José Benito Quintana, PhD University of Santiago de Compostela jb.quintana@usc.es http://webspersoais.usc.es/jb.quintana Castellón Training Course
Overview LOD/LOQs: definition(s) LOD/LOQs: theoretical background Ways of estimating LODs/LOQs Examples Low resolution MS Vs High resolution MS (My) recommendations 2
LOD/LOQ - Terminology Limit of detection / Detection limit / Method detection limit / Minimum detectable value : LOD, LoD, LD, L D, MDL Limit of Quantification / Quantification limit : LOQ, LoQ LQ, L Q, MQL Critical value/limit of decision: L c Decision Limit: CC (same as L c ) Detection capability: CCβ (same as LOD) More at: http://www.iupac.org/publications/analytical_compendium/ 3
LOD - Definition IUPAC The limit of detection, expressed as the concentration, c L, or the quantity, q L, is derived from the smallest measure, x L, that can be detected with reasonable certainty for a given analytical procedure. The value of x L is given by the equation: X l = X blank + k s blank where X blank is the mean of the blank measures, s blank is the standard deviation of the blank measures, and k is a numerical factor chosen according to the confidence level desired. Typically k=3 http://goldbook.iupac.org/l03540.html 4
LOD/LOQ - Definition In general LOD: concentration/quantity that can be detected with reasonable certainty X l = X blank + k s blank Typically k=3 for LOD LOQ: concentration/quantity that can be quantified with reasonable certainty k=10 or 9 or 6 for LOQ (not a clear consensus) WHAT IS A REASONABLE CERTAINTY? ESTIMATING THE BLANK MEAN AND SD 5
LOD - Background Hypothesis testing - H 0 : the signal measured is not significantly different from the blank (the analyte is not present in the sample) - H 1 : the signal measured is different from the blank (the analyte is present in the sample) For a value of (e.g. 0.05 or 5%) the null hypothesis can be rejected or accepted If accepted, then the signal in the sample is accepted to be due to random variations in our determination 6
LOD - Background Normal (Gaussian) distribution - Type I ( ) errors: possibility of producing a false positive - Type II (β) errors: possibility of producing a false negative L c : critical level. Value with a probability of producing a false positive Figures from Boqué and Vander Heyden. LCGC Europe 22(2), 2009: http://www.chromatographyonline.com/limit-detection?id=&pageid=1&sk=&date= 7
LOD - Background β=0.5 (50%) Let s imagine =0.05 L C =5 ng/l, LOD=5 ng/l? Figures from Boqué and Vander Heyden. LCGC Europe 22(2), 2009: http://www.chromatographyonline.com/limit-detection?id=&pageid=1&sk=&date= 8
LOD - Background 3.28*S blank =β=0.05 If 3*S blank Then =β=0.07 If LOD is set to10ng/l? Figures from Boqué and Vander Heyden. LCGC Europe 22(2), 2009: http://www.chromatographyonline.com/limit-detection?id=&pageid=1&sk=&date= 9
LOD - Background ISO 11483-1 LOD: the true net concentration (or quantity) of component in the material subject to analysis that will lead, with a probability (1-β), to the conclusion that the concentration (or quantity) of component in the material analyzed is greater than that of a blank sample Similar to an older IUPAC definition of minimum detectable value 10
2002/657/EC LOD - Background CC and CCβ Two possibilities: No permitted (regulated) limit Permitted (regulated) limit 11
2002/657/EC LOD - Background No permitted (regulated) limit Decision Limit: CC (=L c ) Detection capability: CCβ (=LOD) 12
LOD - Background 2002/657/EC Permitted (regulated) limit Decision Limit: CC ( L c ) Detection capability: CCβ ( LOD) Minimum Required Performance Level (MRPL) 13
Measuring the blank Blank Matrix similar to the sample NOT containing the analyte Not that easy 1. Sewage will likely contain the analyte: use something simpler 2. Ultrapure water may present a peak of the analyte: real blank signal (and problem) 3. If there is no peak what is the chromatographic signal? 4. We could also use standards and then use a factor to convert that to sample LOD by using some factors 14
Measuring the blank Case 2. We perform blanks and there are peaks Best scenario Measure the area several blank replicates (how many?) Calculate the mean and standard deviation Apply the formula(s) and stablish your LOD, LOQ, CC or CCβ X l = X blank + k s blank 2002/657/EC: n 20 15
Measuring the blank Case 1, 3-4. Peak from natural concentration or no peak Get a matrix similar to your sample containing a (or several) known concentration(s) of analyte The concentration(s) should be close to the LOD Use an indirect approach to estimate the mean and SD of the blank 16
The signal-to-noise approach European Pharmacopeia LOD: S/N=3 LOQ: S/N=10 Noise determined in a peak-to-peak basis (maximum amplitude) over a range of 20 times the width of the peak at half-maximum Figure from Boqué and Vander Heyden. LCGC Europe 22(2), 2009: http://www.chromatographyonline.com/limit-detection?id=&pageid=1&sk=&date= 17
S/N Low Res systems (QQQ) Chromatogram Plot File: c:\varianws\data\tania\150317\17-03-2015_p_2.5ppb.xms Sample: P_2.5ppb Operator: Scan Range: 1-39457 Time Range: 0.10-20.09 min. Date: 17/03/2015 16:31 400 400 100 kcounts 136.1>91.0 [-14.0V] S/N (PP): 44 S: 448092 N: 10143 AMP_1 17-03-2015_P_2.5ppb.xms 91.0 (136.1>91.0 [-14.0V]) Filtered S/N (PP): 44 S: 448092 N: 10143 300 1A 200 100 0 0 300 2.5 5.0 7.5 10.0 Seg 1, Time: 0.10-20.09, Scan Functions: 17 2.5 5.0 7.5 minutes Seg 1, Time: 0.10-20.09, Scan Functions: 17 4734 9671 14608 19545 Scans In some instruments it is quite unclear how it is calculated 4734 9671 14608 Do it yourself! Remember to measure height! In this case noise is ca. 45,000 18
S/N Low Res Chromatogram Plots In low res systems you have to measure secondary ions 90 ng/l of amphetamine File: c:\varianws\data\tania\150317\18-03-2015_s1_f2_3.xms Sample: S1_F2_3 Operator: Scan Range: 1-39372 Time Range: 0.11-20.10 min. Date: 18/03/2015 17:03 MCounts AMP_1 18-03-2015_S1_F2_3.xms 91.0 (136.1>91.0 [-14.0V]) Filtered 136.1>91.0 [-14.0V] 1.00 From 1 st MRM: 0.75 S/N: 91 S/N (PP): 91 S: 1.1e+006 N: 12158 LOQ: ca. 10 ng/l 0.50 LOD: ca. 3.3 ng/l 0.25 0.00 But 2 nd MRM should be visible: S/N 3 15 ng/l necessary kcounts 136.1>119.0 [-6.0V] 800 700 600 500 400 AMP-2 18-03-2015_S1_F2_3.xms 119.1 (136.1>119.0 [-6.0V]) Filtered S/N (PP): 23 S: 542175 N: 23684 S/N: 23 300 LOD=LOQ=15 ng/l 200 100 0 4.5 5.0 5.5 6.0 6.5 Seg 1, Time: 0.11-20.10, Scan Functions: 17 minutes 8632 9618 10604 11590 12578 Scans 19
100 0 kcounts 343.2>245.0(-) [26.0V] 100 S/N Low Res THCCOOH_2 24-03-2015_S1_F1_1.xms 245.0 (343.2>245.0(-) [26.0V]) Filtered 170 ng/l of carboxy-thc 75 50 S/N (PP): 450 S: 105364 N: 234 S/N: 450 LOQ ca 3 ng/l 25 0 2 3 4 5 6 7 8 9 10 Is this realistic? Seg 1, Time: 0.11-15.08, Scan Functions: 6 Is it better to use another matrix with a lower concentration? Does it really matter anyway? minutes 377 576 775 975 1174 1373 1572 1771 1970 Scans 20
S/N High res 20 ng/ml standards of nitrosamines in GC-QTOF Noise can be zero! 21
S/N High res A wastewater containing 200 ng/l NDMA: 74.0475 m/z NMEA: 88.0631 m/z YES! Noise can be zero! Even with a complex matrix! 22
S/N High res The same 20 ng/ml standard in profile mode of acquisition The noise is here!! Why? 23
NDMA spectrum S/N High res 24
S/N High res Background spectrum 25
S/N High res Background spectrum 26
Background spectrum S/N High res The reality is not centroid! 27
Alternatives to S/N Basically two options: 1. Based on certainty, i.e. acceptable RSD. LOD/LOQ: analyte concentration where the standard deviation should be larger than 10% (IUPAC) or 20% (Eurachem) or variable (2002/657/EC depending on concentration level) RSD calculated from n 20 (IUPAC or 2002/657/EC) or n 10 (Eurachem) 2. Deriving the blank parameters indirectly from the calibration plot 28
Alternatives to S/N The nitrosamines example (NDEA): 4-replicates of standards in the 0.1/0.5-20 ng/l range RSD relationship with concentration can be modelled, e.g.*: RSD = a 1 Conc (+b) ng/ml RSD % 0,1 0,3 55,7 0,5 4,1 1 5,7 2 4,0 3 3,4 5 5,4 10 1,9 20 2,0 *Eppe et al. Analytica Chimica Acta 519 (2004) 243 253 29
Alternatives to S/N The nitrosamines example (NDEA): R=0.88 ng/ml RSD % 0,1 0,3 55,7 0,5 4,1 1 5,7 2 4,0 3 3,4 5 5,4 10 1,9 20 2,0 RSD=10% LOQ= 1.2 ng/ml RSD=20% LOD= 0.6 ng/ml 30
Alternatives to S/N Deriving the blank parameters indirectly from the calibration plot (ISO 11843-2): Intercept blank signal S y/x : std. dev. of the estimate blank std. dev. Figure from J. Miller and J. Miller. Statistics and Chemometrics for Analytical Chemistry. 7 th Edition. Pearson. Essex, UK. 31
Alternatives to S/N The nitrosamines example (NDEA): 0.5-20 ng/ml a=225 b=545 S y/x =269 R=0.997 Blank signal at LOD = 225 + 3*269 = 1032 LOD = 1032/545 = 1.9 ng/l 32
Alternatives to S/N The nitrosamines example (NDEA): 0.5-5 ng/ml (X 1000,0) 4 Plot of Fitted Model NDEA = 168,854 + 598,629*Conc NDEA 3 2 a=169 b=599 S y/x =98 R=0.995 1 0 0 1 2 3 4 5 Conc Blank signal at LOD = 169+ 3*98 = 463 LOD = 463/599 = 0.77 ng/l Calibration range should be close to LOD and LOQ 33
My recommendations Report clearly how LOD/LOQs are calculated If you have blank problems, minimize them and use them for calculation of LOD/LOQ Use the S/N approach with a matrix similar to your samples But at a level closer to LOD Remember your confirmation ion(s) Otherwise use something else (e.g. river water or ultrapure water) and take into account matrix effects (and recovery) Use profile mode in HR-MS (if feasible) If there is no noise, use the RSD approach (with standards) and be pragmatic 34
My recommendations Check your calculations Check LODs/LOQs from time to time DO NOT GET MAD!! IT IS AN ESTIMATION! 35