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RE: Log transformation of concentration

From: Bob Leary <bleary>
Date: Fri, 27 Mar 2009 09:14:02 -0400

Dear all,
I suspect any improved numerical behavior of the log transformed model =
relative to the untransformed model
 is due to the fact that with the untransformed model with a =
proportional residual error, typically
FOCE with INTERACTION would be used. But with the log transformed =
model, the
error becomes additive and INTERACTION becomes irrelevant. INTERACTION =
overall seems to have
a somewhat negative effect on numerical performance in terms of =
convergence behavior.
There is another effect - the fidelity of the FOCE approximation (with =
interaction in the untrasformed case,
without interaction in the log transformed case) to the true marginal =
likelihood is going to be different in the
two cases. The overall effect is difficult to predict, but my intuition =
is that the approximation may on average be
better in the log transformed case, since the model then is at least =
linear in EPS . Recall that if the
model is linear in both ETAS and EPS, then the FOCE approximation is =
exact . The log transform at least insures
linearity in EPS, although the effect on the ETAS may or may not be =

Robert H. Leary, PhD

Pharsight - A Certara(tm) Company
5625 Dillard Dr., Suite 205
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Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871
Email: bleary

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-----Original Message-----
From: owner-nmusers
Sent: Friday, March 27, 2009 1:54 AM
To: nmusers
Subject: Re: [NMusers] Log transformation of concentration

Dear all,

log-transformation has also some practical value. It adds stability to =
the parameter estimation process when the observations cover a wide =
range. I just had an example running with data from a phase I dose =
ranging study . The doses increased during the execution of the study =
over a 50-fold range. With fairly complete profiles I had =
concentrations which differed up to 500-fold. I fit the data on the =
linear scale and then log-transformed. Only with the log-transformed =
data was I able to fit a full BLOCK(5) OMEGA matrix. Rounding error =
terminations were diminished. The VPC was much easier as I had no =
negative predictions.

These are all just practical observations, and I cannot give you an =
eloquent statistical explanation (Leonid may). But I will log-transform =
my concentration data in the future, especially when they cover a wide =
range. Thanks also to Mats for pointing that out in his workshop.


Joachim GREVEL, Ph.D.
Merck Serono S.A. - Genève
Human Pharmacology
1202 Geneva
Tel: +41.22.414.4751
Fax: +41.22.414.3059
Email: joachim.grevel

Leonid Gibiansky <LGibiansky
Sent by: owner-nmusers

03/26/2009 11:52 PM

"Elassaiss - Schaap, J. \(Jeroen\)" <jeroen.elassaiss


Re: [NMusers] Log transformation of concentration



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 =


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 =
> 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 =
> 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 =
> 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 =
> for F. Then, after you obtain F, you take the log. In the DV =
> 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 =
> group about the log-transformed concentration. But I am still
> not very clear about this. Could anybody give me a reason to =
> 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 =
> 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 =
> solution of that equation might be different from the original
> one. If it is different, how can I explain the theta1 in the =
> transformed model?
> Would anyone please give me some explainations or references?
> Thanks a lot!
> Chenguang
> =
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Received on Fri Mar 27 2009 - 09:14:02 EDT

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