## U as a futility criterion [Two-Stage / GS Designs]

❝ Are there any rules or recommendations for setting up the pre-specified limit (U) as a futility criterion?

Not really. You have to find a balance between the maximum study costs you are accepting to spend and the potential loss in power. Xu

*et al*.* recommend a futility of 42 on n

_{total}for CV ≤30% and 180 for CV >30%. Generally a small stage 1 sample size is not a good idea.

`library(Power2Stage)`

power.tsd.fC(method="B", alpha=c(0.0249, 0.0357), CV=0.25, n1=24,

fCrit="CI", fClower=0.9374, max.n=42) # fixed GMR 0.95

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0249 0.0357

Interim power monitoring step included

Target power in power monitoring and sample size est. = 0.8

Power calculation via non-central t approx.

CV1 and GMR = 0.95 in sample size est. used

Maximum sample size max.n = 42

Futility criterion 90% CI outside 0.9374 ... 1.06678

BE acceptance range = 0.8 ... 1.25

CV = 0.25; n(stage 1) = 24; GMR = 0.95

1e+05 sims at theta0 = 0.95 (p(BE) = 'power').

p(BE) = 0.83087

p(BE) s1 = 0.6057

Studies in stage 2 = 33.2%

Distribution of n(total)

- mean (range) = 27.9 (24 ... 42)

- percentiles

5% 50% 95%

24 24 42

power.tsd.fC(method="B", alpha=c(0.0249, 0.0357), CV=0.25, n1=24,

fCrit="CI", fClower=0.9374, max.n=42, usePE=TRUE)

# fully adaptive

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0249 0.0357

Interim power monitoring step included

Target power in power monitoring and sample size est. = 0.8

Power calculation via non-central t approx.

CV1 and PE1 in sample size est. used

Maximum sample size max.n = 42

Futility criterion 90% CI outside 0.9374 ... 1.06678

BE acceptance range = 0.8 ... 1.25

CV = 0.25; n(stage 1) = 24

1e+05 sims at theta0 = 0.95 (p(BE) = 'power').

p(BE) = 0.87839

p(BE) s1 = 0.6057

Studies in stage 2 = 33.2%

Distribution of n(total)

- mean (range) = 30 (24 ... 42)

- percentiles

5% 50% 95%

24 24 42

Remember that if you deviate from one of the published methods (except by adding a futility which leads to early stopping) you have to assess the Type I Error. Fine with the setting above:

`power.tsd.fC(method="B", alpha=c(0.0249, 0.0357), CV=0.25, n1=24,`

fCrit="CI", fClower=0.9374, max.n=42, usePE=TRUE,

theta0=1.25)

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0249 0.0357

Interim power monitoring step included

Target power in power monitoring and sample size est. = 0.8

Power calculation via non-central t approx.

CV1 and PE1 in sample size est. used

Maximum sample size max.n = 42

Futility criterion 90% CI outside 0.9374 ... 1.06678

BE acceptance range = 0.8 ... 1.25

CV = 0.25; n(stage 1) = 24

1e+06 sims at theta0 = 1.25 (p(BE) = TIE 'alpha').

p(BE) = 0.045069

The maximum inflation of the TIE is often observed at combinations of small n

_{1}and low CV. The minimum n

_{1}for Xu’s method is 18. With CV 10% we get a TIE of 0.035744.

- Xu J, Audet C, DiLiberti CE, Hauck WW, Montague TH, Parr AF, Potvin D, Schuirmann DJ.
*Optimal adaptive sequential designs for crossover bioequivalence studies.*Pharm Stat. 2016;15(1):15–27. doi:10.1002/pst.1721.

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- Two-stage design and 'forced bioequivalence' Mikalai 2018-06-06 08:28 [Two-Stage / GS Designs]
- Two-stage design and 'forced bioequivalence' ElMaestro 2018-06-06 10:53
- Two-stage design and 'forced bioequivalence' Yura 2018-06-07 10:24
- But what is the real problem? ElMaestro 2018-06-07 13:53
- But what is the real problem? Yura 2018-06-07 14:59
- But what is the real problem? Mikalai 2018-06-07 15:47
- But what is the real problem? Helmut 2018-06-07 17:33
- But what is the real problem? Mikalai 2018-06-08 12:24
- U as a futility criterionHelmut 2018-06-08 14:00

- But what is the real problem? Mikalai 2018-06-08 12:24

- But what is the real problem? Helmut 2018-06-07 17:33

- But what is the real problem? Mikalai 2018-06-07 15:47

- But what is the real problem? Yura 2018-06-07 14:59

- But what is the real problem? ElMaestro 2018-06-07 13:53

- Two-stage design and 'forced bioequivalence' Yura 2018-06-07 10:24

- Two-stage design and 'forced bioequivalence' ElMaestro 2018-06-06 10:53