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Strategic Process Control Technologies, LLC
SPCWWW.SPCTECHLLC.COM 2007 © SPCTech, All Rights Reserved
Building Calibrations from Knowledge:
Applying Synthetic Calibration Techniques for Efficient Method Development and Realistic Robustness Testing
Robert P. Cogdill
IFPAC 2007Life Cycle Management of Analyzer and Method Reliability
31 January 2007, Baltimore MD
SPCTechnologies, LLC
2SPCWWW.SPCTECHLLC.COM 2007 © SPCTech, All Rights Reserved
Process monitoring & controlProduct quality testing (i.e. release testing)Root cause investigationData collection for formulation & process development
2. What are the jobs of multivariate calibrations?Calibrations are filters for transformation of multivariate data into (useful) univariate signals and informationFacilitate understanding of the factors affecting product quality and performanceProvide mechanisms to gauge the performance and condition of theanalytical system
3. What are the performance requirements for calibration models?
Accuracy & SensitivityPrecisionLinearityRangeRobustness
1. What are the jobs of PAT sensors?
3.
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The “main effects” of calibration dataset design on performance:
The Spectroscopic “Universe”
Synthetic Calibration
Lab-Scale/DOE
BatchSpectraP
hysi
cal V
aria
tion
Composition Variation
Accuracy, Sensitivity, Linearity, Range
Precision,Robustness
4SPCWWW.SPCTECHLLC.COM 2007 © SPCTech, All Rights Reserved
What are the most important factors in NIR calibration data?
Calibration Spectra
=Pure-ComponentVariation +
Baseline/PhysicalFactors
InstrumentNoise+
5SPCWWW.SPCTECHLLC.COM 2007 © SPCTech, All Rights Reserved
What are the most important factors in NIR calibration data?
Calibration Spectra
Pure-ComponentVariation
Baseline/PhysicalFactors
InstrumentNoise
=
+ +
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Calibration Development Flow Path
Feasibility Tests
DOE Calibration
Validation
Deployment
ModelUpdate
Current MethodDevelopment Path:
Feasibility Tests
Efficient Calibration
Deployment
Validation
ModelUpdate
Efficient CalibrationDevelopment Path:
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Synthetic Calibration ModelingPure-component methods have demonstrated the utility of a priori information in the pure-component spectraThe ideal pure-component estimation method would be:
easily deployed using common software routinesaccurate on an absolute basisFlexible enough to accommodate update information
If the error covariance matrix can be estimated, it should be possible to create a synthetic calibration databasewhich accurately reflects true expected variation, therefore allowing calibration without standards
In many respects,synthetic calibration represents the “holy grail” for NIR calibration
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Case Study: NIR Analysis of Intact Tablets
Objective: Generate a NIR calibration model suitable for process control & real-time release using only production-scale tablets (no “designer” or DOE tablets)
Calibration Data:NIR spectra and reference chemistry data from parallel testing during two full-scale production campaigns: 321 TabletsInstrument precision estimate: 3 tablets scanned 10 times without repositioningLong-term instrument stability: 12 tablets scanned periodically during one year (no reference data)Raw material pure-component scans
Validation Data:90 production- and laboratory-scale tablets having extreme concentration variation
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Green = Campaign I, N = 241Blue = Campaign II, N = 80
On-line NIR tablet spectra and parallel test data (full-scale production):
Calibration via Parallel Testing:
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Green = 1st Derivative, Blue = 2nd DerivativeRegression Coefficients
- Form of regression vectors suggests poor-generalization capability- Many non-specific features
Calibration via Parallel Testing:
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25 30 35 40 45 50 5534
35
36
37
38
39
40
Reference API Concentration (%)
Pre
dict
ed A
PI C
once
ntra
tion
(%)
Green = 1st Derivative, Blue = 2nd Derivative
- Calibration is apparently sensitive, but robustness is questionable- Slope is completely under-estimated
Calibration via Parallel Testing:
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Synthetic Calibration ModelingAssumptions:
Nominal-composition samples are plentifulParallel test samples, instrument noise testing, etc.
Spectral data follows a pure additive modelPure-component spectra are representative and comprehensive
Synthetic Calibration Procedure:1. Partitioning of available data (batches, days, etc.)2. Analyze error covariance matrix (baseline, inter-batch)3. Generate synthetic calibration database from design matrix,
use to augment any available “real” data4. PLS Calibration
13SPCWWW.SPCTECHLLC.COM 2007 © SPCTech, All Rights Reserved
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
Reference Concentration (%)
Pre
dict
ed C
once
ntra
tion
(%)
PLS Prediction Plot
Robustness Testing
Synthetic Calibration
Synthetic Calibration Modeling
1200 1400 1600 1800 2000 2200 2400-3
-2
-1
0
1
2
3
Wavelength (nm)
Arb
itrar
y In
tens
ity
1200 1400 1600 1800 2000 2200 2400-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Wavelength (nm)R
elat
ive
Log 10
(1/R
)
1200 1400 1600 1800 2000 2200 2400-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Wavelength (nm)
Rel
ativ
e Lo
g 10(1
/R)
1200 1400 1600 1800 2000 2200 2400Wavelength (nm)
1200 1400 1600 1800 2000 2200 24000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength (nm)
Log 10
(1/R
)
+
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 10
10
20
30
40
50
60
Intensity
Freq
uenc
y
-3 -2 -1 0 1 2 30
5
10
15
20
25
30
35
Intensity
Freq
uenc
y
SpectralDecomposition
eESY~XX~ T ++⋅+=
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Synthetic Cal. Parameters Effects Table (effect on Val R2):
15SPCWWW.SPCTECHLLC.COM 2007 © SPCTech, All Rights Reserved
Comparison of Real and Synthetic NIR Spectra:
Real Calibration Spectra Synthetic Calibration Spectra
Shape Errors
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Optimization StatisticsGreen = 1st Derivative, Blue = 2nd Derivative
RMSE R2
S/N Sensitivity
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Synthetic Model CoefficientsGreen = 1st Derivative, Blue = 2nd Derivative
Regression Coefficients
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Estimation of Slope Correction Factor
Can slope/bias correction factors be reliably estimated using only parallel test data?
NO
Green = 1st Derivative, Blue = 2nd Derivative
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Estimation of Slope Correction Factor
Calculation of slope coefficient:
Traditionally: X = Reference, Y = Predicted (e.g. NIR)
For noise-free data, calculation of slope correction is essentially the same regardless of which is X or Y
For real data (finite reference and prediction noise):
Accuracy of covariance estimate (X’Y) is reducedMagnitude of slope coefficient (b) is reduced because variance of X is over-estimatedBoth sources of error are mitigated by increasing the magnitude of variance and covariance relative to the noise (increase S/N)
X'XY'Xb =
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Estimation of Slope Correction FactorIf the precision of the methods is known with confidence, the slope estimate can be corrected: ( )
( )X'XY'Xb
precision
NIR
σσ
=
R2 = 0.962RMSE = 0.054
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Estimation of Slope Correction Factor
(For perfect data) The slope is equal to the ratio of standard deviations between X and Y
A more robust correction factor can be estimated using a ratio of observed standard deviations The slope correction estimate will be more robust when the slope is near unity, and when there are outlying samples
2onREFprecisi
2X
2ionPREDprecis
2Yb
σσ
σσ
−
−= R2 = 0.982
RMSE = 0.037~30% less error
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Estimation of Slope Correction Factor
Can slope/bias correction factors be reliably estimated using only parallel test data? (Note: Not corrected for precision)
Maybe
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Synthetic Calibration (slope corrected)Green = 1st Derivative, Blue = 2nd Derivative
RMSEP = 3.05%R2
val = 0.939No laboratory-scale batches!
DOE Calibration:R2
val = 0.948500 cal samples, 13 lab batches!
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SummarySynthetic calibration has been applied successfully for NIR monitoring of multi-component blending and intact tablet analysis
Publication of results is in process…Synthetic calibration was used to produce a sensitive, linear calibration model using zero high-leverage reference samples
By correcting for measurement precision, parallel testing data may be used to estimate slope and bias coefficients for process controlcalibrations
Synthetic calibration should be considered as an extension of current efforts in efficient calibration
PCP, NAS, GLS, maximum-likelihood weighting, direct orthogonalization, etc.
Synthetic calibration can be applied incrementally, and is not an “all or nothing solution”
Use synthetic calibration to create a “starter model” to “cherry pick”production samples for validationAugment synthetic calibration with process development or parallel test data