crap [Two-Stage / GS Designs]

Dear Helmut,

❝ ...

$$\small{\begin{matrix} \textsf{Name} & \textsf{Method} & \textsf{Type} & GMR & \pi & \alpha & CV & n_1 & E[N] & \text{TIE} & n_{2,min} & E[N] & \textsf{ANVISA} & \textsf{comp}\\\hline \textsf{SLF} & \textsf{B} & 1 & 0.90 & 0.8 & 0.0272 & 0.20 & 12 & 40.8 & 0.04997 & 6 & 40.8 & 0.04999 & \textsf{higher}\\ \textsf{SLF} & \textsf{B} & 1 & 0.90 & 0.9 & 0.0268 & 0.22 & 16 & 60.3 & 0.04985 & 8 & 60.3 & 0.04977 & \textsf{lower}\\ \textsf{Potvin} & \textsf{B} & 1 & 0.95 & 0.8 & 0.0294 & 0.24 & 12 & 29.8 & 0.04876 & 6 & 29.9 & 0.04879 & \textsf{higher}\\ \textsf{Potvin-SLF} & \textsf{B} & 1 & 0.95 & 0.8 & 0.0302 & 0.24 & 12 & 29.5 & 0.04999 & 6 & 29.6 & 0.05020 & \textsf{higher}\\ \textsf{Fuglsang} & \textsf{B} & 1 & 0.95 & 0.9 & 0.0284 & 0.22 & 12 & 31.7 & 0.04960 & 6 & 31.7 & 0.04958 & \textsf{lower}\\ \textsf{Fuglsang-SLF} & \textsf{B} & 1 & 0.95 & 0.9 & 0.0286 & 0.22 & 12 & 31.6 & 0.04999 & 6 & 31.6 & 0.05032 & \textsf{higher}\\ \textsf{Montague} & \textsf{D} & 2 & 0.90 & 0.8 & 0.0280 & 0.20 & 12 & 40.3 & \color{Red}{0.05180} & 6 & 40.3 & \color{Red}{0.05181} & \textsf{higher}\\ \textsf{Montague-SLF} & \textsf{D} & 2 & 0.90 & 0.8 & 0.0268 & 0.18 & 12 & 32.7 & 0.04998 & 6 & 32.7 & 0.04980 & \textsf{lower}\\ \textsf{Fuglsang} & \textsf{C/D} & 2 & 0.90 & 0.9 & 0.0269 & 0.18 & 12 & 41.8 & 0.05021 & 6 & 41.8 & 0.05011 & \textsf{lower}\\ \textsf{Fuglsang-SLF} & \textsf{C/D} & 2 & 0.90 & 0.9 & 0.0266 & 0.18 & 12 & 42.0 & 0.04995 & 6 & 42.0 & 0.04967 & \textsf{lower}\\ \textsf{Potvin} & \textsf{C} & 2 & 0.95 & 0.8 & 0.0294 & 0.22 & 12 & 24.9 & \color{Red}{0.05143} & 6 & 24.9 & \color{Red}{0.05136} & \textsf{lower}\\ \textsf{Potvin-SLF} & \textsf{C} & 2 & 0.95 & 0.8 & 0.0282 & 0.10 & 16 & 16.0 & 0.05010 & 8 & 16.0 & 0.05010 & \textsf{equal}\\ \textsf{Fuglsang} & \textsf{C/D} & 2 & 0.95 & 0.9 & 0.0274 & 0.10 & 16 & 16.0 & 0.05010 & 8 & 16.0 & 0.05010 & \textsf{equal}\\ \textsf{Fuglsang-SLF} & \textsf{C/D} & 2 & 0.95 & 0.9 & 0.0275 & 0.20 & 12 & 25.8 & 0.04962 & 6 & 25.8 & 0.04985 & \textsf{higher} \end{matrix}}$$

❝ TIE which is significantly >0.05 in red (limit of the binomial test 0.05036). I don’t understand why in some scenarios the TIE is lower with a minimum n2.

❝ Counterintuitive.

I'm quite sure: This is because of the simulation error. The differences of the TIE without and with min.n2 are so small. See the last column above.
Any try with a different seed of the random number generator may and will change the comparison.

Regards,

Detlew