- On 31 Dec 1999 at 18:35:02, e.helmer.at.fournier.fr sent the message

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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 - On 1 Jan 2000 at 18:51:39, "David Foster" (dmfoster.at.u.washington.edu) sent the message

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The answer to your question depends upon how you calculate your AUC. - On 3 Jan 2000 at 22:17:39, "Joseph Balthasar" (jbalthasar.-at-.pharm.utah.edu) sent the message

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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)

*********** - On 4 Jan 2000 at 21:07:47, ml11439.-a-.goodnet.com sent the message

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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 - On 11 Jan 2000 at 21:28:32, HARRY.MAGER.HM.-at-.bayer-ag.de sent the message

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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 - On 12 Jan 2000 at 22:47:34, jwu.-a-.coromed.com sent the message

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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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