- On 26 Nov 2002 at 09:02:40, martin.schumacher.-at-.pharma.novartis.com sent the message

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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 - On 26 Nov 2002 at 22:16:33, "Edmond B. Edwards" (editr.at.sympatico.ca) sent the message

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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. - On 27 Nov 2002 at 08:34:19, martin.schumacher.-a-.pharma.novartis.com sent the message

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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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