## Inflation of the TIE with Xu’s ‘Method F’? [Two-Stage / GS Designs]

Dear Helmut,

» I’m confused. Xu et al. (doi:10.1002/pst.1721) claim that for a range of CV 10–30% and n1 12–? and design constraints (α0 0.05, α1 0.0248, α1 0.0364, maximum total sample size 42, stopping for futility in the first stage if the (1–2α1) CI is entirely outside 0.9492–1/0.9492) the maximum Type I Error (assessed at a true GMR 0.80) is 0.050. ... But:
»

library(Power2Stage)» power.2stage.fC(method="C", alpha0=0.05, alpha=c(0.0248, 0.0364), »                 CV=0.2, n1=12, GMR=0.95, theta0=0.8, max.n=42, »                 fCrit="CI", fClower=0.9492, targetpower=0.8, »                 pmethod="shifted", nsims=1e6)» ...» » 1e+06 sims at theta0 = 0.8 (p(BE)='alpha').» p(BE)    = 0.053425» ...» 

What? Am I missing sumfink?

IMHO no. Another claim of the authors not fulfilled was already reported some times ago here. Not every claim contains gold .
Ask our Ol'Captain to forget his task to get a "philosophical" understanding of SD and fire up his Compiler instead to verify this ominous Power2Stage::power.2stage.fC().

But ... Do the authors really claim that n1=12 and CV=0.2 together with the other TSD characteristics do not lead to an alpha-inflation?
If I remeber the paper correctly they have an "optimized" n1=18 in their method F. Optimized w.r.t. (quote from the paper) "An optimal design is defined as the design that has at least 80% power and at most 5% overall type I error rate for all ISCV values within the specified ISCV range and achieves the smallest cost function value described ...".
That does not necessarily mean that all designs they had choosen from during optimization had a TIE <=0.05 itself.
Another quote: "Unacceptable designs (my explanation: TIE>0.05, power<80%) were assigned an extremely high cost value in order to keep the search within the acceptable region of the design space."

Regards,

Detlew