- On 5 Sep 1997 at 10:54:12, Tony Lee (p2149z.aaa.hotmail.com) sent the message

Back to the Top

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 - On 8 Sep 1997 at 10:20:45, Hans Proost (J.H.Proost.aaa.farm.rug.nl) sent the message

Back to the Top

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 - On 9 Sep 1997 at 10:46:11, "Gentry, Tom" (TGENTRY.-a-.willco.niaaa.nih.gov) sent the message

Back to the Top

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

********************************************************************** - On 15 Sep 1997 at 15:12:58, Hans Proost (J.H.Proost.-a-.farm.rug.nl) sent the message

Back to the Top

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 - On 17 Sep 1997 at 10:57:56, Roger Jelliffe (jelliffe.-a-.hsc.usc.edu) sent the message

Back to the Top

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/

************************************************

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Calculation of F and PK/PD Modeling" as the subject

PharmPK Discussion List Archive Index page

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)