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In calculating the AUC for any particular profile. it is normally correct to
use a linear method for the ascending portion of the curve (up to Cmax) and a
log method for the descending portion. This is very straight-forward when
dealing with nice, smooth "up and down" profiles. The question is this - what
method(s) should be utilised when a profile rises to Cmax, then starts to fall,
but during the descending phase perhaps concentrations rise again, but not as
high as Cmax, then fall again. Should a linear method be used between two data
points when the second point is higher than the first, irrespective of whether
it is post-Cmax, or should a log method be used for all points post-Cmax??
Any thoughts will be greatfully received.
Chris Davie
Department of Pharmacokinetics
SmithKline Beecham Pharmaceuticals R&D
christopher_c_davie.at.sbphrd.com
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> In calculating the AUC for any particular profile. it is normally correct to
> use a linear method for the ascending portion of the curve (up to Cmax) and a
> log method for the descending portion. This is very straight-forward when
> dealing with nice, smooth "up and down" profiles. The question is this - what
> method(s) should be utilised when a profile rises to Cmax, then starts to
>fall,
> but during the descending phase perhaps concentrations rise again, but not as
> high as Cmax, then fall again. Should a linear method be used between two data
> points when the second point is higher than the first, irrespective of whether
> it is post-Cmax, or should a log method be used for all points post-Cmax??
The theoretical basis for using the log AUC method is founded on the
assumption that it is describing an exponential decline. While wobbling
in the region of the peak conc there is no advantage of the log method
(but it is probably not much worse). Trapezoidal AUC is after all only an
approximation suitable for generating initial estimates for non-linear
regression models so its not really a big deal either way :-)
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
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This is a very interesting question. We have done PK data analysis for
Pharmaceutical companies where multiple peaks in plasma conc-time profile
were observed. We used linear method for the ascending (generally
convex in nature) as well as descending (generally concave and log-linear)
portion of the curve (the results of the PK data analysis were also
submitted to FDA). The reasoning being that the linear method usually
underestimates the AUC in the ascending phase, which is somewhat balanced by
the overestimation of the AUC in the descending phase. However, the presence
of multiple peaks further complicates the calculation of AUC. So my suggestion
is to use linear method for whole profile unless you have very strong reasons
to use log method for descending portion of the profile.
If it is imperative to use log method for descending profile, I
think, real answers can not be easily found without doing simulation
studies with some type of sensitivity analysis.
Hope this helps you.
G. Krishna
Medical College of Virginia, Virginia Commonwealth University
--
Gopal Krishna, Ph.D. Candidate (Pharmacokinetics/Biopharmaceutics)
Maintainer: PK/PD/Biopharmaceutics Home Page-
http://griffin.vcu.edu/~gkrishna/PK/pk.html
Email: Gkrishna.-a-.Gems.VCU.EDU
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This is a very interesting question. We have done PK data analysis for
Pharmaceutical companies where multiple peaks in plasma conc-time profile
were observed. We used linear method for the ascending (generally
convex in nature) as well as descending (generally concave and log-linear)
portion of the curve (the results of the PK data analysis were also
submitted to FDA). The reasoning being that the linear method usually
underestimates the AUC in the ascending phase, which is somewhat balanced by
the overestimation of the AUC in the descending phase. However, the presence
of multiple peaks further complicates the calculation of AUC. So my suggestion
is to use linear method for whole profile unless you have very strong reasons
to use log method for descending portion of the profile.
If it is imperative to use log method for descending profile, I
think, real answers can not be easily found without doing simulation
studies with some type of sensitivity analysis.
Hope this helps.
G. Krishna
Ph.D. Candidate (Pharmacokinetics/Biopharmaceutics)
Medical College of Virginia, Virginia Commonwealth University
P.S. I sent this email earlier but it seems that it was not distributed.
--
Maintainer: PK/PD/Biopharmaceutics Home Page-
http://griffin.vcu.edu/~gkrishna/PK/pk.html
Email: Gkrishna.aaa.Gems.VCU.EDU
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The linear trapezoidal rule has been proven to give biased estimates
of AUC both at the ascending and descending parts of concentration
-time curves. However, since the sampling is usually more frequent
before the peak as compared to the tail of the curve, the bias can be
neglected at the ascending part, and also near the peak(s). The
log-trapezoidal rule also results in bias at the ascending part of the
curve, however, it gives the exact estimate of areas under descending
log-linear profiles (noiseless). If the noise is low (less than 10 %),
the log-trapezoidal rule is preferable, especially in cases of long
half-lives. It becomes even more important when calculating the first
moment (AUMC).
Vladimir Piotrovskij, Ph.D. Fax: +32-14-603768
Janssen Research Foundation Email: vpiotrov.at.janbe.jnj.com
Clinical Pharmacokinetics
B-2340 Beerse
Belgium
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One approach is based on the sign of the second derivative as described by
Proost ( J Pharm Sci 74: 793-794, 1985) which we have implemented into a
"deconvolution " program (Pharm Res 5: 247-248, 1988).
Hope it helps.
Gary A. Thompson, Ph.D.
Clinical Pharmacology
Procter and Gamble
11450 Grooms Rd.
Cincinnati, OH 45242
513-626-2058
thompson.ga.-a-.pg.com
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Concerning the discussion about estimating AUC for noisy or multiple
concentration peak data, people should remember that interpolation and then
integration by Lagrange polynomials is an entirely general method of
integration and is independent of the local concavity or convexity of the
data. The Lagrange method was implemented several years ago by ML Rocci, Jr
and WJ Jusko, "LAGRAN program for area and moments in pharmacokinetic
analysis" Computer Programs in Biomedicine 16: 203-216 (1983). One problem
with Lagrange method is that it occasionally suffers from oscillations
yielding poor estimates of area. The Lagrange method and the issue of
oscillations is discussed in 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).
R. Purves has done a rigorous comparison of many methods of estimating AUC
and AUMC. I recommend his paper: "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). In the paper, Purves describes what he
found to be the optimal algorithm for estimating AUC and AUMC. This method
involves a parabola through the origin for regions of the concentration curve
having negative curvature and the standard log trapezoidal method elsewhere.
Finally, in the forthcoming April issue of J Pharm Sci is an article by
JM Gallo and myself describing our program NCOMP which implements both
the Lagrange method and the Purves method for noncompartmental analysis of
pharmacokinetic data. This Windows 3.1 program, designed for use with the
Excel spreadsheet, can be obtained by sending me email (p_laub.at.fccc.edu).
Paul Laub
Paul B. Laub numerical analysis and mathe. modeling of biomedical data
Dept. of Medical Oncology 364 West Bldg.
Fox Chase Cancer Center 7701 Burholme Ave. Phila. PA 19111 USA
p_laub.at.fccc.edu (215)728-3890 (voice) (215) 728-2741 (fax)
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13, 591-608 for estimating AUC of drugs undergoing enterohepatic cycling.
Hope this information is useful.
J. Vora
vora.-a-.butler.edu
Butler University
College of Pharmacy
Indianapolis, IN
from: VORA 940-9216
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From: Maria Durisova
>>Dear Chris Davie,
>>to reply your question concerning AUC calculation for a
>>multiple peak profile we are sending you the auc.uue file.
>>How to use this file:
>>1. Decode the auc.uue file using uudecode command. You will
>> receive the file auc.exe.
>>2. Transfer the file auc.exe (in the binary mode) to an
>> empty directory at a hard disk of your PC.
>>3. Run the auc.exe file. You will receive the following
>> files:
>> 9_matrix.fx
>> laser.hp
>> prn_9_m.bat
>> prn_las.bat
>>5. To print out the file 9_matrix.fx or laser.hp use the
>> file prn_9_m.bat or prn_las.bat, respectively.
[db-Actually this message was intercepted and the file 'auc.exe' has been
placed on the ftp server at:
ftp://ftp.cpb.uokhsc.edu/anonymous/pk/auc.exe
Either enter this URL into your WWW browser and it should retrieve the file
or use ftp software to log onto the ftp.cpb.uokhsc.edu machine as anonymous
and move to the /anonymous/pk/auc.exe using the 'cd' command. Then follow
Maria's instructions above.]
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