Bioequivalence and Bioavailability Forum

Hi Ghannam,

Please!

❝ Futility design is a type of two stage design studies. In this design you may dose a group of volunteers then based on the results of the first group you may complete the study by adding a second group of subjects. alpha value will be 0.05 % and will not be changed to 0.0294 %.

Splendid. Do you have a reference?

The EMA’s GL states “[…] the choice of how much alpha to spend at the interim analysis is at the company’s discretion”. ‘Splitting’ α to 0, 0.05 is tough. Of course you need a futility criterion in the interim. Which one do you have in mind? The GMR, the CI, an upper total sample size? Even more moderate splits (Haybittle/Peto or O’Brien/Fleming) lead to an inflation of the type I error (see this post).

library(Power2Stage)
power.2stage.fC(alpha=c(0, 0.05), n1=12, CV=0.24, fCrit="PE",
                fClower=0.8, theta0=1.25, powerstep=FALSE)

TSD with 2x2 crossover
Method B: alpha (s1/s2) = 0 0.05
No interim power monitoring step used
Target power in sample size est. = 0.8
Power calculation via non-central t approx.
CV1 and GMR = 0.95 in sample size est. used
Futility criterion PE outside 0.8 ... 1.25
BE acceptance range = 0.8 ... 1.25

CV = 0.24; n(stage 1) = 12; GMR= 0.95

1e+06 sims at theta0 = 1.25 (p(BE)='alpha').
p(BE)    = 0.058721
p(BE) s1 = 0.010094
Studies in stage 2 = 46.59%

Distribution of n(total)
- mean (range) = 19.3 (12 ... 108)
- percentiles
 5% 50% 95%
 12  12  40

I changed the category of the thread. Before we can discuss regulatory acceptance, you should tell us the exact background of your statistical method.

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.

---

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)