Bioequivalence and Bioavailability Forum

Dear Yung-jin!

❝ Can this CV_intra from a pilot study really represent a CV_intra from a main study?

Well, you may see CV_intra as an estimate from the population of possible main studies. This estimate is uncertain. Therefore, based on the sample size of the pilot study, you may calculate a confidence interval of the CV (see this post). Generally one is only interested in the one-sided (upper) limit. If the CV in the main study is lower than expected, you will loose some money, but still demonstrate BE. If you base your sample size calculation one the ‘carved-from-stone’ CV in the pilot study, and the actual CV is higher - you loose money and fail to show BE. Bad luck.
In the thread mentioned above I used a 95% CI, which is quite over-weary… Patterson & Jones (2006) recommend an 80% one-sided-interval (or the common producer's risk of 20%). If sponsors have some problems in understanding this concept, just tell them, that if they use the carved-from-stone CV the chance of a higher CV in the main study is 50%.

❝ What sample size will be required for a pilot study?

Hey, that’s a really good question! We should leave this to some Bayesian statisticians, because we would need some priors in this case. 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?
Main hint: The larger, the better. OK, that's trivial, but let's play around with the formula (balanced 2×2 studies), upper 80% CL of CV_intra:

 n  10%   15%   20%   30%   40%    50%
 4  21.4  32.4  43.8  68.7  97.2  131
 6  15.6  23.6  31.6  48.2  65.8   84.8
12  12.7  19.1  25.6  38.7  52.1   66.0
16  12.2  18.3  24.4  36.9  49.5   62.5
24  11.6  17.5  23.3  35.1  47.1   59.8
32  11.3  17.0  22.7  34.2  45.8   57.6

For an expected CV of 20% I would say 12 subjects are OK, for HVDs the minimum in a pilot is 16-24. Well, of course you can perform a pilot study in six subjects, obtain a CV of 50% and run the main study as a 4×2 replicate study (PE 95%, 80% power, conventional AR) in 50 subjects. But: you have a 50% chance, that the CV will be >50% and the study will fail. Or you use the upper CL (84.8%), which will call for 118 subjects. Now you have only a 20% chance of failure. Since it's a HVD, perform the pilot in 24 subjects, base the sample size on 59.8% and have an expected chance of success in 68 subjects.

❝ Usually we use 4-6 subjects as the sample size in a BE pilot study here.

Wow, four! That’s brave. Six is Vinod Shah’s magic number – I call that a dice game with the devil. See one of my old lectures (1.7MB, slides 60-63). I cheated in the example: I took a real dataset (24 subjects) and sliced it into either four subsets of six subjects each, or in two subsets of twelve subjects. Again: the bigger, the better.