Assessing Calibration-Related
Measurement Bias Near the Limit of
Quantitation
By Troy Strock US Environmental Protec1on Agency, Region V Laboratory 536 S. Clark St. 10th floor (ML-­‐10C), Chicago IL 60605 [email protected] Disclaimer
The opinions expressed herein are the author’s and do not represent any official posi1on of the US EPA Maximizing Sensitivity: How low can you
go? on: Depends • Data user needs (Exposure thresholds, nutrient limits, allowable tolerance for precision and bias) • Instrumenta1on (sensi1vity, stability, condi1on) • Purity of reagents, standards, laboratory environment • Material tested Shemika Charles, world record holder for limbo, image from hVp://www.cambio.com/2015/06/18/this-­‐girl-­‐can-­‐literally-­‐limbo-­‐under-­‐anything/ What do we measure in analytical
chemistry?
•  Detector response – not concentra1on! •  Calibra1on func1ons are built using response as the dependent variable, and then applied in reverse •  Applying the calibra1on func1on is a transforma1on of response to concentra1on, and we can lose some informa1on on the way Definitions
•  Calibra1on—The act of evalua1ng and adjus1ng the precision and accuracy of measurement equipment. Instrument calibra1on is intended to eliminate or reduce bias in an instrument’s readings over a range of con1nuous values. h,p://www.chemwiki.ucdavis.edu/Analy>cal_chemistry/Data_analysis/
Instrument_Calibra>on_Over_A_Regime/ •  Bias—a systema1c error that contributes to the difference between the mean of a large number of test results and an accepted reference value. h,p://www.astm.org/ILS/precisionbias.html •  Limit of quan1ta1on— The lowest concentra1on at which the analyte can not only be reliably detected but at which some predefined goals for bias and imprecision are met. h,p://www.ncbi.nlm.nih.gov/pmc/ar>cles/PMC2556583/ •  Calibra1on related measurement bias -­‐-­‐ Loss of propor1onality between measured response and calculated concentra1on due to applica1on of the calibra1on model Where good calibrations go bad:
Two types of calibration related measurement
bias
Posi1ve x-­‐intercept: Curve produces a posi1ve calculated concentra1on at response = 0 Posi1ve y-­‐intercept: Curve produces a calculated concentra1on of 0 at a response > 0 Two types of calibration related measurement
bias
For calibration models that do not pass through (0,0),
modeled response per unit concentration is not linear
10 10 10 posi1ve posi1ve forced 10 ug/L x-­‐intercept 8 y-­‐intercept through (0,0) 8 LOQ: 8 As response approaches 0, / RF400 = 0.187 4 RF10concentra1on approaches x-­‐
intercept ug/L 8.2 2 x-­‐intercept: 6 Response per unit Concentra1on 0 As response approaches y-­‐
intercept, concentra1on approaches 0 6 4 2 6 4 2 0 0 50 Response per unit concentra1on is constant across calibra1on range 0 100 0 50 100 0 Concentra1on 50 100 Positive X-Intercept: 2-ethyl-1-hexanol by 5030/8260,
80°C
(external standard curve shown; x-­‐intercept is ~60% of 1 ppb standard concentra>on) % change in concentra>on resul>ng from change in area 10 8 6 4 2 0 -­‐2 0 -­‐4 -­‐6 -­‐8 -­‐10 10 20 30 40 Standard concentra>on (ng/mL) +5% change in area -­‐5% change in area +1% change in area -­‐1% change in area 50 Positive X-Intercept: 2,4-dintrophenol by
8270D
2.5 ug/mL cal std, response = 5962 Calc concentra1on = 3.05 ug/mL Response factor2.5 = 0.073 Method blank, response = 9 Calc concentra1on = 2.05 ug/mL 0.15% of response, 67% of concentra1on Positive x-intercept: Pentachlorophenol by
8270D
Linear 1/x weighted R2 = 0.993 RSE=18% (no 0.5 ug/mL std) Standard Conc (ug/mL) 0.5 1 2.5 5 10 25 50 75 100 Calc RF 0.031 0.031 0.056 0.076 0.093 0.119 0.128 0.137 0.134 Positive x-intercept: Pentachlorophenol by
8270D
m/z 266 response LLOQ std Cal range conc (ug/ X-­‐int * IS conc Blank conc Blank area / (ug/mL) (ug/mL) (ug/mL) low std area mL) 0.5-­‐100 1 0.77 0.80 24% 1-­‐100 2.5 1.25 1.28 14% 2.5-­‐100 2.5 2.03 2.03 2.1% 5-­‐100 5 2.74 2.77 0.7% *LLOQ: Lower Limit of Quan1ta1on, set as lowest standard whose calculated concentra1on was within ±50% of expected. From SW-­‐846 method 8000D. Black: 2.5 ug/mL cal standard Blue: method blank Positive x-intercept: Methylated 4,6-dinitro-2sec-butyl phenol
Method Detec1on Limit Study (2.5 ug/L spike level, n=7) Std Dev (ug/L) 0.086 2.5-­‐125 ug/L MDL (s*tα=0.01, df=6) Quad 1/x weighted R2 = 0.998 RSE=9.1% (X-­‐int) (IS conc) = 1.7 ug/L 0.27 Positive x-Intercepts – Measurement Quality
Considerations
•  Responses close to the x-­‐intercept of the calibra1on func1on can change by orders of magnitude without much change in concentra1on •  Concentra1ons extrapolated below the lowest calibra1on point tend to have posi1ve bias rela1ve to responses •  Calibra1ng to a lower concentra1on and weigh1ng the regression tends to push the x-­‐intercept of the regression line closer to the origin •  Response may be more useful for data evalua1on (e.g., when comparing concentra1ons in blanks to samples) (y-­‐intercept is 93% of low standard response) Range of responses with calculated concentra1on between 0 and LOQ Range of responses with nega1ve calculated concentra1on { { % change in concentra>on resul>ng from change in area Positive y-intercept: Octylphenol 12-ethoxylate
by LC/MS/MS
100 80 60 40 20 0 -­‐20 0.0 -­‐40 -­‐60 -­‐80 -­‐100 0.5 1.0 1.5 Standard concentra>on, ug/L +5% change in area -­‐5% change in area +1% change in area -­‐1% change in area 2.0 Positive Y-intercept: Method of standard
additions
Developed to determine chemical concentra1ons in a sample, but can also be used to es1mate ‘Background Equivalent Concentra1on’ in calibra1on standards • Assump1ons: • Calibra1on is linear • Calibra1on passes through origin 10 forced through (0,0) 8 Response per unit Concentra1on 6 Response per unit concentra1on is constant across calibra1on range 4 2 0 0 50 100 Concentra1on hVps://www.tau.ac.il/~advanal/StandardAddi1onsMethod.htm Positive Y-intercept: Acetone in water by
5030/8260
Extracted ion (m/z 43) chromatogram CAL 250 ug/L Quad 1/x weighted R2 = 0.924 RSE = 71% Y-­‐intercept: 1.29 CAL 125 ug/L CAL 50 ug/L CAL 25 ug/L CAL 12.5 ug/L
CAL 5 ug/L, Instr Blank Storage Blank, Samples Positive Y-intercept: Acetone in water by
5030/8260
Extracted ion (m/z 43) chromatogram CAL 250 ug/L Calculated concs Between 0 and LOQ { { Calculated conc is nega1ve Linear 1/x weighted R2 = 0.997 RSE=11% Y-­‐intercept: 1.8 X-­‐intercept*C(IS) = -­‐170 ug/L CAL 125 ug/L CAL 50 ug/L CAL 25 ug/L CAL 12.5 ug/L
CAL 5 ug/L, Instr Blank Storage Blank, Samples Background Equivalent concentra1on (Y=0): 170 ug/L Positive Y-intercept: Vinyl chloride in water
by 5030/8260 (Single Quad SIM)
Extracted ion m/z 62 response CAL 1 ug/L R2 = 0.994 RSE = 27.2% Y-­‐intercept = 0.0235 X-­‐intercept * C(IS) = -­‐0.15 ug/L Background Equivalent concentra1on: 0.15 ug/L CAL 0.75 ug/L CAL 0.5 ug/L CAL 0.2 ug/L CAL 0.1 ug/L Sample Positive Y-intercept: Bisphenol A by LC/MS/
MS
calc conc % of cal std % of expected BPA (13C12) response conc 103 recovery (%) 19 60 77 -­‐ 21 76 67 82 77 Background equivalent conc = ~ 5 ug/L 140000 120000 100000 80000 60000 40000 20000 0 Response (area) response (ug/L) 5 ug/L cal std 8200 5.26 75 ug/L cal std 62752 75.5 Blank 1 1577 < 0 5 ug/L LCS1 4914 1.02 75 ug/L LCS1 48197 56.8 Y = 776.6 x + 4118 R2 0.9998 0 50000 100000 150000 Concentra1on (ug/L) Positive y-intercept: Chromium in water by
200.8
Cal Cal standard m/z 52 m/z 52 %RSD counts/ Calc conc %RSD conc (ug/L) counts/sec counts/sec Calc conc (ug/L) 0
48815
2.3
0
500 39862190
4.7
501
100
7387971
3.1
94.1
50
3896709
5.3
49.1
Blank 10
771698
4.6
9.7
response is 5
424927
6.7
4.9
85% of 0.1 1
124901
5.5
0.91
ug/L 0.5
82720standard 1.2
0.49
0.1
54387
1.7
0.095
0
44098
4.3
0.0017
Background Equivalent conc (ug/L): 0.61
standard counts/sec conc (ug/L) 0
500
100
50
10
5
1
0.5
0.1
0
sec 77210
1.5
34780452
1.4
6786515
3.3
Blank 4.9
3454558
is 722462response 5.9
.1 39786798% of 06.3
129129ug/L 3.4
95822standard 1.1
71578
0.9
69861
0.8
Background Equivalent conc (ug/L)
Current MDL: 0.10 ug/L Current LOQ: 0.50 ug/L (ug/L) 0
501
97.3
49.0
9.4
4.7
0.78
0.28
-0.066
-0.083
1.1
“Negative x-intercept”:
Vanadium in digested waters by 200.8, May
2016
Prepared Standard m/z 51 response m/z 51 m/z 51 corrected Calc conc Calc conc Conc (ug/L)
Cal Blank 500 100 (Counts/sec)
%RSD response (Counts/sec)
1322988
39829325
8485545
1.6
1.0
3.7
50 10 5 1 0.5 0.1 Cal Blank 4740824
1844754
1439137
1042337
1015341
992022
977752
3.8
4.6
3.4
1.6
1.3
1.5
1.4
(ug/L)
%RSD
112690
38104271
7481939
0
501
97.0
N/A
1.2
2.9
3774345
845278
458032
69206
36467
4599
-1855
48.4
9.9
4.7
-0.54
-0.99
-1.4
-1.5
5.0
10.5
8.6
N/A
N/A
N/A
N/A
Background equivalent concentration: 17.2 ug/L (uncorrected)
Current MDL: 0.15 ug/L Current LOQ: 1 ug/L “Negative x-intercept”: Vanadium in digested
waters by 200.8
•  Increased background a likely cause •  Calibra1on intercept flipped from nega1ve to posi1ve Positive Y-Intercepts – Measurement Quality
Considerations
•  Background present in calibra1on standards can be calibrated out, but: •  Measurement uncertainty near LOQ increases exponen1ally •  Poten1al for low bias measurements or false nega1ves exists near LOQ if standards have background that samples do not •  When necessary, measurement uncertainty or bias can be limited by raising effec1ve LOQ to a calibra1on standard level clearly dis1nguishable from the background •  When low level measurements are important, carefully evaluate poten1al sources of background, and minimize those associated with standards that are not also in samples, if possible •  Consider using response in addi1on to concentra1on for data evalua1on Another Approach: FDA Method for Preparation
and LC/MS/MS Analysis of Honey for
Fluoroquinolone Residues (enrofloxacin,
cyprofloxacin)
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External standard calibra1on in blank honey matrix linear regression, not forced through (0,0) 1/x weigh1ng op1onal Correla1on coefficient ≥0.99 Calibra1on range: 2.5-­‐50 ng/g Max concentra1on limit: 5 ng/g < 2.5 ng/g reported as non-­‐detect 2.5 ng/g -­‐ 5.0 ng/g reported as posi1vely iden1fied, but below quan1fica1on limit ≥ 5.0 ng/g reported as a numerical concentra1on value hVp://www.fda.gov/Food/FoodScienceResearch/LaboratoryMethods/ucm071495.htm FDA: Preparation and LC/MS/MS
Analysis of Honey for Fluoroquinolone
Residues
Conclusions
•  For calibra1on models not forced through the origin, the intercept can be an important indicator of the poten1al for measurement bias near the LOQ. •  Background in reagents and standards used for instrument calibra1on and instrument sensi1vity can vary by over 1me, and the cause is not always apparent. •  Evalua1ng the calibra1on intercepts and comparing responses of blanks, samples and standards during data evalua1on may help lab staff beVer understand data limita1ons and root cause of QC problems. •  Most important: Define data quality needs first. Not a lab func1on, but we can help! Careful with that extrapolated data!
Thanks for listening!