From: Nick Holford <*n.holford*>

Date: Sun, 22 Mar 2009 08:08:55 +0200

Mats,

This is an interesting idea but it seems to be more complicated than

just a consideration of the residual variability (RV%) when using log

transformation with transform both sides (TBS) estimation.

First of all you appear to assume that the RV% is only a proportional

residual error but if could also include an additive component when

using TBS so that there is not a single RV% that would describe a

particular situation because it would change with concentration.

A model based estimate of AUC would typically be based on an empirical

Bayes estimate (EBE) of CL. This estimate is of course a shrinkage

estimate which will typically be biased towards the population CL but I

have realized that there is also EBE bias from the choice of

transformation used in parameter estimation. Thus I would not expect the

model based estimate to be additionally biased because of using EBEs

with TBS. This is probably something you have thought about so please

inform me.

Turning to the NCA method - I dont know if a bias is expected from the

NCA calculated AUC but I would naively assume that the trapezoidal part

would not be biased. I am ready to learn if there is a bias expected

with trapezoidal NCA. I expect this has been investigated and reported

but I am not familiar with it. The extrapolated portion typically relies

on a log linear transformation to estimate the elimination rate constant

which so in this respect the log transformed model based and NCA based

methods would seem to be similar.

Another source of difference between model and NCA based AUCs might

arise from the use of different statistics to describe the central

tendency of the indidual estimates. NCA estimates could be based on the

arithmetic mean of the individual AUC sor on the geometric mean (most

commonly used for bioequivalence analysis). The model based estimates

based on the arithmetic mean of the EBE predicted AUCs would be biased

towards the geometric mean because the population value would typically

be estimated with an exponential ETA.

If you have the time would you expand on the details of your assertion

so that I and others can understand the basis more clearly? It seems to

me that comparison of model based AUCs with NCA based AUCs is more

complicated than just a consideration of the typical value of the

residual error.

Nick

Mats Karlsson wrote:

*>
*

*> Dear Ethan,
*

*>
*

*>
*

*>
*

*> Just a caution when comparing model-based AUCs with NCA calculated
*

*> AUCs. If you have done your modeling using log-transformation of
*

*> observations and model predictions and then compared AUCs on the
*

*> linear scale, you should not expect a perfect agreement between the
*

*> two. The reason is that the mean of an exponentiated distribution of
*

*> epsilons is not the same as the median, but higher. Thus, the AUCs of
*

*> model-predicted individual profiles will be expected to be lower than
*

*> either simulated or observed. The magnitude of the difference will
*

*> depend on the residual error magnitude and will typically be:
*

*>
*

*>
*

*>
*

*> %RV expected AUC difference
*

*>
*

*> 10 0.50%
*

*>
*

*> 20 2%
*

*>
*

*> 30 5%
*

*>
*

*> 40 9%
*

*>
*

*> 50 14%
*

*>
*

*> 70 29%
*

*>
*

*>
*

*>
*

*> Best regards,
*

*>
*

*> Mats
*

*>
*

*>
*

*>
*

*> Mats Karlsson, PhD
*

*>
*

*> Professor of Pharmacometrics
*

*>
*

*> Dept of Pharmaceutical Biosciences
*

*>
*

*> Uppsala University
*

*>
*

*> Box 591
*

*>
*

*> 751 24 Uppsala Sweden
*

*>
*

*> phone: +46 18 4714105
*

*>
*

*> fax: +46 18 471 4003
*

*>
*

*>
*

*>
*

*> *From:* owner-nmusers *

*> [mailto:owner-nmusers *

*> *Sent:* Friday, March 20, 2009 6:52 PM
*

*> *To:* Michael.J.Fossler *

*> *Subject:* Re: [NMusers] calculation of AUC
*

*>
*

*>
*

*>
*

*> sorry for being lazy this morning and wish relying on others knowledge
*

*>
*

*> just to share, I used DADT=C method, and it didn't depend on sampling
*

*> after I tried with my model (which took quite a while to get results)
*

*>
*

*> -- I could do as Bill suggested setting up some small dataset and
*

*> simple model to check first, then would share with the group ealier :-)
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> ------------------------------------------------------------------------
*

*>
*

*> *From:* "Michael.J.Fossler *

*> *To:* nmusers *

*> *Sent:* Friday, March 20, 2009 9:42:59 AM
*

*> *Subject:* Fw: [NMusers] calculation of AUC
*

*>
*

*>
*

*> I second Bill's suggestion to work this out on your own for your
*

*> specific problem. This forum can help you with general questions and
*

*> overall approaches, but very specific queries like this are for you
*

*> and your colleagues to hash out.
*

*>
*

*> *Error! Filename not specified.*
*

*> ----- Forwarded by Michael J Fossler/PharmRD/GSK on 03/20/2009 09:40
*

*> AM -----
*

*>
*

*> *"Bill Bachman" <bachmanw *

*> Sent by: owner-nmusers *

*>
*

*> 20-Mar-2009 09:17
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> To
*

*>
*

*>
*

*>
*

*> "'Martin Bergstrand'" <martin.bergstrand *

*> <ethan.wu75 *

*>
*

*> cc
*

*>
*

*>
*

*>
*

*> Subject
*

*>
*

*>
*

*>
*

*> RE: [NMusers] calculation of AUC
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> The easiest answer is to work it out. Do some simulations (without
*

*> variability) with multiple subjects with identical PK parameters BUT
*

*> different sampling times. Tabulate your AUCs and compare the results
*

*> for different sampling times!
*

*>
*

*>
*

*>
*

*>
*

*> ------------------------------------------------------------------------
*

*>
*

*>
*

*> *From:* owner-nmusers *

*> [mailto:owner-nmusers *

*> Sent:* Friday, March 20, 2009 8:45 AM*
*

*> To:* 'Ethan Wu'; nmusers *

*> Subject:* RE: [NMusers] calculation of AUC
*

*>
*

*> Dear Ethan,
*

*>
*

*> You need to provide more information on how you plan to calculate AUC
*

*> otherwise the question canâ€™t be answered. It is of course possible to
*

*> calculate the AUC without any influence of the sampling frequency. You
*

*> should be able to find examples of how to do this in the NMusers
*

*> archive. See for example the answer from Mats Karlsson in this thread
*

*> (http://nonmem..org/nonmem/nm/98apr032002.html
*

*> <http://nonmem.org/nonmem/nm/98apr032002.html>).
*

*>
*

*> Kind regards,
*

*>
*

*> Martin Bergstrand, MSc, PhD student
*

*> -----------------------------------------------
*

*> Department of Pharmaceutical Biosciences,
*

*> Uppsala University
*

*> -----------------------------------------------
*

*> P.O. Box 591
*

*> SE-751 24 Uppsala
*

*> Sweden
*

*> -----------------------------------------------
*

*> martin.bergstrand *

*> -----------------------------------------------
*

*> Work: +46 18 471 4639
*

*> Mobile: +46 709 994 396
*

*> Fax: +46 18 471 4003
*

*>
*

*>
*

*> *From:* owner-nmusers *

*> [mailto:owner-nmusers *

*> Sent:* den 20 mars 2009 13:05*
*

*> To:* nmusers *

*> Subject:* [NMusers] calculation of AUC
*

*>
*

*> Hi all, to calculate AUC of one of the compartments using ADVAN6, if
*

*> it is a fixed time interval, will the AUC be influenced by the
*

*> frequncy of sampling of the dataset within this interval or not?
*

*> thanks
*

*>
*

*>
*

*> ------------------------------------------------------------------------
*

*>
*

*> No viruses found in this incoming message
*

*> Scanned by *iolo AntiVirus 1.5.6.4*_
*

*> _http://www.iolo.com <http://www.iolo.com/iav/iavpop3>
*

*>
*

*>
*

*>
*

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand

n.holford

http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Sun Mar 22 2009 - 02:08:55 EDT

Date: Sun, 22 Mar 2009 08:08:55 +0200

Mats,

This is an interesting idea but it seems to be more complicated than

just a consideration of the residual variability (RV%) when using log

transformation with transform both sides (TBS) estimation.

First of all you appear to assume that the RV% is only a proportional

residual error but if could also include an additive component when

using TBS so that there is not a single RV% that would describe a

particular situation because it would change with concentration.

A model based estimate of AUC would typically be based on an empirical

Bayes estimate (EBE) of CL. This estimate is of course a shrinkage

estimate which will typically be biased towards the population CL but I

have realized that there is also EBE bias from the choice of

transformation used in parameter estimation. Thus I would not expect the

model based estimate to be additionally biased because of using EBEs

with TBS. This is probably something you have thought about so please

inform me.

Turning to the NCA method - I dont know if a bias is expected from the

NCA calculated AUC but I would naively assume that the trapezoidal part

would not be biased. I am ready to learn if there is a bias expected

with trapezoidal NCA. I expect this has been investigated and reported

but I am not familiar with it. The extrapolated portion typically relies

on a log linear transformation to estimate the elimination rate constant

which so in this respect the log transformed model based and NCA based

methods would seem to be similar.

Another source of difference between model and NCA based AUCs might

arise from the use of different statistics to describe the central

tendency of the indidual estimates. NCA estimates could be based on the

arithmetic mean of the individual AUC sor on the geometric mean (most

commonly used for bioequivalence analysis). The model based estimates

based on the arithmetic mean of the EBE predicted AUCs would be biased

towards the geometric mean because the population value would typically

be estimated with an exponential ETA.

If you have the time would you expand on the details of your assertion

so that I and others can understand the basis more clearly? It seems to

me that comparison of model based AUCs with NCA based AUCs is more

complicated than just a consideration of the typical value of the

residual error.

Nick

Mats Karlsson wrote:

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand

n.holford

http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Sun Mar 22 2009 - 02:08:55 EDT