Limit Of Detection, Limit Of Quantification And Limit Of Blank

EurachemA FOCUS FORANALYTICAL CHEMISTRYIN EUROPELimit of detection, limit ofquantification and limit of blankElvar Theodorsson

LoB, LoD, LoQ Limit of blank (LoB), limit of decision, limit of detection (LoD) andlimit of quantitation (LoQ) and are concepts and terms used todescribe the lowest concentration of a measurand that can be reliablymeasured by a particular measurement procedure . The literature in this area has previously been and is unfortunatelystill confusing regarding concepts, nomenclature and methods. The approach recommended here is primarily based on recentrecommendations by ides/pdf/MV guide 2nd ed EN.pdf

CLSI - IFCC

Imprecision profile

Common notion of limit of quantitation inclinical chemistry The concentration at which imprecision (coefficient of variation)of the method is 5%However Medical laboratories are already and increasingly faced with thequestion of the possible presence of a measurand for medical(tumor markers, infectious agents, carcinogens, pollutants) orlegal reasons (drugs of abuse). More formal understanding ofthe detection limit and limit of quantitation is therefore needed

Detection limit is basically a familiar conceptAbsence of diseaseAbsence of measurand blankPersons with diseaseMeasurand present

Detection limit is basically a familiar conceptPositive testNegative testParticipantsWith diseaseWithout diseaseTrue positivesFalse positives(type I error)False negatives True negatives(type II error)Total withTotal al [PPV]positiveTotal [NPV]negative

Three levels Decision limit, limit of blank, critical value CCα (term used in the EU directives) LOD Limit of Detection, minimum detectable value,detection limit, CCβ (term used in the EU directives) LOQ quantification limit, quantitation limit, limit of quantitation, limit ofdetermination, reporting limit, limit of reporting and application limit.9

Critical value in clinical chemistry The concept critical value in the context of detection should be usedwith care in clinical chemistry since it is most commonly used todenote the concentration at which the laboratory needs to notify theclinic in an extraordinary manner

The limit of decision (CCα) The limit of decision (CCα) is theconcentration of the measurand thatis significantly different from zero. Limit of decision CCα s*1.65 The concept is e.g. used whendetermining whether a material iscontaminated or not. The limit of blank (LoB) or criticalvalue is not a concept defined in VIM3 but has been defined as the highestapparent concentration of ameasurand expected when replicatesof a blank sample containing nomeasurand are measured.Limit of decision CCαLimit of blankCritical value1.65*sNull hypothesis:measurand absentAlternative hypothesis:measurand present50% false negatives if thetrue concentation is equalto the limit of decisionα 0.05

The limit of detection (LOD or CCβ) The limit of detection (LOD orCCβ) is the lowest concentrationof the measurand that can bedetected at a specified level ofconfidence. Limit of detection LOD s*3.3Detection decisionNull hypothesis:measurand absentAlternative hypothesis:measurand present3.30*sLODβ 0.05α 0.05

Limit of detection (LOD or CCβ) – VIM 3Detection decisionNull hypothesis:measurand absentAlternative hypothesis:measurand present3.30*sLODβ 0.05α 0.0513

The limit of detection (LOD or CCβ) The detection limit of the measurementsystem/instrument and of the methodshould be kept apart. The detection limitof the measurement system isdetermined by presenting the systemdirectly with the reagent blank or withother types of samples. When thedetection limit of the measurementmethod is determined the sample isprocessed through the all steps of themeasurement procedure.Detection decisionNull hypothesis:measurand absentAlternative hypothesis:measurand present3.30*sLODβ 0.05α 0.05

Limit of quantitation (LoQ)Limit of quantitation The “limit of quantitation” (LoQ) is not aconcept defined in VIM 3 but has beendefined as “the lowest concentration ofmeasurand that can be determined with anacceptable level of repeatability precisionand trueness”. The limit of quantification (LOQ) is “thelowest concentration at which theperformance of a method or measurementsystem is acceptable for a specified use”. Limit of quantitation LOQ s*1010 * sNull hypothesis:measurand absentAlternative hypothesis:measurand present15

Measuring interval Set of quantities of the same kind that can be measured by agiven measuring instrument or measuring system with specifiedinstrumental uncertainty, under defined conditions The measuring interval is dependent on the extent to which themeasuring system can produce results which are fit for theintended purpose The lower limit of the measuring interval coincides with the limitof quantitation (LOQ) (the lowest concentration of themeasurand that can be measured with an acceptableuncertainty) which is higher than the detection limit (LOD)16

Measuring interval

Theory of hypothesis testingJertzy NeymanEgon PearsonRoland Fisher

Limit of decision CCαLimit of blankCritical value1.65*sNull hypothesis:measurand absentAlternative hypothesis:measurand present50% false negatives if thetrue concentation is equalto the limit of decisionα 0.05

Errors in detection Alpha (α) error Type I error Falsepositive – The probability of falselyrejecting the null hypothesis that asubstance is not present when it isactually present Beta (β) error Type II error Falsenegative – The probability of falselyaccepting the null hypothesis that asubstance is absent, when in fact thesubstance is present at thedesignated concentrationDetection decisionNull hypothesis:measurand absentAlternative hypothesis:measurand presentβα

M.C. Ortizet al. /AnalyticaChimicaActa 674(2010)123–142

ISO-11843 standards (1997) The most common protocols forestimation of the LoD and LoQincluding the ISO-standards assumethat the instrument output at lowconcentrations can result in negativereadings/concentrations

CLSI - IFCC

https://eurachem.org/images/stories/Guides/pdf/MV guide 2nd ed EN.pdf

Limit of decision (CCα) – straightforwardprocedure applicable in clinical chemistry Determine the standard deviation (s) of ten independentmeasurements of a blank sample or of a sample with very lowconcentrations of the measurand Limit of decision CCα s*1.65

Limit of detection (LOD CCβ) – straightforwardprocedure applicable in clinical chemistry Determine the standard deviation (s) of ten independentmeasurements of a blank sample or of a sample with very lowconcentrations of the measurand Limit of detection LOD s*3.3

Limit of quantitation (LOQ) – straightforwardprocedure applicable in clinical chemistry Determine the standard deviation (s) of ten independentmeasurements of a blank sample or of a sample with very lowconcentrations of the measurand Limit of quantitation LOQ s*10 The multiplier is usually 10, but that number is historical andarbitrary. Other values such as 5 or 6 are commonly used(based on ‘fitness for purpose’ criteria). Consider the fitness of purpose of using the concentration atwhich imprecision (coefficient of variation) of the method is 5%

Talanta Volume 129, 1 November 2014, Pages 606–616

Linnet & Kondratovich 2004 In clinical chemistry, asymmetric, nongaussian blank distributions arecommon, and the calibration curve may be nonlinear. For sample size n, the nonparametrically determined 95th percentileof the blank measurements {obtained as the value of the[n(95/100) 0.5]th ordered observation} defines the limit for resultssignificantly exceeding zero [limit of blank (LoB)]. The LoD is the lowest value that is likely to yield a result exceedingthe LoB. LoD is estimated as: LoB cβxSDS, where SDS is the analytical SDof a sample with a low concentration cβ is approximately equal to1.65 for a type II error of 5%.

s0 The estimated standarddeviation of m singleresults at or near zeroconcentrations’0 The standard deviationused for calculating LODand LOQn The number of replicateobservations averagedwhen reporting resultswhere each replicate isobtained following theientire measurementprocedurenb The number of blankobservations averagedwhen calculating theblank correctionaccording to theFrom the results of m replicatemeasurements during validation calculatethe standard deviation, s0Will the resultsbe blank correctedduring routine useof the method?YesNomeasuremernt procedureUse the calculated standarddeviation, s’0 for calculating theLOD and LOQ

Calculation of LODWhat to doa) Replicate measurements of blanksamples, i.e. matrices containing nodetectable measurand or replicatemeasurement of test samples withlow concentrations of the measurandb) Replicate measurements ofreagent blanks or replicatemeasurements reagent blanks spikedwith low concentrations of measurandHowmanytimes10What to calculate from the dataCommentsCalculate the standard deviation,s0 of the results.Calculate s 0 from s0 as shown inFig. 1.CalculateLOD 3* s 010Calculate the standard deviation,s0 of the results.Calculate s 0 from s0 as shown inFig. 1.CalculateLOD 3* s 0Approach b) is acceptable, when it isnot possible to obtain blank samplesor test samples at lowconcentrations.When these blanks do not gothrough the whole measurementprocedure the calculation will giveinstrumental LOD

Calculation of LOQWhat to doHowmanytimesa) Replicate measurements ofblank samples, i.e. matricescontaining no detectablemeasurand or replicatemeasurements of test sampleswith low concentrations ofanalyte.10b) Replicate measurements ofreagent blanks or replicatemeasurements of reagent blanksspiked with low concentrations ofmeasurand.10What to calculate from the CommentsdataCalculate s 0 from s0 asshown.Calculate LOQ asThe value for the multiplier kQ is usually 10,but other values such as 5 or 6 arecommonly used (based on ”fitness forpurpose” criteria).LOQ kQ s 0.Calculate the standardApproach b) is acceptable, when it is notdeviation, s0 of the results. possible to obtain blank samples or testsamples at low concentrations.Calculate s from s as0shown in Fig. 1.Calculate LOQ asLOQ kQ s 0.0When these reagent blanks are not takenthrough the whole measurement procedureand are presented directly to the instrumentthe calculation will give the instrument LOQ.

The limit of detection (LOD) is.A. The lowest concentration that can be measuredB. The concentration at which we can decidewhether an element is present or notC. The point where we can just distinguish a signalfrom the backgroundD. The lowest concentration that should be repoted0%A.0%B.0%C.0%D.

The limit of quantification (LOQ)A. Is a purely statistical conceptB. Is based on fitness of purpose criteria – onlyC. Combines fitness of purpose criteria withstatistical criteriaD. Can be lower than LOD0%A.0%B.0%C.0%D.

Take a home message Decision limit, limit of blank, critical value, CCα (term used in the EUdirectives) Determine the standard deviation (s) of ten independent measurements of a blanksample or of a sample with very low concentrations of the measurand. Limit ofdecision CCα s*1.65 LOD, Limit of Detection, minimum detectable value,detection limit, CCβ (term used in the EU directives) Determine the standard deviation (s) of ten independent measurements of a blanksample or of a sample with very low concentrations of the measurand Limit ofdetection LOD s*3.3 LOQ, quantification limit, quantitation limit, limit of quantitation, limit ofdetermination, reporting limit, limit of reporting and application limit. Determine the standard deviation (s) of ten independent measurements of a blanksample or of a sample with very low concentrations of the measurand Limit ofquantitation LOQ s*10. Consider the fitness of purpose of using theconcentration at which imprecision (coefficient of variation) of the method is 5%

Limit of quantitation (LOQ) - straightforward procedure applicable in clinical chemistry Determine the standard deviation (s) of ten independent measurements of a blank sample or of a sample with very low concentrations of the measurand Limit of quantitation LOQ s 10 The multiplier is usually 10, but that number is historical and arbitrary.