Sunday, June 23, 2013

Closing in on a Media Selection

In the last post, the augmented design gave some results that provided deeper insight into how the different media components were affecting the viable cell density.  Presently, the model for the VCD is made of both main effects and pairwise interactions.
Parameter Estimates from Fit to Full-Factorial Model
Term

Estimate
Std Error
t Ratio
Prob>|t|
Intercept

7.5838154
0.228814
33.14
<.0001*
Glutamine

-0.572075
0.209098
-2.74
0.0170*
EAA

0.0998006
0.27464
0.36
0.7222
NEAA

1.2100318
0.331635
3.65
0.0029*
ITS

0.5629417
0.202966
2.77
0.0158*
Lipids

-0.727668
0.368208
-1.98
0.0697
Glutamine*EAA

-1.04495
0.268457
-3.89
0.0019*
EAA*NEAA

0.8313522
0.344822
2.41
0.0314*
EAA*Lipids

1.2371315
0.334539
3.70
0.0027*
NEAA*ITS

-1.070604
0.260279
-4.11
0.0012*
NEAA*Lipids

0.840536
0.276571
3.04
0.0095*

The ANOVA results indicate the model is significantly better at fitting the data than normal process variations.
ANOVA Results of Fit to Full-Factorial Model
Source
DF
Sum of Squares
Mean Square
F Ratio
Model
10
237.42417
23.7424
26.6759
Error
13
11.57041
0.8900
Prob > F
C. Total
23
248.99458

<.0001*

The resulting prediction profiler shows linear responses (no square terms used at this point), and at the coded point 0, the middle of the ranges explored, the expected viable cell density is 7.58x10^6.  Note that the exponents were omitted from the plot to improve visualization.
Prediction Profiler for Fit to Full-Factorial Model


Stepping back for a minute, let's recall the purpose of this exercise: I wanted to find the minimum number of experiments needed to explain how the different media components affected the viable cell density.  I reasoned that this could be achieved in fewer than the 54 experiments that were used in the cited paper.  At the moment, I'm 24 experiments into the analysis and most of the effects that were observed in the results from the CCD analysis are present.  My current problem is that when the center point data is included, the full factorial model is unable to predict the measured values (red triangles).
Actual by Predicted with Center Points Shown but Excluded from Fit to Model


Despite the 24 experiments, the process space has yet to be fully explored from a full-factorial perspective - as a result, trying to include square terms to the model would be useless because they continue to be aliased against each other.  The only path forward is to augment the data further to see if the results allow model refinement.

Augmenting the experiment to a total of 32 now and selecting only the statistically significant terms from a fit to the full-factorial model gives the same results as obtained from the previous analysis.  The key differences are the reduction in the F ratio and the loss of the pairwise interaction of NEAA and EAA.

ANOVA Results from Fit of Augmented Data to Full Factorial Model
Source
DF
Sum of Squares
Mean Square
F Ratio
Model
9
228.02583
25.3362
15.8153
Error
22
35.24409
1.6020
Prob > F
C. Total
31
263.26992

<.0001*

Parameter Estimates from Fit of Augmented Data to Full Factorial Model
Term

Estimate
Std Error
t Ratio
Prob>|t|
Intercept

7.5813733
0.228694
33.15
<.0001*
Glutamine

-0.560817
0.22865
-2.45
0.0226*
EAA

0.170159
0.241575
0.70
0.4886
NEAA

1.3289597
0.23971
5.54
<.0001*
ITS

0.4425618
0.226401
1.95
0.0634
Lipids

-0.191069
0.228817
-0.84
0.4127
Glutamine*EAA

-1.2019
0.238782
-5.03
<.0001*
EAA*Lipids

0.9275438
0.24142
3.84
0.0009*
NEAA*ITS

-0.775146
0.240365
-3.22
0.0039*
NEAA*Lipids

0.7488445
0.239475
3.13
0.0049*

The model is still unable to predict the VCD at the midpoint of the range explored (solid red triangles).  In spite of completing enough runs for a full factorial (32), the square terms of each of the main effects remain indistinguishable from each other!  What to do next?  Stay tuned!
Actual versus Predicted of Augmented Design


Singularity Details 

Glutamine*Glutamine = EAA*EAA = NEAA*NEAA = ITS*ITS = Lipids*Lipids




No comments:

Post a Comment