \right)}. $$

As an illustration, from Table 4, we have

$$ {\text{Mean}}(x_{5} ) = 100 - {\left( {63.92 + 2.24 + 9.59 + 8.17} \right)} = 16.08 $$
$$ {\text{Var}}(x_{5} ) = {\left( {3.34 + 0.04 + 0.28 + 0.22} \right)} + 2{\left( { - 0.26 - 0.86 - 0.63 + 0.07 + 0.03 + 0.11} \right)} = 0.81 $$
$$ \begin{aligned}{} {\text{Cov}}(x_{1} ,x_{5} ) & = - {\left( {3.44 - 0.26 - 0.86 - 0.63} \right)} = - 1.59 \\ {\text{Cov}}(x_{2} ,x_{5} ) & = - {\left( { - 0.26 + 0.04 + 0.07 + 0.03} \right)} = 0.12 \\ \end{aligned} $$
$$ {\text{Cov}}(x_{3} ,x_{5} ) = - {\left( { - 0.86 + 0.07 + 0.28 + 0.11} \right)} = 0.39 $$
$$ {\text{Cov}}(x_{4} ,x_{5} ) = - {\left( { - 0.63 + 0.03 + 0.11 + 0.22} \right)} = 0.27. $$

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Zhang, L., Van Campenhout, C., Devleeschouwer, N. et al. Statistical analysis of serum protein electrophoresis results in External Quality Assessment schemes. Accred Qual Assur 13, 149–155 (2008). https://doi.org/10.1007/s00769-008-0388-4

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