Review Electronic supplementary material available online for this article. Estimation of the measurement uncertainty and practical suggestion for the description of the metrological traceability in clinical laboratories Raúl Rigo-Bonnin*1, Noelia Díaz-Troyano1, Laura García-Tejada1, Albert Marcè-Galindo1, Míriam Valbuena-Asensio1, Francesca Canalias2 1 LaboratoriClínic, IDIBELL, Hospital Universitari de Bellvitge, L’Hospitalet de Llobregat, Barcelona, Spain 2 Laboratoride Referència d’Enzimologia Clínica, Departament de Bioquímica i Biologia Molecular, Universitat Autònoma de Barcelona, Bellaterra, Spain *Corresponding author: raulr@bellvitgehospital.cat Abstract Clinicians request a large part of measurements of biological quantities that clinical laboratories perform for diagnostic, prognostic or diseases monitoring purposes. Thus, laboratories need to provide patient’s results as reliable as possible. Metrological concepts like measurement uncerta- inty and metrological traceability allow to know the accuracy of these results and guarantee their comparability over time and space. Such is the importance of these two parameters that the estimation of measurement uncertainty and the knowledge of metrological traceability is required for clinical laboratories accredited by ISO 15189:2012. Despite there are many publications or guidelines to estimate the measurement uncertainty in clinical laboratories, it is not entirely clear what information and which formulae they should use to calculate it. On the other hand, unfortunately, there are a small number of clinical laboratories that know and describe the metrological traceability of their results, even though they are aware of the lack of comparability that currently exists for patient’s results. Thus, to try to facilitate the task of clinical laboratories, this review aims to provide a proposal to estimate the measurement uncertainty. Also, different suggestions are shown to describe the metrological traceability. Measurement uncertainty estimation is partially based on the ISO/TS 20914:2019 guideline, and the metrological traceability described using the ISO 17511:2020. Different biological quantities routinely measured in clinical laboratories are used to exemplify the proposal and suggestions. Keywords: biostatistics; quality control; standardization; traceability; uncertainty Submitted: June 21, 2020 Accepted: October 5, 2020 Introduction The measured values of biological quantities facili- Metrological concepts like measurement uncer- tated by clinical laboratories provide essential in- tainty (MU) and metrological traceability (MT) al- formation that conditions the correct clinical ori- low to know the degree of accuracy of the meas- entation, optimisation of patients’ healthcare pro- ured values that a clinical laboratory provides, and cess, and lead to appropriate therapeutic, diag- the comparability or transferability of these results nostic, or healthcare actions. Therefore, these val- over time and space. Currently, such is the impor- ues must be reliable (exact) and comparable with tance of these two concepts that the estimation of other ones obtained in different periods and plac- MU and the knowledge of MT are required for clin- es (traceable) (1,2). ical laboratories accredited by ISO 15189:2012 (3). https://doi.org/10.11613/BM.2021.010501 Biochem Med (Zagreb) 2021;31(1):010501 1 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description Measurement uncertainty complements a meas- mate the MU, but there is still no consensus on ured value of a biological quantity, indicating the how they should calculate the MU (6-18). On the magnitude of the doubt about this value and pro- contrary, there does seem to be an agreement on viding a quantitative indication of its quality and how laboratories should describe the MT of the reliability (4). Nowadays, there are two main ap- measurement results they provide. Nevertheless, proaches for estimating MU: so-called bottom-up there are a small number of clinical laboratories and top-down. The bottom-up approach is based that know the MT of their results, even though on a comprehensive categorisation of the meas- they are aware of the lack of comparability that urement where each potential uncertainty source currently exists for patient’s results (13,17-19). Thus, is identified and quantified. The estimates of un- with the intention to facilitate the task of clinical certainty expressed as standard deviations (stand- laboratories, this review aims to provide a propos- ard uncertainties) are assigned to individual com- al to estimate the measurement uncertainty in ponents of the procedure, which are then mathe- clinical laboratories showing examples to decide matically combined using propagation rules to what information and which formulae they should provide a combined standard uncertainty. Finally, use to calculate the MU. Also, practical sugges- an expanded uncertainty is estimated, multiplying tions are provided to enable laboratories to de- the combined uncertainty by an appropriate cov- scribe the MT of their results. erage factor (1). Conversely, the top-down approach considers un- Measurement uncertainty estimation certainty as a whole. First, the most significant un- certainty sources are identified and grouped. The top-down approach is particularly well suited Then, their standard uncertainties are estimated to measuring systems commonly encountered in using available laboratory tests performance infor- clinical laboratories. So, the MU should be estimat- mation, such as measurement procedure valida- ed using this approach and taking into account tion or verification data, and intra-laboratory or in- the following steps (6): ter-laboratory data (e.g. internal and external qual- ity control data). Subsequently, the combined un- Specification of the measurand certainty is obtained from the standard uncertain- A measurand is defined as the quantity intended ties for, finally, to estimate the expanded uncer- to be measured (4). So, the measurand must be tainty (1). unequivocally defined and the measurement pro- Furthermore, MT is defined as the property of a cedure used must be exhaustively detailed; other- measurement result whereby the result can be re- wise, an insufficient specification of the measur- lated to a reference through a documented unbro- and may itself be a significant uncertainty source ken chain of calibrations, each contributing to the (definitional or intrinsic uncertainty) that could be measurement uncertainty (4). In other words, to difficult to estimate. To specify the measurand, it is achieve comparability of results over space and necessary to include at least the following infor- time, it is essential to link all the individual meas- mation (6,20): urement results to some common reference. In • The name of the biological system containing this way, results can be compared through their the component (analyte), e.g. blood, plasma, relationship to that reference. Ideally, this refer- serum, urine, etc. ence should be an International System (SI) unit of • The name of the biological component (so- measurement materialised by a primary reference called analyte), e.g. glucose, sodium ion, siroli- measurement procedure and a primary measure- mus, troponin T, etc. ment standard (5). • The kind-of-property, e.g., substance concen- At present, there are several guidelines and publi- tration, mass concentration, number concen- cations that clinical laboratories could use to esti- tration, catalytic concentration, etc. Biochem Med (Zagreb) 2021;31(1):010501 https://doi.org/10.11613/BM.2021.010501 2 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description • The measurement unit, e.g., mmol/L, mg/L, Instead, when clinical laboratories prepare their entities/L, µkat/L, etc. calibration materials, they are entirely responsible Sometimes, it is also necessary to include addi- for estimating the ucal. In these cases, the ucal can tional information such as the measuring system be calculated taking into account all information (or the measurement method or the measurement used to prepare the calibration materials, and sta- principle) used to measure the quantity, and the tistically combining the uncertainties associated conditions under which the measurements are with each one of the sequential value assignment performed (e.g., the temperature for enzymes). steps utilising the law for the propagation of uncer- tainty (8,9,22). Identification of the uncertainty sources Uncertainty related to the long-term intermediate According to different clinical laboratory guide- imprecision lines, the most significant uncertainty sources con- Most of the components of the MU are included in tributions to the overall MU are captured by the the long-term intermediate imprecision. This im- uncertainties related to the assigned value of the precision can be calculated from internal quality end-user calibrator (ucal), the long-term intermedi- control (IQC) data (6). ate precision (uRw), and the bias (ub) (6,7). Thus, it would be sufficient that clinical laboratories con- When clinical laboratories estimate the uRw, there sider only these three uncertainty sources to pro- are different considerations that they should take vide reasonable estimates of MU that help ensure into account (6,7,13): that patient results are fit for medical use. a) The IQC materials used for estimating the uRw should comply with specific attributes or char- Estimation of the standard uncertainties acteristics. For example, the materials should be commutable and different from that used to Uncertainty related to the assigned value of the check the correct alignment of the measuring end-user calibrator systems. A correct estimate of MU is indeed not possible b) The IQC material data must be collected for a without the ucal because it includes all uncertain- sufficiently long-time-interval to reflect most of ties contributions accumulated across the entire the sources of variability influencing the mea- traceability chain of a measurement result (13). surement process. Thus, clinical laboratories should include the ucal in the uncertainty budget when they estimate the c) Different IQC material levels at mean values close MU. The in vitro diagnostic (IVD) manufacturers are to important medical decision limits should be requested to comply with the European Regula- used to know the uRw behaviour across the mea- tion 2017/746 on in vitro medical diagnostics and suring interval of the measuring systems. must be provided with this information to clinical d) A precision study (e.g., comparing variances us- laboratories (21). Usually, manufacturers present ing the F-test) of representative human sam- this information as the calibration material as- ples and IQC materials should be performed signed value (xcal) jointly with its expanded uncer- to verify that the magnitude of imprecision for tainty (Ucal or %Urel(cal)) using a coverage factor (k) both materials is similar. An example of how equal to 2. So, the ucal can be obtained as: to assess this type of studies was published by Fuentes-Arderiu et al. (23). xcal × %Urel(cal) (Equation ucal = (Eq.) 1) e) In clinical laboratories, it is common to indis- 2 × 100 tinctly measure a biological quantity with more or than one identical measuring system (or differ- Ucal ent modules of the same measuring system). ucal = (Eq. 2). Therefore, it would be advisable to obtain an 2 https://doi.org/10.11613/BM.2021.010501 Biochem Med (Zagreb) 2021;31(1):010501 3 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description estimate of MU that would have the variation system i), xi is the IQC mean value obtained using overall measuring systems. the calibrator lot i (or the IQC mean value obtained f) To avoid the effect of IQC material lot changes using the IQC lot i, or the IQC mean value obtained on estimating uncertainty, as well as for practi- using the measuring system i), xp is the IQC pooled cal reasons, the use of a single IQC material lot mean calculated using all calibrator lots (or IQC during the estimation study it would be advis- pooled mean calculated using all IQC lots, or IQC able (6,8). mean value calculated using all measuring sys- tems) and N is the total number of IQC replicate As far as possible, clinical laboratories should com- measurements. ply with most of these considerations to perform an adequate uRw estimation, as well as to avoid a Uncertainty related to the bias possible over-estimate of the uRw. At present, how to deal with the bias on clinical When only one calibrator lot, IQC lot, and a unique measurements and how to calculate the bias com- measuring system are used during a specified ponent of uncertainty continues to be a matter of time interval, the uRw can be calculated as the clas- debate. Some authors firmly state that the bias (or sical standard deviation (s): its uncertainty) must not be included in the uncer- tainty budget because the bias component is al- ∑ni = 1 (xi – x)2 ready will be part of the ucal (13). In other words, it uRw = s = (Eq. 3), n–1 is expected that IVD manufacturers must ensure the traceability of their measuring systems to the where xi represents IQC values obtained in a speci- highest-order available references. This statement fied time-interval, n the number of IQC replicate is partially correct because it is known that, in sev- measurements in a specified time-interval and x eral cases, the IVD manufacturers continue to pre- the IQC mean value obtained in a specified time- pare their calibration materials in-house without interval. any traceability to high-order metrological refer- Furthermore, when two or more lots of calibration ences, although they are requested to comply or IQC materials are involved in a specified time in- with European Regulation 2017/746. terval, or when two or more identical measuring In contrast, other authors opine that when a sig- systems are used to measure the same biological nificant bias is detected this one should be elimi- quantity, the uRw can be calculated as a pooled nated (24,25). If the bias cannot be eliminated, standard deviation (sp) (22): there are two ways of proceeding: 1) to correct the bias by applying a correction factor and incorpo- 1 [ × ∑ ni = 1(ni – 1) × si2 + ∑ ni = 1 ni × xi2 – 1 × ( ∑ ni = 1 ni × xi)2 [ uRw = sp = N–1 N rating its uncertainty to the uncertainty budget, or 2) to include the bias itself in the uncertainty (Eq. 4) budget. It should be noted that the first point with a pooled mean (xp) given by: would only be applicable for those cases in which the bias study is assessed using certified reference 1 × ∑n material (CRM), and when the traceability declared xp = i = 1 ni × xi (Eq. 5), N by the IVD manufacturer is to the same CRM used where ni is the number of IQC replicate measure- to evaluate the bias study (24,25). ments using the calibrator lot i (or the number of Regarding the ub, different procedures allow esti- IQC replicate measurements using the IQC lot i; or mating the measuring system bias, is the one the number of IQC replicate measurements using based on the use of reference materials the most measuring system i), si is the standard deviation widely used. Reference material can be a CRM, an obtained using the calibrator lot i (or the standard IQC material (with or without an associated IQC in- deviation obtained using the IQC lot i, or the ter-laboratory scheme), or a control material be- standard deviation obtained using the measuring longing to an external quality assurance service Biochem Med (Zagreb) 2021;31(1):010501 https://doi.org/10.11613/BM.2021.010501 4 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description (EQAS) (6,7,25). Of all of them, CRM or commutable 2 IQC or EQAS control materials with values assigned sLabsi,k uμi,k = 1.25 × ∑ Ni = 1 ∑ m k=1 by an international conventional or primary meas- qi,k urement procedures should be used whenever (Eq. 10). possible. In the absence of these CRM or commut- able control materials, inter-laboratory IQC fol- In the previous equations R represents the total lowed by control materials from an EQAS can be pool size (total number of replicate measure- used (14). ments, i.e., of IQC values), N the number of IQC ma- When a CRM is used to estimate the bias (b), the b terials levels used, m the number of calibrator lots and its uncertainty (ub) can be calculated as (24): (or IQC material lots or measuring systems) used, ni,k the number of replicate measurements using b=x–μ (Eq. 6) the IQC material level i for the calibrator lot k (or IQC material k, or measuring system k), bi the ub = uμ (Eq. 7), mean bias over ni replicates, using the IQC materi- where x designates the mean value obtained after al level i for the calibrator lot k (or IQC material k, processing the CRM in a specific time-interval, μ is or measuring system k), xi the pooled mean value the CRM assigned value and uμ the uncertainty as- obtained using the IQC material level i for the cali- sociated with the CRM assigned value. Note that brator lot k (or IQC material k, or measuring system Eq. 5 should be used to calculate the x value if k), μi,k the reference value using the IQC material more than one calibration lot or measuring system level i for the calibrator lot k (or IQC material k, or is used. measuring system k) - this value can be the value assigned by the manufacturer of the IQC material Bias studies using IQC materials can be performed or conventional value calculated as the mean of following the Farrance et al. recommendations (22): arithmetic means of peer-group laboratories par- • When two or more lots of calibrator or IQC ma- ticipating in an inter-laboratory IQC program (e.g. terials are involved in a specified time interval, UNITY from Bio-Rad Laboratories) using the IQC or when two or more identical measuring sys- material level i for the calibrator lot k (or IQC mate- tems are used to measure the same biological rial k, or measuring system k), uμi,k is the uncertain- quantity, the bias can be calculated as a weight- ty associated with the reference value μi,k, sLabsi,k ed mean value of bias (bw) (24): is the robust peer-group standard deviation ob- bw = 1 × ∑ Ni = 1 ∑ m n × bi,k = 1 × ∑ Ni = 1 ∑ m n × (xi,k – μi,k) tained using the IQC material level i for the calibra- k = 1 i,k k = 1 i,k R R tor lot k (or IQC material k, or measuring system k), qi,k the number of peer-group laboratories partici- (Eq. 8) pating in the IQC material level i for the calibrator and its uncertainty (ubw) as: lot k (or IQC material k, or measuring system k). • When only one calibrator lot, IQC lot, and a ubw = 1 N m × 2 1 N m ( × ∑ i = 1 ∑ k = 1 ni,k uμi,k ) + ( × ∑ i = 1 ∑unique 2 × bi,k n measuring 2 ) – (bwsystem ) are used during a k = 1 i,k R R specified time interval, equations become: ni,k × uμi,k ) + ( 1 × ∑ Ni = 1 ∑ m 1 1 2 2 2 m =1 n × bi,k ) – (bw) k = 1 i,k bw = × ∑ Ni = 1 ni × bi = × ∑ Ni = 1 ni × (xi – μi) R M M (Eq. 9) (Eq. 11) The ICQ manufacturer must provide the μi,k. 1 ubw = ( 1 × ∑ Ni = 1 ni × uμi ) + ( × ∑ Ni = 1 ni × bi ) – (bw) 2 2 2 Otherwise, if the IQC material presents an associ- M M ated IQC inter-laboratory scheme, it can be esti- mated as (26): (Eq. 12) https://doi.org/10.11613/BM.2021.010501 Biochem Med (Zagreb) 2021;31(1):010501 5 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description The IQC manufacturer must provide the μi,k. Oth- where R is the total pool size (total number of erwise, if the IQC material presents an associated measurements including all measuring systems IQC inter-laboratory scheme, it can be estimated and EQAS participations, N is the number of EQAS as (26): participations, ei,k is the measurement error for the EQAS participation i and the measuring system k, sLabsi2 xi,k is the measured value obtained for the EQAS uμi = 1.25 × ∑ Ni = 1 (Eq. 13), participation i and the measuring system k, μi is qi thre reference value assigned by the EQAS manu- where N represents the number of IQC material facturer for the EQAS participation i, uμi is the un- levels used, ni the number of replicate measure- certainty associated with the reference value μi, ments using the IQC material level i, M the total sLabsi is the robust peer-group standard deviation number of replicate measurements, bi the bias facilitated by the EQAS manufactured for partici- over ni replicates using the IQC material level i, xi pation i and qi is the number of peer-group labo- the mean value obtained using the IQC material ratories for the EQAS participation i. level i, μi the reference value for the IQC material • When only one measuring system is used, the level i (this value corresponds to the conventional bias (b) and its uncertainty (ub) can be calculat- value calculated as the mean of arithmetic means ed as: of peergroup laboratories participating in an in- ter-laboratory IQC program (e.g. UNITY from Bio- 1 × N e = 1 × N (x – μ ) b= ∑i=1 i ∑i=1 i i Rad Laboratories), uμi the uncertainty associated N N with the mean reference value μi, sLabsi the robust (Eq. 17) peer-group standard deviation obtained for the IQC material level i and qi the number of peer- group laboratories participating in the IQC mate- 1 × n u 2 + 1 × N e 2– b2 rial level i. ub = ∑ i = 1 μi ∑i=1 i N N The bias can also be estimated from EQAS. In these (Eq. 18) cases, the bias and its uncertainty can be calculat- ed as described above. Thus: • When more than one measuring system is used sLabsi2 uμi = 1.25 × ∑ Ni = 1 (Eq. 19), to measure the same quantity, a mean bias (b) qi can be calculated as (24): 1× N e = 1 × ∑ Ni = 1 ∑ m b= ∑ i = 1 ∑m k = 1 i,k (x μ) k = 1 i,k – i where N represents the number of EQAS participa- R R tions, ei the measurement error for the EQAS par- (Eq. 14), ticipation i, xi the measured value obtained for the EQAS participation i, μi the reference value as- and its uncertainty (ub) as: signed by the EQAS manufacturer for the EQAS 1 participation i, uμi the uncertainty associated with ( 1 × ∑ Ni = 1 uμi ) + ( × ∑ Ni = 1 ∑ m 2 2 2 ub = k = 1 ei,k) – (b) the reference value μi, sLabsi the robust peer-group N R standard deviation facilitated by the EQAS manu- (Eq. 15). facturer for participation i and qi the number of peer- The EQAS’ manufacturer must provide the uμi or, if group laboratories for the EQAS participation i. not, could be calculated as (26): Once the bias and its uncertainty have been esti- mated, metrological compatibility studies can be sLabsi2 carried out to know whether the biases are or are uμi = 1.25 × ∑ Ni = 1 (Eq. 16), not statistically significant. Thus, a bias is consid- qi Biochem Med (Zagreb) 2021;31(1):010501 https://doi.org/10.11613/BM.2021.010501 6 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description ered significant if the absolute value of the bias it- Calculation of the expanded uncertainty self is higher than its relative expanded uncertain- ty, i.e. if |b| > 2 × ub (4). Expanded uncertainty (U) is calculated multiplying the uc by a coverage factor k: If a significant bias is detected, its treatment should be different depending on the kind-of-ref- U = k × uc (Eq. 23). erence material used. If a CRM is used, the bias This k-value depends on the type of probability should be eliminated by applying a correction fac- distribution, the level of statistical significance se- tor to every individual measured value obtained, lected and the number of independent measure- dividing the assigned value of the CRM by the ments made to obtain the uc. Under typical clinical mean value obtained in the bias study. Also, the laboratory working conditions, it is acceptable to MU associated with this correction factor (ucf ), cal- use a k-value of 2 (6,7). culated such as the ub, should be included in the uncertainty budget. On the contrary, if IQC or Comparison of the expanded uncertainty EQAS control materials are used, it is not recom- obtained with the maximum allowable mended to apply a correction factor to eliminate expanded uncertainty the bias, and the bias itself should be included in the uncertainty budget (6,22,25). Finally, to know if a U value is acceptable, it must be compared with the maximum allowable (per- Calculation of the combined standard missible) expanded uncertainty (Umax). Thus, an U uncertainty value is considered acceptable if it is lower or equal than the previously selected Umax by the lab- Wen the individual contribution of each standard oratory. uncertainty source has been estimated, the com- bined standard uncertainty can be calculated by Another controversial point that currently exists is adding estimates of the standard uncertainties how the Umax should be established. Measure- considered above, according to one of the follow- ment uncertainty requirements for defining fit- ing equations: ness-for-purpose limits may be based on clinical outcome studies, biological variation or state-of- 2 uc = ucal 2 + uRw the-art, being those based on biological variation, (Eq. 20) despite their limitations, generally accepted and used (27-30). However, it should be noted that un- less a country has established legal metrological 2 uc = ucal 2 + uRw + ucf2 = ucal 2 2 + uRw + ub2 requirements (e.g. the German RiliBÄK), the selec- tion of one type of requirement or another is a (Eq. 21) matter of consensus and depends on the clinical laboratory itself. So, despite there are several ways to select the 2 2 2 uc = ucal + uRw + b (Eq. 22) Umax, we show here a procedure based on state- of-the-art to calculate the Umax using on the Clinical laboratories should use Eq. 20 when the RiliBÄK concept named “root mean square of compatibility study shows that the bias is not sta- measurement error” (∆) (31-33): tistically significant. Equation 21 should be used %∆rel(max) × μa μa 2 2 when a CRM is used to estimate the bias, the bias is Umax = ∆max = = × CVmax + %brel(max) 100 100 significant, and it has been “eliminated” applying a correction factor. Equation 22 should use if IQC or (Eq. 24), EQAS materials are used to estimate the bias, and where ∆max represents the maximum allowable the laboratory cannot “eliminate” the bias. absolute root mean square of measurement error, https://doi.org/10.11613/BM.2021.010501 Biochem Med (Zagreb) 2021;31(1):010501 7 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description %∆rel(max) the maximum allowable pecent relative bility in Laboratory Medicine (JCTLM) database root mean square of measurement error, μa the (39). For each biological quantity, the strategy to reference value for which the requirement has follow can be based on: been established, CVmax the maximum allowable • Obtaining the MT declared by the manufactur- coefficient of variation and %brel(max) the maxi- ers. If this information is not present in bro- mum allowable percent relative bias. chures or incomplete information is found, this The %∆rel(max) values can be selected directly from one can be acquired directly asking the manu- RiliBÄK (31). Otherwise, they can be calculated facturers, or in some cases, from websites of gov- from the CVmax and %brel(max) using biological vari- ernment agencies, such as the Food and Drug Ad- ation data, state-of-the-art data, or data from dif- ministration (FDA) (40). ferent organizations such as CLIA, National Choles- • Obtaining additional information related to the terol Education Program for lipid-related quanti- references (units of measurement, measure- ties, European Medicine Agency (EMA) for drugs, ment procedures, or reference materials) to de- among others (34-38). scribe the calibration hierarchies and the se- To illustrate the proposal for the estimation of MU, quence of result assignments up the point at some biological quantities that are routinely meas- which metrological traceability begins. This in- ured in clinical laboratories using both already formation can be obtained from the reagent’s “commercial” (i.e., those with CE marking) and “in- manufacturers, CRM certificates, or the JCTLM house” validated measurement procedures have database (39). been selected (see Supplementary material 1). Ta- • Performing a table or flow chart from all infor- ble 1 shows the MU budget and the maximum al- mation previously collected to describe the lowable relative expanded uncertainty. Besides, metrological traceability chain and the calibra- Supplementary materials 2, 3 and 4 contain spread­­ tion hierarchy of the measurement results. sheets that allow calculating the primary measure- As an example, Table 2 and Supplementary Mate- ment uncertainty sources (ucal, uRw and ub), the uc, rial 5 show the MT description for some biological and the U. Also, they include a study to know if the quantities. U obtained is or is not acceptable compared with the Umax, and show an example of how to specify Conclusions the measurand. Every supplementary material considers the use of the three kind-of-materials to This review provides practical suggestions of how estimate the bias, CRM, IQC materials (with an as- clinical laboratories could estimate the MU and de- sociated IQC inter-laboratory scheme), and EQAS scribe the MT of biological quantities results to materials. help and motivate clinical laboratories to: 1) con- duct this type of studies, 2) incorporate informa- Metrological traceability description tion regarding uncertainty and traceability in their reports, and 3) allow them a greater understand- As we commented before, the description of MT in ing of the importance that these concepts have in clinical laboratories is a less controversy matter the laboratory medicine sciences. Also, in the “clin- than the MU uncertainty and can be made simply ical laboratory accreditation era”, this review could based on the ISO 17511:2020 (5). All information help laboratories in meeting those ISO 15189 re- needed to its description can be provided by the quirements related to these two metrological con- manufacturers of the reagents or calibration mate- cepts. rials, as well as from certificates of analysis of CRM declared by international or national metrology in- Potential conflict of interest stitutes, and from the Joint Committee for Tracea- None declared. Biochem Med (Zagreb) 2021;31(1):010501 https://doi.org/10.11613/BM.2021.010501 8 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description Table 1. Measurement uncertainty budget for different biological quantities commonly measured in clinical laboratories Biochemical IQC measured U %Urel Unit ucal uRw† b‡ u b‡ uc %Urel(max) quantity value* (N) (k = 2) (k = 2) S-Alanine 23.4 (614) 0.5280 1.1523 - 0.1523 1.2347 1.2675 2.5 10.8 transaminase; U/L 11.5 cat.c. 181 (643) 0.5280 2.3892 - 0.1523 1.2347 2.4468 4.9 3 S-Albumin; 27.1 (639) 0.1490 0.7537 1.2639 0.8140 0.7683 1.5 5.7 g/L 12.50 mass c. 47.6 (606) 0.1490 1.1801 1.2639 0.8140 1.1895 2.4 5.0 22.00 (from 1.7 to 8.52 (414) 0.5850 0.5314 - 0.5530 1.0540 0.7903 1.58 18.55 S-Bilirubin; < 34 µmol/L) μmo/L subst.c. 16.00 (from > 34 to 107 (410) 0.5850 1.9651 - 0.5530 1.0540 2.0503 4 4 513 μmol/L) S-Cholesterol; 2.93 (385) 0.0220 0.0527 - 0.0107 0.0621 0.0571 0.11 3.90 mmol/L 4.20 subst.c. 7.01 (389) 0.0220 0.0842 - 0.0107 0.0621 0.0871 0.17 2.48 S-Clozapine; 618 (131) 16.2486 28.0565 113.6000 96.4195 32.4219 65 11 nmol/L 21.2 subst.c. 1689 (131) 28.6875 36.8283 113.6000 96.4195 47.2660 95 6 S-Glucose; 3.42 (645) 0.0453 0.0721 0.0159 0.0943 0.0851 0.17 4.98 mmol/L 11.00 subst.c. 19.1 (632) 0.0453 0.3811 0.0159 0.0943 0.3838 0.7 4.0 7.084 (1723) 0.0071 0.0113 0.0081 0.0599 0.0133 0.027 0.377 P(aB)-Hydrogen 1 7.415 (1748) 0.0071 0.0098 0.0081 0.0599 0.0121 0.024 0.326 0.400 ion; pH (37 °C) 7.622 (1725) 0.0071 0.0094 0.0081 0.0599 0.0118 0.024 0.309 2.72 (758) 0.0100 0.0414 0.0057 0.0199 0.0426 0.09 3.13 S-Potassium mmol/L 4.27 (243) 0.0100 0.0379 0.0057 0.0199 0.0392 0.08 1.84 4.50 ion; subst.c. 7.89 (783) 0.0250 0.0621 0.0057 0.0199 0.0669 0.13 1.70 4.31 (210) 0.0492 0.3300 0.6301 0.3122 0.4494 0.90 20.85 B-Sirolimus; nmol/L 7.94 (210) 0.0792 0.4838 0.6301 0.3122 0.5753 1.15 14.49 21.20 subst.c. 12.4 (210) 0.1417 0.6282 0.6301 0.3122 0.7109 1.4 11.5 0.74 (333) 0.0100 0.0475 0.2723 0.8914 0.0485 0.01 13.12 S-Thyrotropin; mIU/L 6.79 (196) 0.0100 0.2731 0.2723 0.8914 0.2733 0.55 8.05 13.50 arb.subst.c. 36.9 (149) 0.0100 1.7180 0.2723 0.8914 1.7180 3.4 9.3 IQC - internal quality control. *IQC measured values correspond to the pooled mean values obtained after processing IQC materials for all identical measuring systems used to measure the quantities. ucal - uncertainty associated with the values assigned to the calibrator. uRw - uncertainty related to the long-term intermediate imprecision. b - measurement bias. ub - uncertainty associated with the bias. uc - combined standard uncertainty. U - expanded uncertainty. %Urel - percent relative expanded uncertainty. k - coverage factor. %Urel(max) - maximum allowable per cent relative expanded uncertainty. Biochemical quantities nomenclature (20): aB - arterial blood; B - blood; P - plasma; S - serum; arb.subst.c. - arbitrary substance concentration; cat.c. - catalytic concentration; mass c. - mass concentration; and subst.c - substance concentration. †To estimate the uRw, one calibrator and IQC material lot, and two or more identical measuring systems to measure the selected quantities were used. Instead, for the mass concentration of sirolimus in blood and mass concentration of clozapine in serum, only one calibrator, IQC material lot and measuring system were used. ‡The b and the ub for the substance concentration of sirolimus in blood were estimated using the certified reference material (CRM) ERM-DA111a. This CRM was processed twice per week for six months, and only one measuring system and calibration lot were used. The manufacturer provided the CRM assigned value and its uncertainty, and they were 10.64 nmol/L and 0.301 nmol/L, respectively. The b and the ub for the mass concentration of clozapine in serum and the pH in arterial blood were estimated using data from 10 external quality assessment scheme participations during the survey period 2019. The b and the ub for the rest of biological quantities using IQC materials, which they have the inter-laboratory quality control scheme associate it. The IQC data and the conditions used were the same that those described for estimating the uRw. https://doi.org/10.11613/BM.2021.010501 Biochem Med (Zagreb) 2021;31(1):010501 9 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description Table 2. Metrological traceability for different biochemical quantities results usually measured in clinical laboratories Biochemical IVD Calibration- Metrological traceability declared by Highest metrological quantity manufacturer material the manufacturer traceability of quantity results Measurement Reference procedures used to material prepare/assign their calibration materials Calibrator for S-Alanine IFCC/ERM-AD454k Roche automated systems *ICRMP: IFCC’s procedure (41) transaminase; n.d. IFCC’s method (41) Diagnostics (C.f.a.s) *ICS: cat.c. ERM-AD454k/IFCC (Ref. 10759350190) Calibrator for S-Albumin; Roche automated systems BCR470/ USNRP 12-0575C n.d. *ICS: mass c. Diagnostics (C.f.a.s) CRM470 USNRP 12-0575C (42) (Ref. 10759350190) Calibrator for S-Bilirubin; Roche automated systems Doumas’ procedure n.d. Doumas’ method (43) *ICRMP: subst.c. Diagnostics (C.f.a.s) Doumas’ procedure (43) (Ref. 10759350190) Calibrator for ID-GC/MS Abell-Kendall’s S-Cholesterol; Roche automated systems Abell-Kendall n.d. method (44) and *ICRMP: Abell-Kendall (44) and subst.c. Diagnostics (C.f.a.s) ID-MS (45) (Ref. 10759350190) ID-GC/MS procedures (45) Clinical Laboratory of Hospital Clozapine 100 de Bellvitge’s calibrators S-Clozapine; “In-house” “In-house” mg [USP] (ref. Gravimetry MSMP: Gravimetry subst.c. 1142107) CRM: Clozapine, 100 mg [USP] (Ref. 1142107) Calibrator for S-Glucose; Roche automated systems Roche Diagnostics’s calibrators n.d. ID-MS subst.c. Diagnostics (C.f.a.s) MSMP: ID-MS (Ref. 10759350190) SI GEM Premier 5000 PRMP: Potentiometry using P(aB)-Hydrogen Instrumentation PAK BG/ISE/GL/COOX SRM 186g n.d. the Harned’s cell without ion; pH(37 °C) Laboratory (ref. 55360011) transference and liquid junction *PMS: SRM 186g Primary SI calibrators ISE Standard low PRMP: Gravimetry and (not specified) S-Potassium ion; Roche and high (Ref. coulometry based on prepared Gravimetry subst.c. Diagnostics 11183974216/ DerSimonian-Laird procedure. gravimetrically 11183982216) Spark-source MS from purified *PMS: SRM 918c salts ClinCal Whole SI Blood Calibrator PRMP: Gravimetry, HPLC-UV, B-Sirolimus; Set, lyophil., for Recipe ERM-AC021a LC-MS/MS HPLC-MS, TLC, Karl-Fisher subst.c. Immunosuppressants titration, TGA, 1H NMR (Level 0 – 6) *PMS: ERM-AC021a (Ref. 9933) S-Thyrotropin; Roche TSH Calset WHO 3rd IRP WHO NIBSC 3rd IRP 80/558 n.d. *ICS: arb.subst.c. Diagnostics (Ref. 04738551190) 80/558 WHO NISNC 3rd IRP 80/558 Biochem Med (Zagreb) 2021;31(1):010501 https://doi.org/10.11613/BM.2021.010501 10 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description Table 2. Continued CRM - Certified reference material. ERM - European Reference Material. 1H NMR - nuclear magnetic resonance of hydrogen 1. HPLC-MS - high-performance liquid chromatography with mass spectrometry detection. HPLC-UV - high-performance liquid chromatography with ultraviolet detection. ICS - international conventional standard. ICRMP - International conventional reference measurement procedure. ID-MS - isotope dilution-mass spectrometry. ID-GC/MS - isotope dilution-gas chromatography-mass spectrometry. IFCC - International Federation of Clinical Chemistry and Laboratory Medicine. IRP - International Reference Preparation. IVD - in vitro diagnostic. LC-MS/MS - liquid chromatography-tandem mass spectrometry. MS - mass spectrometry. MSMP - Manufacturer’s selected measurement procedure. n.d. - not declared. NIBSC - National Institute for Biological Standards and Control. PMS - primary measurement standard. PRMP - primary reference measurement procedure. RM - Reference material. SI - International System of Units. SRM - Standard Reference Material. TGA - thermogravimetric analysis. TLC - thin-layer chromatography. USNRP - United States National Reference Preparation for Human Serum Proteins. USP - United States Pharmacopeia. WHO - World Health Organization. *Included in the JCTLM database (39). Biochemical quantities nomenclature (20): aB - arterial blood; B - blood; P - plasma; S - serum; arb.subst.c. - arbitrary substance concentration; cat.c. - catalytic concentration; mass c. - mass concentration; and subst.c - substance concentration. References 1. Rigo-Bonnin R, Alía P, Canalias F. Measurement uncertainty 10. Nordic Innovation Center. Handbook for calculation of and metrological traceability of whole blood cyclosporin A measurement uncertainty in environmental laboratories, mass concentration results obtained by UHPLC-MS/MS. Clin NORDTEST Technical report 537. Ed 3.1. Available at: http:// Chem Lab Med. 2018;56:1458–68. https://doi.org/10.1515/ www.nordtest.info/index.php/technical-reports/item/ cclm-2018-0120 handbook-for-calculation-of-measurement-uncertainty- 2. Plebani M, Simundic AM. Quality in laboratory diagno- in-environmental-laboratories-nt-tr-537-edition-3.html. stics: from theory to practice. Biochem Med (Zagreb). Accessed August 15th 2020. 2010;20:126-30. https://doi.org/10.11613/bm.2010.014 11. European Federation of National Associations of Measure- 3. International Organization for Standardization (ISO). Medi- ment, Testing and Analytical Laboratories. Measurement cal laboratories. Requirements for quality and competence. uncertainty revisited: Alternative approaches to uncertainty ISO 15189. Geneva, Switzerland: ISO, 2012. evaluation, EUROLAB Technical report No. 1/2007. Available 4. Joint Committee for Guides in Metrology (JCGM). Internati- at: http://www.eurolab.org/documents/1-2007.pdf. Acce- onal vocabulary of metrology - Basic and general concepts ssed August 15th 2020. and associated terms; VIM 3rd ed. JCGM 200. Sèvres, Fran- 12. European Federation of National Associations of Me- ce: JCGM, 2012. Available at: https://www.bipm.org/utils/ asurement, Testing and Analytical Laboratories, Gu- common/documents/jcgm/JCGM_200_2012.pdf. Accessed ide to the evaluation of measurement uncertainty for qu- August 15th 2020. antitative test results, EUROLAB Technical report No. 5. International Organization for Standardization (ISO). In vi- 1/2006. Available at: http://www.eurolab.org/documents/ tro diagnostic medical devices. Requirements for establishi- EL_11_01_06_387%20Technical%20report%20-%20Gu- ng metrological traceability of values assigned to calibra- ide_Measurement_uncertainty.pdf. Accessed August 15th tors, trueness control materials and human samples. ISO 2020. 17511. Geneva, Switzerland: ISO, 2020. 13. Braga F, Panteghini M. The utility of measurement un- 6. International Organization for Standardization (ISO). Medi- certainty in medical laboratories. Clin Chem Lab Med. cal laboratories — Practical guidance for the estimation of 2020;58:1407-13. https://doi.org/10.1515/cclm-2019-1336 measurement uncertainty. ISO/TS 20914. Geneva, Switzer- 14. Martinello M, Snoj N, Skitek M, Jerin A. The top-down land: ISO, 2019. approach to measurement uncertainty: which formu- 7. Clinical and Laboratory Standards Institute (CLSI). Expre- la should we use in laboratory medicine? Biochem Med. ssion of measurement uncertainty in laboratory medicine; 2020;30:020101. https://doi.org/10.11613/bm.2020.020101 approved guideline. CLSI EP29-A. Wayne, PA: CLSI, 2012. 15. Milinković N, Ignjatović S, Šumarac Z, Majkić-Singh N. Un- 8. Joint Committee for Guides in Metrology (JCGM). Evaluati- certainty of measurement in laboratory medicine. J Med on of measurement data - Guide to the expression of uncer- Biochem. 2018;37:279–88. https://doi.org/10.2478/jomb- tainty in measurement; 3rd edition. JCGM 100. Sèvres, Fran- 2018-0002 ce: JCGM; 2008. Available at: https://www.bipm.org/utils/ 16. Ćelap I, Vukasović I, Juričić G, Šimundić AM. Minimum requ- common/documents/jcgm/JCGM_100_2008_E.pdf. Acce- irements for the estimation of measurement uncertainty: ssed August 15th 2020. Recommendations of the Joint Working Group for Uncer- 9. EURACHEM/CITAC, Guide CG4: Quantifying uncertainty in tainty of Measurement of the CSMBLM and CCMB. Biochem analytical measurement, 3er ed. Eurachem, 2012. Available Med (Zagreb). 2017;27:030502. https://doi.org/10.11613/ at: https://www.eurachem.org/index.php/publications/gui- bm.2017.030502 des/quam. Accessed August 15th 2020. https://doi.org/10.11613/BM.2021.010501 Biochem Med (Zagreb) 2021;31(1):010501 11 Rigo-Bonnin R. et al. Uncertainty estimation and traceability description 17. Oosterhuis WP, Bayat H, Armbruster D, Coskun A, Freeman 29. Fuentes-Arderiu X, Padró-Miquel A, Rigo-Bonnin R. Disad- KP, Kallner A, et al. The use of error and uncertainty methods vantages of using biological variation data for reference in the medical laboratory. Clin Chem Lab Med. 2018;56:209– change values. Clin Chem Lab Med. 2012;50:961. https:// 19. https://doi.org/10.1515/cclm-2017-0341 doi.org/10.1515/cclm.2011.827 18. Kallner A. Estimation of uncertainty in measurements in the 30. Carobene A. Reliability of biological variation data availa- clinical laboratory. Clin Chem Lab Med. 2013;51:2249–51. ble in an online database: need for improvement. Clin Chem https://doi.org/10.1515/cclm-2013-0749 Lab Med. 2015;53:871–7. https://doi.org/10.1515/cclm- 19. Panteghini M, Braga F. Implementation of metrological tra- 2014-1133 ceability in laboratory medicine: where we are and what is 31. Bundesärztekammer. Guidelines of the German Medical missing. Clin Chem Lab Med. 2020;58:1200–4. https://doi. Association on quality assurance in medical laboratory te- org/10.1515/cclm-2019-1128 sting. GMS Zeitschrift zur Förderung der Qualitätssicherung 20. International Union of Pure and Applied Chemistry, Interna- in medizinischen Laboratorien. 2015;6:1-41. Available at: tional Federation of Clinical Chemistry. Properties and units http://iacld.ir/DL/elm/94/guidelinesofthegermanmedicala- in the laboratory sciences. Part X. Properties and units in ge- ssociationonqualityassuranceinmedicallaboratorytesting. neral clinical chemistry. Pure Appl Chem. 2000;72:747-972. pdf. Accessed August 15th 2020. https://doi.org/10.1351/pac200072050747 32. Braga F, Panteghini M. Defining permissible limits for the 21. Regulation (EU) 2017/746 of the European Parliament and combined uncertainty budget in the implementation of me- of the Council of 5 April 2017 on in vitro diagnostic medical trological traceability. Clin Biochem. 2018;57:7–11. https:// devices and repealing Directive 98/79/EC and Commission doi.org/10.1016/j.clinbiochem.2018.03.007 Decision 2010/227/EU, Official Journal of the European Uni- 33. Haeckel R, Wosniok W, Gurr E, Peil B. Permissible limits for on, L117/176-332. uncertainty of measurement in laboratory medicine. Clin 22. Farrance I, Frenkel R, Badrick T. ISO/TS 20914:2019 – a cri- Chem Lab Med. 2015;53:1161–71. https://doi.org/10.1515/ tical commentary. Clin Chem Lab Med. 2020;58:1182–90. cclm-2014-0874 https://doi.org/10.1515/cclm-2019-1209 34. European Federation of Clinical Chemistry and Laboratory 23. Fuentes-Arderiu X, González-de-la-Presa B. Interchange- Medicine (EFLM). EFLM biological variation database. Ava- ability of estimates of day-to-day imprecision between ilable at: https://biologicalvariation.eu/. Accessed August commercial control materials and serum pools. Clin Chem. 15th 2020. 2002;48:573–4. https://doi.org/10.1093/clinchem/48.3.573 35. Fuentes-Arderiu X, Rigo-Bonnin R. Maximum permissible 24. Frenkel R, Farrance I, Badrick T. Bias in analytical chemi- day-to-day imprecision and ISO 15189. Accred Qual Assur. stry: a review of selected procedures for incorporating un- 2006;11:593–4. https://doi.org/10.1007/s00769-006-0166-0 corrected bias into expanded uncertainty of analyti- 36. Clinical Laboratory Improvement Amendments (CLIA). cal measurements and a graphical method for evalua- Requirements for Analytical Quality. Available at: https:// ting the concordance of reference and test procedures. Clin www.westgard.com/clia.htm. Accessed August 15th 2020. Chim Acta. 2019;495:129–38. https://doi.org/10.1016/j. 37. Caudill SP, Cooper GR, Smith SJ, Myers GL. Assessment of cca.2019.03.1633 current National Cholesterol Education Program guideli- 25. Ceriotti F. Deriving proper measurement uncertainty from nes for total cholesterol triglyceride, HDL-cholesterol, and internal quality control data: An impossible mission? Clin LDL-cholesterol measurements. Clin Chem. 1998;44:1650– Biochem. 2018;57:37–40. https://doi.org/10.1016/j.clinbio- 8. https://doi.org/10.1093/clinchem/44.8.1650 chem.2018.03.019 38. European Medicines Agency (EMA). Guideline on bioanalyti- 26. International Organization for Standardization (ISO). Sta- cal method validation. EMEA/CHMP/EWP/192217/2009; tistical methods for use in proficiency testing by interlabo- 2011. Available at: https://www.ema.europa.eu/en/docu- ratory comparisons. ISO 13528. Geneva, Switzerland: ISO; ments/scientific-guideline/guideline-bioanalytical-met- 2005. hod-validation_en.pdf. Accessed August 15th 2020. 27. Sandberg S, Fraser CG, Horvath AR, Jansen R, Jones G, Oo- 39. Joint Committee for Guides in Metrology (JCGM). JCTLM da- sterhuis W, et al. Defining analytical performance specifica- tabase: Laboratory medicine and in vitro diagnostics. Ava- tions: Consensus Statement from the 1st Strategic Confe- ilable at: https://www.bipm.org/jctlm/. Accessed August rence of the European Federation of Clinical Chemistry and 15th 2020. Laboratory Medicine. Clin Chem Lab Med. 2015;53:833–5. 40. United States Food & Drug Administration (FDA). Devices@ https://doi.org/10.1515/cclm-2015-0067 FDA. Available at: https://www.accessdata.fda.gov/scripts/ 28. Cooper G, De Jonge N, Ehrmeyer S, Yundt-Pacheco J, Jan- cdrh/devicesatfda/index.cfm. Accessed August 15th 2020. sen R, Ricós C, et al. Collective opinion paper on findings of the 2010 convocation of experts on laboratory quality. Clin Chem Lab Med. 2011;49:793–802. https://doi.org/10.1515/ cclm.2011.149 Biochem Med (Zagreb) 2021;31(1):010501 https://doi.org/10.11613/BM.2021.010501 12