From: Mats Karlsson <*mats.karlsson*>

Date: Wed, 25 Mar 2009 22:15:46 +0100

Nick,

See comments below.

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

-----Original Message-----

From: owner-nmusers

On Behalf Of Nick Holford

Sent: Tuesday, March 24, 2009 8:07 PM

To: nmusers

Subject: Re: [NMusers] calculation of AUC

Mats,

Thanks for trying to explain things further but I am still confused. I

agree for the moment we can forget about shrinkage and about computing

the central tendency over a group of subjects.

Lets just fit one individual with a model and estimate clearance then

calculate AUC from Dose/CL. If we take the same concentration

observations and compute an AUC using a trapezoidal rule then I still

dont follow your example.

M> AUCs from a model are usually calculated either to drive PD or to =

compare with NCA AUCs of observed data, as an internal validation. I was =

making a point regarding the second use of model based AUCs. Of course =

there are many situations where AUC is not dose/CL, whenever AUC is =

calculated by trapezoidal rule is one of them.

If you want to compare like with like - model-based trapezoidal rule =

AUCs with real data trapezoidal rule AUCs - you should also take into =

the error generation structure. If you get data that have reported =

negative concentration (as you discuss below) it is appropriate to use a =

simulation that mimics that. I never see that type of data and try to =

mimic the error generation process of more common structure. Naturally =

you should treat your simulated data just as the real data.

You say:

"The exponentiation of (LOG(F)+EPS(1)) will not give the expected mean =

of F, but something higher. [this is what you can calculate =

model-simulated NCA AUCs from]"

but I dont understand what you mean by "this is what you calculate

model-simulate NCA AUCs from".

I am not thinking of calculating NCA AUCs from simulated concentrations. =

I expect to use real measured concentrations.

Simulating concentrations which force all concentrations to be

non-negative is a biased simulation of reality. If there is any

possibility of an additive error then there is a possibility of a

negative measured concentration. Real assays can have additive errors so =

real assays must be capable of measuring values that appear to be

negative. Note the difference between the true concentration which must

be non-negative and the measured concentration, i.e. the truth plus

error, which can be negative if the error is additive.

Nick

Mats Karlsson wrote:

*> Dear Nick,
*

*>
*

*> I did not discuss shrinkage because it didn't concern the point I was =
*

trying (and maybe failing) to make. [However, I don't think that if one =

wants to compare with NCA AUCs, data are likely to be rich with =

reasonably small shrinkage]

*>
*

*> I used proportional residual error as an example. Doesn't really =
*

matter which residual error you use - going from the normality =

assumption on the log scale to normal scale would always make the mean =

of a simulated observation higher than the mean. Mean(exp(epsilon)) is =

going to be higher than 1 regardless of residual error model.

*>
*

*> The point I'm trying to make is not how you calculate the central =
*

tendency of several AUCs, it concerns the calculation of individual =

AUCs.

*>
*

*> The problem I point out is relevant when you compare NCA AUCs from =
*

observed data with NCA AUCs from model predictions, regardless if you =

use linear or log-linear trapezoidal rules. Observed NCA AUCs are =

expected to be higher than NCA AUCs from model-predicted (but not higher =

than model simulated) AUCs calculated by NCA (from the same sampling =

schedule).

*> For a model:
*

*> Y=LOG(F)+EPS(1)
*

*> The exponentiation of LOG(F) will give the expected mean of F [from =
*

which model-predicted NCA AUC will be calculated]

*> The exponentiation of (LOG(F)+EPS(1)) will not give the expected mean =
*

of F, but something higher. [this is what you can calculate =

model-simulated NCA AUCs from]

*>
*

*> Thus model-predicted and model-simulated NCA AUCs will be =
*

systematically different if they are calculated in this way. I expect =

that if the model is correct, the observed NCA AUCs will be more similar =

to the simulated NCA AUCs.

*>
*

*> Hope this makes it clearer.
*

*>
*

*> 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
*

*>
*

*>
*

*> -----Original Message-----
*

*> From: owner-nmusers *

[mailto:owner-nmusers

*> Sent: Sunday, March 22, 2009 7:09 AM
*

*> To: nmusers
*

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

*>
*

*> 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 *

Bergstrand*

*>> 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 *

<mailto: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 Wed Mar 25 2009 - 17:15:46 EDT

Date: Wed, 25 Mar 2009 22:15:46 +0100

Nick,

See comments below.

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

-----Original Message-----

From: owner-nmusers

On Behalf Of Nick Holford

Sent: Tuesday, March 24, 2009 8:07 PM

To: nmusers

Subject: Re: [NMusers] calculation of AUC

Mats,

Thanks for trying to explain things further but I am still confused. I

agree for the moment we can forget about shrinkage and about computing

the central tendency over a group of subjects.

Lets just fit one individual with a model and estimate clearance then

calculate AUC from Dose/CL. If we take the same concentration

observations and compute an AUC using a trapezoidal rule then I still

dont follow your example.

M> AUCs from a model are usually calculated either to drive PD or to =

compare with NCA AUCs of observed data, as an internal validation. I was =

making a point regarding the second use of model based AUCs. Of course =

there are many situations where AUC is not dose/CL, whenever AUC is =

calculated by trapezoidal rule is one of them.

If you want to compare like with like - model-based trapezoidal rule =

AUCs with real data trapezoidal rule AUCs - you should also take into =

the error generation structure. If you get data that have reported =

negative concentration (as you discuss below) it is appropriate to use a =

simulation that mimics that. I never see that type of data and try to =

mimic the error generation process of more common structure. Naturally =

you should treat your simulated data just as the real data.

You say:

"The exponentiation of (LOG(F)+EPS(1)) will not give the expected mean =

of F, but something higher. [this is what you can calculate =

model-simulated NCA AUCs from]"

but I dont understand what you mean by "this is what you calculate

model-simulate NCA AUCs from".

I am not thinking of calculating NCA AUCs from simulated concentrations. =

I expect to use real measured concentrations.

Simulating concentrations which force all concentrations to be

non-negative is a biased simulation of reality. If there is any

possibility of an additive error then there is a possibility of a

negative measured concentration. Real assays can have additive errors so =

real assays must be capable of measuring values that appear to be

negative. Note the difference between the true concentration which must

be non-negative and the measured concentration, i.e. the truth plus

error, which can be negative if the error is additive.

Nick

Mats Karlsson wrote:

trying (and maybe failing) to make. [However, I don't think that if one =

wants to compare with NCA AUCs, data are likely to be rich with =

reasonably small shrinkage]

matter which residual error you use - going from the normality =

assumption on the log scale to normal scale would always make the mean =

of a simulated observation higher than the mean. Mean(exp(epsilon)) is =

going to be higher than 1 regardless of residual error model.

tendency of several AUCs, it concerns the calculation of individual =

AUCs.

observed data with NCA AUCs from model predictions, regardless if you =

use linear or log-linear trapezoidal rules. Observed NCA AUCs are =

expected to be higher than NCA AUCs from model-predicted (but not higher =

than model simulated) AUCs calculated by NCA (from the same sampling =

schedule).

which model-predicted NCA AUC will be calculated]

of F, but something higher. [this is what you can calculate =

model-simulated NCA AUCs from]

systematically different if they are calculated in this way. I expect =

that if the model is correct, the observed NCA AUCs will be more similar =

to the simulated NCA AUCs.

[mailto:owner-nmusers

I

the

part

relies

constant

the

typically

to

knowledge

sampling

:-)

------------------------------------------------------------------------

------------------------------------------------------------------------

Bergstrand*

possible to

You

<mailto:martin.bergstrand

------------------------------------------------------------------------

--

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 Wed Mar 25 2009 - 17:15:46 EDT