## Now what? w & w* examples [Two-Stage / GS Designs]

Hi Helmut,

❝ Not necessarily good but a “guesstimate”.

Got it. Well... whatever a guesstimate is

❝ ❝ … but in case we observe some unforeseen value we have the possibility to add some extra subjects.

❝ ❝ However, in such a case we could just go with a fixed design and adapt the Power.

❝ I’m not sure what you mean here. In a fixed sample design I would rather work with the upper CL of the CV or – if not available – assume a reasonably higher CV than my original guess rather than fiddling around with power.

I try to explain. In case the argument is that a TSD approach should be performed not because of an uncertain CV per se (e.g. quite a big range observed so far) but because it is desired to safeguard against an unfavorable outcome of the CV (i.e. an extreme realization / random deviate of the CV), then: stop right there. To protect against such an outcome is exactly the definition of Power (type II error) and I would question whether a TSD is really the right tool - maybe a fixed design already suffices (with a proper Power).

❝ ❝ In a TSD setting we typically have no good understanding about the CV... Do I miss something here?

❝ (1) Yep and (2) no.

❝ ❝ Based on what assumptions would we select n1 (= fixed design sample size)? We typically have some range of possible values and we don't know where we will be.

❝ I was just quoting a regulatory statistician (don’t want to out him). Others didn’t contradict him. So likely he wasn’t alone with his point of view.

❝ Very interesting. I expected that the sample size penalty (n2) will be higher if we use a low n1.

Me too.

❝ If we base n1 on the lower end and the CV is close to the guesstimate that’s the winner. One the other hand there is a ~56% chance of proceeding to the second stage which is not desirable – and contradicts the concept of a “safety net”.  A compromise would be 75% of the fixed sample design.

❝ The pessimistic approach would be crazy.

I agree to all of it.

Best regards,
Ben.