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Re: Log transformation of concentration

From: Chenguang Wang <>
Date: Thu, 26 Mar 2009 14:39:38 +0100

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



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:
> 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
> 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:
> e-mail: LGibiansky at
> 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 about this.
>> 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 - 09:39:38 EDT

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