Abstract
The international standard ISO 15189 requires that medical laboratories estimate the uncertainty of their quantitative test results obtained from patients’ specimens. The standard does not provide details how and within which limits the measurement uncertainty should be determined. The most common concept for establishing permissible uncertainty limits is to relate them on biological variation defining the rate of false positive results or to base the limits on the state-of-the-art. The state-of-the-art is usually derived from data provided by a group of selected medical laboratories. The approach on biological variation should be preferred because of its transparency and scientific base. Hitherto, all recommendations were based on a linear relationship between biological and analytical variation leading to limits which are sometimes too stringent or too permissive for routine testing in laboratory medicine. In contrast, the present proposal is based on a non-linear relationship between biological and analytical variation leading to more realistic limits. The proposed algorithms can be applied to all measurands and consider any quantity to be assured. The suggested approach tries to provide the above mentioned details and is a compromise between the biological variation concept, the GUM uncertainty model and the technical state-of-the-art.
Acknowledgments
Suggestions from Dr W. J. Geilenkeuser, Referenzinstitut für Bioanalytik, are gratefully acknowledged.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Financial support: None declared.
Employment or leadership: None declared.
Honorarium: None declared.
Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication.
Appendix
Calculation of CVE in the case of a normal distribution
In Equation (18), M is the arithmetic mean: (RL1+RL2)/2
Calculation of CVE* in the case of a log-normal distribution
a) for a RI covering a 95% interval (RL1=RL2.5and RL2=RL97.5are known)
On the logarithmic scale, sE and median (Med) can be calculated by the following equations:
CVE derived of sE,ln (CVE* ) can be calculated by equation (20) according to Aitchison [41].
b) if other information than RL2.5and RL97.5is given, e.g., RL2=RL99and Mln(which is identical to the median on the ln-scale),then RL2.5and RL97.5can be obtained by Equations (22) and (23)
ln RL2.5 and ln RL97.5 [Equations (22) and (23)] are inserted in Equation (19) to obtain the standard deviation on the ln scale which is needed to calculate CVE* by Equation (20).
Permissible bias (pB) as fraction of analytical variation according to Fraser [10]
In this equation sB means the inter-individual variation.
Assuming sA=0.5·sB or sB=2·sA
Calculation of the random variation uB of pB estimation [42]
The random variation of uB is derived from the estimation of a confidence interval (x) and amounts to:
If the mean value of a control material is determined from n=15 (or n=20) measurements, the t-value of the two-sided t-distribution (α=0.05) is 2.14 (2.09) and uB becomes 0.55·psA (or 0.47·psA). If 15–20 measurements are used, an average value of uB=0.5·psA is appropriate.
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