# Uncertainty of measurement in clinical laboratory sciences.

To the Editor:

Random and systematic errors can act together to produce an error of measurement (total error) and generate a doubt (uncertainty) about the true value of the measured quantity.

The international metrological organizations, keeping in mind these facts, have developed the concept of uncertainty of measurement. This concept has become an important issue in general metrology, and by extension, its importance is increasing in clinical laboratory sciences. It is thus important to clarify the concept and to identify the practical difficulties in the use of uncertainty of patients' results.

Uncertainty of measurement (hereafter referred to as uncertainty) is a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand (i.e., the measured quantity) (1); in other words, uncertainty is numerical information that complements a result of measurement, indicating the magnitude of the doubt about this result. Uncertainty is described by means of one of the following three parameters (2):

* "Standard uncertainty" (u) is the standard deviation that denotes the uncertainty of the result of a single measurement.

* "Combined standard uncertainty" ([u.sub.c]) is the standard deviation that denotes the uncertainty of the result obtained from other results of measurement. It is obtained by combining the standard uncertainties of all individual measurements according to the law of propagation of uncertainty.

* "Expanded uncertainty" (U) is the statistic defining the interval within which the value of the measurand is believed to lie with a particular level of confidence. It is obtained by multiplying the combined standard uncertainty by a coverage factor, k, the choice of which is based on the level of confidence (1 - [alpha]) desired. If k = 2, then 1 - [alpha] [approximately equal to] 0.95; if k = 2.6, then 1 - [alpha] [approximately equal to] 0.99.

The international scientific and standardization bodies recommend that the uncertainty of patients' results obtained in clinical laboratories should be known (3-5); the rationale for this recommendation is that full interpretation of the value of a quantity obtained by measurement also requires evaluation of the doubt attached to its value. The common opinion of these bodies is that clinical laboratories should supply information about the uncertainty of their results of measurement when applicable; ideally, this information should be attached to the patients' results as shown in this example:

S-Almandine aminotransferase; cat.c. = (1.15 [+ or -] 0.23) [micro]kat/L, where 1.15 [micro]kat/L is the result given by the system of measurement, and 0.23 [micro]kat/L is the expanded uncertainty multiplied by 2 as coverage factor. (According to IFCC and IUPAC, S is serum, and cat.c. is the catalytic concentration.)

Institutional guidelines for estimating uncertainty of measurement, containing examples in fields of application other than clinical laboratory sciences, have been published (2, 6-8). An excellent review of uncertainty (and traceability) in clinical chemistry was published recently (9).

Depending on the field of application, uncertainty is attributable to different sets of elements. Each element of uncertainty, expressed as a standard deviation, may be estimated from the probability distribution of values with repeated measurements, termed "type A standard uncertainty", or estimated by use of an assumed probability distribution based on experience or other available information, termed "type B standard uncertainty".

In general, in clinical laboratory sciences the most relevant elements that can contribute to uncertainty for a given system of measurement are:

* Incomplete definition of the particular quantity under measurement,

* Unrepresentative sampling,

* Withdrawal conditions,

* Centrifugation conditions,

* Storage conditions,

* Day-to-day (or between-run) imprecision,

* Systematic error,

* Lack of specificity,

* Values assigned to calibrators

Estimation of the combined uncertainty, expressed as a variance, is the sum of the values, all expressed as variances, corresponding to several of the above elements. Perhaps variances corresponding to these elements can be easily estimated in some clinical laboratories, but for others their evaluation is certainly not easy, as may be derived from the following points:

(a) Manufacturers do not give the uncertainty of the values assigned to calibrators.

(b) In the majority of measurement procedures used in clinical laboratories, the metrological standard deviation varies with the value of the measurand; this phenomenon, called "heteroscedasticity" (the opposite is called homoscedasticity), should be always taken into account when estimating uncertainty.

(c) Premetrological variation should not be considered negligible even when the premetrological process seems to be well standardized (10, 11).

Bearing in mind these points, the following questions arise:

* When will manufacturers supply the uncertainties of the values assigned to calibrators?

* How many clinical laboratories know--or really can know--the mathematical or graphical relationship between metrological standard deviation and concentration for each measurement procedure?

* How many clinical laboratories know--or really can know--the standard deviation of their pre-metrological variation for each quantity?

* Is there heteroscedasticity for premetrological variation, and if it exists, can it be evaluated?

* When a clinical laboratory has produced biological reference values according to IFCC recommendation, should systematic error be referred to as the conventional true value of the calibrators used during the production of reference values?

Although some of the most relevant elements contributing to uncertainty can potentially be evaluated in clinical laboratories, the effort required to undertake such an endeavor might be so great that it will be difficult to bring into general use the uncertainty of patients' results.

References

(1.) International Bureau of Weights and Measures, International Electrotechnical Commission, International Organization for Standardization, International Organization of Legal Metrology, International Federation of Clinical Chemistry, International Union of Pure and Applied Chemistry, International Union of Pure and Applied Physics. International vocabulary of basic and general terms in metrology Geneva: ISO, 1993.

(2.) International Organization for Standardization, International Electrotechnical Commission, International Organization of Legal Metrology, International Bureau of Weights and Measures. Guide to the expression of uncertainty in measurement. Geneva: ISO, 1993.

(3.) International Union of Pure and Applied Chemistry, International Federation of Clinical Chemistry. Compendium of terminology and nomenclature of properties in clinical laboratory sciences. Recommendations 1995. [Prepared for publication by JC Rigg, SS Brown, R Dybkaer, H Olesen.] Oxford: Blackwell Science, 1995.

(4.) European Committee for Standardization. Medical informatics-expression of the results of measurement in health sciences. ENV 12435. Brussels: CEN, 1997.

(5.) International Organization for Standardization. Quality management in the medical laboratory. ISO/DIS 15189. Geneva: ISO, 2000.

(6.) Taylor BN, Kuyatt CE. National Institute of Standards and Technology. Guidelines for evaluating and expressing the uncertainty of NIST measurement results. NIST Technical Note 1297, 1994 edition. http://physlab.nist.gov/ Pubs/guidelines/outline.html (accessed March 22, 1999).

(7.) Eurachem. Quantifying uncertainty in analytical measurement. London: Eurachem, British Standards Institute, 1995.

(8.) Deutsches Institut fur Normung. Basic concepts in metrology. Evaluating measurements of a single measurand and expression of uncertainty. DIN 1319-3. Berlin: DIN, 1996.

(9.) Kristiansen J, Christensen JM. Traceability and uncertainty in analytical measurements. Ann Clin Biochem 1998;35:371-9.

(10.) Fuentes-Arderiu X, Acebes-Frieyro G, Gavaso-Navarro L, Castineiras-Lacambra MJ. Pre-metrological (pre-analytical) variation of some biochemical quantities. Clin Chem Lab Med 1999; 37:987-9.

(11.) Fuentes-Arderiu X, Gonzalez-Alba JM, Baltuille-Peiron F, Navarro-Moreno MA. Premetrological variation of thyrotropin, thyroxine (non-protein bound), and triiodothyronine concentrations in serum. Clin Chem 2000;46:431-2.

Xavier Fuentes-Arderiu

Servei de Bioquimica Clinica

Ciutat Sanitaria i

Universitaria de Bellvitge

08907 L'Hospitalet de Llobregat

Catalonia, Spain

Fax 34-93-260-7546

E-mail xfa@csub.scs.es
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