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# Clinical Chemistry and Laboratory Medicine (CCLM)

### Published in Association with the European Federation of Clinical Chemistry and Laboratory Medicine (EFLM)

Editor-in-Chief: Plebani, Mario

Ed. by Gillery, Philippe / Greaves, Ronda / Lackner, Karl J. / Lippi, Giuseppe / Melichar, Bohuslav / Payne, Deborah A. / Schlattmann, Peter

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# Optimizing the use of the “state-of-the-art” performance criteria

Rainer Haeckel
/ Werner Wosniok
/ Thomas Streichert
Published Online: 2015-03-20 | DOI: https://doi.org/10.1515/cclm-2014-1201

## Abstract

The organizers of the first EFLM Strategic Conference “Defining analytical performance goals” identified three models for defining analytical performance goals in laboratory medicine. Whereas the highest level of model 1 (outcome studies) is difficult to implement, the other levels are more or less based on subjective opinions of experts, with models 2 (based on biological variation) and 3 (defined by the state-of-the-art) being more objective. A working group of the German Society of Clinical Chemistry and Laboratory Medicine (DGKL) proposes a combination of models 2 and 3 to overcome some disadvantages inherent to both models. In the new model, the permissible imprecision is not defined as a constant proportion of biological variation but by a non-linear relationship between permissible analytical and biological variation. Furthermore, the permissible imprecision is referred to the target quantity value. The biological variation is derived from the reference interval, if appropriate, after logarithmic transformation of the reference limits.

## Introduction

The organizers of the first EFLM Strategic Conference “Defining analytical performance goals” identified three models for defining analytical performance goals in laboratory medicine. Whereas the highest level of model 1 (outcome studies) is difficult to implement, the other levels are more or less based on subjective opinions of experts, with models 2 (based on biological variation) and 3 (defined by the state-of-the art) being more objective. The benefits and disadvantages of models 2 and 3 have already been discussed elsewhere [1, 2].

Problems with the biological variation model are the large variability between studies (e.g., 2.3%–31.9% for triglycerides [3]), data are often generated from relatively young and healthy subjects, dependence on the time span studied (hours to years), and possible effects of measurand concentrations. Owing to the great diversity of literature reports, many authors consider biological variation not suited to set metrological requirements. Problems with the state-of-the-art model are lack of scientific reasoning, often based on “old” data, which may be outdated, lack of transparency, lack of neutrality (dependency on industry), and the lack of relationship between what is achievable and what is needed clinically.

A working group of the German Society of Clinical Chemistry and Laboratory Medicine (DGKL) has developed a combination of models 2 and 3 to overcome some disadvantages inherent to both models [2].

## New concept for defining permissible performance criteria

Three types of biological variation (CVB) have been described: (1) intra-individual variation (CVI), (2) inter-individual variation (CVG), and (3) combined CVB (combined CVI and CVG). As a surrogate for the biological variation [2], the empirical (biological) coefficient of variation (CVE) has been proposed [1, 2]. According to Simundic et al. [4], CVE could be termed CVA+I+G.

The empirical biological variation CVE derived from the reference interval (RI) was proposed because laboratories are obliged to provide RI for all measurands, must check their transferability (if taken from external sources), and should review the RI periodically as required by ISO 15189 [5]. Furthermore, reference limits (RL) usually vary less than data on biological variation in the literature and often are from consensus groups.

RLs reflect the biological variations, including the analytical variation. If values are normally distributed, the empirical (biological) standard deviation, sE, can be estimated by (upper RL–lower RL)/3.92 [2]. However, a “true” empirical normal distribution does not exist in laboratory medicine. For small reference ranges and relatively high mean values (e.g., sodium and chloride concentrations in plasma or hematological quantities), the distribution usually looks close to “normal”, but a log-normal distribution has the same shape under these conditions. For relatively large reference ranges (e.g., thyreotropin, triglycerides, enzymes in plasma), it is obvious that the data are not normally distributed. Generally, it may be assumed that laboratory data follow a power normal distribution, i.e., (xλ–1)/λ has a normal distribution, where the coefficient λ controls the shape of the distribution. Important special cases are λ=1, indicating a normal distribution, and λ=0, the lognormal distribution. The λ value for a specific data set can be estimated by numerical methods.

If λ is unknown and cannot be estimated from data, e.g., because only RLs are given, but there are no individual values, the assumption of a logarithmic distribution was recommended [6]. Assuming a lognormal distribution, the empirical standard deviation (sE) is calculated from the lower reference limit (RL1) and the upper reference limit (RL2) by Eq. (1), as recently explained [2]:

$sE,ln=(lnRL2−lnRL1)/3.92. (1)$(1)

Then, the CVE of a logarithmic normal distribution expressed on the linear scale (CVE*) can be calculated from Eq. (1), as explained in the Appendix:

$CVE∗=(exp(sE,ln2)−1)0.5⋅100. (2)$(2)

CVE* can be considered as a surrogate for the conventional biological variation (CVB), although it also contains the analytical variation. The CVE* values were compared (Figure 1) with the combined CVB values [CVB=(CVI2+CVG2)0.5] for 64 quantities (in blood, serum, and plasma) listed in the RiliBÄK [8]. The CVB data were taken from Ricos et al. [7]. Although this list is already very comprehensive, CVB data are available for only 80% of the RiliBÄK measurands. As shown in Figure 1, CVB and CVE* correlate quite well. The greatest divergences (above the regression line=black line in Figure 1) are obtained with C-reactive protein, CA 19-9, and prostate-specific antigen (PSA). In the Ricos et al. [7] list, a relatively high CVG value of 130% is presented for CA 19-9. Erden et al. [9] more recently published a CVG=64.2%, a value that appears more realistic. In Table 1, the intra-individual biological variation (CVI) of PSA is compared from several reports. The most comprehensive survey was published by Söletormos et al. [10] on behalf of the European Group on Tumor Markers. The CVI values from 13 studies varied between 2.1% and 22.9%. These large differences between studies make a choice of the correct CVB value difficult. Ricos et al. [7] selected a CVI=18.1, whereas a CVI of about 13% (close to the mean of the reported span) would correlate with the CVE* quite well.

Figure 1:

Comparison of CVE* values with combined CVB values taken from Ricos et al. [7].

PSA, prostate-specific antigen; CRP, C-reactive protein.

Table 1:

The intra-individual variability of plasma PSA reported by several researchers.

The empirical biological variation CVE* derived from the reference range can be applied to derive permissible analytical uncertainty and to determine quantity quotients standardizing reporting laboratory results.

## Proposal for determining permissible analytical uncertainty

Various approaches have been presented to define permissible analytical uncertainty as a proportion of biological variation. Cotlove et al. [16] proposed to multiply CVB with a constant factor of 0.5. Fraser [11] suggested a three-class model with factors 0.25, 0.5, and 0.75, and Haeckel and Wosniok [1] suggested a five-class model. All models use more or less arbitrary factors. If permissible limits derived of the present state-of-the-art [root-mean-square of measurement deviation (RMSD) in Figure 2] are compared with biological variation data (CVE*), a curved relationship may be observed (analog to the curved line in Figure 2). With the Cotlove et al. [16] model (analog to the straight line in Figure 2), too stringent requirements are postulated, which can hardly be reached by the present technology for measurands with relatively small CVE* values. For measurands with larger biological variation, the requirements may be too permissive. The curved relationship for the present technology can be simply described by Eq. (3):

Figure 2:

Comparison of empirical biological variation (CVE*) with permissible analytical variation derived of the present state of the art (technical feasibility). RMSD (circles), root-mean-square measurement deviation (column 3 of Table 2a of the German Guideline 2008); straight line, 0.5·CVE* line; diamonds, present proposal.

$pCVA=(CVE∗−0.25)0.5. (3)$(3)

This equation approximately describes the empirical relation between CVE* and the major part of the presently used permissible imprecision values. Eq. (3) describes a curved relation between permissible analytical CV (pCVA) and CVE*. It can be easily adapted to future technical improvements by modifying its parameters. The exponent in Eq. (3) may be reduced from 0.5 to, e.g., 0.45 if one wishes more stringent permissible limits.

An algorithm to estimate pCVA values for a single target or measured values has been recently proposed [2].

## Permissible limits for combined and expanded measurement uncertainty

Three types of measurement uncertainty supported by many international organizations (BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, and OIML) are described in the Guide to the Expression of Uncertainty in Measurement [17]: standard uncertainty uS (imprecision, standard deviation), combined uncertainty uC (u12+u22+u32)0.5, and expanded uncertainty U=kuC (if coverage factor k=1.96, the level of confidence is 95%). In laboratory medicine, at least two components have to be combined, imprecision and bias.

The permissible uncertainty (of measurement) can be given by Eq. (3), e.g., u1 in uC. For permissible bias (pB) (e.g., u2 in uC), 0.5·pCVA was previously suggested [2]. According to the GUM concept [17], an uncertainty component should be added for which also 0.5·pCVA was proposed [2]:

$pB=(0.5 pCVA2+0.5 pCVA2)0.5=0.7⋅pCVA. (4)$(4)

Then, the permissible limit of uC is (pCVA2+pB2)0.5:

$uC=1.22⋅pCVA.$

Considering a 95% probability of uC, the expanded uncertainty can be calculated by Eq. (5):

$pU%=1.96⋅puC=2.39⋅pCVA, (5)$(5)

where pU% corresponds to the RMSD value of the RiliBÄK 2008 [8, column 3 in Table B1a]. The pU% in relation to CVE* values were compared with the RMSD for several measurands (Figure 2). Mean limits for 64 plasma quantities were about 5% lower than those required by the new RiliBÄK [8]. The straight line represents the 0.5 multiplication factor for the biological variation as proposed by Fraser [11]. The problem with this more or less arbitrary classification is the difficulty to which a single measurand may be attributed. The expanded uncertainty also leads to a curved relation with CVE* (like pCVA vs. CVE*).

## Permissible limits for ring trials (EQAS)

Recently, we have proposed that permissible limits in external quality assessment schemes (EQAS) may be derived of pCVA, respectively, of pU% values [18]. Analogous to this approach, the 90% interval of the permissible limits for EQAS may be

$pUEQAS%=1.64⋅pU%=3.92⋅pCVA (6)$(6)

and the 95% interval may be

$pUEQAS%=1.96⋅pU%=4.68⋅pCVA. (7)$(7)

Examples for the various permissible uncertainties were recently published [2]. Mean limits for 64 plasma quantities were similar to those required by the new RiliBÄK [8].

## Discussion

The empirical (biological) variation (CVE*) derived from the reference range is suggested as a surrogate for the biological variation. RLs are available to all measurands, and most probably, the laboratories have more experience with these data because they have to validate them before their introduction in the diagnostic service and then to verify them periodically according to good laboratory practice [5]. CVE* values can be used to derive permissible uncertainty by algorithms that may reconcile the presently competing biological variation model and the state-of-the-art model.

Although CVE values correlate quite well with biological variation data (Figure 1), they combine intra- and inter-individual variations (CVC). The relation between both is not constant. The better choice would be to use only CVI data. Presently, however, these data vary considerably in the literature (see example presented in Table 1). Therefore, several authors refused to use CVI to derive permissible performance criteria [1, 2, 19]. The application of CVE data may be an acceptable compromise until more reliable data on intra-individual variations are available. Furthermore, CVE data vary between laboratories.

The working group “Guide limits” of the DGKL developed easily to handle Excel tools for the estimation of RIs from intra-laboratory data pools and the estimation of the permissible uncertainty. These tools are distributed gratuitously, e.g., via website of the DGKL [20] or from the authors and could be implemented by software companies in their information systems.

## Appendix

Estimation of CVE*

1. Assuming a logarithmic normal distribution for the measurand, the biological standard deviation derived of the RLs is on the logarithmic scale

$sE,ln=(lnRL2−lnRL1)/3.92.$

2. The mean on the logarithmic scale is

$meanln=(lnRL2+lnRL1)/2.$

3. The corresponding mean on the linear scale is [21]

$meanlin=exp(meanln+0.5∗sE,ln2).$

However, this mean is not needed to calculate CVE*, as is shown below.

4. sE,ln can be transformed to the linear scale according to Aitchison and Brown [21]:

$sE,lin=meanlin⋅(exp(sE,ln2)−1)0.5.$

5. CVE*=sE,lin·100/meanlin.

6. CVE*=meanlin·(exp sE,ln2–1)0.5·100/meanlin.

7. CVE*=(exp(sln2)–1)0.5·100.(2)

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

Financial support: None declared.

Honorarium: None declared.

Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication.

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Corresponding author: Rainer Haeckel, Bremer Zentrum für Laboratoriumsmedizin, Klinikum Bremen Mitte, 28305 Bremen, Germany, Phone: +49 412 273448, E-mail:

Accepted: 2015-02-09

Published Online: 2015-03-20

Published in Print: 2015-05-01

Citation Information: Clinical Chemistry and Laboratory Medicine (CCLM), Volume 53, Issue 6, Pages 887–891, ISSN (Online) 1437-4331, ISSN (Print) 1434-6621,

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