## Two-Stage Sequential Potvin Designs [Two-Stage / GS Designs]

Hi BEQool,

❝ I just have a question regarding 1st stage study(ies) here. If I am not mistaken, the paper describes two studies in the 1st stage - each with their own test formulation (A or B + reference) ("At the end of the day, even though the two trials at stage 1 are conducted as 2-treatment, 2-sequence, 2-period trials").

❝ Could we also perform one study in the 1st stage with 2 test treatments (so 3-treatment, 6-sequence, 3-period) instead of 2 studies seperately? But then probably all of these calculations (alphas, TIE, power...) mentioned in the article wouldnt apply? Or would they?

The results in the paper would apply to just that kind of design, but it might not be too far off to assume it would be very similar .... but not identical due to df's. So we'd need new simulations for a design where stage 1 combines two tests and one ref. Certainly this can be done.

❝ In the paper you calculated power and alphas for different combinations of CV (0.1-1.0 by 0.1), N (12, 24, 36, 48 and 60) and GMR. So if one goes into a 1st stage with any deviations from these combinations (for example N1=20 or CV=0.25), one would have to perform additional simulations with this combination?

Potvin's idea, one that was copied in subsequent papers form various authors is to evaluate a range of CV's and GMR's that cover most naturally occurring combinations. You never know the true GMR or a true CV - you just get some estimates. The grid of combinations (CV, GMR) is then chosen so as to be dense enough that we're comfortable to conclude that once we've found good alphas there will not be overall alpha inflation even for a true (CV, GMR) not falling exactly on a grid point. Some like it, some don't.
Potvin and co-workers later used bounded optimisation to relax the worry anyone might still have. And then those who had worries just found some other reasons to worry, leaving the impression that this is not always about science and the concern for the patient's risk but occasionally about something else entirely.

Pass or fail!
ElMaestro