## Use of lower bound for power of two combined TOST [Power / Sample Size]

Dear All!

Let me ask another question regarding the quote from the Patterson/Jones book:

Seems to me that the authors recommend to use the lower bound as criterion for setting the targetpower, i.e. if an overall power of 0.8 is aimed for, the powers for the two metrics have to be chosen such that the lower bound >= 0.8.

Example with both metrics with equal variabilities (CV of both metrics 0.25):
sampleN.TOST(CV=0.25, targetpower=0.9) gives n=38 and power=0.908890.
power.TOST(CV=0.25, n=38) gives also power=0.908890.
lbound = 0.908890 + 0.908890 -1 = 0.81778

Example with different variabilities (CVs 0.2 and 0.25):
sampleN.TOST(CV=0.25, targetpower=0.9) gives n=38 and power=0.908890.
power.TOST(CV=0.2, n=38) gives power=0.9805344
lbound = 0.908890 + 0.9805344 -1 = 0.8894244
Here we could set the targetpower for the first step lower than 0.9:
sampleN.TOST(CV=0.25, targetpower=0.85) gives n=32 power=0.857257.
power.TOST(CV=0.2, n=32) gives power=0.9595363
lbound = 0.857257 + 0.9595363 -1 = 0.8167933

Do I understand that paragraph correct or read to much into it?
If I'm correct, do you think that such an approach is resonable?

Regards,

Detlew