## Validated frameworks; observed GMR not relevant [Two-Stage / GS Designs]

Hi Yura,

» If the ratio of AUC and Cmax T / R beyond 0.95 - 1.05, whether it is a violation of the conditions of the calculation for algorithm of adaptive design?

Adjusted alphas of the published frameworks are only valid for certain ranges of n1/CV-combinations, fixed GMRs, and target powers assessed (see this presentation, slide 20). F.i. Potvin’s αadj 0.0294 in ‘Method B’ (“Type 1”) is valid for n1 12–60, CV 10–100%, fixed GMR 0.95, and target power 80%. The maximum Type I Error is generally seen at small stage 1 sample sizes and low CVs. Hence, even if the n1 and/or CV were outside the validated range on the upper end (say for ‘Method B’ >60 and/or >100%) you can be pretty sure that the patient’s risk is still controlled. However, in such a case picky assessors might ask for simulations.
I would avoid performing the first stage in 12 subjects. Due to dropouts one may end up outside the validated range. Example for ‘Method B’:

library(Power2Stage) power.2stage(CV=0.2, n1=12, alpha=c(0.0294, 0.0294), theta0=1.25,              targetpower=0.8, pmethod="shifted", nsims=1e6)$pBE # [1] 0.046352 # n1 within validated range: TIE <0.05. power.2stage(CV=0.2, n1=10, alpha=c(0.0294, 0.0294), theta0=1.25, targetpower=0.8, pmethod="shifted", nsims=1e6)$pBE # [1] 0.048389 # n1 outside validated range: higher TIE but still <0.05.

The GMR observed in the first stage is not relevant.

Cheers,
Helmut Schütz

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