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Re: calculation of AUC

From: Nick Holford <n.holford>
Date: Sun, 22 Mar 2009 08:28:00 +0200

Sorry -- this sentence need a 'not' as follows:

"This estimate is of course a shrinkage estimate which will typically be
biased towards the population CL but I have NOT realized that there is
also EBE bias from the choice of transformation used in parameter
estimation."

Nick Holford wrote:
> 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 can’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
>>
>>
>> ------------------------------------------------------------------------
>>
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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 - 02:28:00 EDT

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