## GMR, theta 0 and that all [Two-Stage / GS Designs]

Dear d_labes

Many thanks for your explanations. So just to clarify my mind…

Using theta0 in power2stage as 0.8 or 1.25, I’m informing the system that, after studies have been simulated based on expected GMR, n1, CV and target power, test product is truly non bioequivalent, because true T/R is 0.8 or 1.25 and therefore the respective 90% CI will always be outside the [0.80.1.25] bioequivalence range.

The algorithm will then calculate the number of simulated studies that wrongly rejected the Null Hypothesis and divide this number by the total number of simulated studies. The ratio represents TIE.

Considering a study design under Potvin’s method B framework (type I TSD), i.e. and expected GMR of 0.95, an n1 between 12 and 60 subjects, a CV between 10 and 100% and a target power of 0.8, no simulations are required if, on the end of the study, GMR was 0.95 and CV between 10 and 100%. Am I thinking appropriately?

But if expected GMR is for example 0.91, n1 between 12 and 60 subjects, CV between 10 and 100% and target power is 0.8, there is a violation of method B assumptions, right?

And therefore simulations are needed based on true data at the end of trial in order to calculate if TIE was below the nominal alpha of 0.05. So, assuming a final GMR of 0.91, a CV of 34%, n1 = 16, a target power of 0.8, and no futility rule, power2stage simulation conditions would be:

Based on this results:

Best rgs and thks for all the patience!

Many thanks for your explanations. So just to clarify my mind…

Using theta0 in power2stage as 0.8 or 1.25, I’m informing the system that, after studies have been simulated based on expected GMR, n1, CV and target power, test product is truly non bioequivalent, because true T/R is 0.8 or 1.25 and therefore the respective 90% CI will always be outside the [0.80.1.25] bioequivalence range.

The algorithm will then calculate the number of simulated studies that wrongly rejected the Null Hypothesis and divide this number by the total number of simulated studies. The ratio represents TIE.

Considering a study design under Potvin’s method B framework (type I TSD), i.e. and expected GMR of 0.95, an n1 between 12 and 60 subjects, a CV between 10 and 100% and a target power of 0.8, no simulations are required if, on the end of the study, GMR was 0.95 and CV between 10 and 100%. Am I thinking appropriately?

But if expected GMR is for example 0.91, n1 between 12 and 60 subjects, CV between 10 and 100% and target power is 0.8, there is a violation of method B assumptions, right?

And therefore simulations are needed based on true data at the end of trial in order to calculate if TIE was below the nominal alpha of 0.05. So, assuming a final GMR of 0.91, a CV of 34%, n1 = 16, a target power of 0.8, and no futility rule, power2stage simulation conditions would be:

`power.2stage(method = c("B"), alpha0 = 0.05, alpha = c(0.0294, 0.0294),n1=16, GMR=0.91, CV=0.34, targetpower = 0.8, pmethod = c("nct"), usePE = FALSE, Nmax = Inf, min.n2=0, theta0=0.8, theta1=0.8, theta2=1.25, npct = c(0.05, 0.5, 0.95), setseed = TRUE, details = TRUE)`

With this simulation scenario:

1e+05 sims. Stage 1 - Time consumed (secs):

user system elapsed

0.4 0.0 0.4

Keep calm. Sample sizes for stage 2 (98482 studies)

will be estimated. May need some time.

Time consumed (secs):

user system elapsed

1.3 0.0 1.3

Total time consumed (secs):

user system elapsed

2 0 2

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

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

BE margins = 0.8 ... 1.25

CV = 0.34; n(stage 1)= 16; GMR = 0.91

GMR = 0.91 and mse of stage 1 in sample size est. used

Futility criterion Nmax = Inf

1e+05 sims at theta0 = 0.8 (p(BE)='alpha').

p(BE) = 0.04385

p(BE) s1 = 0.01512

Studies in stage 2 = 98.48%

Distribution of n(total)

- mean (range) = 100.5 (16 ... 332)

- percentiles

5% 50% 95%

46 96 170

Based on this results:

- Type I error with the 2 stages was 0.04385 (and therefore <0.05) for the 1e+05 simulated studies

- Type I error for the first stage was 0.01512

- 98.48% of the simulated studies went into stage 2. The other 1.52% of the studies ended on stage 1 (either as BE or non BE)

Best rgs and thks for all the patience!

### Complete thread:

- Data for 2nd stage of Potvin’s designs BE-proff 2017-02-18 06:40
- Data for 2nd stage of Potvin’s designs ElMaestro 2017-02-18 10:20
- Data for 2nd stage of Potvin’s designs BE-proff 2017-02-18 13:29
- GMR = fixed! Helmut 2017-02-18 16:23

- Data for 2nd stage of Potvin’s designs BE-proff 2017-02-18 13:29
- “Type 1” slightly higher power than “Type 2” for the same adj. α Helmut 2017-02-18 11:51
- “Type 1” slightly higher power than “Type 2” for the same adj. α BE-proff 2017-02-18 13:31
- Terminology Helmut 2017-02-18 16:27
- Terminology Yura 2017-02-20 11:28
- Which GMR to plug in ElMaestro 2017-02-20 11:46
- Which GMR to plug in BE-proff 2017-02-21 11:35
- Which GMR to plug in ElMaestro 2017-02-21 11:47

- Which GMR to plug in BE-proff 2017-02-21 11:35
- Validated frameworks; observed GMR not relevant Helmut 2017-02-22 12:03
- Validated frameworks; observed GMR not relevant Silva 2017-03-09 01:26
- GMR, theta 0 and that all d_labes 2017-03-09 09:21
- GMR, theta 0 and that allSilva 2017-03-09 12:38
- GMR, theta 0 and that all ElMaestro 2017-03-09 12:56
- GMR, theta0 and that all d_labes 2017-03-09 13:55
- GMR, theta0 and that all Silva 2017-03-09 18:01

- GMR, theta 0 and that allSilva 2017-03-09 12:38

- GMR, theta 0 and that all d_labes 2017-03-09 09:21

- Validated frameworks; observed GMR not relevant Silva 2017-03-09 01:26

- Which GMR to plug in ElMaestro 2017-02-20 11:46

- Terminology Yura 2017-02-20 11:28

- Terminology Helmut 2017-02-18 16:27
- “Type 1” slightly higher power than “Type 2” for the same adj. α BE-proff 2017-02-21 11:31

- “Type 1” slightly higher power than “Type 2” for the same adj. α BE-proff 2017-02-18 13:31

- Data for 2nd stage of Potvin’s designs ElMaestro 2017-02-18 10:20