Bioequivalence and Bioavailability Forum

Hi ElMaestro,

❝ this thread is extremely interesting!

Nice to read!

❝ […] the line converts the expected CV to a kind of "almost worst-case"-CV within reason as defined by alpha. I can see why, but it makes the resulting curve somewhat pessimistic. "On average" (pardon!) the total sample sizes will tend to be lower.

Correct. That’s why I added the second (somewhat more optimistic) table. Of course everybody is free to choose another α. Try it: Any value >0.1 likely will tell you that the ideal pilot should have just 12 subjects. What about the reliability of the GMR? Which leads to…

❝ […] we also argued a few times here that observed GMR from a pilot must be taken into account. It gets complicated...

Indeed. Actually the expected GMR lies somewhere within the CI – which might be terribly wide if estimated from a small pilot. I’m not aware whether anybody played around with the CI (maybe a larger α would make sense).

BTW, here are the tables for Potvin’s Methods B/C (average total sample sizes from 10⁶ simulations):
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│                                      Method B: stage 1 sample size                               │
├──────────────────────────────────────────────────────────────────────────────────────────────────┤
│    12   14   16   18   20   22   24   26   28   30   32   34   36   38   40   42   44   46   48  │
├───┬──────────────────────────────────────────────────────────────────────────────────────────────┤
│CV%│                                    average total sample size                                 │
├───┼──────────────────────────────────────────────────────────────────────────────────────────────┤
│ 30│46.4 45.7 44.7 43.5 42.1 40.8 39.8 39.2 38.9 38.9 39.3 39.9 40.7 41.7 42.9 44.2 45.7 47.2 48.9│
│ 25│32.4 31.3 30.1 29.2 28.6 28.6 29.0 29.7 30.7 31.9 33.3 34.9 36.6 38.3 40.2 42.1 44.1 46.0 48.0│
│ 20│20.6 20.0 20.0 20.6 21.7 23.0 24.6 26.3 28.2 30.1 32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0│
│ 15│13.5 14.7 16.3 18.1 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0│
│ 10│12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0│
└───┴──────────────────────────────────────────────────────────────────────────────────────────────┘
┌──────────────────────────────────────────────────────────────────────────────────────────────────┐
│                                      Method C: stage 1 sample size                               │
├──────────────────────────────────────────────────────────────────────────────────────────────────┤
│    12   14   16   18   20   22   24   26   28   30   32   34   36   38   40   42   44   46   48  │
├───┬──────────────────────────────────────────────────────────────────────────────────────────────┤
│CV%│                                    average total sample size                                 │
├───┼──────────────────────────────────────────────────────────────────────────────────────────────┤
│ 30│46.6 45.8 44.9 43.6 42.2 40.9 39.9 39.2 38.9 38.9 39.2 39.7 40.4 41.4 42.5 43.8 45.3 46.9 48.6│
│ 25│32.5 31.4 30.2 29.2 28.6 28.5 28.9 29.5 30.5 31.7 33.1 34.7 36.4 38.2 40.1 42.0 44.0 46.0 48.0│
│ 20│20.6 20.0 20.0 20.5 21.5 22.9 24.5 26.2 28.1 30.0 32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0│
│ 15│13.4 14.6 16.2 18.1 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0│
│ 10│12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0│
└───┴──────────────────────────────────────────────────────────────────────────────────────────────┘
We see a similar pattern of the “ideal” stage 1 sample sizes, which relies on a best guess of the CV again. But there’s a major difference to the pilot/pivotal-combo. It might not be the primary interest of the sponsor to pass with the minimum total sample size, but already in the first stage. So for CV 20% likely the best choice of n₁ should not be based on the smallest total sample size 20 (with n₁ 14 chance to proceed to the second stage 44%) but we rather would opt for n₁ 24 (only 8% in stage 2) – which is also the sample size in a fixed sample design with α 0.0294.

❝ How bout something along these lines: [1–7]

Have mercy and show more respect for my peanut-sized brain! Have to think it over. As you know, futility rules might kick power in the arse.