## Binding / Nonbinding futility rule - alpha control [Two-Stage / GS Designs]

Dear Detlew,

» Avoiding the conditional sample size re-estimation, i.e. using the conventional sample size re-estimation via
» interim.tsd.in(GMR1=0.89, CV1=0.2575165, n1=38, ssr.conditional = "no")
» gives n2=4. Ooops? Wow!

Ok, again: the recommendation here is to stop due to futility because the power of stage 1 is greater than the target power 80%. The result of n2 = 4 is correct in this situation. The reason is (i) we calculate n2 based on GMR which is 95% and (ii) we are not using conditional error rates, i.e. we ignore the magnitude of the p-values from stage 1.

» » » Binding, nonbinding - does it have an impact on the alpha control? I think not, but are not totally sure.
» » Non-binding: Type 1 error is protected, even if the futility criterion is ignored.
»
» Was also my thought because I didn't find any relationship to a futility rule in the proof of alpha control in the paper of Maurer et al. Or do I err here?

You are correct.

» » Binding: Type 1 error is protected only if the futility criterion will be adhered to. ('Binding' is not common practice, authorities don't want this).
»
» Are you sure for the binding case?

I believe so, yes.

» Of course the power may be compromized.

Agreed!

» I think that your statement for the binding case is only valid if you make a further adaption of the local alpha / critical values taking the futility rule into consideration.

No, I don't think that a further adaptation needs to be made. Should be mentioned in e.g. the book of Wassmer and Brannath. I will check this when I have more time.

» Do you have any experinces for your statement 'Binding' is not common practice, authorities don't want this'.
» If yes, what is/are the reason(s) given by authorities to abandon binding futility rule(s) or not to 'like' them?

Should also be mentioned in the book, but I haven't checked. I learned that in a workshop. I think the problem is that people may not believe you that you will always adhere to the stopping rule.

Best regards,
Ben.