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The following message was posted to: PharmPK
Dear Colleagues,
Following the recent contributions of M. Wasserman and E. Edwards re.
the
sample size estimation for the assessment of bioequivalence in a 2x2
crossover trial I would like to add a few comments.
Given that we apply the 80-125% confidence interval approach for the
assessment of bioequivalence the following 2 parameters are needed for
the
estimation of the sample size:
i. The expected T/R ratio.
ii. The intrasubject CV.
The intrasubject CV depends on several exp. conditions, e.g. the
formulation of the drug, and is highly variable. It's estimate should be
based on some experimental data. However, if only data from a very
limited
number of subjects is available, as is usually the case, the CV carries
a
large uncertainty. I would suggest to use not only the CV
(point)estimate
in the sample size calculations, but at least also the upper limit of
it's
95% confidence interval in order to get a more realistic estimate of the
needed sample size. CVs with just a few degrees of freedom might be
gross
underestimates of the true CV.
To illustrate the influence of T/R and CV on the sample size please find
below a few results, supplementing the results of E. Edwards. The alpha
was
set at 0.05 and power at 0.8.
T/R CV=0.30 CV=0.35
0.90 80 106
0.95 40 54
1.00 32 42
1.05 38 50
1.10 68 90
I would appreciate if somebody could give some guidance, literature
references, etc. about the "best" choice of the T/R ratio and how to
estimate sample sizes for nxn crossover trials with n>2.
Best regards,
Martin
Martin M. Schumacher, Ph.D.
Principal Scientist
Novartis Pharma AG
PCS Modeling & Simulation Group
WKL-136.1.19
CH-4002 Basel
Switzerland
Email martin.schumacher.at.pharma.novartis.com
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The following message was posted to: PharmPK
Dr. Schumacher:
I do not know of any 'best' expected T/R ratio, but I use an expected
T/R
ratio of 0.95 because it provides a guesstimate with slightly larger
subject
numbers that 1.05. Here is the reasoning I use:
1) the main problem is the fluctuation of the intrasubject CV between
studies - this can only be know approximately before the actual data are
collected - and, as is evident, this value will greatly affect the
number of
subjects.
2) unless the proper number of subjects is chosen, the power may be
insufficient, and the entire trial may have to be redone - time and
money
are at stake here
3) if the CV is overestimated you'll have used more subjects than
necessary,
but the power will be sufficient, and 'only' money will be lost.
However,
if you've underestimated the CV, the power will be compromised, and
might
require extra time to redo the trial - time and money are lost.
Therefore,
if you can afford it, it is better to spend money for extra subjects and
save the time that would be lost if the study had to be repeated
4) one hopes (expects) that the T/R would be close to 1.00 but, failing
that, if one assumes 0.95 instead of 1.05, one will estimate a slightly
larger number of subjects.
This is preferred, because if the CV estimate errs on the low side,
using
the expected ratio of 0.95 will calculate more subjects and this might
be
enough to compensate for a higher unexpected CV.
As for other types of crossover studies. The FDA has published a
guidance,
found at URL: http://www.fda.gov/cder/guidance/1716dft.pdf
which gives suggested numbers for crossover studies with n=4 in a table
in
the Appendices - based on simulation studies. There may be others.
Hope
this helps.
Edmond Edwards, Ph.D.
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The following message was posted to: PharmPK
Dear Edward,
Thanks for your thoughtful comments about the choice of the T/R ratio in
the context of sample size estimation.
Here are 2 references re. this subject I found:
T. Ng, The coice of delta in equivalence testing, Drug Inf. J. 35,
1517-27
(2001)
D. Hauschke, Choice of delta: a special case, Drug Inf. J. 35, 875-9
(2001)
Best regards,
Martin
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