Impact of minimum stage 2 sample size on the TIE: example [Two-Stage / GS Designs]
Hi ElMaestro,
I’ll give two examples. Both at the location (n1 12, CV 20%) of the maximum TIE.
Simulating for power (at 0.95):
Yes, it does – and this was my point. This time simulating for the TIE (at 1.25):
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 (n1 12, CV 20%) of the maximum TIE.
Simulating for power (at 0.95):
- No lower limit of n2
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 n2 = 1.5 × n1
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
❝ 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 n2
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 n2 = 1.5 × n1
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
❝ 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
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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
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:
- 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