Bioequivalence and Bioavailability Forum

Dear Yung-jin,

❝ ❝ Actually the questions is: how small can a pilot study be that with a certain confidence the sample size estimation for the pivotal study is reliable?

❝

❝ Exactly.

Yes, but I think the only tools we have is either the confidence limit approach or bootstrapping. Both methods may give us a nasty (i.e., large CV) if the sample size of the pilot is small - or on the other hand will suggest a small size, because the CV in the pilot was low due to pure chance. But that's trivial. The larger any sample size is, the lower the variability (aka the 1/sqrt(N) game). I'm afraid, there is not a simple answer to the question above.

❝ ❝    n  20%

❝ ❝    4  43.8

❝ ❝   16  24.4

❝

❝ Uhh... Sorry about that I don't know how to interpret/use this table.

That's easy. You have a pilot study (n=4) which gave you a CV of 20%. The upper 80% confidence interval of the CV is 43.8%. In other words you have a 50% chance that in the main study the CV will be larger than 20% (trivial, because it's an estimate) and a 20% chance that the CV will be larger than 43.8%.
Now it's up to you: Believe in the CV of 20% (well, that't like flip of a coin, or just a little bit better than red/black in roulette) or go with the CV of 43.8%. Oops, is it a HVD?
Now look at the second row: The pilot study was larger (n=16) and again we got a CV of 20%. But now the upper CL is only 24.4%. Due to the larger pilot, we are more certain about the value of the CV.

❝ ❝ Wow, four! That's brave. Six is Vinod Shah's magic number - I call that a dice game with the devil. [cut]

❝ That's commonly used with 4-6 subjects in a BE pilot study here... I just cannot believe that the subj# like that could give a good estimation of CV_intra at all. It almost becomes SOP with local CROs here to use 4-6 subjects to perform a BE pilot study.

Haha. I guess they apply a nice safety margin on the sample size.

❝ Then they replicate the values they get from these 4-6 subjects up to 24 or so, and finally do an anova to obtain the MSE. And they get their estimated CV_intra!

I'm not sure whether I understand this procedure. Sounds like some kind of resampling (bootstraping), but I don't get the point. Why 24? Bootstraping relies on a sufficiently large and representative sample. If the sample is small and the variability is particularly small or high due to chance, any resampling will reproduce this behaviour in the simulated data set. Sorry, but n=4 is rubbish, IMHO.

❝ Yes, but the question is: how bigger is the better? It's a pilot study only, but it seems very critical.

Well, easy question - difficult answer. I'm really in favour of sequential designs; you guessed right: D Potvin et al. (2008) is my favourite method.

It's nice to have a method to deal with the uncertainty of CV, but another point is the variability of the point estimate. To my knowledge, there is no statistical method available to deal with that. So again, what to use? The ratio in the pilot (the ‘carved-from-stone-method’)? A safety margin? How large; ±5% - or what?