From: Elassaiss - Schaap, J. <*jeroen.elassaiss*>

Date: Thu, 26 Mar 2009 22:04:15 +0100

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

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 <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 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

This message and any attachments are solely for the intended recipient. =

If you are not the intended recipient, disclosure, copying, use or =

distribution of the information included in this message is prohibited =

--- Please immediately and permanently delete.

Received on Thu Mar 26 2009 - 17:04:15 EDT

Date: Thu, 26 Mar 2009 22:04:15 +0100

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

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 <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 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

This message and any attachments are solely for the intended recipient. =

If you are not the intended recipient, disclosure, copying, use or =

distribution of the information included in this message is prohibited =

--- Please immediately and permanently delete.

Received on Thu Mar 26 2009 - 17:04:15 EDT