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Re: Log transformation of concentration

From: Leonid Gibiansky <LGibiansky>
Date: Thu, 26 Mar 2009 18:52:37 -0400


I think that the goal of modeling is to recover (predict) the underlying
quantity (concentration, pd effect, whatever we are modeling). Our
assumptions about the model (error model, in particular) help us (if
they are correct) to recover those quantities. So there is no such thing
as "prediction mode": we should always predict the underlying quantity.
If the "true" error model is additive or proportional, then, given 1000
observations at the same true-concentration level, true concentration is
equal to the mean of those observations. If the "true" error model is
exponential, then, given the same 1000 observations, concentration is
equal to the geometric mean of the observations. If the true model is
exponential but we fit an additive model, then the fit is biased
(relative to the true value), and vice versa. Investigation of the data
should allow (in theory, given sufficient amount of data) to recover the
true model, including the true error model. Log-transformation is just
the trick that allows to implement the exponential error model in nonmem.


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Elassaiss - Schaap, J. (Jeroen) wrote:
> 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
> [mailto:owner-nmusers
> *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
> about this.
> Regards!
> Chenguang
> 2009/3/26 Leonid Gibiansky <LGibiansky
> <mailto: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
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Received on Thu Mar 26 2009 - 18:52:37 EDT

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