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

Dear Ben,

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?

Are you sure for the binding case?

I thought: If the TIE is controlled without adhering to any futility rule, then it is more than ever controlled also by applying a futility criterion. The probability of deciding BE is lowered by doing so, and therefore also the TIE.

Of course the power may be compromized.

Example (some sort of 'forced BE', whatever this is):

gives pBE('empiric power')= 0.68452 (!). Increasing n1 doesn't help. Try it.

Empiric TIE (theta0=1.25) is: pBE= 0.034186.

Without the futility criterion w.r.t. the CI

you obtain pBE('empiric power')= 0.80815.

Power much more raised if you also forget the power futility rule:

gives a pBE= 0.90658.

Empiric TIE (theta0=1.25) is: pBE= 0.050012. Nitpickers! Don't cry "alpha inflation"! The +0.000012 to 0.05 is the simulation error. Try

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. But I don't know

Do you have any experinces for your statement

If yes, what is/are the reason(s) given by authorities to abandon binding futility rule(s) or not to 'like' them?

❝ ❝ 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?

❝ 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 thought: If the TIE is controlled without adhering to any futility rule, then it is more than ever controlled also by applying a futility criterion. The probability of deciding BE is lowered by doing so, and therefore also the TIE.

Of course the power may be compromized.

Example (some sort of 'forced BE', whatever this is):

`power.tsd.in(CV=0.25, theta0=0.9, GMR=0.9, n1=36)`

gives pBE('empiric power')= 0.68452 (!). Increasing n1 doesn't help. Try it.

Empiric TIE (theta0=1.25) is: pBE= 0.034186.

Without the futility criterion w.r.t. the CI

`power.tsd.in(CV=0.25, theta0=0.9, GMR=0.9, n1=36, fCrit="no")`

you obtain pBE('empiric power')= 0.80815.

Power much more raised if you also forget the power futility rule:

`power.tsd.in(CV=0.25, theta0=0.9, GMR=0.9, n1=36, fCrit="no", fCpower=1)`

gives a pBE= 0.90658.

Empiric TIE (theta0=1.25) is: pBE= 0.050012. Nitpickers! Don't cry "alpha inflation"! The +0.000012 to 0.05 is the simulation error. Try

`setseed=F`

and you will get something like p(BE)= 0.049858 or in the next run p(BE)= 0.04982.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. But I don't know

**how**this could be done. The implementation in Power2Stage anyhow doesn't make such an adaption, if I see it correctly.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?

—

Regards,

Detlew

Regards,

Detlew

### Complete thread:

- Finally: Exact TSD methods for 2×2 crossover designs Helmut 2018-04-21 17:17 [Two-Stage / GS Designs]
- Exact TSD methods: Example Helmut 2018-04-21 20:33
- Finally: Exact TSD methods for 2×2 crossover designs ElMaestro 2018-04-21 20:49
- Flow chart (without details) Helmut 2018-04-21 21:41
- naive questions regarding new functions in Power2Stage mittyri 2018-04-28 15:54
- Some answers Helmut 2018-04-28 17:29
- Some more "answers" d_labes 2018-04-29 21:11
- clarification regarding user Power2Stage guides mittyri 2018-04-30 13:41

- naive questions regarding new functions in Power2Stage mittyri 2018-04-28 15:54

- Flow chart (without details) Helmut 2018-04-21 21:41
- Technicality: Weigths for the inverse normal approach d_labes 2018-04-25 14:19
- Selection of w and w* Helmut 2018-04-26 09:51
- Selection of w and w* d_labes 2018-04-26 20:02
- Now what? w & w* examples d_labes 2018-05-09 13:53
- Now what? w & w* examples Ben 2018-06-10 20:12
- Now what? w & w* examples Helmut 2018-06-11 13:57
- Now what? w & w* examples Ben 2018-06-12 19:14

- a bug in interim.tsd.in()? mittyri 2018-06-11 23:27
- a bug in interim.tsd.in()? Ben 2018-06-12 19:32
- Nonbinding futility rule d_labes 2018-06-13 16:59
- Bad weather? Helmut 2018-06-13 19:23
- NLYW? d_labes 2018-06-14 10:18

- Nonbinding futility rule Ben 2018-06-13 20:26
- Nonbinding futility rule d_labes 2018-06-14 10:47
- Nonbinding futility rule Ben 2018-06-15 17:58
- Binding / Nonbinding futility rule - alpha controld_labes 2018-06-16 19:42
- Binding / Nonbinding futility rule - alpha control Ben 2019-03-30 09:52

- Binding / Nonbinding futility rule - alpha controld_labes 2018-06-16 19:42

- Nonbinding futility rule Ben 2018-06-15 17:58

- Nonbinding futility rule d_labes 2018-06-14 10:47

- Bad weather? Helmut 2018-06-13 19:23

- Nonbinding futility rule d_labes 2018-06-13 16:59

- a bug in interim.tsd.in()? Ben 2018-06-12 19:32

- Now what? w & w* examples Helmut 2018-06-11 13:57

- Now what? w & w* examples Ben 2018-06-10 20:12

- Selection of w and w* Helmut 2018-04-26 09:51