# RE: calculation of AUC

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

The NONMEM Users Network is maintained by ICON plc. Requests to subscribe to the network should be sent to: nmusers-request@iconplc.com.

Once subscribed, you may contribute to the discussion by emailing: nmusers@globomaxnm.com.