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Dear All
I am now suprising that there are still be quite a few people estimate the
AUC by using the linear trepazoid. According to Gabrielsson textbook for
PK and PD data analysis, their group strongly suggested the log/linear
trepazoid. I myself teach my students to do the log/linear trepazoid.
However, i found that in pharm industry, quite a few of people still used
the linear one. Could anybody please contribute to comment on using linear
or log/linear trepazoid. Thank you very much.
Best regards
Asoc. Prof. Dr. Korbtham Sathirkaul
Faculty of Pharmacy
Mahidol University
Bangkok, Thailand.
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My own preference is to dispense with either of the two methods below
(which I label AUTs - Area Under the Trapezoids) that were originally
developed as a quick and dirty approximations to the real
AUC - Area under the Curve.
I prefer to use the real Area under the Curve from the fitted model.
For example, in the simple exponential model, this is easily estimated
as Co/ke, where Co is the estimated concentration at time 0
and ke is the estimated elimination coefficient.
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Dear Dr. Sathirakul:
About AUC's. Why not make a model of the behavior of the
drug, and then simulate with the model and compute the AUC that way?
You could use a Bayesian approach based first on a population model
and then on whatever serum data you obtain from an individual
patient. You would also capture the relationships between the doses,
the concentrations found, and the AUC, and it would be easy to
compute the regimen to achieve a desired concentration for a desired
time, or a desired profile until a desired AUC is reached? Any
comments, anyone?
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
****
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Here are several useful papers on the AUC / noncompartmental analysis topic --
Robert Purves
"Optimum Numerical Integration Methods for Estimation of Area-Under-the-Curve
(AUC) and Area-Under-the-Moment-Curve (AUMC)" in JPB 20: 211-226 (1992).
KC Yeh and KC Kwan, "A Comparison of Numerical Integrating Algorithms by
Trapezoidal, Lagrange, and Spline Approximation" Journal of
Pharmacokinetics and
Biopharmaceutics (JPB) 6: 79-98 (1978).
ML Rocci, Jr and WJ Jusko, "LAGRAN program for area and moments in
pharmacokinetic analysis" Computer Programs in Biomedicine 16: 203-216 (1983)
P.B. Laub and J.M. Gallo
"NCOMP - A Windows-based Computer Program for
Noncompartmental Analysis of Pharmacokinetic Data"
J. Pharm. Sci. 85: 393-395 (1996)
Paul
--
-- 30 -- 30 -- 30 --
Mr. Paul B. Laub Expression Bioinformatics (650) 845-5411 (voice)
Incyte Genomics (650) 855-0572 (fax)
3160 Porter Dr. Palo Alto, CA 94304 plaub.-a-.incyte.com
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I find this post needs some comment.
>
> My own preference is to dispense with either of the
> two methods below
> (which I label AUTs - Area Under the Trapezoids)
> that were originally
> developed as a quick and dirty approximations to
> the real
> AUC - Area under the Curve.
Really? This method is used in every other field of
science to calculate the area under a curve. I can
assure you it was not developed as a quick and dirty
approximation - it was just good mathematics (and
still is).
If the rate of change of concentration is first-order
with respect to concentration, the Log-linear method
gives the *exact* area between two data points. No
quick and dirty here.
>
> I prefer to use the real Area under the Curve from
> the fitted model.
Models are never perfect, therefore you will still
only find an estimate of the "real" AUC in this way.
Why rely on the accuracy of any model when you can use
one of the trapezoid methods?
=====
Stephen Day
Merck-Frosst Centre for Therapeutic Research
Kirkland, QC CANADA
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Dear Drs. Jelliffe, Sathirakul, et al,
While we are on the subject of AUC's. I analyzed some data on a 3rd
generation cephalosporin after IV, IM and subcutaneous administration in
animals. The AUC after IM and sub Q came out significantly higher than
after IV, so bioavailability is >100%. I determined the AUC using the
trapezoidal approximations. Since I am going to have to go back and try to
determine how this happened, could anyone suggest why? I suppose, that
after IV the drug is more rapidly cleared via the kidney than after IM/SQ.
Any thoughts for a beginner?
Jeff Lakritz DVM, PhD.
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[A few replies from over the weekend - db]
Sender: PharmPK.aaa.boomer.org
Reply-To: Nick Holford
MIME-Version: 1.0
From: Nick Holford
Date: Sat, 05 Aug 2000 08:46:49 +1200
To: david.-at-.boomer.org
Subject: Re: PharmPK Re: Log-linear or linear trapezoid
The following message was posted to: PharmPK
"Derrick J (Rick) Bates (by way of David_Bourne)" wrote:
> My own preference is to dispense with either of the two methods below
> (which I label AUTs - Area Under the Trapezoids) that were originally
> developed as a quick and dirty approximations to the real
> AUC - Area under the Curve.
The "AUT"s (0-inf or over SS Dosing Interval) are themselves only of
any real PK value as initial estimates of Clearance/F.
> I prefer to use the real Area under the Curve from the fitted model.
> For example, in the simple exponential model, this is
>easily estimated
> as Co/ke, where Co is the estimated concentration at time 0
> and ke is the estimated elimination coefficient.---
More generally (any number of compartments) "real" AUC can be
computed from Dose*F/CL. Any (linear) PK model should be
parameterizable in terms of CL/F so you only need to know one
parameter (CL/F) (rather than two, C0,ke, as Derrick suggests).
But if I have an estimate of CL/F why would I have any
pharmacokinetic reason to bother calculating AUC? Perhaps the only
reason is to satisfy regulatory bioequivalance guidelines -- but in
this context any pharmacokinetic science (e.g. compartmental models)
is typically too hard for the regulators and one must resort to
empirical AUC, Tmax, Cmax statistics developed at the Walt Disney
School of Pharmacokinetics.
AUC (derived from Dose*F/CL) has some use as an empirical "exposure"
quantity in pharmacodynamics. But because information about time is
necessarily lost by integration of C wrt t learning about schedule
dependence is very hard. I believe the AUC approach to
pharmacodynamics was also developed at the Walt Disney School of
Pharmacokinetics. Many graduates of WDSP seem to be working in the
anti-cancer field which is perhaps a reflection of why it is
difficult to find examples that demonstrate that AUC is any better
than dose as a predictor of drug response in this area.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
---
Sender: PharmPK.aaa.boomer.org
Reply-To: "J.G. Wright"
MIME-Version: 1.0
From: "J.G. Wright"
Date: Mon, 7 Aug 2000 12:07:42 +0100 (GMT)
To: david.at.boomer.org
Subject: Re: PharmPK Re: Log-linear or linear trapezoid
The following message was posted to: PharmPK
Dear Stephen,
Let say I give a bolus dose, and then take a couple of samples. In all
but a few cases (eg enterohepatic recycling), concentration will decrease
with time. So if I put my
first point at time zero, concentration zero, I will miss a big chunk
of the AUC and obtain
correspondingly biased estimates of clearances. If you back-extrapolate
in some way, then you are modelling and you may a well do it in a
statistical manner, acknowledging uncertainty.
Join-the-dots pharmacokinetics (whatever good mathematics it calls upon)
ignores two fundamental factors - the dosing history and the existence of
error. You say that the loglinear trapezoidal gives an exact area between
two points - this would only be true if the samples are error-less. They
are measured with error and it probably will not be the same at both
points.
There is a common misconception that noncompartmental methods are
model-independent. This is not the case, they are simply based on
assumptions which are somewhat physiologically strange (straight lines
join the dots,
on some scale) and hence unstated. As the use of
AUC to calculate clearance depends on many of the assumptions required for
a simple compartmental model, speed and perhap simplicity are all that is
gained.
In a pharmacological context, there is a lot to understand. Join-the-dots
pharmacokinetics doesn't acknowledge its assumptions and furthermore
provides no diagnostics for when they are violated. A method cannot be
divorced from its context - trapezoidal AUCs are quick and very dirty.
On the other hand,
timing error won't make much difference...
Regards,
James Wright
---
Sender: PharmPK.-a-.boomer.org
Reply-To: "Bhatti, Masood"
MIME-Version: 1.0
From: "Bhatti, Masood"
Date: Mon, 7 Aug 2000 09:22:52 -0400
To: david.-a-.boomer.org
Subject: RE: PharmPK Re: Log-linear or linear trapezoid
The following message was posted to: PharmPK
Dear Jeff,
Is it possible that your drug is undergoing first pass lung metabolism after
I.V. administration?
Masood Bhatti
Section Leader
Purdue Pharma
---
Sender: PharmPK.-a-.boomer.org
Reply-To: zhao wang
Mime-Version: 1.0
From: zhao wang
Date: Mon, 07 Aug 2000 09:05:01 -0500
To: david.at.boomer.org
Subject: Re: PharmPK Re: Log-linear or linear trapezoid
The following message was posted to: PharmPK
I think:
1) IV does not make kidney clearance "more rapidly"and this the one
of the assumptions that is made to estimate BA;
2) Try normalize the dose by body weight for each subject being studied;
3) Try use the same subject for different administration;
4) Simultaneously IV, oral and sub Q modeling to estimate BA will be
more accuracy but you need a software like SAAM II.
5) If each study (different dose administration ) is from different
subject, there will be some variation of Vd and Cle from either
inter-or intra individuals and therefore, if the variation of BA
estimation is within this range, it should be acceptable, 105% of BA
does not mean BA > 100%, but the variation of estimation.
Just some thoughts.
Zhao Wang, M.D.
Northwestern University Medical School
Anesthesia Research
---
Sender: PharmPK.aaa.boomer.org
Reply-To: "David S. Farrier"
Mime-Version: 1.0
From: "David S. Farrier"
Date: Mon, 07 Aug 2000 10:35:49 -0400
To: david.-at-.boomer.org
Subject: Re: PharmPK Re: Log-linear or linear trapezoid
The following message was posted to: PharmPK
A group from Phoenix International's PK Department presented a poster in
1996 at the AAPS annual meeting. They ran simulations comparing the results
of calculating AUC using trapezoid, log-trapezod, and spline smoothing
methods. Their conclusion was: given the normal variability of plasma level
data, the log-trapezoid and spline methods did not give a statistically
better estimate of the AUC than the standard trapezoid rule.
We built and tested a module for PK Solutions that produced a side-by-side
comparison of AUC values (partials and cumulative) calculated by both the
standard trapezoid and log-trapezoid methods. The overall results were
statistically so similar, except with rare and unlikely plasma profiles,
that we decided to only use the standard trapezoid method for our software.
Not that log-trapezoid is any more difficult or sophisticated, but why make
things more esoteric when the simpler approach is adequate and justified.
David
David S. Farrier, Ph.D.
Summit Research Services
1374 Hillcrest Drive
Ashland, OH 44805 USA
Tel/Fax: (419)-289-9207
Email: DFarrier.aaa.SummitPK.com
Web Site: www.SummitPK.com
[I seem to remember a paper by Kwan (some time back) that came to a
similar conclusion...I had a graduate student do some (limited)
simulations once and we came to same conclusion. However, Purves
paper and suggestion convinced to add a one after the other
comparison in Boomer output. Linear trapezoid and Purves' linear /
log-linear method - db]
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Dr.Lakritz,
The reason why bioavailability(F)= AUCoral/AUCiv is that
the first order absorption equation Cp= [KaFd/Vd(Ka-Ke)][e-Ket- e-Kat]
when integrated from infinity->0 reduces to:
AUCoral= FD/VdKe
When compared to AUCiv= D/VdKe
AUCoral= (F)*AUCiv
Since an F value greater than one is not possible, the possibility
of a decreased Ke when given by the IV route is one of the most likely
possibilities. At any rate, some factor is affecting the determination
of the Ke value when given by different routes.
Mike Leibold, PharmD, RPh
ML11439.aaa.goodnet.com
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Dear Friends,
I've been following your interesting discussion concerning the AUC
determination. I'd like to add one more aspect to the discussion
that, in my understanding, nobody has addressed yet.
The analytical error at the end of a concentration vs. time curve
increases (especially when the concentrations are analyzed to the
limit of the method). There appears to be a possibility that only
data points that fall on the "positive" side of the LOQ will be
recorded while those on the "negative" side would fall in the
category of non-quantifiable. This seems to be a possibility
especially with shallow curves.
My question is: What is the effect of the analytical error at or
close to the LOQ on the determination of AUC by curve fitting
especially when weighting is used?
With best regaards,
Stefan Soback, DVM, PhD
Kimron Veterinary Institute
Beit Dagan
Israel
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by way of David_Bourne wrote:
>
> The reason why bioavailability(F)= AUCoral/AUCiv is that
> the first order absorption equation Cp= [KaFd/Vd(Ka-Ke)][e-Ket- e-Kat]
> when integrated from infinity->0 reduces to:
>
> AUCoral= FD/VdKe
> Since an F value greater than one is not possible, the possibility
> of a decreased Ke when given by the IV route is one of the most likely
> possibilities. At any rate, some factor is affecting the determination
> of the Ke value when given by different routes.
Algebra CL=Vd x Ke
Biology Ke=CL / Vd
From a biological perspective clearance and volume of distribution are
quite distinct. Ignoring random variation one can consider them to be
"constant". The elimination rate "constant" is only a constant if CL and
Vd do not change. A change in either CL or Vd will alter Ke.
However, ONLY a change in CL will change AUC. A change in Vd cannot
change AUC (for a drug wihe linear kinetics integrated from 0-inf for a
single dose or over a dosing interval at steady state).
The asssumption of linear kinetics is easily violated when oral doses
are given. Rate dependent extent of absorption can occur easily because
portal vein concs can be high enough to cause the mixed order
elimination during first pass. Inspection of plasma conc profiles may
only support first order elimination.
A higher AUCoral than AUCiv can occur if the oral absorption rate is
rapid. This can lead to erroneous conclusions. One of the most infamous
examples is the widely cited but erroneous assertion that the stomach is
a major source of first pass metabolism of ethanol. Frezza M. di Padova
C. Pozzato G. Terpin M. Baraona E. Lieber CS. High blood alcohol levels
in women. The role of decreased gastric alcohol dehydrogenase activity
and first-pass metabolism [published errata appear in N Engl J Med 1990
May 24;322(21):1540 and 1990 Aug 23;323(8):553] New England Journal of
Medicine. 322(2):95-9, 1990 Jan 11. These authors completely ignored the
mixed order elimination of ethanol and interpreted the ratio of
AUCoral/AUViv as a measure of extent of absorption. The NEJM is not an
authoratative source for PK issues!
--
Nick Holford, Division of Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, 85 Park Road, Auckland, NZ
email: n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
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"stefans (by way of David_Bourne)" wrote:
>
> The analytical error at the end of a concentration vs. time curve
> increases (especially when the concentrations are analyzed to the
> limit of the method). There appears to be a possibility that only
> data points that fall on the "positive" side of the LOQ will be
> recorded while those on the "negative" side would fall in the
> category of non-quantifiable. This seems to be a possibility
> especially with shallow curves.
>
> My question is: What is the effect of the analytical error at or
> close to the LOQ on the determination of AUC by curve fitting
> especially when weighting is used?
The role of analytical error (and other sources of random variation) can
be recognized by using a model based approach and bypassing the Walt
Disney AUC step all together.
--
Nick Holford, Division of Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, 85 Park Road, Auckland, NZ
email: n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
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Dear Members
My opinion on the issue is as follows
1. In case of biological research field especially like PK, we can closely
approximate the facts and not determine them exactly. And I feel it
impossible and un-necessary as well to have 100% accuracy. (one of the
factors is cost involved).
With the accuracy and precision levels currently prevailing, the purpose of
studying the PK of drugs is generally seved.
2. The impact of the values close to LOQ on AUC can be ignored. Because the
contribution of the corresponding AUC(Tm to Tn) to the total AUC is
generally small.
3. In very few cases it may not be so. Then the analytical method needs
'upgradation'
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>The role of analytical error (and other sources of random variation) can
>be recognized by using a model based approach and bypassing the Walt
>Disney AUC step all together.
>
>--
>Nick Holford, Division of Pharmacology & Clinical Pharmacology
True Nick, except FDA only accepts the Disney-like, model-independent
approach for bioequivalence studies.
David S. Farrier, Ph.D.
Summit Research Services
1374 Hillcrest Drive
Ashland, OH 44805 USA
Tel/Fax: (419)-289-9207
Email: DFarrier.-a-.SummitPK.com
Web Site: www.SummitPK.com
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Dear Members:
About accuracy and precision. They ARE important. At least
for potentially toxic drugs, we are not playing with data, we are
modeling it so we can act on it OPTIMALLY, that is, to develop dosage
regimens to achieve desired target goals with maximal precision.
The issue of LOQ is also important here. I hate to belabor
this point, but when we have no other info about the specimen except
the measured value itself, then there most certainly IS a LOQ.
However, when we do most PK work, that is not the case. We know, with
reasonable precision, when the doses were given and when the samples
were obtained. So we know the drug is really present. Even simple
linear models show us that the last molecule is never excreted. So,
instead of having to ask, as we must in toxicological work, if the
drug is PRESENT OR NOT, and having therefore to develop a LOQ, we
know the drug is present. The question being asked is not the same as
in toxicology. It is instead - HOW MUCH drug is present?
Now comes the question of weighting the data optimally. Most
people agree that weighting data by its Fisher information is
appropriate - the reciprocal of the variance of the data point. It
works quite well. The point is that when you determine the assay
error and express it as a polynomial function of the concentration,
that important relationship continues over the entire range of the
assay, down to and including the blank, if you set it up correctly.
This point is discussed in more detail in an article in Therap Drug
Monit 15:380-393, 1993, especially the section on Evaluating the
Credibility of Population Parameter Values and Serum Level Data, pp.
386-391.
Best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.-a-.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
*******
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> I've been following your interesting discussion concerning the AUC
> determination. I'd like to add one more aspect to the discussion
> that, in my understanding, nobody has addressed yet.
>
> The analytical error at the end of a concentration vs. time curve
> increases (especially when the concentrations are analyzed to the
> limit of the method).
First, a digression from your main point below.
Well, it is true that the analytical error/precision at the end of
a concentration vs. time curve typically increases in a RELATIVE
sense, i.e, the analytical error relative to the result increases.
It is also true that the analytical error/precision at the end of
a concentration vs. time curve generally decreases in an ABSOLUTE
sense, i.e. the analytical error/precision itself gets smaller and
smaller towards the end of the concentration vs. time curve
(basically the low end of the calibration curve).
> There appears to be a possibility that only
> data points that fall on the "positive" side of the LOQ will be
> recorded while those on the "negative" side would fall in the
> category of non-quantifiable. This seems to be a possibility
> especially with shallow curves.
>
Happens all the time in the data I see.
But this is a topic that I will avoid getting mired in here.
Oops, now a second digression just occurred to me.
Another reason I prefer to use AUCs (Area Under Curve)
instead of AUTs (Area under Trapezoids)
is because of the ability to generate uncertainty estimates
(measures of quality) for AUCs whereas I seem to have to accept
AUTs with no concept of uncertainty or quality measure for them.
> My question is: What is the effect of the analytical error at or
> close to the LOQ on the determination of AUC by curve fitting
> especially when weighting is used?
>
Since the model fitting programs I am aware of try to minimize
the ABSOLUTE errors instead of the RELATIVE errors then
analytical error at the end of the curve should have minimal
effect on the determination of the AUC.
Having said that, it must of course be caveated when weighting
is used. The end effect of weighting is minimize what become
"relative" errors.
My personal experience has been that LOQ and weighting seem to
have minimal effect on the AUC estimates except in those cases
where the terminal elimination becomes very flat and gets
extrapolated to infinity. It is this extrapolation to infinity
that is the source of the problem. The same problem would exist
for the AUT if it was extrapolated to infinity by the terminal
elimination estimate.
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Dear Derrick:
Good for you! You are right - the absolute error, not the
relative error, is the important thing. The SD and the variance, not
the CV%, are what is important in determining the credibility of a
data point by its Fisher information
Best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
*****
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