# RE: Log transformation of concentration

From: Elassaiss - Schaap, J. <jeroen.elassaiss>
Date: Thu, 26 Mar 2009 22:04:15 +0100

Dear Chenguang,

There is one difference that could be added to the excellent explanation
by Leonid; this has been previously brought forward by Mats in another
thread (Calculation of AUC) this week. When log-transforming on both
sides (TBS) your model will predict the median (geometric mean) rather
than the average of your data on the normal scale. This only will be
noticable when the residual error is large, see the values provided by
Mats. This effect does not depend on between-subject variability, i.e.
it also holds for single-subject models.

So while the log-transformation does not change the meaning of the
parameters, it will change the prediction 'mode' from average to median.

Best regards,
Jeroen

Jeroen Elassaiss-Schaap, PhD
Modeling & Simulation Expert
Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3)
Early Clinical Research and Experimental Medicine
Schering-Plough Research Institute
T: +31 41266 9320

_____

From: owner-nmusers
On Behalf Of Chenguang Wang
Sent: Thursday, 26 March, 2009 14:40
To: Leonid Gibiansky
Cc: nmusers
Subject: Re: [NMusers] Log transformation of concentration

Dear Leonid,
Thank you very much for your explaination! I think I am now much clearer

Regards!

Chenguang

2009/3/26 Leonid Gibiansky <LGibiansky

Hi Chenguang,
The main reason to do the log transformation is the numerical
algorithm used in nonmem for error model. If you try to fit the error
model
Y=F*EXP(eps)
nonmem will take only the first term of the EXP function
expansion and will use the error model
Y=F*(1+EPS)

Therefore, the only way to get true exponential (not
proportional) model is to log-transform both parts:
LOG(Y)=LOG(F)+EPS

Note that this is done on the very last step. All parameters
have the same meaning. All differential equations are written and solved
for F. Then, after you obtain F, you take the log. In the DV column, you
put the log of observed concentrations, so that your actual code is
Y=LOG(F)+EPS

Last year I compared the performance of FOCE with interaction
for models with and without log-transformation, and found the
performance to be similar (in terms of bias and precision of parameter
estimates): you can find the poster on PAGE web site. Still, for several
real data sets, I've seen that the log-transformed model provided
slightly better fit, especially for data with large residual error.

Leonid

--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com <http://www.quantpharm.com/>
e-mail: LGibiansky at quantpharm.com <http://quantpharm.com/>
tel: (301) 767 5566

Chenguang Wang wrote:

Dear NONMEM users,

I am working on a PK model and using the log-transformed
concentration data. I'v read some discussions in the NONMEM user group
about the log-transformed concentration. But I am still not very clear
concentration? Also, I am curious that after the transform, will the
fixed effect have the same meaning as that in the untransformed model?
For example, theta1 is the clearance, after log-transform of
concentration, would the estimation of theta1 still stands for the
population clearance? To my simple thinking about the differential
equation,

d(lnc)/dt= (dc/dt)*(1/c). Therefore, a "c" will be
multiplied to the right term of the orginal differential equation. I
think the solution of that equation might be different from the original
one. If it is different, how can I explain the theta1 in the log
transformed model?

Would anyone please give me some explainations or
references?

Thanks a lot!

Chenguang

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Received on Thu Mar 26 2009 - 17:04:15 EDT

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