## Impact of minimum stage 2 sample size on the TIE: example [Two-Stage / GS Designs]

Hi ElMaestro,

» So let me ask the forbidden question: "Can you reformulate?"

»

» » Higher sample size ⇒ more degrees of freedom ⇒ narrower CI ⇒ higher probability to pass BE.

» » In other words, the TIE will also increase and one would have to use a

»

» This is one thing I did not get.

I’ll give two examples. Both at the location (

Simulating for power (at 0.95):

» Does that logic also work when we simulate true GMR 0.8 or 1.25 for type I error? I find it hard to convince myself.

Yes, it does – and this was my point. This time simulating for the TIE (at 1.25):

» Somehow I guess regulators just wanted to say that inclusion of a single subject in stage 2 would not be ok. They are right and that is not rocket science.

I think not to perform the second stage with one subject is a no-brainer. I guess that two was a compromise. AFAIK, Alfredo suggested 12 subjects to the BSWP.*

» So let me ask the forbidden question: "Can you reformulate?"

»

» » Higher sample size ⇒ more degrees of freedom ⇒ narrower CI ⇒ higher probability to pass BE.

» » In other words, the TIE will also increase and one would have to use a

*lower*adjusted α.»

» This is one thing I did not get.

I’ll give two examples. Both at the location (

*n*_{1}12, CV 20%) of the maximum TIE.Simulating for power (at 0.95):

- No lower limit of
*n*_{2}

`library(Power2Stage)`

power.2stage(method="B", alpha=rep(0.0294, 2), CV=0.2,

n1=12, GMR=0.95, targetpower=0.8, min.n2=0)

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0294 0.0294

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

No futility criterion

BE acceptance range = 0.8 ... 1.25

CV = 0.2; n(stage 1) = 12; GMR= 0.95

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

p(BE) = 0.84174

p(BE) s1 = 0.41333

Studies in stage 2 = 56.34%

Distribution of n(total)

- mean (range) = 20.6 (12 ... 82)

- percentiles

5% 50% 95%

12 18 40

- Lower limit of
*n*_{2}= 1.5 ×*n*_{1}

`power.2stage(method="B", alpha=rep(0.0294, 2), CV=0.2,`

n1=12, GMR=0.95, targetpower=0.8, min.n2=18)

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0294 0.0294

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

No futility criterion

Minimum sample size in stage 2 = 18

BE acceptance range = 0.8 ... 1.25

CV = 0.2; n(stage 1) = 12; GMR= 0.95

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

p(BE) = 0.91564

p(BE) s1 = 0.41333

Studies in stage 2 = 56.34%

Distribution of n(total)

- mean (range) = 23.5 (12 ... 82)

- percentiles

5% 50% 95%

12 30 40

*n*_{1}, naturally the same percent of studies will proceed to the second stage. However, the expected total sample sizes will be larger (*E*[*N*] 23.5*vs.*20.6, median 30*vs.*18). The sponsor gains power (91.6% vs. 84.2%).» Does that logic also work when we simulate true GMR 0.8 or 1.25 for type I error? I find it hard to convince myself.

Yes, it does – and this was my point. This time simulating for the TIE (at 1.25):

- No lower limit of
*n*_{2}

`library(Power2Stage)`

power.2stage(method="B", alpha=rep(0.0294, 2), CV=0.2,

n1=12, GMR=0.95, targetpower=0.8, min.n2=0, theta0=1.25)

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0294 0.0294

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

No futility criterion

BE acceptance range = 0.8 ... 1.25

CV = 0.2; n(stage 1) = 12; GMR= 0.95

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

p(BE) = 0.046262

p(BE) s1 = 0.028849

Studies in stage 2 = 87.86%

Distribution of n(total)

- mean (range) = 23.1 (12 ... 98)

- percentiles

5% 50% 95%

12 22 40

- Lower limit of
*n*_{2}= 1.5 ×*n*_{1}

`power.2stage(method="B", alpha=rep(0.0294, 2), CV=0.2,`

n1=12, GMR=0.95, targetpower=0.8, min.n2=18, theta0=1.25)

TSD with 2x2 crossover

Method B: alpha (s1/s2) = 0.0294 0.0294

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

No futility criterion

Minimum sample size in stage 2 = 18

BE acceptance range = 0.8 ... 1.25

CV = 0.2; n(stage 1) = 12; GMR= 0.95

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

p(BE) = 0.048816

p(BE) s1 = 0.028849

Studies in stage 2 = 87.86%

Distribution of n(total)

- mean (range) = 29.2 (12 ... 98)

- percentiles

5% 50% 95%

12 30 40

*n*_{2}) to 0.048816 (minimum*n*_{2}= 1.5 ×*n*_{1}). No problem with ‘Method B’ but gets nasty with ‘Method C’ (see the plot in my OP).» Somehow I guess regulators just wanted to say that inclusion of a single subject in stage 2 would not be ok. They are right and that is not rocket science.

I think not to perform the second stage with one subject is a no-brainer. I guess that two was a compromise. AFAIK, Alfredo suggested 12 subjects to the BSWP.*

- García-Arieta A, Gordon J.
*Bioequivalence Requirements in the European Union: Critical Discussion.*AAPS J. 2012;14(4):738–48. doi:10.1208/s12248-012-9382-1

—

Helmut Schütz

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

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

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

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### Complete thread:

- Impact of minimum stage 2 sample size on the Type I Error Helmut 2016-12-30 01:22
- Impact of minimum stage 2 sample size on the Type I Error ElMaestro 2016-12-30 12:12
- Impact of minimum stage 2 sample size on the TIE: exampleHelmut 2016-12-30 14:01
- Impact of minimum stage 2 sample size on the TIE: example ElMaestro 2016-12-30 17:19
- Impact of minimum stage 2 sample size on the TIE: example Helmut 2016-12-30 18:00
- Impact of minimum stage 2 sample size on the TIE: example ElMaestro 2016-12-30 18:50
- Bingo! Helmut 2016-12-30 19:00

- Impact of minimum stage 2 sample size on the TIE: example ElMaestro 2016-12-30 18:50

- Impact of minimum stage 2 sample size on the TIE: example Helmut 2016-12-30 18:00

- Impact of minimum stage 2 sample size on the TIE: example ElMaestro 2016-12-30 17:19

- Impact of minimum stage 2 sample size on the TIE: exampleHelmut 2016-12-30 14:01

- Impact of minimum stage 2 sample size on the Type I Error ElMaestro 2016-12-30 12:12