# PharmPK Discussion - AUC calculation methods

PharmPK Discussion List Archive Index page
• On 14 Oct 2002 at 16:37:59, "Dr. Tanuja Kulshrestha" (tkulshrestha.at.lambda-cro.com) sent the message

Dear sir,

could you put up this case on the discussion board , for opinion

14 October 2002

Case study

A Pharmacokinetic study protocol was entitled “ An experimental
pharmacokinetic evaluation of XXXXX ER Tablets in comparision to
conventional XXXXX Capsules in healthy human volunteers”.

Protocol under statistical analysis stated that, “The ratio of ln-
transformed least square means for the pharmacokinetic parameter
AUC0-24 will be computed after administration of Treatment – I and
Treatment – II.”

Evaluation parameters under statistical analysis stated “ The ratio of
ln-tranformed least square means for pharmacokinetic parameter
AUC0-24 after administration of Treatment I and Treatment II should be
greater than or equal to 80%.”

During data analysis the study AUC0-24  was first computed by
summation method . The results determined that The ratio of
ln-tranformed least square means for pharmacokinetic parameter
AUC0-24 after administration of Treatment I and Treatment II was found
to be 75%.

So, computation of results AUC0-24 was done by two ways

1.  By summation of AUC0-8 + AUC8-16 + AUC16-24
2.  By multiplication of AUC0-8 by 3

The result obtained by multiplication method i.e. multiplication
of AUC0-8 by 3 , gave a ratio of ln-tranformed least square means for
pharmacokinetic parameter AUC0-24 after administration of Treatment I
and Treatment II as 80.1%

The Report, reported both results i.e.

1. AUC0-24 by summation
2. AUC0-24 by multiplication i.e. (3 X AUC0-8)

We have two questions here

1. Is this approach of handling the problem acceptable by regulatory?
I.e. Can you analyze the data in two ways, when the Protocol did not
categorically say so. (The stand of the report preparing group would
generally be – we did not say which way we would do it , so we can do
it by both the methods .)
2. Does this need to be recorded as a Protocol deviation in raw data
and report?

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• On 15 Oct 2002 at 11:18:16, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

> During data analysis the study AUC0-24 was first computed by
> summation method . The results determined that The ratio of
> ln-tranformed least square means for pharmacokinetic parameter
> AUC0-24 after administration of Treatment I and Treatment II was found
> to be 75% .
>
What was the design of the study? Single dose with sampling from 0-24
h? Multiple doses every 8 h with the same sampling design over each of
3 successive 8 h periods once steady state had been reached? Something
else?

> So, computation of results AUC0-24 was done by two ways
>
> 1. By summation of AUC0-8 + AUC8-16 + AUC16-24
> 2. By multiplication of AUC0-8 by 3

Method 2 is no different from doing the statistics on AUC0-8. You can
multiply by any positive number and the test result will not change.

It is a bad idea to do two tests and then decide which one to use. This
is because doing two tests and then deciding which results you like
best does not correctly preserve the probabilities used to decide if
you should reject the null hypothesis.

So the answer to your questions; Just use one method for your
statistics. If its a single dose study then method 1 is probably
preferable. If its a multiple dose steady state study then method 2 is
preferable (but do not bother multiplying by 3).

Nick

Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.at.auckland.ac.nz
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

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• On 15 Oct 2002 at 09:28:15, "Wolna, Peter" (Wolna.at.IKP.DE) sent the message

Dear Tanuja,
this approach will not be accepted. A unique approach to the decision
should
always be fixed in the protocol.
Furthermore, with your multiplication method the ratio of AUC(0-8) is
calculated, and not the ratio of AUC(0-24). A factor can be dropped in
case
of ratios.
By the way, why do you calculate AUC(0-24) using the three terms
AUC(0-8),
AUC(8-16) and AUC(16-24)?

Regards
Peter

Peter Wolna
Inst. f. Klin. Pharmakologie

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• On 15 Oct 2002 at 03:45:16, "Doc, Frederic" (Frederic.Doc.aaa.pfizer.com) sent the message

Dear Tanuja,

you did not mention if the comparison was made with one dosing only or
if
the IR form was administered more than once daily.
Reading your message I would assume that it was given 3 times as you
report
the multiplying method (AUC0-8 x3).
Regarding both methods they give results that are very slightly
different.
Did this report mention any statistical analysis to compare both
methods ?
Is 75% really significantly different from 80.1% ? I would not conclude
without any statistical analysis.
Answer to question 1: On a practical point, if you choose to report both
methods you will have to explain your choices (why did you first use the
summation method? Why did you choose to try and analyse with a different
method?) and your conclusions (would you say that your ER tablet is
"bioequivalent" to 3 times dosing with the IR dosage form?).
My answer to question 2 would be that if the protocol did not mention
that
you should use one particular method then it does not seem to be a
deviation. But once again I would say that you really have to clearly
explain what led you to the choice of analysis methods.

I hope this helps,

Frederic

PFIZER Global R&D
Fresnes Laboratories
FRANCE

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• On 15 Oct 2002 at 04:16:04, "Doc, Frederic" (Frederic.Doc.at.pfizer.com) sent the message

Nick,

But in your answer "If its a single dose study then method 1 is probably
preferable." I would reinforce this point saying that you do not have
any
choice in fact. The previously described multiplying method (AUC0-8 x3)
represents an approximation of what should be relevant to 3 times dosing
with 8 hours between administrations. So if you only dose once daily
you can
not use this method.

Regards,
Frederic

PFIZER Global R&D
Fresnes Laboratories
FRANCE

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• On 15 Oct 2002 at 18:49:18, Walt Woltosz (walt.aaa.simulations-plus.com) sent the message

At 04:07 AM 10/14/02, you wrote:

A Pharmacokinetic study protocol was entitled ì An experimental
pharmacokinetic evaluation of XXXXX ER Tablets in comparision to
conventional XXXXX Capsules in healthy human volunteersî.

From the title, can one assume that the comparison is between ER
(extended release) tablets given once per day to immediate release
tablets given three times per day?

If so, is Treatment I the ER formulation and Treatment II the immediate
release formulation?

My earlier comment was predicated on this assumption.

Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (SIMU)
1220 W. Avenue J
Lancaster, CA 93534-2902
U.S.A.
http://www.simulations-plus.com
E-mail: walt.at.simulations-plus.com

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• On 15 Oct 2002 at 22:12:30, sunil v (sunil_nish.-at-.yahoo.com) sent the message

Dear Frederic, Nick,

Perhaps I can throw some light on the issue. The study Dr.Tanuja
mentions is concerned with comparison of PK/PD of a immediate release
formulation (which is administered three times a day) versus a
controlled release formulation meant for once a day administration. The
comparison against summation of all three doses of immediate release
was done to mimic real life usage of the drug. However this may not be
a fair comparison as the dosing condition of both immediate and
controlled release products are identical only in during first dose
(i.e AUC 0-8), hence the option of multiplying AUC 0-8 by three (to
equalise dose between immediate release and controlled release).

While by regulatory point, I agree with your view that

one can not pick and choose the favourable method, I am interested in
your openion on scientific basis for such calculation.

Regards,

Sunil V

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• On 16 Oct 2002 at 16:52:16, bangarurk.-a-.drreddys.com sent the message

Pharmacodynamics and related topics

Dr.Tanuja,

I suppose that in first place your protocol you need to mention
the
evaluation criteria,
eg: the geometric mean ratios to be 80-125% for Test to
Reference in
AUC.

Secondly when you have done the study on repeated administration of
the
conventional product on three days (it appears from your mail, you
are
supposed to calculate the AUC using method of summation and not
the
multiplication of AUC0-8 by 3, by doing so probably you are not
confirming
to the protocol (as you have sampled through 3 days).

In a regulatory perspective you can not use any method selectively,
further
to finding that the earlier method did not give favorable results.(if
your
later results are favorable over earlier results?)

I hope that this helps you.

thanks,

Ramakrishna Bangaru
Dr.Reddy's Laboratories Ltd.,
Generics,
India

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Dear Dr. Tanuja,

What i understand from ur mail that u want to prove the validity of the
"controlled release claim" of ur proposed product against the immediate
release counterpart and the study is essentially a single dose
bioavailability study OK.

In my opinion, you dont have any other choice but to go for the
summation approach thats what we follow when truncate the AUC and thats
what u are supposed to do to prove that T/R ratio is not less than 80%
thus no potential bioavailability/suprabioavailability issues.Its a
cummulative AUC determination approach that needs summation over the
dosing period.Sometimes it happens due to flip flop phenomenon or
saturation kinetics we get the subsequent AUC ( 8-16 and 16-24)a bit
less and that needs to be taken into consideration but u avaoid it if u
multiply it.

Moreover,it makes sense also if u follow summation method as if it
would be a correct approach to multiply the AUC ( 0-8 hrs)by three we
actually need not to continue the study for 24 hours and can stop it at
8 hours that is not preferred from the regulatory standpoint.

I hope this would suffice your purpose.

Research Scientist
Ranbaxy Research Laboratories
India.
Quoting "Dr. Tanuja Kulshrestha" :

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• On 17 Oct 2002 at 04:44:03, "Doc, Frederic" (Frederic.Doc.aaa.pfizer.com) sent the message

> Dear Frederic, Nick,
>
> Perhaps I can throw some light on the issue. The study Dr.Tanuja
> mentions is concerned with comparison of PK/PD of a immediate release
> formulation (which is administered three times a day) versus a
> controlled release formulation meant for once a day administration. The

I understand from you message that your protocol design is: IR
formulation 3 times a day for one day and ER formulation once a day for
one day. Is it OK ?

> AUC comparison against summation of all three doses of immediate
> release
> was done to mimic real life usage of the drug. However this may not be
> a fair comparison as the dosing condition of both immediate and
> controlled release products are identical only in during first dose
> (i.e AUC 0-8), hence the option of multiplying AUC 0-8 by three (to
> equalise dose between immediate release and controlled release).

If your IR formulation does not show significant concentrations at t=8h
(before second IR dosing) then the next administration expected AUC is
supposed to be similar as the first one. In these conditions why not
use the multiplying method ? On a regulatory point I would say that if
you give an evidence that your 8h - plasma concentration is equal to
zero then your calculation method should be considered as acceptable by
the FDA or others.

But if there is a remaining significant blood concentration at t=8h
(before second IR dosing) then there is no doubt that you should use
the summation method.

Hope this helps,

Regards,

Frederic - PFIZER Global R&D

[I hope I have the message quoting correct - db]

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