# RE: calculation of AUC

From: Mats Karlsson <mats.karlsson>
Date: Sun, 22 Mar 2009 21:46:47 +0100

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
On Behalf Of Nick Holford
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
>
>
> =
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>

--
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 - 16:46:47 EDT

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