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Dear all,
Here is an animal PK study design: 3 animals for each sampling time. So,
for 10 sampling time, 30 animals are used.
Afterwards, you can calculate an AUC using the mean of the concentration
measured for each sampling time.
Is it possible (and if yes how ?) to correlate a variability (sd for
example) with the AUC calculated ?
Any suggestion would be appreciated.
Eric Helmer, Pharm D
Pre-Clinical Study Manager, Animal Pharmacokinetics
Laboratoires Fournier, France
Tel: 03-80-44-78-13 / 01-47-10-88-42
Fax: 03-80-44-77-10
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The answer to your question depends upon how you calculate your AUC.
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Dear Eric:
A good method is given in:
Nedelman JR, Gibiansky E and Lau DT, Applying Bailer's method for AUC
confidence intervals to sparse sampling. Pharmaceutical Research 12(1):
124-8, 1995.
Hope this helps.
Joe Balthasar
***********
Joseph P. Balthasar, Ph.D.
Assistant Professor
Department of Pharmaceutics
517 Hochstetter Hall
University at Buffalo
Buffalo, New York 14260
716-645-2842, ext. 256 (telephone)
716-645-3693 (fax)
***********
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Hello Eric,
The variance in the mean plasma concentration measured for each
sampling time would be a measure of the variance in the AUC. The
overall within-groups variance could then be calculated as the average
variance of the ten sampling time variances.
1) Variance in mean plasma concentration per sample time
Variance= Sum(i-3)[Xi-Xn]/[N-1]
2) Variance within-groups
Variance(wit)= 1/10[Var1+Var2+Var3......+Var10]
The within-groups variance would estimate the overall population
variance in the mean sample times, and would provide an estimate of
dispersion in the calculated AUC. This is since the AUC is calcuated
using the means of the three plasma concentrations for each of the
10 sample times.
The above is actually the first part of analysis of variance found
in most basic statistic books.
Mike Leibold, PharmD, RPh
ML11439.at.goodnet.com
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Dear Eric,
I do not know what Jun Wu has in mind when claiming that var(AUC) should not=
be
estimable even under the linear trap. approximation (covariance between
adjacent time points is zero, for more details see the paper by Bailer and t=
he
list of publications provided by Jawien).
Although the methods referenced by Wojciech Jawien have their merits (e.g.,
Bailer (1988), Gagnon and Peterson (1998)), they all rely on specific
assumptions on how you calculate the AUC (Bailer: linear trap. rule, Gagnon
logarithmic approximation) etc.
Analysing destructive sampling data / independent-data concentration "profil=
es"
is quite easy using resampling techniques. One major advantage is that they
are completely independent of the algorithm you use to approximate the AUC
(log-linear, parabolas-through-the-origin then log-linear etc.). In addition=
,
they can be applied both in a parametric and in a nonparametric context and =
can
be also used to calculate T1/2, micro-/macro constants and their correspondi=
ng
variabilities percentiles, and many other statistical measures [cp H. Mager
and G. G=F6ller (1998). Resampling methods in sparse sampling situations in
preclinical pharmacokinetic studies. JPharmSci 87, 372-378].
We have developed a corresponding SAS application (Bay-Bootstech 1.1) that i=
s
available on request free of charge. At present, version 2.0 is under
development. It will also cover bioequivalence and dose-response tests, a
beta-release should be available around 05/2000.
Maybe this is of some help.
Harry Mager
Bayer AG
Clinical Pharmacology
D-42096 Wuppertal
Phone 0049-202-368891 (Fax -364788)
E mail Harry.Mager.HM.aaa.Bayer-AG.de
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Harry,
I agree cov(x1bar, x2bar)=0, I should not have used the phrase "covariance
between adjacent time points". What I am trying to add is
Var(ai*(X(i-1)bar+Xibar),a(i+1)*(xibar+x(i+1)bar))=a1*a2*var(xibar).
This is the term that also contributes to the var(AUC). Also,the trapzoidal
expression I wrote was wrong in the sign that involve the second mean
concentration term- (Xibar+X(i+1)bar)/2. It is a silly mistake.
I have to read Bailer's paper, but before I could acquire that paper, I have
these questions about how to estimate from just one experiment the Var(AUC).
Is it OK to use Var(Xbar)=var(X)/n at each time point, where n=3?
Or treating the total of 30 rats under study as the population, and
the sampling
sheme is random without replacement, but what to do with the last
three animals?
Maybe the "resampling techniques" is the way to go. I will get on hold of your
paper. I would really appreciate also to have a copy of your SAS program too.
I appreciate any elabortation on this topic. Thanks.
Jun
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