RE: Log transformation of concentration

From: Elassaiss - Schaap, J. <jeroen.elassaiss>
Date: Fri, 27 Mar 2009 07:57:13 +0100

Leonid,

Agreed! (the quotes around true are important of course). There
obviously is a better phrase for "prediction 'mode'" as I used it, but
it is more technical and general: "expectation".

It is important to be aware of these differences in expectation between
untransformed and log-transformed models (only) when comparing typical
subject predictions to a data average.

In general the differences in expectation and the differences in the
error model, as you elegantly described in your preceding post, are not
clearly mentioned when introducing students to the method of
log-transformation, to my opinion something that should be improved
upon.

Best regards,
Jeroen

-----Original Message-----
From: Leonid Gibiansky [mailto:LGibiansky
Sent: Thursday, 26 March, 2009 23:53
To: Elassaiss - Schaap, J. (Jeroen)
Cc: nmusers
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:* 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
>
> 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:
> 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
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 Fri Mar 27 2009 - 02:57:13 EDT

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