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Dear Readers:
I would like to get your opinions on the following
questions.
First one is on the calculation of relative bioavailability.
To calculate the relative bioavailability of a oral
formulation
in individual subject, we can use (1) the ratio of
individual
AUC from oral dosing to average AUC from IV dosing to
a group of subjects or (2) the ratio of individual AUC from
oral dosing to individual AUC from IV dosing. I call second
method self-comparison method. I would like to know which
method is more accurate? Any statistical or physiological
justification?
Second question is on PK/PD correlation.
I would to know how to deal with PK/PD
correlation problems in the situations such as
plasma concentration measurement and efficacy
determination on different time intervals (PK in
hours and PD in days) or different dosage regimen
for PK and PD (PK-single dosing and PD-multiple
dosing). Your answers or suggestions for references
will be greatly appreciated.
Tony Lee
Mailto:p2149z.aaa.hotmail.com
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The topic is more complicated than is suggested in this question.
There can be hardly any debate about the question which method should
be used to calculate the relative (or absolute) bioavailability FOR
AN INDIVIDUAL: method (2). The reason is simple: AUC comparison is
based on the assumption that clearance is constant. Since clearance
is, in general, a pharmacokinetic parameter with relatively high
interindividual variability, it is essential that AUC of the same
individual are compared.
However, the question is more complicated if you are interested in
the 'best' (unbiased) estimate of 'average' bioavailability of a group
of subjects (or, in terms of population PK, a typical value of
bioavailability of the population), and its variance.
In this case, some assumption on the statistical distribution are
necessary. In my opinion, it is both realistic and practical to
assume a log normal distribution of the pharmacokinetic parameters.
The calculation is easy: (a) calculate the bioavailability of each
individual subject (ratio of dose-adjusted individual AUCs)
(b) calculate the mean and sd of the log(base e)-transformed ratio's
(c) mean bioavailability is inversed of log-mean
(d) coefficient of variation (CV, expressed as fraction) is the sd of
the log(base e)-transformed ratio's
(e) sd of bioavailability is product of mean bioavailability and CV.
If AUCs from the same individual are not available, the
aforementioned procedures don't work correctly! In this case a
different approach is necessary.
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-a-.farm.rug.nl
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To: Tony Lee
Re: Calculation of Bioavailability.
What you refer to as the "self-comparison method" is the better
way to assess the bioavailability (F) of a drug in an "individual
subject". The ratio of AUCpo / AUCiv both obtained from the same
individual (under all the same conditions, other that route of
administration) would control for between-subject sources of variance
which would have an equivalent influence on the AUCs regardless of the
route of administration. Such sources of variance would include for
example, the apparent distribution volume of the drug and it's rate of
clearance.
The only instance this might not be true is when the error of
measurement is much greater than individual differences in the
post-absorptive determinants of AUC. But if that were true, the whole
question of "the relative bioavailability of a oral formulation in
individual subject" would be compromised. If it's not already obvious,
the best method is to assess the AUCpo / AUCiv for each individual in a
group of subjects and then describe bioavailability by descriptive
statistics.
By the way, there is at least one important drug for which the
comparison of AUCpo / AUCiv is not appropriate for assessment of its
bioavailability. (hint: it accounts for > 5% of the total American
caloric intake).
Tom Gentry
================================================== R. Thomas Gentry, Ph.D.
Office of Collaborative Research Activities
National Institute on Alcohol Abuse and Alcoholism
Willco Bldg., Suite 400, 6000 Executive Blvd.
Bethesda, MD, 20892-7003
tel. 301-443-6009 fax. 301-443-7043
Email: tgentry.-at-.willco.niaaa.nih.gov
================================================------------------------------
Date: Wed, 10 Sep 1997 10:47:20 -0500
From: Ofer Spiegelstein
Subject: Grapefruit juice-drug interaction warnings
Dear Fellows,
Should drugs that have or are suspected of having possible clinically
significant interaction with grapefruit juice, have warnings against it in
patient=EDs inserts and/or doctor=EDs data sheets?
I am asking this because of the replies to my question (ANCHODD and
PharmCare) regarding the existence of such warnings. As you may have seen
there are warnings for terfenadine in the UK, felodipine in Australia and
indinavir and saquinavir as well.
Both felodipine and terfenadine have proven interaction with grapefruit
juice. On the other hand neither indinavir nor saquinavir have been shown
to interact with grapefruit juice. Yet they both have the potential of such
an interaction as they have low bioavailability and major CYP 3A4 metabolism.
What about cyclosporin and nisoldipine, both having documented interactions
with grapefruit juice?
Should cisapride have a warning as well?
Sincerely,
Ofer Spiegelstein
*********************************************************************
Ofer Spiegelstein
Department of Pharmacy
The Hebrew University of Jerusalem
P.O.Box 12065, Jerusalem 91120
Israel
ofersp.-at-.cc.huji.ac.il
**********************************************************************
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Again, the situation is more complicated than in my first answer!
My first answer to the PK/Pharm group was an approximation,
which will be sufficiently accurate in most cases.
Here is a more complete answer, with the exact solution.
The only, almost complete reference to log normal distributions can
be found in:
Biostatistics in Pharmacology (volume I, pp. 544- )
by AL Delaunois, LJ Martin, E Olbrich, AA Weber
Pergamon Press - Oxford 1973 (ISBN 0 08 016556 7)
(series 'International encyclopedia of pharmacology and therapeutics)
According to this reference, the relationship mentioned in my note to
the PK/Pharm group is only valid for the case CV is small.
For variance, the following relationship is given in the
aforementioned reference (symbols modified to text):
var = s^2 = ln(1+CV^2)
where var is the variance of the ln-transformed data,
s is the standard deviation of the ln-transformed data, and
CV is the coefficient of variation (^2 = square)
If CV is small, var is almost equal to CV^2.
E.g., if s = 0.1, it follows that CV = 0.10025,
if s = 0.25, then CV = 0.25396
if s = 0.4 (rather large!), CV = 0.41655
Note: always use 'ln', natural logarithm, base e
(using logarithms with base 10 requires co factors; I don't
like them, and they should be banned from the whole field of
pharmacokinetics).
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.aaa.farm.rug.nl
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About bioavalaibility. The fraction absorbed can also be computed directly
from a mixed dosage regimen containing both IV and PO dosage in individual
patient regimens. This can be done in both parametric and nonparametric
population models, using iterative Bayesian and nonparametric EM software
for such modeling. This avoids comparison of AUC's, obtained possibly under
differeing clinical circumstances, and permits it to be done in the
patients of interest, in their often changing clinical circumstances. If
one would like more info, call me at (213)342-1300, or check our web site
for more info.
Sincerely,
Roger Jelliffe
************************************************
Roger W. Jelliffe, M.D.
USC Lab of Applied Pharmacokinetics
CSC 134-B, 2250 Alcazar St, Los Angeles CA 90033
Phone (213)342-1300, Fax (213)342-1302
email=jelliffe.aaa.hsc.usc.edu
************************************************
Take a look at our Web page for announcements of
new software and upcoming workshops and events!!
It is http://www.usc.edu/hsc/lab_apk/
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