an efficient design of experiment (doe)
TRANSCRIPT
An efficient Design of Experiment (DOE) approach to cell culture upstream media optimization
Mayank GargManager-MSAT
Biologics Development CenterDr. Reddy’s Laboratories Ltd.
3-4 March 2011 1 of 31
GE Bioprocess SymposiumBangalore
• Prerequisites
• Rational DOE approach• Conventional vs Optimal• Stepwise evaluation of approach
• Case study
Overview
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Well defined target
Navigator
Appropriate tools
Prerequisites
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Screening
Path to optima
Optimiza
tion
Conventional approach
Plackett Burman
Fl/Fr factorial
Steepest movement
RSM
Custom Design
Augmentation
Steepest movement
RSM
Optimal approach
DOE Approach
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Plackett Burman (FrF)
Fl/Fr factorialSteepest movement RSM
Custom Design (FrF) Augmentation Steepest movement RSM
All factors
Point of max response
All significant
factors
Insignificant factors
Sig. factors w/o
interaction
Sig. factorsWith
interactions
All sig. factors
+ interactions
Point of max response
Optima
Optima
Insignificant factors
DOE Approach
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DOE Approach
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•Expectations from a good DesignNumber of Experiments to be lowDesign efficiency to be highAverage variance of prediction to be lowRelative variance of coefficient to be lowPower of design to be high
• Expectations from results to rely interpretationModel should fit with:
High significance ( low p value: <0.05) High correlation (R2 and adjusted R2) No lack of fit
Screening: Sig. Factors
Conventional approach
D Optimal DesignD Efficiency 100
G Efficiency 100
A Efficiency 100
Average Variance of Prediction 0.388889
Design Creation Time (seconds) 0
Design DiagnosticsD Optimal DesignD Efficiency 100
G Efficiency 100
A Efficiency 100
Average Variance of Prediction 0.291667
Design Creation Time (seconds) 0
Design Diagnostics
25%
Plackett Burman (Fr Fct) 11F, 2L (12 runs)
Fixed matrix and number of run
Custom design (Fr Fct)11F, 2L (16 runs)
Custom matrix and number of runs
Optimal approach
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Significance Level 0.050
Signal to Noise Ratio 1.000
InterceptX1X2X3X4X5X6X7X8X9
X10X11
Effect0.0830.0830.0830.0830.0830.0830.0830.0830.0830.0830.0830.083
Variance0.2140.2140.2140.2140.2140.2140.2140.2140.2140.2140.2140.214
Power
Relative Variance of CoefficientsSignificance Level 0.050
Signal to Noise Ratio 1.000
InterceptX1X2X3X4X5X6X7X8X9
X10X11
Effect0.0630.0630.0630.0630.0630.0630.0630.0630.0630.0630.0630.063
Variance0.8430.8430.8430.8430.8430.8430.8430.8430.8430.8430.8430.843
Power
Relative Variance of Coefficients
294%24%
Conventional approach Optimal approach
Screening: Sig. Factors
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Path to optima: How far we are ???
• Fit first order• No lack of fit
•Lack of fit for first order
i≤j
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Factor
Resp
onse
•Far from optima
•Near Optima•Fit for second order•No lack of fit
Path to optima: Steepest movement
Steepest movementPost screening
• Not efficient when applied to:
• Main effects (if) having• Interaction• Curvature
Steepest movementPost Interaction identification
• Very efficient when applied to :
• Only main effects having• No interaction• No curvature
Conventional approach Optimal approach
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Full factorial: 4F, 2L (16 runs) Augmentation: 4F, 2L (8 runs)
D Optimal DesignD Efficiency 100
G Efficiency 100
A Efficiency 100
Average Variance of Prediction 0.1875
Design Creation Time (seconds) 0
Design DiagnosticsD Optimal DesignD Efficiency 96.83878
G Efficiency 88.64053
A Efficiency 93.61702
Average Variance of Prediction 0.131944
Design Creation Time (seconds) 0.05
Design Diagnostics
3%
11%
6%
Path to optima: Sig. factors + Interactions
Conventional approach Optimal approach
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30%
Significance Level 0.050
Signal to Noise Ratio 1.000
InterceptX1X2X3X4
X1*X2X1*X3X1*X4X2*X3X2*X4X3*X4
Effect0.0420.0420.0470.0470.0470.0420.0420.0420.0470.0470.047
Variance0.9950.9950.9890.9890.9890.9950.9950.9950.9890.9890.989
Power
Relative Variance of CoefficientsSignificance Level 0.050
Signal to Noise Ratio 1.000
InterceptX1X2X3X4
X1*X2X1*X3X1*X4X2*X3X2*X4X3*X4
Effect0.0630.0630.0630.0630.0630.0630.0630.0630.0630.0630.063
Variance0.8870.8870.8870.8870.8870.8870.8870.8870.8870.8870.887
Power
Relative Variance of Coefficients
Full factorial: 4F, 2L (16 runs) Augmentation: 4F, 2L (8 runs)
12%33%
Conventional approach Optimal approach
Path to optima: Sig. factors + Interactions
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All Main effects
• Not efficient• Significantly high no. of Experiments
Main effect having interaction(Post steep movement of main effects, having no interactions)
• Very efficient• Low number of experiments
Optimization: Response Surface
Conventional approach Optimal approach
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•Objective : To improve productivity•Product : A Mab•Cell line : CHO•Strategy : Feed composition optimization
Bolus feed (serum free chemically defined)11 components (grouped and individual)
•Approach : DOE•Scale : 4 x 3, 500 ml bench top reactors
Introduction Case study
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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 Y-1 -1 -1 1 -1 1 -1 1 -1 -1 -1-1 -1 -1 1 1 1 1 -1 -1 1 -10 0 0 0 0 0 0 0 0 0 01 -1 1 1 1 -1 -1 -1 1 -1 -10 0 0 0 0 0 0 0 0 0 01 1 -1 1 -1 1 1 -1 1 -1 11 -1 1 -1 -1 1 1 1 -1 -1 11 1 1 -1 -1 1 -1 -1 -1 1 -1-1 -1 1 -1 1 1 -1 1 1 1 11 -1 -1 -1 1 -1 -1 -1 -1 -1 11 1 -1 -1 1 -1 1 1 -1 1 -1-1 1 1 1 -1 -1 -1 -1 -1 1 1-1 1 1 1 1 -1 1 1 -1 -1 1-1 1 -1 -1 -1 -1 -1 1 1 -1 -11 -1 1 1 -1 -1 1 1 1 1 -1-1 -1 -1 -1 -1 -1 1 -1 1 1 11 1 -1 1 1 1 -1 1 1 1 10 0 0 0 0 0 0 0 0 0 0-1 1 1 -1 1 1 1 -1 1 -1 -1
Screening: Sig. Factors Case study
• Factors : 11• Levels : 2 (-1,+1)• Response : Yield• Design : Custom
(D optimal)
• Center points : 3• No. of exp : 19
Experimental Design
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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 Y-1 -1 -1 1 -1 1 -1 1 -1 -1 -1 1.182-1 -1 -1 1 1 1 1 -1 -1 1 -1 1.2270 0 0 0 0 0 0 0 0 0 0 1.0001 -1 1 1 1 -1 -1 -1 1 -1 -1 0.7270 0 0 0 0 0 0 0 0 0 0 0.9551 1 -1 1 -1 1 1 -1 1 -1 1 1.0911 -1 1 -1 -1 1 1 1 -1 -1 1 0.9091 1 1 -1 -1 1 -1 -1 -1 1 -1 0.773-1 -1 1 -1 1 1 -1 1 1 1 1 1.0001 -1 -1 -1 1 -1 -1 -1 -1 -1 1 0.9091 1 -1 -1 1 -1 1 1 -1 1 -1 0.591-1 1 1 1 -1 -1 -1 -1 -1 1 1 1.182-1 1 1 1 1 -1 1 1 -1 -1 1 1.136-1 1 -1 -1 -1 -1 -1 1 1 -1 -1 0.6821 -1 1 1 -1 -1 1 1 1 1 -1 0.545-1 -1 -1 -1 -1 -1 1 -1 1 1 1 0.8641 1 -1 1 1 1 -1 1 1 1 1 1.2730 0 0 0 0 0 0 0 0 0 0 1.091-1 1 1 -1 1 1 1 -1 1 -1 -1 1.091
0.50.60.70.80.9
11.11.21.3
Y A
ctua
l
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3Y Predicted P=0.0037
RSq=0.93 RMSE=0.0886
Actual by Predicted PlotRSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)
0.9348420.8324520.0885740.959368
19
Summary of Fit
ModelErrorC. Total
Source117
18
DF0.787930500.054917920.84284842
Sum ofSquares
0.0716300.007845
Mean Square9.1302
F Ratio
0.0037*Prob > F
Analysis of Variance
Lack Of FitPure ErrorTotal Error
Source527
DF0.045317250.009600670.05491792
Sum ofSquares
0.0090630.004800
Mean Square 1.8881F Ratio
0.3815Prob > F
0.9886Max RSq
Lack Of Fit
Fitted model analysis
Screening: Sig. Factors Case study
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X6X1X11X4X5X9X8X2X3X7X10
Term0.119375
-0.0966250.096625
0.09650.045375-0.03975
-0.0341250.0285
-0.0285-0.017125
-0.017
Estimate0.0221440.0221440.0221440.0221440.0221440.0221440.0221440.0221440.0221440.0221440.022144
Std Error5.39
-4.364.364.362.05
-1.80-1.541.29
-1.29-0.77-0.77
t Ratio0.0010*0.0033*0.0033*0.0033*0.07960.11570.16720.23900.23900.46460.4678
Prob>|t|
Sorted Parameter Estimates
0.50.7
0.91.1
1.3
Y0
.95
93
68
±0
.04
80
5
-1
-0.5 0
0.5 1
0X1
-1
-0.5 0
0.5 1
0X2
-1
-0.5 0
0.5 1
0X3
-1
-0.5 0
0.5 1
0X4
-1
-0.5 0
0.5 1
0X5
-1
-0.5 0
0.5 1
0X6
-1
-0.5 0
0.5 1
0X7
-1
-0.5 0
0.5 1
0X8
-1
-0.5 0
0.5 1
0X9
-1
-0.5 0
0.5 1
0X10
-1
-0.5 0
0.5 1
0X11
Prediction Profiler
Parameter estimate analysis
Screening: Sig. Factors Case study
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X1 X4 X6 X11 Y-1 1 1 -1 1.182-1 1 1 -1 1.2270 0 0 0 1.0001 1 -1 -1 0.7270 0 0 0 0.9551 1 1 1 1.0911 -1 1 1 0.9091 -1 1 -1 0.773-1 -1 1 1 1.0001 -1 -1 1 0.9091 -1 -1 -1 0.591-1 1 -1 1 1.182-1 1 -1 1 1.136-1 -1 -1 -1 0.6821 1 -1 -1 0.545-1 -1 -1 1 0.8641 1 1 1 1.2730 0 0 0 1.091-1 -1 1 -1 1.091-1 1 1 11 1 -1 1-1 1 -1 -11 1 1 -11 -1 1 -1-1 -1 -1 -11 -1 -1 1-1 -1 1 1
• Factors : 4• Levels : 2 (-1,+1)• Response : Yield• Design : Augmentation: Custom
(D optimal)• No. of exp : 8
Experimental Design
Path to optima: Sig. Factors + Interactions Case study
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X1 X4 X6 X11 Y-1 1 1 -1 1.182-1 1 1 -1 1.2270 0 0 0 1.0001 1 -1 -1 0.7270 0 0 0 0.9551 1 1 1 1.0911 -1 1 1 0.9091 -1 1 -1 0.773-1 -1 1 1 1.0001 -1 -1 1 0.9091 -1 -1 -1 0.591-1 1 -1 1 1.182-1 1 -1 1 1.136-1 -1 -1 -1 0.6821 1 -1 -1 0.545-1 -1 -1 1 0.8641 1 1 1 1.2730 0 0 0 1.091-1 -1 1 -1 1.091-1 1 1 1 1.3641 1 -1 1 1.136-1 1 -1 -1 1.1821 1 1 -1 0.7271 -1 1 -1 0.455-1 -1 -1 -1 0.9091 -1 -1 1 0.909-1 -1 1 1 1.091
0.40.50.60.70.80.9
11.11.21.31.4
Y A
ctua
l
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4Y Predicted P<.0001
RSq=0.88 RMSE=0.1019
Actual by Predicted PlotRSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)
0.8828060.8095610.101905
0.96327
Summary of Fit
ModelErrorC. Total
Source101626
DF1.25161300.16615301.4177660
Sum ofSquares
0.1251610.010385
Mean Square12.0526F Ratio
<.0001*Prob > F
Analysis of Variance
Lack Of FitPure ErrorTotal Error
Source6
1016
DF0.040890810.125262170.16615298
Sum ofSquares
0.0068150.012526
Mean Square 0.5441F Ratio
0.7645Prob > F
0.9116Max RSq
Lack Of Fit
Fitted model analysis
Path to optima: Sig. Factors + Interactions Case study
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X1X11X4X1*X11X6X1*X6X4*X11X1*X4X4*X6X6*X11
Term-0.1193750.1155417
0.1078750.08803120.0587917-0.0340310.0284688-0.028469-0.008469
3.125e-5
Estimate0.0208010.0208010.0208010.0220630.0208010.0220630.0220630.0220630.0220630.022063
Std Error-5.745.555.193.992.83
-1.541.29
-1.29-0.380.00
t Ratio<.0001*<.0001*<.0001*0.0011*0.0122*0.14250.21530.21530.70610.9989
Prob>|t|
Sorted Parameter Estimates
0.40.60.8
11.21.4
Y0.
963
±0.0
4157
5
-1
-0.5 0
0.5 1
0X1
-1
-0.5 0
0.5 1
0X4
-1
-0.5 0
0.5 1
0X6
-1
-0.5 0
0.5 1
0X11
Prediction Profiler
Parameter estimate analysis
Significant terms
X1, X4, X6, X11X1*X11
Path to optima: Sig. Factors + Interactions Case study
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Model re-fitting for significant terms: Stepwise regression
Path to optima: Steepest movement Case study
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0.40.50.60.70.80.91.01.11.21.31.4
Y A
ctua
l
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4Y Predicted P<.0001
RSq=0.85 RMSE=0.1021
Actual by Predicted Plot
X1X11X4X1*X11X6
Term-0.1193750.1155417
0.1078750.08520830.0587917
Estimate0.0208390.0208390.0208390.0208390.020839
Std Error-5.735.545.184.092.82
t Ratio<.0001*<.0001*<.0001*0.0005*0.0102*
Prob>|t|
Sorted Parameter Estimates
Model re-fitting for significant terms: Stepwise regression
Path to optima: Steepest movement Case study
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Y = 0.963– 0.119 X1 + 0.108 X4 + 0.059 X6 + 0.116 X11 + 0.085 X1*X11
ΔX4 = 0.50 unitΔX6 = (0.059/0.108)*0.5 = 0.273 unit
Steps Coded X4
Coded X6
Response
Origin 0 0 1.000
Δ 0.500 0.273 ---
Origin + 2Δ 1.000 0.546 1.120
Origin + 4Δ 2.000 1.092 1.317
Origin + 6Δ 3.000 1.638 1.474
Origin + 8Δ 4.000 2.184 1.561
Origin + 9Δ 4.500 2.457 1.415
Origin + 7Δ 3.500 1.911 1.588
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Origin + n delta
Resp
onse
Re-fitting model equation
Path to optima: Steepest movement Case study
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Pattern X1 X11 Y00 0 000 0 0+− 1 -100 0 0−+ -1 10A 0 1.41421
a0-
1.41421 000 0 0
0a 0-
1.41421A0 1.41421 000 0 0−− -1 -1++ 1 1
• Factors : 2• Levels : 2 (-1,+1)• Response : Yield• Design : RSM• Axial points : (a, A)• Center points : 6• No. of exp : 13
Experimental Design
Optimization: Response Surface Case study
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Pattern X1 X11 Y00 0 0 1.47300 0 0 1.418+− 1 -1 0.89100 0 0 1.455−+ -1 1 1.0000A 0 1.41421 1.345
a0-
1.41421 0 1.09100 0 0 1.473
0a 0-
1.41421 0.964A0 1.41421 0 1.21800 0 0 1.509−− -1 -1 1.182++ 1 1 1.527
0.80.91.01.11.21.31.41.51.6
Y A
ctua
l
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6Y Predicted P<.0001
RSq=0.99 RMSE=0.0286
Actual by Predicted Plot
ModelErrorC. Total
Source57
12
DF0.614450870.005714420.62016529
Sum ofSquares
0.1228900.000816
Mean Square150.5370
F Ratio
<.0001*Prob > F
Analysis of Variance
RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)
0.9907860.9842040.0285721.272727
13
Summary of Fit
Lack Of FitPure ErrorTotal Error
Source347
DF0.001350780.004363640.00571442
Sum ofSquares
0.0004500.001091
Mean Square 0.4127F Ratio
0.7534Prob > F
0.9930Max RSq
Lack Of Fit
Fitted model analysis
Optimization: Response Surface Case study
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X11*X11X1*X1X1*X11X11X1
Term-0.156591-0.1565910.20454550.12431470.0520443
Estimate0.0108330.0108330.0142860.0101020.010102
Std Error-14.46-14.4614.3212.31
5.15
t Ratio<.0001*<.0001*<.0001*<.0001*0.0013*
Prob>|t|
Sorted Parameter Estimates
Parameter estimate analysis
0.80.91.01.11.21.31.41.51.6
Y1.
5342
11±0
.031
92
-1
-0.5 0
0.5 1
0.5X1
-1
-0.5 0
0.5 1
0.7X11
Prediction Profiler
Optimization: Response Surface Case study
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-1
-0.5
0
0.5
1
X11
Y
1.209091
1.129545
1.05
1.288636
1.368182
1.447727
1.527273
0.9704550.890909
-1 -0.5 0 0.5 1X1
Contour plot
Optimization: Response Surface Case study
Surface plot
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Results Case study
0 48 96 144 192 240 288 336 3840.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Before Feed optimizationAfter feed optimization
Age (hours)
Nom
alize
d IV
CC
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Before Feed optimization After Feed optimization0.0
0.5
1.0
1.5
2.0
2.5
Summary and Conclusions
•Set Target•Define Strategy•Select Appropriate Statistical Tools •Rationalize Approach•Evaluate Design At Every Step•Scrupulously Execute And Accurately Analyze•Interpret data coalescing Statistical & Scientific knowledge•Verify and confirm resutls•Enjoy
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3-4 March 2011 30 of 31Mayank Garg, DRL India
3-4 March 2011 31 of 31Mayank Garg, DRL India
Thank You