Bioequivalence and Bioavailability Forum

Dear Ghannam86,

like Helmut I await more infos on the background of your "futility design". A term I never heard up to now.
Meanwhile for me this sounds like something that is called sample size re-estimation (SSR) design, blinded or not.^1,2

Naively applied one would expect to be able to use alpha = 0.05 since no BE decision is taken in the "first" stage and therefore no alpha has to be spent. There is some rumor out there that some (leading?) regulatory authority has accepted such thinking.

But as Helmut has already shown above using a variant of Potvin Method B and alpha in stage 1 = 0:

library(Power2Stage)
power.2stage.ssr(alpha=0.05, n1=12, CV=0.25, blind=FALSE, theta0=1.25)

TSD with 2x2 crossover
 with sample size re-estimation (only)
Nominal alpha = 0.05
Sample size est. based on power calculated via non-central t approx.
with CV1, GMR = 0.95 and targetpower = 0.8
BE acceptance range = 0.8 ... 1.25

CV= 0.25; n(stage 1) = 12

1e+06 sims at theta0 = 1.25 (p(BE)='alpha').
p(BE)    = 0.059582
Studies in stage 2 = 94.82%

Distribution of n(total)
- mean (range) = 28.6 (12 ... 124)
- percentiles
 5% 50% 95%
 12  26  50

There is an alpha-inflation! Should (!) be not acceptable for regulators.
This was noticed by Golkowski¹ for blinded SSR, and is well known, although in the context of superiority testing with parallel groups, back to 1990.³ Or even back to Stein's paper in 1945.⁴ See also.⁵

How "futility" comes into play I await your specification.

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1. Golkowski D, Friede T, Kieser M
   "Blinded sample size re-estimation in crossover bioequivalence trials"
   Pharm Stat. 2014 May-Jun;13(3):157-62. Epub 2014 Apr 9
   
2. Jones B, Kenward MG
   "Design and Analysis of Cross-Over Trials"
   Third edition, Chapman and Hall/CRC, Boca Raton, Oct 2014
   Chapter 12
   
3. Wittes J, Brittain E
   "The role of internal pilot studies in increasing the efficiency of clinical trials"
   Stat Med, Vol. 9, 65-72 (1990)
   
4. Stein, C.
   "A two-sample test for a linear hypothesis whose power is independent of the variance"
   Annals of Mathematical Statistics 16, 243-258 (1945)
   
5. Wittes et al.
   "Internal Pilot Studies I: Type I Error Rate of the NAIVE t-Test"
   Statist. Med. 18, 3481-3491 (1999)