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

Namaste Naksh,

❝ 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.

According to the paper, yes. However, for HVD(P)s 0.95 is 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.

Such a T/R-ratio is the end of the story in RSABE with any (‼) sample size (see below).

❝ 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%).

RSABE allows unlimited scaling (check the ‘implied limits’):

round(scABEL(CV = CVwR, regulator = "FDA"), 4)  lower  upper 0.5700 1.7545

The FDA’s decision tree:

Even if you would pass in the first step of RSABE (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??

Yes. Apart from the bug in the function (see the Comment in the previous post) …

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)

… that’s nonsense. Even if we ignore the irreproducible results due to the random seed, N < n1 is yet another bug.

❝ not the additional sample size (plz correct me if i am wrong)

See above. Since you didn’t specify the 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?

Yes, you do.
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

If you would perform the second stage with 76 subjects …

power.RSABE(alpha = adj, theta0 = GMR, CV = CVwR, n = 24 + 76, design = "2x2x4") [1] 0.04751

… the study would fail because any power <0.5 is a failure by definition (see this article).

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

With any ’worse’ T/R-ratio the sample size will go through the roof.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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