## PE outside {0.80, 1.25} not possible [Two-Stage / GS Designs]

❝ Should't we calculate stage-2 sample size with GMR of 0.95??

❝ I am trying to understand if this will be helpful in case of drugs which are very highly variable e.g. Mesalamine.

*extremely*risky.

First of all let’s attach the libraries and define some variables.

`suppressMessages(library(PowerTOST))`

suppressMessages(library(adaptIVPT))

CVwR <- 0.6978

swR <- CV2se(CVwR)

GMR <- 0.72

adj <- 0.0294

n1 <- 24

❝ Hypothetically, if study conducted with N=24, fully replicate design but T/R ratio observed worse like 0.72.

❝ And if calculate power with reduced alfa in study using actual result of T/R=0.72, ISCV=0.6978 and N=24 using powerTOST package.

❝ `power.RSABE(alpha = 0.0294, theta0 = 0.72, CV = 0.6978, n = 24, design = "2x2x4")`

❝ `[1] 0.18378`

(which is less than 80%).

*unlimited*scaling (check the ‘implied limits’):

`round(scABEL(CV = CVwR, regulator = "FDA"), 4)`

lower upper

0.5700 1.7545

*bound*≤0), you would fail with the PE of 0.72 because it has to lie within 0.8000 – 1.2500 (details in this article). Confirmed (with

*any*

`alpha`

and `targetpower`

you like):`sampleN.RSABE(theta0 = GMR, CV = CVwR, design = "2x2x4")`

Error: True ratio 0.72 not within margins 0.8 ... 1.25!

❝ To recalculate the sample size with actual variability and assumed **T/R of 95%** and reduced alfa.

❝ `rss(n = 24, r = 2, S_WR = 0.630, params = list(sig_level=0.0294))`

❝ `$rss`

❝ `21`

❝ this N=21 is total sample size right??

`N <- integer(20) # multiple calls to assess reproducibility`

for (j in seq_along(N)) {

N[j] <- unlist(rss(n = n1, r = 2, S_WR = swR, params = list(sig_level = adj)))[["rss"]]

}

cat(paste(N, collapse = ", "), "\n")

21, 21, 21, 22, 21, 21, 21, 22, 22, 21, 21, 21, 21, 21, 20, 20, 22, 21, 21, 21

(will be different if you call it)

`N < n1`

is yet another bug.❝ not the additional sample size (plz correct me if i am wrong)

`GMR`

, the function’s default `0.95`

is used – which is much better than the 0.72 you expect.❝ Since, we have already started study with N=24, we cant go ahead with stage-2.

❝ Am i missing something?

`rss()`

is buggy. Though the PE-constraint is implemented (`m = 1.25`

) in the list of parameters, the function should throw an error like `sampleN.RSABE()`

if you specify a T/R-ratio outside `1/m … m`

. Instead it returns `nmax`

, which defaults to 100.`unlist(rss(n = n1, r = 2, S_WR = swR, params = list(sig_level = adj, GMR = GMR)))[["rss"]]`

100

`power.RSABE(alpha = adj, theta0 = GMR, CV = CVwR, n = 24 + 76, design = "2x2x4")`

[1] 0.04751

*any*power <0.5 is a failure by definition (see this article).

LALA mesalamine is a nasty drug. It’s not the high

*CV*

_{wR}which is problematic but the T/R-ratio. If you know already (say, from a pilot study or a failed one) that it’s outside 0.8000 – 1.2500, forget it. Even with a ‘better’ one:

`sampleN.RSABE(theta0 = 0.84, CV = CVwR, design = "2x2x4", details = FALSE)`

++++++++ Reference scaled ABE crit. +++++++++

Sample size estimation

---------------------------------------------

Study design: 2x2x4 (4 period full replicate)

log-transformed data (multiplicative model)

1e+05 studies for each step simulated.

alpha = 0.05, target power = 0.8

CVw(T) = 0.6978; CVw(R) = 0.6978

True ratio = 0.84

ABE limits / PE constraints = 0.8 ... 1.25

Regulatory settings: FDA

Sample size

n power

120 0.80100

*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:

- Adaptive Design for the FDA’s RSABE? Helmut 2023-12-18 11:20 [Two-Stage / GS Designs]
- Likely it does not work (potentially inflated Type I Error) Helmut 2023-12-19 11:10
- Exploring package adaptIVPT, function rss() Helmut 2023-12-20 13:27
- Extreme test case Helmut 2023-12-24 13:01
- Extreme GMR Naksh 2023-12-25 04:16
- PE outside {0.80, 1.25} not possibleHelmut 2023-12-25 10:54
- PE outside {0.80, 1.25} not possible Naksh 2023-12-25 11:42
- Forget rss() Helmut 2023-12-25 13:15
- Forget rss() Naksh 2023-12-26 04:49
- TSD useful at all? Helmut 2023-12-26 12:50

- Forget rss() Naksh 2023-12-26 04:49

- Forget rss() Helmut 2023-12-25 13:15

- PE outside {0.80, 1.25} not possible Naksh 2023-12-25 11:42

- PE outside {0.80, 1.25} not possibleHelmut 2023-12-25 10:54

- Extreme GMR Naksh 2023-12-25 04:16

- Extreme test case Helmut 2023-12-24 13:01

- Exploring package adaptIVPT, function rss() Helmut 2023-12-20 13:27

- Likely it does not work (potentially inflated Type I Error) Helmut 2023-12-19 11:10