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Reporte breveMetrologa

* Department of Clinical ChemistryKarolinska University Hospital, Stockholm SWEDENE-mail: anders.kallner@karolinska.ki.se

Correspondencia:Anders Kallner, PhD MDDepartment of Clinical ChemistryKarolinska University Hospital, Stockholm SWEDENE-mail: anders.kallner@karolinska.ki.se

Recibido: 16-03-2007Aceptado: 28-03-2007

The uncertainty concept and its implications forlaboratory medicine

Anders Kallner, PhD MD*

MEASUREMENT PERFORMANCE

Laboratory measurement performance needs to be es-timated in a uniform and standardized manner to al-low comparison of results and become scientifically

valid. A much-used measure is the variation of re-peated measurements and the agreement of the re-sult with a reference or true value. There are thusprincipally two types of variation of results of mea-surements, systematic and random. Information onboth types needs to be attached to the result of themeasurement; that information shall be informativeand understood by the end-users. Provided somerules are observed that can be achieved by relying onthe concept ofuncertainty.

Systematic variations result in changes in theagreement between the obtained value and the truevalue, i.e. the trueness of the result. If the bias, the

statistic used to measure trueness, can be assessed,the results can be compensated for the deviation. Biasis however difficult to assess and particularly so in bio-logical systems since the true value is rarely known.Bias can then be expressed as the deviation from a refe-rence value obtained by reference methods.

The random variation,precision, is the closenessof the average of the results of a large number of re-plicate measurements. The statistic that is used to des-cribe precision numerically is imprecision. The over-

all concept precision can be subdivided into repeata-bility, reproducibility and intermediate precision.The repeatability describes the performance if themeasurement is repeated without any changes in theconditions, reagents etc. whereas reproducibility is

the performance if all conditions have been changed.Intermediate precision is when but a few of the con-ditions have been changed; those changed shall bestated.*

The total error, which is a long-standing conceptin clinical chemistry, is the sum of a systematic anda random error contribution. It is usually reportedin relative form, i.e. percentage. It can be criticized,e.g. bias is often both absolute and relative to the re-sult and it is not always correct to add the two com-ponents linearly. Likewise the concept ofaccuracycomprises precision and trueness because it describesthe closeness of the result of one measurement to a

reference or true value. Accuracy cannot be given anumerical value.Accuracy must not be incorrectlyused for trueness.

An alternative to using the concept of errors thatmay be embedded in the results is to estimate andstate the uncertainty of the result. The most impor-tant differences between the Error model and theUncertainty model are listed in table I. A well-known parameter that describes the dispersion ofresults is the standard deviation, which thus isequal to the standard uncertainty, a measure of theimprecision.

ESTIMATION OF IMPRECISION

Imprecision can be estimated by several differentmethods. It is often obtained under repeatability con-

* Definitions of a selection of metrological terms used in thedocument are given in the Appendix.

Artemisamedigraphic en lnea

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SUSTRADODE-M.E.D.I.G.R.A.P.H.I.C

:ROP ODAROBALE FDP

VC ED AS, CIDEMIHPARG

ARAP

ACIDMOIB ARUTARETIL :CIHPARGIDEM

ditions, e.g. the quantity, e.g. the concentration ismeasured several times in a reference or patient sam-ple in one series. Samples of several different concen-trations are often used to create an imprecision pro-file since there is no universal rule that either theabsolute or relative variation is constant within ameasuring interval. Another technique is to measure

samples of different concentrations in duplicates andestimate the uncertainty from the difference betweenthe paired results. In clinical laboratories, the re-sults of measuring the quantity of control materialsduring a certain period of time e.g. approaching in-termediate conditions are frequently used in the cal-culation. Only rarely, the imprecision is estimatedunder reproducibility conditions, e.g. all conditionschanged.

If given the choice and possibility, it is an advan-tage to use patient materials to estimate the impreci-sion. The end-user also needs to know how the im-

precision has been estimated to benefit optimallyfrom that knowledge. It is therefore important thatan agreement is reached between laboratories andend-users (clinicians) on how the imprecision shallbe estimated.

Laboratories that are accredited according to theEN/ISO 15189 or ISO/IEC 17025 are obliged to re-port the uncertainty in their measurements. The EN/ISO 15189 states (5.6.3): "The laboratory shall deter-mine the uncertainty of results, when possible andrelevant. Uncertainty components that are of impor-tance shall be taken into account." This statement isgenerally understood as implying that an uncertain-ty budget shall be established when possible anda combined uncertainty estimated.

UNCERTAINTY BUDGET, COMBINED ANDEXPANDED UNCERTAINTY

The common understanding of "budget" is probablyan act or a document that deals with the future useof available resources. When talking about an uncer-

tainty budget in measurements, however, this meansa description of the size, nature and functional rela-tionship of the sources of uncertainty. Comprehen-sive discussions of the concept of uncertainty andhow it shall be estimated and interpreted can befound in references 1 to 4 of which "Guide to the ex-pression of uncertainty in measurement", GUM, is

the parent document.1Briefly, the GUM method is to identify and

quantify the standard uncertainty of all processesthat together constitute the measurement proce-dure (input variables) and their functional rela-tionship. The standard uncertainties are then com-bined according to certain rules to form thecombined uncertainty. The standard uncertainty ofa process is the same as its standard deviation andcan be estimated either by any of the methods men-tioned above, e.g. repeated measurements (Type A)or by assuming other distributions e.g. a rectangu-

lar distribution that allows the estimation of thestandard uncertainty (Type B). Both process canbe applied to the entire procedure and thus give thecombined uncertainty directly. A most importantassumption in the GUM is that all known biaseshave been eliminated or compensated, leaving anuncertainty of the success that can be added as an-other input variable to the combined uncertainty.The combined uncertainty thus describes the totaluncertainty and is favorably compared with the to-tal error concept (Table I).

In their universal form, the uncertainty propa-gation rules1-4 are based on partial derivatives ofthe function that describes the relation betweenthe input variables. Few laboratorians are familiarwith this mathematical procedure. There is howe-ver a convenient method of numerical approxima-tion of the general rules. 2 This procedure has beenrealized in a Microsoft Excel sheet.5 For simple ope-rations like addition-subtraction and multiplica-tion-division manual procedures, which are appli-cable the rules are:

Table I. Comparison of key elements of the error model and uncertainty model.

Error model Uncertainty model

Single unknowable value. Defines an interval within which the true value is assumed.Could be corrected if known. Cannot be used for correction or corrected.

Two types of component: One type of component. systematic error random error

Applies to a single quantity value. Applies to a ll values obtained according to a given procedure.

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( ) ( )22

BAC

BA

C

uuu

uandu

ifuestimate

;BAC

+=

+=

22

+=

=

Bu

Au

Cu

uandu

ifuestimate

BAC

BAC

BA

C

And

Where ua, u

band u

crepresent the standard uncer-

tainty of input variable A and B and the product C,respectively.

Estimates of a preanalytical variation and the un-certainty of the bias elimination may be entered asseparate input variables into the uncertainty budget.Their functional relations may be additive or multi-plicative.

The combined uncertainty is estimated as 1 SD,

e.g. the result will be found within the interval deli-neated by the reported value the combined uncer-tainty with a probability of about 67%. If a higherprobability of finding the true value within the limitsis desired, then the combined uncertainty shall bemultiplied by a coverage factor (k). This gives theexpanded uncertainty (U). A coverage factor of 2 isusually taken as resulting in a confidence interval of95%. If an expanded uncertainty is reported, then thecoverage factor must also be reported. However, likein scientific literature, it is most convenient, al-though not always conventional, to report the com-

bined uncertainty only.

REPEATABILITY, REPRODUCIBILITY ANDINTRA- OR INTERLABORATORY

UNCERTAINTY

The combined uncertainty does not always satisfythe needs of the laboratories or the clinical end usersof laboratory data. The laboratories need to know therepeatability performance and the intermediary im-precision (e.g. between series or after calibrations, orchange of reagent or calibration lots) to properlymanage monitoring of the quality. Laboratories andclinicians alike also need to know the intralaboratoryvariation e.g. the variation taking all these factorsand the possibility of using several different instru-ments into account. The clinician is particularly in-terested in the latter aspect.

CLSI EP 15 advised an efficient and simple proto-col that allows estimating the components of thecombined uncertainty.6 The protocol comprises re-peated measurements of the quantities on several oc-

casions, usually on different days. The original rec-ommendation is three replicate measurements in fiveseries, but by increasing the number of replicates, se-ries confidence of the results can be increased. Wehave developed a Microsoft Excel spreadsheet that

will carry out these calculations.A similar approach5 can be attempted to estimatethe interlaboratory uncertainty, which is of interestif patients use different laboratories, and the physi-cians thus have to evaluate results that may not becomparable. It might then be appropriate to findmeans to harmonize the measurement procedures toincrease the transferability of the results. Since Pro-ficiency Testing (PT) schemes rather assess the accu-racy of measuring the test sample than the bias ofthe laboratory, they are not helpful for the individuallaboratory to take rational corrective actions.

CLINICAL USE OF THE UNCERTAINTY

The clinician uses the laboratory data for monitoringthe status of a patient or for classifying the patientin relation to a reference value, e.g. in diagnosis. Inboth cases their concern is if the value obtained fromthe laboratory differs from a previous result or a bio-logical reference value. It becomes important to ad-vise a method to objectively estimate the least signifi-cant difference between two results. The principlesfor this have been outlined above. Thus the criteriafor a significant difference between two values are

that it shall be larger than the uncertainty of the dif-ference :

( ) ( )22BA uuu

uk

+=

>

Wherek is the coverage factor.If the sample has been analyzed by the same labo-

ratory it is feasible to assume that the uncertainty ofboth results is the same and the criteria changes to:

2> A

uku . As a rule of thumb, consider-

ing k = 2 and the 2 equal to 1.4, the difference be-tween two consecutive results should be 3 times thecombined uncertainty to rule out at a confidencelevel of 95% - that the difference is due to laborato-ry factors.

If compared with a reference value, the reasoningis the same. However, it is usually agreed that a refe-rence value is without uncertainty; its value is theresult of a consensus or other decision. Therefore,

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SUSTRADODE-M.E.D.I.G.R.A.P.H.I.C

:ROP ODAROBALE FDP

VC ED AS, CIDEMIHPARG

ARAP

ACIDMOIB ARUTARETIL :CIHPARGIDEM

the least significant difference in this case is reducedto Auku > .

However, it is important to remember that all theuncertainty estimates are based on statistical consi-derations that may themselves be liable to considerable

uncertainties! The physicians judgment will there-fore be the basis for a final decision on diagnosis andtreatment of a patient. The laboratories in collabo-ration with the clinicians - should find the necessarylevel of uncertainty to make a rational use of the re-sults possible. A useful basis for such discussionsmay be found in the report by Ricos et al.7 The tablein the Ricos publication is based on biological varia-tions and in many cases the laboratories can performmuch better than the table indicates.

APPENDIX

Definitions

Metrology the science of measuring requires anexact vocabulary based on globally agreed defini-tions. Several international groups that are activelyinvolved in measurements have published a standarddocument. This is theInternational Vocabulary of Ba-

sic and General Terms in Metrology (VIM), first pub-lished by ISO in 1993. A revised 3rd edition will mostlikely appear during 2007. Other standards and re-commendations follow the VIM, e.g. ISO 5725 and theCLSI documents published after 2003.

Ideally the terms should be understood intuitivelybut also be useful in all disciplines that deal withmeasurements. This is not always possible and more-over there may be difficulties to intuitively accept thedifference in meaning of a word in scientific and eve-ryday languages.

The definitions may be difficult to read at firstsight, partly due to the ambition to create generallyapplicable definitions. The vocabulary has beentranslated into major languages but the official lan-guages are English and French.

The ISO format of the entries has been retainedand the terms are sorted in alphabetical order.

Accuracy: closeness of agreement between the re-sult of a measurement and a true value.

Combined standard uncertainty: standardmeasurement uncertainty that is obtained from themeasurement results of the input quantities in ameasurement function.

Commutability of a reference material: proper-ty of a reference material, demonstrated by the close-ness of agreement between the relation among the

measurement results for a stated quantity in this ma-terial, obtained according to two given measurementprocedures, and the relation obtained among the mea-surement results for other specified materials.

Coverage factor: number larger than or equal to

one by which a combined standard measurement un-certainty is multiplied to obtain an expanded mea-surement uncertainty.

Expanded measurement uncertainty: productof a combined standard measurement uncertaintyand a factor larger than the number one.

Intermediate precision condition: condition ofmeasurement in a set of conditions that includes thesame measurement procedure, same location, andreplicated measurements on the same or similar ob-

jects over an extended period of time, but may includeother conditions involving changes.

NOTE1. A specification should contain the conditions

changed and unchanged, to the extent practical.2. In chemistry, the term inter-serial intermediate

precision condition of measurement (between se-ries imprecision) is sometimes used to designatethis concept.

Quantity: property of a phenomenon, body, orsubstance to which a number can be assigned withrespect to a reference.

Repeatability: property of a measuring system to

provide closely similar indications for replicated mea-surements of the same quantity under repeatabilityconditions.

Measurand: quantity intended to be measured.Measurement accuracy: closeness of agreement

between a measured quantity value and a true valueof a measurand.

Measurement bias: systematic measurement er-ror or its estimate, with respect to a reference quan-tity value.

Measurement error: measured quantity valueminus a reference quantity value.

Measurement precision: closeness of agreementbetween indicators obtained by replicate measure-ments on the same or similar objects under statedspecified conditions.

NOTEMeasurement precision is usually expressed numer-ically by measures of imprecision, such as standarddeviation, variance, or coefficient of variation underthe specified conditions of measurement.

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8/4/2019 incertidumbre en qumica clnica

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The uncertainty concept and its implications for laboratory medicine

29Volumen 32 No. 1 Enero-Marzo 2007. p. 25-29

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Measurement repeatability: repeatability, mea-surement precision under the set of repeatability con-ditions of measurement

Measurement reproducibility: reproducibility,measurement precision under reproducibility condi-

tions of measurement.Measurement traceability: property of a mea-surement result whereby the result can be related toa stated reference through a documented unbrokenchain of calibrations, each contributing to the mea-surement uncertainty.

Measurement trueness: closeness of agreementbetween the average of an infinite number of repli-cate measured quantity values and a true value of themeasurand.

Measurement uncertainty: parameter character-izing the dispersion of the quantity values being attrib-uted to a measurand, based on the information used.

Random error: component of measurement errorthat, in replicate measurements, varies in an unpre-dictable manner.

Repeatability condition: condition of measure-ment in the set of conditions that includes the samemeasurement procedure, same operators, same mea-suring system, same operating conditions and samelocation, and replicated measures on the same or sim-ilar objects over a short period of time.

Reproducibility condition: condition of mea-surement in a set of conditions that includes differentlocations, operators, measuring systems, and repli-

cated measurements on the same or similar objects.Standard uncertainty: measurement uncertain-ty expressed as a standard deviation.

Systematic error: component of measurementerror that in replicates measurements remains con-stant or varies in a predictable manner.

Type A evaluation of measurement uncer-tainty: evaluation of a component of measurementuncertainty by a statistical analysis of quantity val-ues obtained under defined conditions of measure-ment precision.

Type B evaluation of measurement uncer-tainty: evaluation of a component of measurementuncertainty determined by means other than a Type

A evaluation of measurement uncertainty.Uncertainty budget: statement of a measure-

ment uncertainty, of the components of that mea-surement uncertainty, and of their calculation andcombination.

REFERENCES

1. Guide to the expression of uncertainty in measurement.Geneva: ISO; 1993.

2. Eurachem/Citac. Guide quantifying uncertainty in analyti-

cal measurement 2000. Available from: URL: http//:www.eurachem.ul.pt (visited 11-03-07).

3. EA. Guidelines on the expression of uncertainty in quanti-tative testing (EA 4-16). 2004 Available from: URL: http//:www.european-accreditation.org (visited 11-03-07).

4. Australasian Association of Clinical Biochemists. Uncer-tainty of measurement in quantitative medical testing2004. Available from: URL: http//: www.AACB.au (visited11-03-07).

5. Kallner A, Khorovskaya L, Pettersson T. A method to esti-mate the uncertainty in measurements in a conglomerateof laboratories/instruments. Scand J Clin Lab Med. 2005;65: 551-567.

6. Clinical and Laboratory Standards Institute. User Verifica-tion of Performance for Precision and Trueness; AprovedGuideline Second Edition. CLSI document EP15-A2(e)

[ISBN 1-56238-574-7].7. Ricos C, lvarez F, Cava F, Garca-Lacio JV, Hernndez A,

Jimnez CV, et al. Current databases on biological varia-tion; pros, cons and progress. Scan J Clin Lab Invest. 1999;59: 491-500. Table updated on the homepage of Dr J West-gard, available from: URL: HTTP//:www.westgard.com(visited 11-03-07).

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