# PharmPK Discussion - Statistical test for three sequence three period BE test

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• On 11 Feb 2005 at 19:34:32, Shruti Agrawal (shrutiagrawal02.aaa.yahoo.co.in) sent the message

Dear all

We have developed two formulations and want to test the bioequivalence
of both the products in coparison to marketed product. the study design
would be three sequence three period (two tests and one reference) BE
study.

What would be the appropriate statistical test to determine BE of both
the formulations from this study design?

Shruti

Dr. Shruti Agrawal
Department of Pharmaceutics
Ernest Mario School of Pharmacy
Rutgers, The State University of New Jersey
Piscataway NJ 08854

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• On 11 Feb 2005 at 15:40:34, "Labadie, Robert" (robert.labadie.at.pfizer.com) sent the message

The following message was posted to: PharmPK

Shruti,

You need to do a six sequence Williams square (special Latin square)
design
for your study which is balanced for carryover effects. Run all your
data
through the same statistical model as your classic 2x2 crossover but
use the
appropriate contrast statements to obtain your unbiased treatment
estimates
and CIs.

Regards.
Rob

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• On 14 Feb 2005 at 17:07:32, =?ISO-8859-1?Q?Helmut_Sch=FCtz?= (helmut.schuetz.aaa.bebac.at) sent the message

The following message was posted to: PharmPK

Dear Shruti,

as Robert already pointed out, you need a six-sequence Williams' design
(a three sequence simply will not work, because it's not balanced both
for
treatment and carry-over).

Bellow you will find the six sequences (T1 and T2 are the test
formulations, R is the reference)

S#|P1|P2|P3
------------
#1|T1|T2|R
#2|T2|R |T1
#3|R |T1|T2
#4|T1|R |T2
#5|T2|T1|R
#6|R |T2|T1

Since Williams' design is balanced, you are also able to extract
pairwise
comparisons - which you may need for nonparametric testing of Tmax ;-)

One Caveat:
According to my experience, such a design is only acceptable for
regulatory applications if you _drop_ one of the formulations in the
later drug development process, i.e., only one of the formulations
will actually be marketed - the study helped you in deciding, which one.

If you want to use both formulations (e.g., two different galenic
forms should _both_ show BE to the reference) you will run into
multiplicity issues: two simultaneous tests at alpha=0.05 lead to an
increased patient's risk of 1-(1-0.05)^2=0.0975!
The calculation of a Bonferroni-corrected 95% confidence interval -
instead of the 90% CI - is needed to keep the overall alpha-risk at 5%:

You will have to adjust the sample size in study planning accordingly.

Regards
Helmut

--
Helmut Schutz
BEBAC
Consultancy Services for Bioequivalence and Bioavailability Studies
Neubaugasse 36/11
A-1070 Vienna/Austria
tel/fax +43 1 2311746
http://BEBAC.at Bioequivalence/Bioavailability Forum at
http://forum.bebac.at
http://www.goldmark.org/netrants/no-word/attach.html

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