## A place to start? [Two-Stage / GS Designs]

Dear Detlew,

» that could indeed be done within the (in)famous package Power2Stage, function power.2stage.fC() using the argument n2.min.

… and power.2stage() without the need of specifying a futility criterion.

» At least partially because n2.min assures a minimum sample size for stage 2, if stage 2 is called for and the estimated sample size is smaller than n2.min.

Right.

» But that's not the problem Helmut has described, at least as I understand it. Here we initiate a stage 2 from the perspective of the AUC evaluation where it is not neccessary to initiate one.

Right as well. I tried to modify 5+ years old code for subject simulations but lost my patience.

» If having more than necessary number of subjects is a problem at all? My gut feeling says no.

From the producer’s perspective, of course, not.
My gut feeling tells me: The adjusted α showed (well, in simulations…) that the TIE is controlled if we follow the frameworks exactly, i.e., initiate the second stage only if necessary based on the interim and with the re-estimated sample size.* If we increase the sample size, the chance of passing BE increases and hence, the TIE.
Misusing Power2Stage:

library(Power2Stage) power.2stage(CV=0.2, theta0=1.25, n1=28)$pBE # [1] 0.029911 power.2stage(CV=0.2, theta0=1.25, n1=28, min.n2=20)$pBE # [1] 0.030917

• A lower sample size – due to dropouts – is not problematic. Lower chance of passing = no inflation of the TIE.

Dif-tor heh smusma 🖖
Helmut Schütz

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