Net Analyte Signal
Based
Multivariate Calibration
Methods
By:
Bahram Hemmateenejad
Medicinal & Natural Products Chemistry Research Center,
Shiraz University of Medical Science
Multivariate Calibration
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CLS
ILS
PCR
PLS
A=CS
c=AS
A = T P, c = T s
A = T P, C = Q U
Q=Tb
Main Problems
• Definition of figures of merit
• Optimization of conditions
• Optimum number of factors
Figure of merit
• Sensitivity
• Selectivity
• Detection Limit
1.2
Univariate Calibration
Absorbance
1
0.8
0.6
0.4
0.2
0
0
5
10
Concentration
15
Optimization of conditions
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Effect of pH
Effect of Temperature
Effect of Ionic Strength
Effect of Concentration
…
Optimum number of factors
120
Cross Validation
100
Minimum PRESS
F-Ratio
PRESS
External Validation
80
60
40
20
0
1
Over-fitting
Under-Fitting
6
Number of Factors
Net Analyte Signal
(NAS)
• A. Lorber, Anal. Chem. 58 (1986) 1167
• The part of mixture spectrum that is useful
for model building
• NAS is unique for the analyte of interest
• NAS is a part of mixture spectrum which is
orthogonal to the spectrum of all existing
components except analyte
• A part of mixture spectra which is directly
related to the concentration of analyte
Net analyte signal, references
• 1986
Proposed by Lorber.
• Spectra of pure compounds available (CLS model).
• 1997-2000
Extensions.
• Inverse calibration (Lorber,Faber,Kowalski)
• Figures of merit (sensitivity, selectivity, limit of detection)
(Faber)
• 1998-2002
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Applications, Software.
Outlier detection.
(Faber, Xu, Ferre)
Biomedical & Pharmaceutical. (Goicoechea, Skibsted)
Spectral preprocessing.
(Faber, Brown, Wentzell)
Wavelength selection.
(Goicoechea, Xu)
Preprocessing and wavelength selection (Skibsted, Boelens)
M1
y
x
M2
2x
3x
M3
3y
2y
M2
y
M1
x
M3
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R (ixj) matrix of mixture spectra
Rk (ixj) matrix of analyte k spectra
R-k (ixj) matrix of background (other analytes + interferences
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R=CS
Rk = sk ck
R = Rk + R-k
F R = F Rk + F R-k, F R-k = 0
F R = F Rk
R* = F sk ck = sk* ck
• F = I – R-k+ R-k
• R* = (I – R-k+ R-k)R = R - R-k+ R-k R
• (I – R-k+ R-k)R-k = 0
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Key Step
R-k
• Rank Annihilation Factor Analysis
(RAFA)
• CLS approach
• Rk = sk ck
• R-k = R – Rk
• ILS approach
• R-k = R -  r ck
• r is a linear combination of the rows of R
• ck = R R-1 ck
•  = 1/ rT R+ ck
• Another approach
• R-k = [ I – ck(ckT ck)-1 ckT]R
• Other approaches
• Xu & Schechter Anal. Chem. 69 (1997) 3722
• Faber
Anal. Chem. 70(1998) 5108
Review of NAS calculation
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Determining No. of analytes (p)
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Preparing mixture standard solutions (j)
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Recording absorbance spectra of solutions at (i) sensors (R matrix)
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Recording absorbance spectrum of unknown (run vector)
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Calculation of R-k
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Calculation of calibration NAS
R* = (I – R-k+ R-k)R
Calculation of the NAS for unknown
r*un = (I – R-k+ R-k)run
Calculation of the pure NAS
s*k = (I – R-k+ R-k)sk
Effect of added noise
NAS-Multivariate calibration
• In some case,
– Nonlinearity
– Interaction between components
– Other source of variables
• The rank of NAS will become greater than 1
• Simple NAS method dose not give perfect
results
• MLR, PCR, PLS and … help to enhance the
results of NAS calculation
• R* is used as input for multivariate models
• R* = c s*
• R* = T* P*
• R* = T* P*
c = T* b*
c= u q
u = T* b*
MLR
PCR
PLS
• R* can be used as input for ANN
In Progress
Figure of merits
• Sensitivity
||ri*|| / ci
or ||s*||
• Selectivity ||ri*|| / ||ri|| or ||s*|| / ||s||
• LOD
3Sc / m,
3 |||| ||bk|| / m
• LOQ
10Sc / m, 10 |||| ||bk|| / m
Applications
• Wavelength region selection
Net Analyte Signal Regression Plot
(NASRP)
• Error Indicator (EI)
• Goicoechea and Olivieri, Analyst 124 (1999) 725
• EI = {s2 [1+(N2s2) / 4 ||r*|| )]}0.5 / ||r*||
• s: standard deviation of the best fitted line
• N: Number of point in the best fitted line
• Temperature insensitive determination of
proteins in electrolyte solutions
• Anal. Chem. 72 (2000) 4985
• Determination of Tetracycline in blood serum
• Anal. Chem. 71 (1999) 4361.
• Determination of drugs in pharmaceutics
• Determination of drugs in serum
• Determination of sorbic and benzoic acids in
fruit juices
Multivariate Standard Addition
Method (MSAM)
• ck = cu + cs
• R = R-k + Rk
• R-k = R -  r ck = R -  r (cu + cs)
• R-k = [ I – ck(ckT ck)-1 ckT]R
• Thanks for you attention