From: Toufigh Gordi 
Subject: [NMusers] Fixed or estimated?
Date:Fri, 28 Mar 2003 13:57:24 -0500

Dear all,

I have a simple PK/PD model of cell binding. I worked on the PK and then 
fixed the PK parameters and got PD estimates. Then I estimated everything 
all together.

The new estimates (when everything is free) are not identical to when PK 
parameters were fixed, although they are very similar. The question is what 
parameters to present, and what is the criteria for choosing the results 
from one model (e.g. fixed PK) over another (nothing fixed). Different 
plots from the two runs are very similar. As one might expect, OFV is lower 
in the "free" model (decreased by 11, #PK parameters=9). My second question 
is whether one can use a decrease in OFV as a guide for choosing the model 
in this case. How much should the drop be to imply a significant advantage 
of the "free" model? Does this model have 9 more parameters compared to a 
fixed PK model (which would require a much larger drop in OFV than 10 to be 
significantly better)?

Personally, I would present the results from a model where nothing is 
fixed. However, I would appreciate some discussion on the matter.

Toufigh Gordi

From: "Bachman, William" 
Subject:RE: [NMusers] Fixed or estimated?
Date: Fri, 28 Mar 2003 14:49:03 -0500

It turns out that OFV is a less than ideal criterion for goodness of fit and
I never use it as the SOLE determinant for model discrimination.  Also take
into consideration the goodness of fit plots and the magnitude of the
variance parameters.

From: Leonid Gibiansky 
Subject:Re: [NMusers] Fixed or estimated?
Date:Fri, 28 Mar 2003 15:00:15 -0500

Toufigh Gordi
This is win-win situation, no matter what you decide you have good a model 
that describe both PK and PK/PD. You may consider similarity of the 
parameters as a confirmation that your overall model is good. Which one to 
choose depend on your goals. In your case, they are nearly identical, so it 
does not matter what you do.

In general, the "fixed parameters" model provides the best fit for the PK 
data. For the PD data, this model uses PK model predictions and PD data to 
describe PK/PD relationship. "Free parameters" model may provide slightly 
worth fit for the PK data with slightly better fit for the PD data (and 
better overall fit).

You should not count PK parameters into the PD model (more precisely, you 
should count parameters even if they are fixed). Difference of 11 points 
evidence that both models are roughly equivalent, but they have the same 
number of the parameters if you  count fixed one as well.

If you need the model to describe PK data only, I would not add PD data 
there (because incorrectly chosen PK/PD model may damage otherwise good PK 
model). If you would like to describe PD data, use the best model (with 
free parameters). Similarity of two models evidence that PD data do not 
disturb PK fit, providing additional comfort.

Good luck,

From:Liping Zhang 
Subject:Re: [NMusers] Fixed or estimated?
Date:Friday, March 28, 2003 2:34 PM -0700

Dear Toufigh,

I agree with Dr. Gibiansky's recommendation completely.

If you are interested in PD model, an additional reason for using the
all-para-free model is that when you simulate (the ultimate goal of
modeling), that is the model you will use. If you use the fixed-PK model
analysis results to simulate, then you are not really simulating from the
same model as your data-analytic model.

About the OFV, I agree with Dr. Bachman, too. For the fixed-PK analysis,
you did not indicate whether you included BOTH PK and PD data to estimate
PD when you fixed the PK para to estimate PD. If you do not include both,
there is no comparison between two OFVs.

Best regards,

Liping Zhang