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
Log transformation of concentration
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
e-mail: LGibiansky at 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
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
_____
Quoted reply history
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.
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
_____
Quoted reply history
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]>
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.
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. - Genve
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
To
"Elassaiss - Schaap, J. \(Jeroen\)" <jeroen.elassaiss
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
> 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:
> 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.
> ------------------------------------------------------------------------
This message and any attachment are confidential and may be privileged or otherwise protected from disclosure. If you are not the intended recipient, you must not copy this message or attachment or disclose the contents to any other person. If you have received this transmission in error, please notify the sender immediately and delete the message and any attachment from your system. Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not accept liability for any omissions or errors in this message which may arise as a result of E-Mail-transmission or for damages resulting from any unauthorized changes of the content of this message and any attachment thereto. Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not guarantee that this message is free of viruses and does not accept liability for any damages caused by any virus transmitted therewith.
Click http://disclaimer.merck.de to access the German, French, Spanish and Portuguese versions of this disclaimer.
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
Quoted reply history
-----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
> 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:
> 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.
>
------------------------------------------------------------------------
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.
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
Quoted reply history
-----Original Message-----
From: Leonid Gibiansky [mailto:[email protected]]
Sent: Thursday, 26 March, 2009 23:53
To: Elassaiss - Schaap, J. (Jeroen)
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
>
>
>
------------------------------------------------------------------------
> 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.
>
------------------------------------------------------------------------
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.
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
>
>
> ------------------------------------------------------------------------
> 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.
> ------------------------------------------------------------------------
This message and any attachment are confidential and may be privileged or
otherwise protected from disclosure. If you are not the intended recipient, you
must not copy this message or attachment or disclose the contents to any other
person. If you have received this transmission in error, please notify the
sender immediately and delete the message and any attachment from your system.
Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not accept
liability for any omissions or errors in this message which may arise as a
result of E-Mail-transmission or for damages resulting from any unauthorized
changes of the content of this message and any attachment thereto. Merck KGaA,
Darmstadt, Germany and any of its subsidiaries do not guarantee that this
message is free of viruses and does not accept liability for any damages caused
by any virus transmitted therewith.
Click http://disclaimer.merck.de to access the German, French, Spanish and
Portuguese versions of this disclaimer.
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
5625 Dillard Dr., Suite 205
Cary, NC 27511
Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871
Email: [email protected]
This email message (including any attachments) is for the sole use of the
intended recipient and may contain confidential and proprietary information.
Any disclosure or distribution to third parties that is not specifically
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message.
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
>
>
> ------------------------------------------------------------------------
> 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.
> ------------------------------------------------------------------------
This message and any attachment are confidential and may be privileged or
otherwise protected from disclosure. If you are not the intended recipient, you
must not copy this message or attachment or disclose the contents to any other
person. If you have received this transmission in error, please notify the
sender immediately and delete the message and any attachment from your system.
Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not accept
liability for any omissions or errors in this message which may arise as a
result of E-Mail-transmission or for damages resulting from any unauthorized
changes of the content of this message and any attachment thereto. Merck KGaA,
Darmstadt, Germany and any of its subsidiaries do not guarantee that this
message is free of viruses and does not accept liability for any damages caused
by any virus transmitted therewith.
Click http://disclaimer.merck.de to access the German, French, Spanish and
Portuguese versions of this disclaimer.