Artemisa. edigraphic.com. The uncertainty concept and its implications for laboratory medicine. medigraphic. en línea. Reporte breve Metrología

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1 medigraphic rtemisa en línea Reporte breve Metrología The ncertainty concept and its implications for laboratory medicine nders Kallner, PhD MD* MESUREMENT PERFORMNE * Department of linical hemistry Karolinska University Hospital, Stockholm SWEDEN anders.kallner@karolinska.ki.se orrespondencia: nders Kallner, PhD MD Department of linical hemistry Karolinska University Hospital, Stockholm SWEDEN anders.kallner@karolinska.ki.se Laboratory measrement performance needs to be estimated in a niform and standardized manner to allow comparison of reslts and become scientifically valid. mch-sed measre is the variation of repeated measrements and the agreement of the reslt with a reference or tre vale. There are ths principally two types of variation of reslts of measrements, systematic and random. Information on both types needs to be attached to the reslt of the measrement; that information shall be informative and nderstood by the end-sers. Provided some rles are observed that can be achieved by relying on the concept of ncertainty. Systematic variations reslt in changes in the agreement between the obtained vale and the tre vale, i.e. the treness of the reslt. If the bias, the statistic sed to measre treness, can be assessed, the reslts can be compensated for the deviation. ias is however difficlt to assess and particlarly so in biological systems since the tre vale is rarely known. ias can then be expressed as the deviation from a reference vale obtained by reference methods. The random variation, precision, is the closeness of the average of the reslts of a large nmber of replicate measrements. The statistic that is sed to describe precision nmerically is imprecision. The overall concept precision can be sbdivided into repeatability, reprodcibility and intermediate precision. The repeatability describes the performance if the measrement is repeated withot any changes in the conditions, reagents etc. whereas reprodcibility is the performance if all conditions have been changed. Intermediate precision is when bt a few of the conditions have been changed; those changed shall be stated. * The total error, which is a long-standing concept in clinical chemistry, is the sm of a systematic and a random error contribtion. It is sally reported in relative form, i.e. percentage. It can be criticized, e.g. bias is often both absolte and relative to the reslt and it is not always correct to add the two components linearly. Likewise the concept of accracy comprises precision and treness becase it describes the closeness of the reslt of one measrement to a reference or tre vale. ccracy cannot be given a nmerical vale. ccracy mst not be incorrectly sed for treness. n alternative to sing the concept of errors that may be embedded in the reslts is to estimate and state the ncertainty of the reslt. The most important differences between the Error model and the Uncertainty model are listed in table I. wellknown parameter that describes the dispersion of reslts is the standard deviation, which ths is eqal to the standard ncertainty, a measre of the imprecision. ESTIMTION OF IMPREISION Imprecision can be estimated by several different methods. It is often obtained nder repeatability con- Recibido: ceptado: * Definitions of a selection of metrological terms sed in the docment are given in the ppendix. 5

2 nders Kallner Table I. omparison of key elements of the error model and ncertainty model. Error model Single nknowable vale. old SUSTRÍDODE-M.E.D.I.G.R..P.H.I. be corrected if known. Two types of component: systematic error :ROP random ODROLE error FDP pplies to a single qantity vale. V ED S, IDEMIHPRG Uncertainty model Defines an interval within which the tre vale is assmed. annot be sed for correction or corrected. One type of component. pplies to all vales obtained according to a given procedre. RP ditions, e.g. the qantity, e.g. the concentration is measred several times in a reference or patient sample in one series. Samples of several different concen- IDÉMOI RUTRETIL :IHPRGIDEM trations are often sed to create an imprecision profile since there is no niversal rle that either the absolte or relative variation is constant within a measring interval. nother techniqe is to measre samples of different concentrations in dplicates and estimate the ncertainty from the difference between the paired reslts. In clinical laboratories, the reslts of measring the qantity of control materials dring a certain period of time e.g. approaching intermediate conditions are freqently sed in the calclation. Only rarely, the imprecision is estimated nder reprodcibility conditions, e.g. all conditions changed. If given the choice and possibility, it is an advantage to se patient materials to estimate the imprecision. The end-ser also needs to know how the imprecision has been estimated to benefit optimally from that knowledge. It is therefore important that an agreement is reached between laboratories and end-sers (clinicians) on how the imprecision shall be estimated. Laboratories that are accredited according to the EN/ISO or ISO/IE 1705 are obliged to report the ncertainty in their measrements. The EN/ ISO states (5.6.3): "The laboratory shall determine the ncertainty of reslts, when possible and relevant. Uncertainty components that are of importance shall be taken into accont." This statement is generally nderstood as implying that an ncertainty bdget shall be established when possible and a combined ncertainty estimated. UNERTINTY UDGET, OMINED ND EXPNDED UNERTINTY The common nderstanding of "bdget" is probably an act or a docment that deals with the ftre se of available resorces. When talking abot an ncertainty bdget in measrements, however, this means a description of the size, natre and fnctional relationship of the sorces of ncertainty. omprehensive discssions of the concept of ncertainty and how it shall be estimated and interpreted can be fond in references 1 to 4 of which "Gide to the expression of ncertainty in measrement", GUM, is the parent docment. 1 riefly, the GUM method is to identify and qantify the standard ncertainty of all processes that together constitte the measrement procedre (inpt variables) and their fnctional relationship. The standard ncertainties are then combined according to certain rles to form the combined ncertainty. The standard ncertainty of a process is the same as its standard deviation and can be estimated either by any of the methods mentioned above, e.g. repeated measrements (Type ) or by assming other distribtions e.g. a rectanglar distribtion that allows the estimation of the standard ncertainty (Type ). oth process can be applied to the entire procedre and ths give the combined ncertainty directly. most important assmption in the GUM is that all known biases have been eliminated or compensated, leaving an ncertainty of the sccess that can be added as another inpt variable to the combined ncertainty. The combined ncertainty ths describes the total ncertainty and is favorably compared with the total error concept (Table I). In their niversal form, the ncertainty propagation rles 1-4 are based on partial derivatives of the fnction that describes the relation between the inpt variables. Few laboratorians are familiar with this mathematical procedre. There is however a convenient method of nmerical approximation of the general rles. This procedre has been realized in a Microsoft Excel sheet. 5 For simple operations like addition-sbtraction and mltiplication-division manal procedres, which are applicable the rles are: 6 ioqimia

3 The ncertainty concept and its implications for laboratory medicine + ; estimate and ( ) + ( ) if nd estimate and if + Where a, b and c represent the standard ncertainty of inpt variable and and the prodct, respectively. Estimates of a preanalytical variation and the ncertainty of the bias elimination may be entered as separate inpt variables into the ncertainty bdget. Their fnctional relations may be additive or mltiplicative. The combined ncertainty is estimated as 1 SD, e.g. the reslt will be fond within the interval delineated by the reported vale ± the combined ncertainty with a probability of abot 67%. If a higher probability of finding the tre vale within the limits is desired, then the combined ncertainty shall be mltiplied by a coverage factor (k). This gives the expanded ncertainty (U). coverage factor of is sally taken as reslting in a confidence interval of 95%. If an expanded ncertainty is reported, then the coverage factor mst also be reported. However, like in scientific literatre, it is most convenient, althogh not always conventional, to report the combined ncertainty only. REPETILITY, REPRODUIILITY ND INTR- OR INTERLORTORY UNERTINTY The combined ncertainty does not always satisfy the needs of the laboratories or the clinical end sers of laboratory data. The laboratories need to know the repeatability performance and the intermediary imprecision (e.g. between series or after calibrations, or change of reagent or calibration lots) to properly manage monitoring of the qality. Laboratories and clinicians alike also need to know the intralaboratory variation e.g. the variation taking all these factors and the possibility of sing several different instrments into accont. The clinician is particlarly interested in the latter aspect. LSI EP 15 advised an efficient and simple protocol that allows estimating the components of the combined ncertainty. 6 The protocol comprises repeated measrements of the qantities on several occasions, sally on different days. The original recommendation is three replicate measrements in five series, bt by increasing the nmber of replicates, series confidence of the reslts can be increased. We have developed a Microsoft Excel spreadsheet that will carry ot these calclations. similar approach 5 can be attempted to estimate the interlaboratory ncertainty, which is of interest if patients se different laboratories, and the physicians ths have to evalate reslts that may not be comparable. It might then be appropriate to find means to harmonize the measrement procedres to increase the transferability of the reslts. Since Proficiency Testing (PT) schemes rather assess the accracy of measring the test sample than the bias of the laboratory, they are not helpfl for the individal laboratory to take rational corrective actions. LINIL USE OF THE UNERTINTY The clinician ses the laboratory data for monitoring the stats of a patient or for classifying the patient in relation to a reference vale, e.g. in diagnosis. In both cases their concern is if the vale obtained from the laboratory differs from a previos reslt or a biological reference vale. It becomes important to advise a method to objectively estimate the least significant difference between two reslts. The principles for this have been otlined above. Ths the criteria for a significant difference between two vales are that it shall be larger than the ncertainty of the difference : > k ( ) ( ) + Where k is the coverage factor. If the sample has been analyzed by the same laboratory it is feasible to assme that the ncertainty of both reslts is the same and the criteria changes to: > k. s a rle of thmb, considering k and the eqal to 1.4, the difference be- tween two consective reslts shold be 3 times the combined ncertainty to rle ot at a confidence level of 95% - that the difference is de to laboratory factors. If compared with a reference vale, the reasoning is the same. However, it is sally agreed that a reference vale is withot ncertainty; its vale is the reslt of a consenss or other decision. Therefore, 7

4 nders Kallner the least significant difference in this case is redced to > k. However, it is important to remember that all the ncertainty estimates are based on statistical considerations SUSTRÍDODE-M.E.D.I.G.R..P.H.I. that may themselves be liable to considerable ncertainties! The physicians jdgment will therefore :ROP be ODROLE the basis for FDP a final decision on diagnosis and treatment of a patient. The laboratories in collaboration V ED S, with IDEMIHPRG the clinicians - shold find the necessary level of ncertainty to make a rational se of the reslts RP possible. sefl basis for sch discssions may be fond in the report by Ricos et al. 7 The table in IDÉMOI the Ricos RUTRETIL pblication :IHPRGIDEM is based on biological variations and in many cases the laboratories can perform mch better than the table indicates. PPENDIX measrement reslts for a stated qantity in this material, obtained according to two given measrement procedres, and the relation obtained among the measrement reslts for other specified materials. overage factor: nmber larger than or eqal to one by which a combined standard measrement ncertainty is mltiplied to obtain an expanded measrement ncertainty. Expanded measrement ncertainty: prodct of a combined standard measrement ncertainty and a factor larger than the nmber one. Intermediate precision condition: condition of measrement in a set of conditions that incldes the same measrement procedre, same location, and replicated measrements on the same or similar objects over an extended period of time, bt may inclde other conditions involving changes. Definitions Metrology the science of measring reqires an exact vocablary based on globally agreed definitions. Several international grops that are actively involved in measrements have pblished a standard docment. This is the International Vocablary of asic and General Terms in Metrology (VIM), first pblished by ISO in revised 3 rd edition will most likely appear dring 007. Other standards and recommendations follow the VIM, e.g. ISO 575 and the LSI docments pblished after 003. Ideally the terms shold be nderstood intitively bt also be sefl in all disciplines that deal with measrements. This is not always possible and moreover there may be difficlties to intitively accept the difference in meaning of a word in scientific and everyday langages. The definitions may be difficlt to read at first sight, partly de to the ambition to create generally applicable definitions. The vocablary has been translated into major langages bt the official langages are English and French. The ISO format of the entries has been retained and the terms are sorted in alphabetical order. ccracy: closeness of agreement between the reslt of a measrement and a tre vale. ombined standard ncertainty: standard measrement ncertainty that is obtained from the measrement reslts of the inpt qantities in a measrement fnction. ommtability of a reference material: property of a reference material, demonstrated by the closeness of agreement between the relation among the NOTE 1. specification shold contain the conditions changed and nchanged, to the extent practical.. In chemistry, the term inter-serial intermediate precision condition of measrement (between series imprecision) is sometimes sed to designate this concept. Qantity: property of a phenomenon, body, or sbstance to which a nmber can be assigned with respect to a reference. Repeatability: property of a measring system to provide closely similar indications for replicated measrements of the same qantity nder repeatability conditions. Measrand: qantity intended to be measred. Measrement accracy: closeness of agreement between a measred qantity vale and a tre vale of a measrand. Measrement bias: systematic measrement error or its estimate, with respect to a reference qantity vale. Measrement error: measred qantity vale mins a reference qantity vale. Measrement precision: closeness of agreement between indicators obtained by replicate measrements on the same or similar objects nder stated specified conditions. NOTE Measrement precision is sally expressed nmerically by measres of imprecision, sch as standard deviation, variance, or coefficient of variation nder the specified conditions of measrement. 8 ioqimia

5 The ncertainty concept and its implications for laboratory medicine Measrement repeatability: repeatability, measrement precision nder the set of repeatability conditions of measrement Measrement reprodcibility: reprodcibility, measrement precision nder reprodcibility conditions of measrement. Measrement traceability: property of a measrement reslt whereby the reslt can be related to a stated reference throgh a docmented nbroken chain of calibrations, each contribting to the measrement ncertainty. Measrement treness: closeness of agreement between the average of an infinite nmber of replicate measred qantity vales and a tre vale of the measrand. Measrement ncertainty: parameter characterizing the dispersion of the qantity vales being attribted to a measrand, based on the information sed. Random error: component of measrement error that, in replicate measrements, varies in an npredictable manner. Repeatability condition: condition of measrement in the set of conditions that incldes the same measrement procedre, same operators, same measring system, same operating conditions and same location, and replicated measres on the same or similar objects over a short period of time. Reprodcibility condition: condition of measrement in a set of conditions that incldes different locations, operators, measring systems, and replicated measrements on the same or similar objects. Standard ncertainty: measrement ncertainty expressed as a standard deviation. Systematic error: component of measrement error that in replicates measrements remains constant or varies in a predictable manner. Type evalation of measrement ncertainty: evalation of a component of measrement ncertainty by a statistical analysis of qantity vales obtained nder defined conditions of measrement precision. Type evalation of measrement ncertainty: evalation of a component of measrement ncertainty determined by means other than a Type evalation of measrement ncertainty. Uncertainty bdget: statement of a measrement ncertainty, of the components of that measrement ncertainty, and of their calclation and combination. REFERENES 1. Gide to the expression of ncertainty in measrement. Geneva: ISO; Erachem/itac. Gide qantifying ncertainty in analytical measrement 000. vailable from: URL: http//: (visited ). 3. E. Gidelines on the expression of ncertainty in qantitative testing (E 4-16). 004 vailable from: URL: http//: (visited ). 4. stralasian ssociation of linical iochemists. Uncertainty of measrement in qantitative medical testing 004. vailable from: URL: http//: (visited ). 5. Kallner, Khorovskaya L, Pettersson T. method to estimate the ncertainty in measrements in a conglomerate of laboratories/instrments. Scand J lin Lab Med. 005; 65: linical and Laboratory Standards Institte. User Verification of Performance for Precision and Treness; proved Gideline Second Edition. LSI docment EP15-(e) [ISN ]. 7. Ricos, Álvarez F, ava F, García-Lacio JV, Hernández, Jiménez V, et al. rrent databases on biological variation; pros, cons and progress. Scan J lin Lab Invest. 1999; 59: Table pdated on the homepage of Dr J Westgard, available from: URL: HTTP//: (visited ). 9