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I would appreciate if any members of PharmPK can advise me on what should
be a very simple question on how to calculate accumulation ratio (AR).
Drugs were administered either once (QD) daily or twice daily (BID) for 8
consecutive days. AUC0-dosing interval and AUC 0-infinity are available
for both days 1 and 8 on QD and BID.
Is AR:
1. AUC0-dosing interval day8/AUC0-dosing interval day1
2. AUC0-infinity day8/AUC0-infinity day1
3. AUC0-dosing interval day8/AUC0-infinity day1
All three ways have been suggested but there must be one correct way of
calculating AR
many thanks in advance
Faruq H Noormohamed
Department of Therapeutics
Chelsea andWestminster Hospital
369 Fulham Road
LONDON
SW10 9NH
Tel +44 (0)181 746 8141
Fax +44 (0)181 746 8887
email f.noormohamed.-at-.cxwms.ac.uk
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>
> Is AR:
> 1. AUC0-dosing interval day8/AUC0-dosing interval day1
This fits closest to my own definition of AR which is the ratio of
the conc at SS (or after N doses) to the conc after the first dose at
the same time after the dose e.g. the ratio of the trough conc at SS to
the conc immediately before the second dose. Using the AUC gives some
kind of time averaged conc on day 8 divided by the conc averaged over the same
period after the first dose.
> 2. AUC0-infinity day8/AUC0-infinity day1
No. Doesnt fit my definition of AR.
> 3. AUC0-dosing interval day8/AUC0-infinity day1
No. This ratio should be <= 1 (approaches 1 as steady state is reached).
The AR should always be > 1.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.at.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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Faruq:
There is no unique definition of the accumulation ratio (AR), so there
is no *correct* way of its calculating. In Gibaldi & Perrier (2nd
edition) you will find 3 versions of AR:
1. AR = C_ss_min/C_1_min,
where the subscript min corresponds to the plasma concentration
immediately before the dose intake. If the dose is administered in the
post-absorbtive, post-distributive phase this definition of AR will
result in a well-known equation:
AR = 1/(1 - exp(-lambda_z*tau)) (1)
2. AR = C_ss_max/C_1_max,
where the subscript max indicates that the peak concentration is used
in calculating AR. If the drug kinetics can be described by the
one-compartment model you will get again Equation (1).
3. AR = C_ss_av/C_1_av,
where average concentrations at steady state and during the first dose
are used. The latter definition is the most common since it results in
a simple non-compartmental formula, and is, therefore, the most
appropriate:
AR = AUC_ss_tau/AUC_1_tau
Thus, in you three formulas:
1. AUC0-dosing interval day8/AUC0-dosing interval day1
2. AUC0-infinity day8/AUC0-infinity day1
3. AUC0-dosing interval day8/AUC0-infinity day1
the first one is consistent with the latter definition. However, to
get an unbiased estimate, steady state should be achieved at day 8,
otherwise you will under-estimate AR.
By the way, if you have steady state at day 8, your third formula will
give unity if the kinetics of your drug is linear and time-invariant.
If there is auto-induction the ratio will be lower than one. In the
case of auto-inhibition it will be higher than one. So, this ratio is
of importance, too.
Best regards,
Vladimir
--------
Vladimir Piotrovskij, Ph.D. Fax: +32-14-603768
Janssen Research Foundation Email: vpiotrov.-at-.janbe.jnj.com
Clinical Pharmacokinetics
B-2340 Beerse
Belgium
from: "Vladimir Piotrovskij"
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Faruq:
By a definition, the AR (or often referred to as "fraction of the
steady state, achieved in the K-th period of the dosing schedule" is
calculated as the ratio between the AUC in the K-th period and the
AUC in a period at steady state.
As AUC in a period at steady state is equal to the AUC to infinity
after the first dosing, obviously the correct way is number 3.
Kind regards,
Ivan Nestorov, PhD
>
> I would appreciate if any members of PharmPK can advise me on what should
> be a very simple question on how to calculate accumulation ratio (AR).
>
> Drugs were administered either once (QD) daily or twice daily (BID) for 8
> consecutive days. AUC0-dosing interval and AUC 0-infinity are available
> for both days 1 and 8 on QD and BID.
>
> Is AR:
> 1. AUC0-dosing interval day8/AUC0-dosing interval day1
> 2. AUC0-infinity day8/AUC0-infinity day1
> 3. AUC0-dosing interval day8/AUC0-infinity day1
> All three ways have been suggested but there must be one correct way of
> calculating AR
>
> many thanks in advance
>
> Faruq H Noormohamed
>
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+ +
+ Dr. Ivan Nestorov +
+ Department of Pharmacy +
+ University of Manchester +
+ Oxford Rd. +
+ Manchester, M13 9PL +
+ UK +
+ Tel: +44-161-275-6886 +
+ Fax: +44-161-273-8196 +
+ E-Mail: IVAN.aaa.fs1.pa.man.ac.uk +
+ +
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