## “Bad” GMR [Power / Sample Size]

Hi Constantinos,

» We have conducted an in-vitro permeation pilot study for confirming the suitability of our design in terms of time points, duration and for estimating the sample size for the pivotal study based on the within-reference %CV and the GMR calculated.

I don’t get the connection.

» The GMR was approximately 1.19 and the %CV around 25%. As it can easily be inferred the 90% C.I did not fall within the 0.80-1.25 interval.

Without the sample size of the pilot we can only guess (see below).

» I realize that no safe conclusions can be drawn from a very small sample size regarding the equivalence of the products but i wonder if there is an established methodology …

Yes.

» … for assessing if there is any point in proceeding with the pivotal study.

No, it isn’t. Try this (assuming a 2×2×2 design, ≥80% power) …

library(PowerTOST) GMR <- 1.19 # terrible! CV  <- 0.25 res <- data.frame(n = seq(12, 20, 2), lower.CL = NA, upper.CL = NA) for (j in 1:nrow(res)) {   res[j, 2:3] <- round(100*CI.BE(pe = GMR, CV = CV, n = res$n[j]), 2) res$n1[j]   <- sampleN.TOST(CV = CV, theta0 = GMR, details = FALSE,                               print = FALSE)[["Sample size"]]   res$n2[j] <- expsampleN.TOST(CV = CV, theta0 = GMR, prior.type = "CV", prior.parm = list(m = res$n[j], design = "2x2x2"),                                  details = FALSE, print = FALSE)[["Sample size"]] } print(res, row.names = FALSE)

… which gives

  n lower.CL upper.CL  n1  n2  12    99.18   142.78 312 366  14   100.81   140.47 312 356  16   102.08   138.72 312 350  18   103.11   137.33 312 344  20   103.97   136.20 312 340

… where n is the sample size of the pilot, n1 the estimated sample size of the pivotal by the “carved in stone” approach (i.e., assuming that you will get exactly the same GMR and CV as in the pilot), and n2 the sample size estimated by the Bayesian approach (taking the uncertainty of the CV observed in the pilot into account). If you would also take the uncertainty of the GMR into account, the algo would fail.
In short: reformulate.

Dif-tor heh smusma 🖖
Helmut Schütz

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