## Extreme test case [Two-Stage / GS Designs]

Dear all,

something is rotten in the state of Denmark…
For the test case you need the script of the previous post and the library PowerTOST.

adj  <- 0.0294 n1   <- 24 CVwR <- 0.25 # mostly no scaling GMR  <- 0.88 # a bad one

First the functions of PowerTOST:

power.RSABE(alpha = adj, CV = CVwR, theta0 = GMR, design = "2x2x4", n = n1) [1] 0.49905 sampleN.RSABE(alpha = adj, CV = CVwR, theta0 = GMR, 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  = 0.0294, target power = 0.8 CVw(T) = 0.25; CVw(R) = 0.25 True ratio = 0.88 ABE limits / PE constraints = 0.8 ... 1.25 Regulatory settings: FDA Sample size  n    power 52   0.80636

Since power in the first stage <0.8, we would initiate a second stage with 52 – 24 = 28 subjects.

Now the function with its defaults. Additionally I set details = FALSE to return the data.frame of results, inter = TRUE to show the intermediate stage 2 sample sizes, and increased the number of calls for the workaround to a crazy number:

RSS(n1 = n1, CVwR = CVwR, GMR = GMR, calls = 2500, details = FALSE, inter = TRUE)  n2 times  22     1  24    24  26   699  76  1776   alpha.adj n1 CVwR  GMR target n2   N futile 1    0.0294 24 0.25 0.88    0.8 76 100   TRUE

What’s going on here – where does the discontinuity in estimated stage 2 sample sizes come from? The study would stop for futility in the first stage!
Another try with a higher nmax:

RSS(n1 = n1, CVwR = CVwR, GMR = GMR, calls = 50, nmax = 250, details = FALSE, inter = TRUE)  n2 times  24     1  26    16  28    26  30     7   alpha.adj n1 CVwR  GMR target n2  N futile 1    0.0294 24 0.25 0.88    0.8 30 54  FALSE

Now the study would proceed to the second stage but with 30 subjects instead of the 28 estimated by sampleN.RSABE().

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

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