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Aldo Marchetto, Gabriele Tartari & Rosario Mosello

Limit of Detection (LOD)and

Limit of Quantification (LOQ)estimation and use in the chemical lab

Life+ FutMon - Working Group on QA/QC in LaboratoriesMeeting of the Heads of the Laboratories

12-13 October 2009 in Warsaw

C.N.R. Institute of Ecosystem Study, Verbania (Italy)

e-mail: a.marchetto@ise.cnr.it http://www.iii.to.cnr.it

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Internal and external QC

calibrationblank control chartsmean control chartsLOD & LOQresult validation using ion balance andconductivity check

Internal quality control

External quality controluse of certified standardanalyses of certified samplesparticipation to WRTs

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Why to estimate LOD and LOQ?

To evaluate the suitability of the used analytical technique and conditions to the aims of the monitoring.

To compare the quality of the determination with other published results in order to evaluate if there is necessity and possibility of improvement.

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Aim of this presentation

To show simple approaches in order to encourage laboratories to start to estimate their LOD and LOQ using data they still have or they can collect at zero cost.

Not to present a state-of-the-art review of the literature about this subject.

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IUPAC definition

The minimum single result which, with a stated probability, can be distinguished from a suitable blank value. The limit defines the point at

which the analysis becomes possible and this may be different from the lower limit of the determinable analytical range.

The Limit of Detection (LOD), expressed as the concentration, cL, or the quantity, qL, is derived from the smallest measure, xL, that can be

detected with reasonable certainty for a given analytical procedure.

The value of xL is given by the equation

xL = xbi + ksbi

where xbi is the mean of the blank measures, sbi is the standard deviation of the blank measures, and k is a numerical factor chosen

according to the confidence level desired

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IUPAC definition

2002

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ISO 13530 1997Water quality - Guidance on analytical quality control for

chemical and physicochemical water analysis

1997

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Eurachem definition

1998

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EPA

2004

Document 815-R-05-006

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EPA Document 815-R-05-006 2004

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EPA Document 815-R-05-006 2004

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EPA Document 815-R-05-006

2004 LCMRLLowest Concentration Minimum Reporting Level

MRL Minimum Reporting LevelUCMR Unregulated Contaminant Monitoring Regulation

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Standard Methods 21° Ed. 2005: definitions

2005

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Standard Methods 21° Ed. 2005: definitions

2005

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Standard Methods 21° Ed. 2005: definitions

LOD LOQ

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Detection Limit in analysisNORDTEST definition

2007

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The Limit of Detection (LOD) expressed as the concentration is derived from the smallest measure, xL, that can be detected with reasonable certainty for a given

analytical procedure.

xL = xbi + ksbi

where xbi is the mean of the blank measures, sbi is the standard deviation of the blank measures, and k is a numerical factor chosen according to the

confidence level desired (2 < k < 3)

To obtain LOD, signals are transformed inconcentrations using the

calibration curve

SD of blank samples

signal

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Calibration curveN-NH4 spectrophotometry indophenol blue

5 cm optical path

-0.1

0.1

0.3

0.5

0.7

0.9

0.000 0.050 0.100 0.150 0.200

concentration (mg N-NH4 /L)

sign

al (A

)

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-0.1

0.1

0.3

0.5

0.7

0.9

0.000 0.050 0.100 0.150 0.200

concentration (mg N-NH4 /L)

sign

al (A

)

Calibration curveN-NH4 spectrophotometry indophenol blue

5 cm optical path

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.000 0.002 0.004 0.006 0.008 0.010

concentration (mg N-NH4 /L)

sign

al (A

)

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Calibration curveChloride by Ion Chromatography determinationDionex AG19-AS19-AAES 100µL sample loop

-0.5

0.0

0.5

1.0

1.5

2.0

0 0.5 1 1.5 2

concentration (mg Cl /L)

sign

al (p

eak

area

)

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Calibration curveChloride by Ion Chromatography determinationDionex AG19-AS19-AAES 100µL sample loop

-0.5

0.0

0.5

1.0

1.5

2.0

0 0.5 1 1.5 2

concentration (mg Cl /L)

sign

al (p

eak

area

)

-0.05

0.00

0.05

0.10

0.15

0.20

0.00 0.05 0.10 0.15 0.20

concentration (mg Cl /L)

sign

al (p

eak

area

)

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In practice…If you have mean control charts at different concentration,

use them to evaluate LOD and LOQ

else, if calibration slope is very stable (i.e. spectrophotometry)

use SD of the blanks (if possible)

or of a control sample of low concentration

or of the lowest standard

else,

apply Hubax-Vos method on as many calibrations possible,

or use the variability of the calibration standards

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SD of blank samplesN-NH4 spectrophotometry indophenol blue

5 cm optical path

Calibrationmg N/L = 0.196 A + 0.0006

LOD 0.005 mg N/L = 0.196 x 0.021 + 0.0006

0.00

0.01

0.02

0.03

0.04

0.05

0.06

gen-05

giu-05

ott-05

feb-06

apr-0

6ag

o-06mar-

07ag

o-07ott-

07ap

r-08

set-0

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Abs

orba

nce

Mean

dataMean = 0.025 mA

SD = 0.007 mAxL = xbi + ksbi

xL = 0.025 + 3 x 0.007 = 0.046 mA

In the daily determinations and in the calibration, blank mean issubtracted from the values, then for estimating LOD

use 3SD (0.021 A), not mean + 3SD (0.046 A)

LOQ 0.014 mg N/L = 0.196 x 0.070 + 0.0006

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Variability of the lowest standardChloride by Ion Chromatograpy determinationDionex AG19-AS19-AAES 100µL sample loop

Ratio Factor = peak area / ST concentrationRF = 0.057/0.05 = 1.14

LOD 0.018 mg Cl/L = 0.021/1.14

Lowest standard0.05 mg Cl/L

Peak area mean = 0.057Peak area SD = 0.007

xL = xbi + ksbi

for lowest standardxL = ksbi

xL = 3 x 0.007 = 0.0210.03

0.04

0.05

0.06

0.07

0.08

0.09

nov-05

feb-06

apr-0

6ag

o-06nov-0

6feb

-07mag

-07ag

o-07nov-0

7feb

-08giu-08ott-

08gen

-09mar-

09giu-09

Peak

are

a

Mean

data

LOQ 0.061 mg Cl/L = 0.070/1.14

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Variability of calibration standardsChloride by Ion Chromatography determinationDionex AG19-AS19-AAES 100µL sample loop

LOD 0.0002 mg Cl/L

0

5

10

15

0 2 4 6 8 10 12Cl (mg L-1)

RSD

pea

k ar

ea RSD = 5.73 (mg/L)-0.2

LOD = RSD 33% = (5.73/33) (1/0.2)

LOQ = RSD 10% = (5.73/10) (1/0.2) LOQ 0.062 mg Cl/L

4.211.43910.004.35.7015.004.62.2772.005.50.5580.50

5.80.2180.208.60.1080.10

13.80.0580.05

RSDPeakarea

Standardmg/L

n >300 and 2-3 years of calibrations

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Statistics mg L-1

Average 0.508Standard Deviation 0.013Standard Deviation recommended 0.025RSD % 2.7RSD % recommended 5.0Minimum 0.47Maximum 0.54N. data 115

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11mg L-1

R.S

.D. C

ontr

ol C

hart

s

Using control chart

ChlorideIon Chromatography

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

0.60

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101

106

111

mg

L-1

UWL

LWL

UCL

LCL

RSD = 3.37 (mg/L)-0.46

Single control chart in use from Nov 2006 to Aug 2007

All control charts used in the lab for IC determinations (in 20 years)

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0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11mg L-1

R.S

.D. C

ontr

ol C

hart

s

Chloride by Ion Chromatography determination (100µL sample loop)

LOD = RSD 33% = (3.37/33) (1/0.46)

LOQ = RSD 10% = (3.37/10) (1/0.46)

RSD = 3.37 (mg/L)-0.46

LOD from control charts

LOD 0.007 mg Cl/L

LOQ 0.094 mg Cl/L

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Hubaux-Vos

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LOD from daily calibration (Hubaux-Vos)

Example from DionexChromeleon Software

Chloride by IC100µL sample loop

Range 0.05 – 10 mg/L7 standards in duplicate

daily calibration

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LOD from daily calibration (Hubaux-Vos)

LOD 0.027 mg Cl/L

Example from DionexChromeleon Software

Chloride by IC100µL sample loop

Range 0.05 – 10 mg/L7 standards in duplicate

daily calibration

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Range 0.05 – 10 mg/L7 standards

More than 300 calibrationsin 2-3 years

4.211.43910.04.35.7015.04.62.2772.05.50.5580.505.80.2180.208.60.1080.1013.80.0580.05

RSDPeakarea

Standardmg/L

Chloride by Ion Chromatography determinationDionex AG19-AS19-AAES 100µL sample loop

LOD from average calibrations (Hubaux-Vos)

LOD 0.038 mg Cl/L

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.07

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08Concentration

Sign

al

Data

Upper prediction limit

Upper confidence limit

Regression line

Lower confidence limit

Lower prediction limit

L.O.D.

yc

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Chloride by Ion Chromatography determinationDionex AG19-AS19-AAES 100µL sample loop

Values obtained:

Lowest standard variability 0.018 0.061

Control charts RSD 33/10% 0.007 0.094

Standards variability RSD 33/10% 0.0002 0.062

Hubaux-Vos daily calibration 0.027 0.089

Hubaux-Vos average calibrations 0.038 0.073 *

Results obtained (mg Cl / L) LOD LOQ

* Gibbons’s AML 2001

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In practice…If you have mean control charts at different concentration,

use them to evaluate LOD and LOQelse, if calibration slope is very stable (i.e. spectrophotometry)

use SD of the blanks (if possible) or of a control sample of low concentrationor of the lowest standard used for calibration

else, apply Hubax-Vos method,

or use the variability of the calibration standardsDon’t calculate the LOD and LOQ for determinations of:

pH, Conductivity

(with Gran’s the negative values of alkalinity indicate acidity)Alkalinity: measured through 2 end points or Gran’s method

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Conclusions

Quality Control is an important tool to criticize analytical

activity, to improve it and to assure that it is suitable for

the purpose of monitoring.

The estimation of LOD and LOQ is an important part of

Quality Control.

LOD and LOQ can be simply evaluated using results of

control charts, blank samples or calibration curves.

If you do not store these data yet, please store them

anywhere and in a few years you will have years of data...

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LOD & LOQ on the web

http://www.chemometry.com/Research/LOD.html

http://www.chemometry.com/Research/References/ReferencesLOD.html

http://goldbook.iupac.org/

http://www.eurachem.org/guides/valid.pdf

http://www.nordicinnovation.net/nordtestfiler/tr569_ed_3.pdf

http://www.epa.gov/OGWDW/methods/pdfs/methods/methods_lcmrl.pdf

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2556583/

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References for LOD & LOQA.P.H.A., A.W.W.A., W.E.F. 2005. Standard Methods for the Examination of Water and Wastewater. (Method 1030 C). Amer. Publ. Health Ass., Washington.

Currie. L.A. 1997. Detection: international update, and same emerging di-lemmas involving calibration, the blank, and multiple detection decisions. Chemometrics and Intelligent Laboratory Systems 37, 151-181.

Currie. L.A. 1999. Nomenclature in evaluation of analytical methods including detection and quantifcation capabilities. (IUPAC Recommendations 1995). Analytica Chimica Acta 391, 105-126.

Currie. L.A. 1999. Detection and quantifcation limits: origins and historical overview. Analytica Chimica Acta 391, 127-134.

De Vos B., S. Lettens, B. Muys & J. A. Deckers. 2007. Walkley–Black analysis of forest soil organic carbon: recovery, limitations and uncertainty. Soil Use and Management 23, 221–229.

EURACHEM Guide. 1998. The Fitness for Purpose of Analytical Methods. A Laboratory Guide to Method Validation and Related Topics

Gibbons R.D. and D.E. Coleman. 2001. Statistical Methods for Detection and Quantification of Environmental Contamination. New York: Wiley, 384 pp.

Munch D. and P. Branson. 2004. Statistical Protocol for the Determination of the Single-Laboratory Lowest Concentration Minimum Reporting Level (LCMRL) and Validation of Laboratory Performance at or Below the Minimum Reporting Level (MRL). EPA Document 815-R-05-006.

Mocak J., A. S. Bond, M. Mitchell, G. Schollary. 1997. A Statistical Overview of Standard (IUPAC and ACS) and New Procedures for Determining the Limits of Detection and Quantification: Application to Voltammetric and Stripping Techniques. Pure Appl. Chem., 69, 297-328.

Thompson M., S. L. R. Ellison and R. Wood. 2002. Harmonized guidelines for single laboratory validation of methods of analysis (IUPAC Technical Report). Pure Appl. Chem., Vol. 74, No. 5, pp. 835–855.

Thomsen V., D. Schatzlein and D. Mercuro. 2003. Limits of Detection in Spectroscopy. Spectroscopy 18(12): 112-114.

Vogelgesang J. J. Hädrich. 1998. Limits of detection, identification and determination: a statistical approach for practitioners. Accred Qual Assur 3: 242–255.

Voigtman E. 2008. Limits of detection and decision. Part 1, 2, 3, 4 Spectrochimica Acta Part B 63: 115–128, 128-141, 142-153, 154-165.

Janiga I., J. Mocak, I. Garaj. 2008. Comparison of Minimum Detectable Concentration with the IUPAC Detection Limit. Measurement Science Review, Vol. 8, Sec. 1, No. 5, 108-110.