# Re: Log transformation of concentration

From: Leonid Gibiansky <LGibiansky>
Date: Thu, 26 Mar 2009 09:21:46 -0400

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
e-mail: LGibiansky at 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
> Could anybody give me a reason to do the transform on 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
>
Received on Thu Mar 26 2009 - 09:21:46 EDT

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