## Two regions: different populations [General Sta­tis­tics]

Hi Brus,

» But, if α is not adjusted, since there are two reference products, even though they are from different regions, would there be no multiplicity issues?

Consider ElMaestro’s post.
The current regulatory thinking is that an α adjustment is not required since the populations of patients are different (as are the local reference products). If you are concerned about tourists, go ahead and adjust.* If you employ a lower α, any agency will accept that. However, depending on the variability expect roughly 25% larger sample sizes.
BTW, what if tourists switch from one regions’ reference to the other one’s? There is no guarantee that they are BE (see this post). Given, generally we don’t have to worry (see the references in this post).

• Thinking about the US and EU: How large is the subpopulation crossing the pond (not to speak of Europeans visiting Trumpistan). How long will tourists stay on the average? How many will run out of the medication brought with them? If you are able to estimate that, possibly you discover that you have to adjust α to 0.049999999.

library(PowerTOST) # defaults: theta0 = 0.95, targetpower = 0.8 CV  <- seq(0.15, 0.4, 0.05) res <- data.frame(CV = CV,                   alpha1 = 0.050, n1 = NA, # unadjusted                   alpha2 = 0.025, n2 = NA) # Bonferroni for (j in 1:nrow(res)) {   res$n1[j] <- sampleN.TOST(alpha = 0.050, CV = CV[j], details = FALSE, print = FALSE)[["Sample size"]] res$n2[j] <- sampleN.TOST(alpha = 0.025, CV = CV[j], details = FALSE,                             print = FALSE)[["Sample size"]] } res$penalty <- sprintf("%+.2f%%", 100 * (res$n2 - res$n1) / res$n1) names(res)[2:5] <- rep(c("alpha", "n"), 2) print(res, row.names = FALSE)    CV alpha  n alpha  n penalty  0.15  0.05 12 0.025 16 +33.33%  0.20  0.05 20 0.025 24 +20.00%  0.25  0.05 28 0.025 36 +28.57%  0.30  0.05 40 0.025 50 +25.00%  0.35  0.05 52 0.025 66 +26.92%  0.40  0.05 66 0.025 82 +24.24%

Dif-tor heh smusma 🖖
Helmut Schütz

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