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

Hi BEQool,

❝ 1. If we dont pass BE in the first stage, why do we have to assume a fixed GMR (i.e. 95% - same as before the 1st stage) when doing sample size estimation for the 2nd stage? Why dont we just use the observed GMR from the 1st stage? Because TIE would increase?

❝ Has anyone ever gone into the 2nd stage with sample size estimation based on observed GMR from the 1st stage and the agency accepted it without any objections?

My views differ perhaps a bit from Helmut's. I think everybody who played around with TSD's tried it and found out it did not work.
The reason is very simple:
After the first stage you will very, very often (painfully often!) end up in a scenario where it is impossible to achieve 80% power or whatever you are aiming for. Often course it depends on the simulated CV and GMR but this is a very concrete and practical drawback that completely kills all practical use of the observed GMR for planning of stage 2.
Remember: Power is the same as alpha when you are on the acceptance border. So, at GMR=0.8 your power can never exceed alpha. Which means that even well within acceptance borders there are areas of GMR where you cannot achieve 80% power regardless of your sample size. It completely does not work.
I played around with all sorts of ways to circumvent it. Didn't come up with anything of practical use. For example, trying to halve the distance from the observed GMR to 1 and plugging this into sample size calc. I.e. if we get a GMR of 1.28 then we do GMR'=1.00+(1.28-1.00)/2 = 1.14 and plug it into the sample size calc. Tried many other variants of such a principle. Nothing that I tried works well.

❝ b) regarding 2 formulations, so there is no way to go into the study with 2 test formulations and then choose the best one to go into the 2nd stage if we dont pass the BE in the 1st stage? Of course alpha should be adjusted both for 2 test formulations and one interim analysis - so I would say Bonferroni (most conservative) alpha correction with alpha 1.667% (3 hypotheses) or alpha 1.25% (4 hypotheses) should be used?

There is a paper about running a stage 1 with two test formulations. Then picking the best one and doing stage 2 with it. I think it was some Danish weirdo who published it. That wasn't a replicate design, though.

Pass or fail!
ElMaestro

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