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Journal of Chromatography A, 1163 (2007) 237–246

A bottom-up approach in estimating the measurement uncertaintyand other important considerations for quantitative analyses

in drug testing for horses

Gary N.W. Leung ∗, Emmie N.M. Ho, W. Him Kwok, David K.K. Leung,Francis P.W. Tang, Terence S.M. Wan ∗∗, April S.Y. Wong,

Colton H.F. Wong, Jenny K.Y. Wong, Nola H. YuRacing Laboratory, The Hong Kong Jockey Club, Sha Tin Racecourse, Sha Tin, N.T., Hong Kong, China

Received 9 January 2007; received in revised form 4 June 2007; accepted 12 June 2007Available online 27 June 2007

bstract

Quantitative determination, particularly for threshold substances in biological samples, is much more demanding than qualitative identification.proper assessment of any quantitative determination is the measurement uncertainty (MU) associated with the determined value. The International

tandard ISO/IEC 17025, “General requirements for the competence of testing and calibration laboratories”, has more prescriptive requirementsn the MU than its superseded document, ISO/IEC Guide 25. Under the 2005 or 1999 versions of the new standard, an estimation of the MU isandatory for all quantitative determinations. To comply with the new requirement, a protocol was established in the authors’ laboratory in 2001.he protocol has since evolved based on our practical experience, and a refined version was adopted in 2004. This paper describes our approach instablishing the MU, as well as some other important considerations, for the quantification of threshold substances in biological samples as appliedn the area of doping control for horses. The testing of threshold substances can be viewed as a compliance test (or testing to a specified limit). Asuch, it should only be necessary to establish the MU at the threshold level. The steps in a “Bottom-Up” approach adopted by us are similar to thoseescribed in the EURACHEM/CITAC guide, “Quantifying Uncertainty in Analytical Measurement”. They involve first specifying the measurand,ncluding the relationship between the measurand and the input quantities upon which it depends. This is followed by identifying all applicablencertainty contributions using a “cause and effect” diagram. The magnitude of each uncertainty component is then calculated and converted tostandard uncertainty. A recovery study is also conducted to determine if the method bias is significant and whether a recovery (or correction)

actor needs to be applied. All standard uncertainties with values greater than 30% of the largest one are then used to derive the combined standard

ncertainty. Finally, an expanded uncertainty is calculated at 99% one-tailed confidence level by multiplying the standard uncertainty with anppropriate coverage factor (k). A sample is considered positive if the determined concentration of the threshold substance exceeds its thresholdy the expanded uncertainty. In addition, other important considerations, which can have a significant impact on quantitative analyses, will beresented.

2007 Elsevier B.V. All rights reserved.

e anal

o

eywords: Threshold substance; Horse; Measurement uncertainty; Quantitativ

. Introduction

The International Standard ISO/IEC 17025 [1], “Generalequirements for the competence of testing and calibration lab-

∗ Corresponding author. Tel.: +52 2966 6469; fax: +852 2601 6564.∗∗ Co-corresponding author. Tel.: +52 2966 6296; fax: +852 2601 6564.

E-mail addresses: gary.nw.leung@hkjc.org.hk (G.N.W. Leung),erence.sm.wan@hkjc.org.hk (T.S.M. Wan).

mGddrsaor

021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2007.06.035

yses; ISO/IEC 17025

ratories”, has more prescriptive requirements on the measure-ent uncertainty (MU) than its superseded document, ISO/IECuide 25. Under the 2005 or 1999 versions of the new stan-ard, an estimation of the MU is mandatory for all quantitativeeterminations. In doping control for horses, the authors’ labo-atory performs quantitative analyses on threshold substances as

tipulated under the provisions of Article 6 of the Internationalgreement on breeding, racing and wagering [2]. For these meth-ds, the MU must be determined in order to meet accreditationequirements. Normally, the MU refers to a concentration range

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38 G.N.W. Leung et al. / J. Chr

ssigned to a measured value within which the measurand’s truealue is expected to lie with a defined probability (or confidenceevel). As the MU often varies with the concentration of the

easurand [3,4], it might be necessary to establish its value forifferent concentration levels within the calibration range. Inhe case of threshold substances, this can be simplified by deter-

ining the MU at the threshold concentration only. Samplesith measurand values greater than the threshold plus the MU

re considered to have the measured concentration exceeded thehreshold with a known confidence level. The same approach ofdding the MU to the threshold, often referred to as the ‘Decisionimit’, to establish a doping offence has also been adopted in theuman sports testing field [5,6]. For a threshold substance, there-ore, the MU normally quoted pertains to the threshold value.

Broadly speaking, there are two approaches in estimatinghe MU, namely the “Top-Down” and “Bottom-Up” methods7]. Examples for these two approaches can be found in theManual on Quality Assurance and ISO/IEC 17025 Accredi-

ation” issued by the Association of Official Racing Chemists8]. For the “Top-Down” approach, the methodology is consid-

red as a whole and the major sources of uncertainty (such asnalyte recovery, reproducibility, matrix effect, etc.) are iden-ified and evaluated. Sources with significant contributions arehen included to derive the MU. The “Bottom-Up” approach is

atmfl

Fig. 1. A schematic diagram outlining the procedures fo

gr. A 1163 (2007) 237–246

ased on statistical and metrological methods where all conceiv-ble sources of uncertainty are systematically evaluated. In theuthors’ laboratory, a “Bottom-Up” protocol for estimating theU was established initially in 2001. The protocol has since

volved based on our practical experience, and a refined ver-ion was adopted in 2004. This paper provides a step-by-stepllustration of our “Bottom-Up” approach using an internationalhreshold substance testosterone (20 ng/mL free and conjugatedestosterone) in gelding urine as an example [2]. While detailedquations and statistical principles used for calculating individ-al uncertainty components are outside the scope of this paper,ome critical calculations and equations are given to facilitate thenderstanding of the “Bottom-Up” approach. In addition, othermportant considerations that can have a significant impact onuantitative analyses will be presented.

. Experimental procedures

In order to provide better understanding of our “Bottom-p” approach in constructing a “cause and effect” diagram and

ccount for all significant uncertainty components, the prepara-ion of calibrators and spiked samples and the sample processing

ethod are detailed below. In addition, a schematic diagram inowcharting the steps of the method is shown in Fig. 1.

r the quantification of testosterone in equine urine.

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G.N.W. Leung et al. / J. Chro

.1. Preparation of calibration standard solution (Solution—2 μg/mL testosterone in methanol) and calibrators

All testosterone standards used for the preparation oftandard solutions were dried in a vacuum oven at 50 ◦C forh before weighing. About 10 mg of oven-dried testosterone

tandard (USP, Rockville, MD, USA) was accurately weighedn a 100-mL volumetric flask (Flask A) and diluted to the markith methanol (Stock Solution A). At the time of analysis,Standard Solution B (2 �g/mL) was prepared by pipetting

Pipette 1) the required volume (∼2 mL) of Stock Solution Anto a 100-mL volumetric flask (Flask B) and diluted to the

ark with methanol. Aliquots of Standard Solution B (0, 10, 20,0, 60 and 80 �L) were pipetted (Pipette 2) to 2-mL portionsf XAD-treated urine (filtered blank gelding urine havingeen stirred with XAD-16 Amberlite resin) to give duplicatealibrators at 0, 10, 20, 40, 60 and 80 ng/mL respectively.AD-treated urine was used to prepare the calibrators because

t is extremely difficult to obtain testosterone-free horse urineue to the endogenous nature of testosterone.

.2. Preparation of spiked control samples for establishinghe control charts and for quality control at the time ofnalysis

About 10 mg of oven-dried testosterone triethylammoniumulfate standard (NMI, Pymble, Australia) was accuratelyeighed in a 10-mL volumetric flask and diluted to the mark withethanol to prepare a stock solution equivalent to ∼0.5 mg/mL

f free testosterone (TS-QC-A). The required volume of TS-QC-was then pipetted into a 10-mL volumetric flask and diluted

o the mark with methanol to give another stock solution equiva-ent to 100 �g/mL of free testosterone (TS-QC-B). The requiredolume (100 �L) of TS-QC-B was then pipetted into a 500-mLolumetric flask and diluted to the mark with XAD-treated urineo give a spike control sample at a final concentration equivalento 20 ng/mL of free testosterone. Five-milliliter portions of thepiked control sample were transferred to capped plastic tubesnd stored in a freezer at below −60 ◦C. One portion was thawedt the time of analysis to be run in parallel with the test samplesn duplicate (in 2-mL aliquots).

.3. Preparation of spiked samples for recovery study

The same testosterone standard solution used to prepare thepiked controls samples was used for preparing samples for theecovery study. TS-QC-B (100 �L) was pipetted into a 10-mLolumetric flask and diluted to the mark with methanol to prepare“1 �g/mL free testosterone” stock solution (TS-QC-C). Each

piked sample was then prepared by pipetting 40 �L of TS-C-C into 2 mL of untreated blank gelding urine to give a final

oncentration of free testosterone equivalent to 20 ng/mL of freeestosterone.

.4. Sample processing procedures

Each analytical batch comprised a set of testosterone calibra-ors in duplicate, a urine blank, samples in duplicate and spiked

ur(h

gr. A 1163 (2007) 237–246 239

ontrols in duplicate. Urine (2 mL; Pipette 3) was added withn internal standard d3-testosterone (20 ng/mL) and then loadednto a C18-Sep-Pak cartridge, which had been pre-conditionedith methanol (5 mL) and deionised water (5 mL × 2). The

oaded cartridge was rinsed with deionised water (5 mL × 2)nd n-hexane (5 mL) and then eluted with methanol (3 mL). Theluate was evaporated to dryness at 60 ◦C under a stream of nitro-en. Anhydrous methanolic hydrogen chloride (1 M, 0.5 mL)as added and the solution was heated at 60 ◦C for 10 min.iisopropyl ether (3.0 mL) was added and the mixture was trans-

erred to a 15-mL graduated centrifuge tube. The organic extractas base washed (2.0 mL; 1 M sodium hydroxide and 0.15 M

odium chloride) and centrifuged (3000 rpm for 0.5 min). Therganic layer was passed through an anhydrous sodium sul-ate drying tube and then evaporated to dryness at 60 ◦C under

stream of nitrogen. The residue was reconstituted in ethylcetate (50 �L) and loaded onto a Supelclean LC-Si normal-hase extraction cartridge, which had been pre-conditioned withhloroform/ethyl acetate (3 mL; 1:1, v/v). The loaded cartridgeas eluted with chloroform/ethyl acetate (3 mL; 1:1, v/v). Therst 0.5 mL of eluate was discarded. The next 2.5 mL of eluateas collected and evaporated to dryness at 60 ◦C under a streamf nitrogen. The residue was then derivatised with pentafluoro-ropionic acid anhydride (PFPA) and transferred to a conicalnsert in a Chrompack autosampler vial for GC/MS analysis.

. Establishing measurement uncertainty

.1. STEP 1: Establish relationship between the measurandnd the input quantities

The first step in MU evaluation is to define the relationshipetween the measurand (in this case testosterone) and the inputuantities it depends on (Eq. (1)).

T = PT/IS − c

δp/δc× 1

R(1)

here CT = concentration of testosterone in the test sample,T/IS = peak area ratio of testosterone and IS (d3-testosterone)

or the test sample, (�p/�c) = change in GC/MS response (areaatio), �p as a function of calibrator concentration, �c = slope ofhe linear regression curve, c = Y-intercept of the linear regres-ion curve and R = recovery factor.

.2. STEP 2: Identifying all applicable uncertaintyontributions using “cause and effect” diagrams

The next step is to identify all conceivable sources of uncer-ainty by using a “cause and effect” diagram as a tool. Basedn Eq. (1), the concentration of testosterone (CT) is related tohree quantities, namely (PT/IS − c), (�p/�c) and R. A “causend effect” diagram is established with these three factors as theain branches of uncertainty (Fig. 2a). The next step is to eval-

ate each of these main uncertainty branches to identify otherelevant uncertainty sources (Fig. 2b). The uncertainty branch�p/�c), which represents the slope of the calibration curve, willave uncertainty contributions from the preparation of the cal-

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40 G.N.W. Leung et al. / J. Chr

brators, whereas the uncertainty for the (PT/IS − c) branch isainly contributed from the preparation of test sample. For the

ecovery branch, there are two main uncertainty sources, namelyethod recovery and sample recovery [9]. The former is due to

he uncertainty associated with the sample-processing method,hereas the latter is from the uncertainty associated with sample-

o-sample matrix variation. Fig. 2b is then rearranged to obtainig. 2c. The uncertainty contributions for the “preparation of testample” and “preparation of calibrators” branches in Fig. 2c can

e identified from their corresponding experimental proceduresFig. 2d). To avoid double counting, uncertainty sources withhe same nature can be grouped together under the same branch.or example, the method precision is always a major source of

sntd

Fig. 2. (a–f) “Cause and effect” diagrams for establishing measurem

gr. A 1163 (2007) 237–246

ncertainty in any quantification method. A new “method pre-ision” branch is therefore included in the “cause and effect”iagram (Fig. 2e). Uncertainty sources such as the precision ofolumetric glassware and the effect of temperature change onolvent expansion are already covered by the method precision.herefore, these can be consolidated under the method precisionranch, resulting in a simpler “cause and effect” diagram. Forome of the procedures that are not required to perform in everynalysis such as the preparation of the primary standard stock

olution, all those uncertainty contributions from precision can-ot be grouped under the method precision branch (in this case,he preparation of Stock Solution A). A final “cause and effect”iagram is shown in Fig. 2f.

ent uncertainty for the quantification of testosterone in urine.

G.N.W. Leung et al. / J. Chromatogr. A 1163 (2007) 237–246 241

Fig. 2. (Continued ).

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42 G.N.W. Leung et al. / J. Chr

.3. STEP 3: Determine the magnitude of the identifiedncertainty components

Based on the final “cause and effect” diagram, the magnitudef all identified uncertainty components are calculated usinghe appropriate equations and statistical principles [9–11]. Thedentified uncertainty sources and their corresponding standardncertainties are summarised in Table 1. Critical calculationsnd equations are listed in Table 2.

.4. STEP 4: Recovery study

The purpose of the recovery study is to determine if theethod bias is significant and whether a recovery factor (R)

wnld

able 1summary of all contributing uncertainty factors and their corresponding standard u

ncertainty in the preparation of the calibrators (UCal)UFA-bias Uncertainty in volume due to the accuracy of the

(Flask A).UFA-precision Uncertainty in volume due to the precision of the

(Flask A).UFA-temp Uncertainty in volume due to temperature variati

UFlaskA Uncertainty of the flask (Flask A) in preparing “S(100 mL).[Derived from UFA-bias, UFA-precision and UFA-temp

Ub-bias Uncertainty of the calibration of the balance (limUb-precision Uncertainty in repeatability of weighing of the b

Ubal Uncertainty of the balance.[Derived from Ub-bias and Ub-precision.]

Upurity Uncertainty of the purity of testosterone standardUWeight Uncertainty of weighing of testosterone (mass of

[Derived from Upurity and Ubal.]UStdA Uncertainty of the concentration of “Stock Solut

[Derived from UFlaskA and UWeight.]UPipette 1 Uncertainty (bias only) of Pipette 1 in transferrin

A” to the volumetric flask.UFlaskB Uncertainty (bias only) of the flask (Flask B) in p

“Standard Solution B” (100 mL).UStdB Uncertainty of the concentration of “Standard So

[Derived from UStdA, UPipette 1 and UFlaskB.]UPipette 2 Uncertainty (bias only) of Pipette 2 in transferrin

Solution B” to 2 mL of XAD-treated urine for prcalibrators.

UCal Uncertainty in the preparation of the calibrators[Derived from UStdB and UPipette 2.]

ncertainty in the preparation of the test sample (UTest-Sample)UPipette 3 Uncertainty (bias only) of Pipette 3 in transferrin

sample.UTest-Sample Uncertainty in the preparation of test sample

[Derived from UPipette 3.]

ncertainty in the method precision (UPrecision)UPrecision This data is derived by analysing 20 spiked contr

duplicate each (control chart).ncertainty in recovery (URecovery)URm Uncertainty of recovery due to the extraction pro

instrumentation of the method. This data is derivrecovery study.

URs Uncertainty of recovery due to matrix variation.derived from the recovery study.

URecovery Uncertainty in recovery.

gr. A 1163 (2007) 237–246

eeds to be applied to the final testosterone value (Eq. (1)). Athe same time, the uncertainty (UR) associated with R is alsoetermined. There are two uncertainty sources for UR, namelyhe recovery uncertainty due to the sample processing methodURm) and that due to variation in sample matrices (URs), ashown in Eq. (2).

R = URm + URs (2)

Our approach in recovery studies is to analyse five sets of dif-erent urine samples with each set in hexaplicate (n = 6) spiked

ith the target analyte (in this case testosterone triethylammo-ium sulfate, but the measurand is testosterone) at the thresholdevel. Five sets of calibrators are also prepared using the fiveifferent urine matrices. A total of 30 spiked samples are anal-

ncertainties (SU) and relative standard uncertainties (RSU)

SU RSU

volumetric flask 0.0924 mL –

volumetric flask 0.0355 mL –

on (Flask A). 0.115 mL –tock Solution A” 0.152 mL 0.00152

.]it of performance) 0.135 mg –alance 0.02 mg –

0.136 mg 0.0136

. 0 0testosterone). 0.136 mg 0.0136

ion A”. 1.37 �g/mL 0.0137

g “Stock Solution 6.53 �L 0.00327

reparing 0.0924 mL 0.000924

lution B” 0.0282 �g/mL 0.0141

g “Standardeparing the

0.577 �L 0.0289

0.642 ng/mL 0.0321

g 2.0 mL of urine 6.53 �L 0.00327

0.0654 ng/mL 0.00327

ol samples in 1.34 ng/mL 0.0654

cedures anded from the

0.0292 –

This data is 0.0405 –

0.0500 0.0509

G.N

.W.L

eungetal./J.C

hromatogr.A

1163(2007)

237–246243

Table 2A summary of critical calculations and equations for deriving the uncertainties of all contributing factorsParameter Value Uncertainty range SU (Note 1) RSU (Note 1) Remarks

Uncertainty in the preparation of the calibrators (UCal)UFA-bias 100 mL ±0.16 mL 0.0924 mL – SU = 0.16/

√3 (Note 2).

UFA-precision 100 mL – 0.0355 mL – SU obtained from 10 repeated fillings using a 100-mL volumetric flask and weigh each filling tocalculate the standard deviation.

UFA-temp 100 mL ±0.2 mL 0.115 mL – Ambient temperature specification is ±2 ◦C; coefficient of expansion of MeOH = 1 × 10−3 ◦C−1

(uncertainty range = 100 × 2 × (1 × 10−3) = 0.2 mL; SU = 0.2/√

3).UFlaskA = SUFlaskA = √

(SU2FA-bias

+ SU2FA-precision

+ SU2FA-temp) = 0.152 mL (Note 3); RSUFlaskA = 0.152 mL/100 mL = 0.0152

Ub-bias 10 mg – 0.135 mg – SU = limit of performance of the analytical balance.Ub-precision 10 mg – 0.02 mg – SU obtained from 10 repeated weighing of a 10 mg standard mass to calculate the standard deviation.

Ubal = SUbal = √(SU2

b-bais+ SU2

b-precision) = 0.136 mg; RSUbal = 0.136 mg/10 mg = 0.0136

Upurity 1 – 0 0 Assume 100% purity (USP Certified Reference Material).RSUweight = √

(RSU2Purity

+ RSU2bal

) = 0.0136; Uweight = SUweight = 0.0136 × 10 mg = 0.136 mg

RSUStdA = √(RSU2

FlaskA+ RSU2

weight) = 0.0137(Note 4); UStdA = SUStdA = 0.0137 × 100 μg/mL = 1.37 μg/mL

UPipette 1 1 mL (1000 �L) ±8.0 �L 4.62 �L – SUPipette 1 (1 mL) = 8.0/√

3.2 mL (2000 �L) – 6.53 �L 0.00327 SUPipette 1(2 mL) = √

(2 × SU2Pipette 1(1 mL)

.

RSUPipette 1 (2 mL) = 6.53 �L/2000 �L (Note 5).UFlaskB 100 mL ±0.16 mL 0.0924 mL 0.000924 SU = 0.16/

√3.

RSUStdB = √(RSU2

StdA+ RSU2

Pipette 1 (2 mL)+ RSU2

FlaskB) = 0.0141; UStdB = SUStd0.0141 × 2 μg/mL = 0.0282 μg/mL

UPipette 2 20 �L (10–80 �L) ±1.0 �L 0.577 �L 0.0289 SU = 1.0/√

3.RSUCal = √

(RSU2StdB

+ RSU2Pipette 2

) = 0.0321; UCal = SUCal = 0.0321 × 20 ng/mL = 0.642 ng/mL

Uncertainty in the preparation of the test sample (UTest-Sample)UPipette 3 2 mL (2000 �L) – 6.53 �L 0.00327 Same calculation as UPipette 1.

RSUTest-Sample = RSUPipette 3 = 0.0037; UTest-Sample = RSUTest-Sample × 20 ng/mL = 0.00327 × 20 ng/mL = 0.0654 ng/mL

Uncertainty in method precision (UPrecision)UPrecision 20.49 ng/mL – 1.34 ng/mL 0.0654 Mean of 20 spiked control samples (in duplicate each) = 20.49 ng/mL.

Standard deviation of mean obtained from 20 spiked control samples (in duplicateeach) = SUPrecision = 1.34 ng/mL.

Uncertainty in recovery (URecovery)

URm Method recovery (Rm) = Observed value

Certified value.

URm = Rm ×

√(UCobs

Cobs

)2

+(

USpike

CSpike

)2

(Note 4).

URm(SU) = 0.9817 ×√(

0.4490

19.63

)2

+(

0.3809

20

)2

= 0.0292

[Refer to “STEP 4: Recovery study” for detailed explanation.]URs URs (SU) = standard deviation of mean recovery = 0.0405 (refer to Table 2).

URecovery = SURecovery = √(U2

Rm + U2Rs) = 0.0500; RSURecovery = SURecovery

Rm= 0.0500

0.9817= 0.0509.

Note 1: SU = standard uncertainty; RSU = relative standard uncertainty.Note: 2: If a range (±a) is given without confidence level, assume a rectangular distribution and use the following equation: SU = half range/

√3 = a/

√3.

Note: 3: For calculation of uncertainties involves addition and subtraction, use the following equation: e.g. Volume = Volume 1 + Volume 2: SUVolume =√

SU2Volume 1 + SU2

Volume 2.

Note 4: For calculation of uncertainties involves multiplication and division, use the following equation: Conc = Mass × Purity

Volume.

RSUConc =√

RSU2Mass + RSU2

Purity + RSU2Volume.

Note 5: The volume of the Stock Solution A used to prepare Standard Solution B is ∼2 mL from two separate 1 mL pipetting (i.e. 1000 �L + 1000 �L).Note 6: If a range (±a) is given with a confidence level of 95%, use the following equation: SU = half range/1.96 = a/1.96.

244 G.N.W. Leung et al. / J. Chromatogr. A 1163 (2007) 237–246

Table 3A summary of the recovery study results and data treatment

Observed testosterone concentration (ng/mL) Mean (ng/mL) SDMa (ng/mL)

Replicate #1 Replicate #2 Replicate #3 Replicate #4 Replicate #5 Replicate #6

Urine 1 20.19 20.54 21.58 20.03 21.07 20.50 20.65 0.2352Urine 2 20.97 19.62 18.03 19.07 19.34 20.76 19.63 0.4490Urine 3 19.89 b 18.01 20.50 21.28 20.20 19.98 0.5429Urine 4 21.38 21.15 22.29 20.73 20.47 20.80 21.14 0.2660Urine 5 21.95 b 20.77 22.79 21.77 20.77 21.61 0.3852

Recovery Mean recovery

Replicate #1 Replicate #2 Replicate #3 Replicate #4 Replicate #5 Replicate #6

Urine 1 1.0095 1.0270 1.0788 1.0017 1.0535 1.0250 1.0326Urine 2 1.0487 0.9811 0.9014 0.9535 0.9671 1.0381 0.9817Urine 3 0.9947 b 0.9006 1.0249 1.0642 1.0101 0.9989Urine 4 1.0688 1.0577 1.1147 1.0363 1.0234 1.0400 1.0568Urine 5 1.0974 b 1.0383 1.1397 1.0885 1.0383 1.0805

Mean of mean recoveries 1.0301S

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sed and quantified using their corresponding matrix-matchedalibrators to minimise matrix variation. All five sets of spikedamples and their corresponding calibrators are analysed at theame time in order to minimise day-to-day variation. Table 3hows the results for the spiked samples and the correspondingata treatment. Data from Urine 2 was found to be consistent forll replicates and to have a mean method recovery (Rm = 0.982)losest to 1, indicating that variation due to sample matrix is theowest among the five sets of urine samples. Data from Urine 2re therefore used for evaluating the significance of the methodecovery (Rm), or method bias, using Eq. (3).

|1 − Rm|URm

(3)

The magnitude of URs is equal to the standard deviation of theean recovery of the five different sets of urine samples, which

epresents the uncertainty associated with interference from theample matrices; whereas that of URm can be obtained from Eq.4).

Rm = Rm ×√(

UCobs

Cobs

)2

+(

USpike

CSpike

)2

(4)

here Rm = method recovery obtained from the recoverytudy (0.982 for this example), Cobs = experimental value ofhe measurand, testosterone (19.63 ng/mL for this example),

Cobs = uncertainty of the experimental value Cobs (0.449 ng/mLor this example), CSpike = spiked level of the measurand, testos-erone (20 ng/mL for this example), USpike = uncertainty of thepiked level (0.381 ng/mL for this example) (Note: The approacho derive USpike is identical to that for UCal, but the uncertainty

ources originate from the procedures used for the recoverytudy.)

If the value derived from Eq. (3) is less than the chosenoverage factor (k), it can be concluded that the method recov-

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an.

ry is not significantly different from 1 and no correction tohe measured value is necessary. In other words, R in Eq.1) may be taken as 1. The coverage factor (k = 2.528) takenor this example is based on a one-tailed confidence level of9% at a degree of freedom of 20, which is the number ofata used to establish the method precision. For this exam-le, the value from Eq. (3) is 0.62 and the corresponding k is.528, implying that no correction for recovery is necessary.lthough it can be demonstrated that there is no significantias, it is still necessary to include the uncertainty associatedith recovery Eq. (2) in the overall uncertainty calculations

Tables 1 and 2).

.5. STEP 5: Deriving the combined uncertainty

The next step is to derive the combined standard uncertaintySU), or relative combined standard uncertainty (RSU), usingalues determined for the main uncertainty sources. Below arehe four main uncertainty sources for the testosterone quantifi-ation (Table 1):

(a) Uncertainty in the preparation of the calibrators:RSUCal = 0.0321;

b) Uncertainty in the preparation of the test sample:RSUTest-Sample = 0.00327;

(c) Uncertainty in the method precision: RSUPrecision = 0.0654;d) Uncertainty in recovery: RSURecovery = 0.0509.

The largest RSU is the uncertainty in the method precision,hich was derived by analysing 20 spiked control samples in

uplicate (Section 2.2) over a period of many months. Morehan one technician and one GC/MS have been involved in thenalyses in order to establish a method precision value whichs more representative of the method’s reproducibility. All rela-

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G.N.W. Leung et al. / J. Chro

ive standard uncertainties (RSU) with values less than 30% ofhe largest RSU (in this case, the uncertainty in method preci-ion) are considered insignificant and can be taken out for theverall RSU derivation. For this example, the combined rela-ive standard uncertainty (RSUCombined) and combined standardncertainty (UCombined) are calculated using Eqs. (5) and (6)espectively.

SUCombined =√

RSU2Cal + RSU2

Precision + RSU2Recovery

= 0.0889 (5)

Combined = RSUCombined × 20 ng/mL = 1.778 ng/mL (6)

.6. STEP 6: Calculating the expanded uncertainty

The final step is to derive an expanded uncertainty (UExpanded)ased on the combined standard uncertainty (UCombined) deter-ined in STEP 5 using Eq. (7).

Expanded = k × UCombined (7)

here k = coverage factor.Using a coverage factor of 2.528 (99% one-tailed confidence

evel at a degree of freedom of 20), the expanded uncertaintyUExpanded) at the testosterone threshold value (20 ng/mL) is cal-ulated to be 4.5 ng/mL. In other words, if a sample is foundith a testosterone concentration at 24.5 ng/mL (i.e. thresh-ld + expanded uncertainty), there is 99% probability that therue value is above the threshold. Currently, there is no consen-us among racing laboratories on the choice of confidence levelsed for describing the uncertainty associated with the quantifi-ation of threshold substances, although a 95% confidence levels stipulated in the International Standard for Laboratories pub-ished by the World Anti-Doping Agency (WADA). An obviousdvantage of a higher confidence level is that it will give a lowerrobability of a “false positive” declaration. However, it alsoeans that the actual cut-off level for reporting a positive find-

ng will be higher. In the authors’ laboratory, a confidence levelf 99% is used to ensure that more benefit of doubt is given to theerson responsible. In addition, a higher confidence level wouldive a bigger spread of the determined value, thus increasinghe probability of matching the result with that from analysinghe split-portion of the biological sample (or B sample) by theeferee laboratory.

The above “Bottom-Up” approach may look intimidating atrst glance, since there are numerous uncertainty componentsequiring considerations. However, a closer look at STEP 5ould reveal that there are in fact only four main sources ofncertainty. Of these, the method precision will always be aajor source of uncertainty regardless of the approach adopted.

n addition, the evaluation of method recovery is essential inrder to assess the extent of method bias. The calculations for

SUCal, may look complicated and would require some efforts

nitially. However, once established, they can be applied to otheruantitative methods, as most apparatus used (such as balance,olumetric flasks, pipettes, etc.) are likely to be the same. The

otap

gr. A 1163 (2007) 237–246 245

se of spreadsheet software can also facilitate the calculationsurther, making the entire process more user-friendly.

. Other considerations for quantitative analyses inquine biological samples

In order to obtain a reliable quantitative determination, someeneral guidelines such as the use of control charts to monitorhe systematic variation of the analytical method and the use ofertified reference material (CRM) or reference material (RM)o establish traceability have been well recognised by racinghemists. Apart from these common practices, some subtle con-ributions to uncertainty that may easily be overlooked will beiscussed below.

The preparation of standard stock solutions can have a sig-ificant contribution to the overall MU if not handled properly.

standard stock solution is usually prepared by weighing outsuitable amount of RM (or CRM) of the analyte and dis-

olved it in a suitable solvent. A typical limit of performance, orias, for an analytical balance (or bias) is in the low milligrams0.1–0.5 mg). In order to minimize the uncertainty in weighing,henever possible, at least 10 mg of the analyte should be used

or preparing the stock solution. Even for a 10 mg weighing,he relative standard uncertainty can be as high as 5%, whichs already a significant contribution to the overall MU. Somerug standards contain water of crystallization or exist in saltorm, and these should be accounted for in weighing. Manytandards contain moisture, particularly if they are not kept inirtight containers. It is therefore always a good practice to dryhe standard (under mild heat in a vacuum oven) for at least aew hours before weighing. Otherwise, a positive bias may notven be recognised. Having said this, if the supplier does notecommend the drying of a certified reference material, this stephould be omitted in order not to invalidate the certification. As auality assurance measure, different sources of RMs (or CRMs)re preferably used to prepare the standard stock solutions for thealibrators and QC samples. This practice can serve as a check todentify possible purity problems with the RMs. For example,estosterone from the United States Pharmacopeia (USP) andestosterone triethylammonium sulfate from the National Mea-urement Institute (NMI) are used respectively for preparing thealibrators and QCs for the method described in this paper. Its recognized that there may only be one source of a RM. Inuch cases, standard stock solutions for the calibrators and QCamples should at least be prepared by separate weighings.

It is of paramount importance to identify the major form of thearget drug (including its conjugation forms) present in genuinequine biological samples. Referring to our worked example,s testosterone is excreted mainly as testosterone sulfate inquine urine [12], the NMI testosterone triethylammonium sul-ate standard is therefore selected to prepare spiked control (QC)amples. Otherwise, there can be significant underestimation ofhe true concentration of total testosterone in the test sample if

nly free testosterone standards are used to prepare the calibra-ors and the spiked control samples. Using the correct form of thenalyte would account for any incomplete hydrolysis or incom-lete recovery associated with the method. This is particularly

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46 G.N.W. Leung et al. / J. Chr

mportant, as significant differences in recoveries and hydrolysisfficiencies are often associated with different conjugated formsf the same drug.

Isotope dilution is by far the preferred technique in quan-ification. Its advantage is that many systematic errors, such as

atrix effect and detector response, etc., can be compensated forecause the analyte and the internal standard have very similarhysical and chemical properties.

Calibrated air displacement pipettes are used commonly inreparing standard stock solutions or performing sample trans-erring steps. While these pipettes may have acceptable precisionor aqueous samples, they may show significant imprecision orias with organic solvents. Our experience is that positive dis-lacement pipettes tend to give better accuracy and precisionhen pipetting either equine urine with wide variation in vis-

osity or volatile organic solvents (such as methanol). These arereferred over air displacement pipettes [13].

. Conclusion

A worked example for the quantification of testosterone

n equine urine has been used to demonstrate the “Bottom-p” approach used by the authors’ laboratory to estimate theeasurement uncertainties (MU) associated with quantificationethods. In addition, some other important considerations with

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gr. A 1163 (2007) 237–246

ignificant impact on quantitative analyses of equine biologicalamples were discussed.

eferences

[1] ISO/IEC, 17025, General requirements for the competence of testing andcalibration laboratories, International Organization for Standardization,2005.

[2] International agreement on breeding, racing and wagering InternationalFederation of Horseracing Authorities, 2006.

[3] T. Drglin, Accred. Qual. Assur. 8 (2003) 130.[4] R.G. Gullberg, Accred. Qual. Assur. 11 (2006) 562.[5] P. Van Eenoo, F.T. Delbeke, Accred. Qual. Assur. 8 (2003) 477.[6] N.M. Faber, R. Boque, Accred. Qual. Assur. 11 (2006) 536.[7] Interpretation and Guidance on the Estimation of Uncertainty of Measure-

ment in Testing, Standards Council of Canada, 2005.[8] Manual on Quality Assurance and ISO/IEC 17025 Accreditation, Associ-

ation of Official Racing Chemists, 2003.[9] Measurement Uncertainty Training Course Manual, National Analytical

Reference Laboratory, 2000.10] Quantifying Uncertainty in Analytical Measurement, second ed.,

EURACHEM/CITAC Guide, 2000.11] Guide to the Expression of Uncertainty in Measurement, International

12] E. Houghton, in: C.R. Short (Ed.), Proceedings of the 9th International Con-ference on Racing Analysts and Vets, Department of Veterinary Physiology,Louisiana State University, vol. 1, 1992, p. 3.

13] K. Ewald, Eppendorf Application Note 10, 2006.