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Figure 9.2.1 Intermediate results from Boomer (DGN Method)
The parameter to watch is the objective function (the number to be minimized) which in this case is the weighted sum of the squared residuals (WSS). It should continue to fall in value as a successful fit continues.
Figure 9.2.2 Intermediate results from Boomer (Simplex Method)
Once the nonlinear regression program has converged to the best fit solution (maybe) the final parameter values with their uncertainty will be presented.
Figure 9.2.3 Final parameter values from Boomer
Are the final results reasonable?
Figure 9.2.4 Linear plot of Cp versus time - Good CV values
Figure 9.2.4 illustrates a good fit to the provided data. Note the values for the parameter CV are all below 20%.
Figure 9.2.5 Linear plot of Cp versus time - High CV values
Figure 9.2.5 looks the same as 9.2.4, why the higher CV values? Have a closer look at the early time points!
Figure 9.2.6 Enlarged view of the early time points
Notice the second and third points are nearly superimposed. Maybe there is data entry error and even an assay error.
Another example. Again the fit looks good but the CV values for the distribution rate constants, k12 and k21, are quite large. Why?
Figure 9.2.7 Linear plot of Cp versus time - fewer data
In Figure 9.2.7 the CV are large because there aren't enough data points (at the right times) to clearly define the chosen model. More, better times data points should help. Or, maybe a smaller model.
It is important to note that the standard deviation and CV values provide by nonlinear regression programs when fitting a single subject data set have no correlation with the population variability (standard deviation) in the parameter values.
Figure 9.2.8 Error message from SAAM II - Hit limit on two parameters
This may result in a less than ideal convergence.
Figure 9.2.9 Linear plot of Cp versus time with fit constrained by parameter limit hit
Notice the poor fit. It is time to consider the parameter limits originally specified. It may be possible to simply expand the limits and refit. It might be an error in the way the model is specified however. This should be fixed. There may be a data entry error. It could be a scaling error. A dose in milligram may be confused with concentration measured in ng/L. In the present case refitting with a slighter wider limit gives a more satisfactory result.
Figure 9.2.10 Linear plot of Cp versus time with better parameter limits
Figure 9.2.11 Correlation matrix from SAAM II
A high correlation between two parameters (absolute value close to 1) might suggest that a smaller model would work. That is, it may not be necessary to include both parameters in the model.
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