## Power.TOST and "3x3" or other 'higher order' designs [🇷 for BE/BA]

Dear d_labes,

thanks a lot for the response.

❝ Good question, next question.

❝ AFAIK it is the power of showing BE for one comparison (of two formulations whatever kind, Test or Reference) if the evaluation of the 90% CIs is done via an ANOVA with all date taken in consideration. Any multiplicity considerations are left out. That's because they depend on the combination of more than one test via and or or.

❝ Hope this is enough explanation. If not, don't hesitate to torture me further .

power.TOST(CV=CVx, theta0=1.25, n=Nx, design="3x3")
for any combo of CVx and Nx, then power is seemingly never exceeding 0.05 i.e. nominal alpha. As I see it power converges to 0.05 with incresing Nx.

If we had two serial tests with nominal alpha =0.05 and without any concern for multiplicity then then I'd expect the result in some scenarios to exceed 0.05. So I think the result emitted from 3x3 for a given CV and sample size in its present form may in practice be the answer to this question:
1. If we have three formulations A, B and C, and the true ratio for A/C is theta0, regardless of the ratio for B/C, what is then the chance that A/C evaluates to BE (without using elimination of irrelevant treatments as per EMA)?

Accordingly I guess it is not the answer to this question:
2. If we have three formulations A, B and C, and the true ratio for A/C is theta0, and the true ratio for B/C is also theta0, what is then the chance that either A/C or B/C or both evaluate to BE (without using elimination of irrelevant treatments as per EMA)?

I wonder if a scenario exists where a sponsor would decide to run a 3-treatment test but where only the chance of showing BE for a particular pair (as in contrast to any pair) is desired or realistically considered. I am thinking the latter question may in practice be a somewhat more relevant question for companies and for regulators (the latter translating into a type I consideration). In my world it is often a matter of also assuming e.g. 0.95 for one pair and 0.90 for another pair.

But I really could be entirely wrong in these considerations? Let me know your thoughts, please.

❝ PS: Since my wife is now also retired and at home, be patient. I have not so much spare time since before .

Yes, I hear people tend to get really busy when they retire. My uncle went into retirement and bought a hammond organ which he had in his sleeping room. I believe there was no space in his living room due to an excess of ugly old furniture. The organ kept him occupied 24/7. He did not let himself be stopped by the fact that he had a complete lack of musical talent and that he was entirely tone deaf. Like his wife, the neighbours in the apartment complex were not entirely enthusiastic about his new hobby. But it kept him very busy and he played on and on. Tinnitus specialists in the area where he lived saw a prominent rise in their income during those years.

Pass or fail!
ElMaestro