RE: Log transformation of concentration
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 beneficial.
Robert H. Leary, PhD
Fellow
Pharsight - A Certara(tm) Company
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Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]on
Behalf Of [email protected]
Sent: Friday, March 27, 2009 1:54 AM
To: [email protected]
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
__________________________________________
Joachim GREVEL, Ph.D.
Merck Serono S.A. - Genève
Human Pharmacology
1202 Geneva
Tel: +41.22.414.4751
Fax: +41.22.414.3059
Email: [email protected]
Leonid Gibiansky <[email protected]>
Sent by: [email protected]
03/26/2009 11:52 PM
To
"Elassaiss - Schaap, J. \(Jeroen\)" <[email protected]>
cc
[email protected]
Subject
Re: [NMusers] Log transformation of concentration
Jeroen,
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.
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
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:* [email protected]
> [mailto:[email protected]] *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
> about this.
>
> Regards!
>
> Chenguang
>
>
>
> 2009/3/26 Leonid Gibiansky <[email protected]
> <mailto:[email protected]>>
>
> 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 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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