## Hey, hey wait another moment.... [General Sta­tis­tics]

Dear Helmut, dear other Disku-Tanten,

» You want to get both T1 and T2 approved.

T1 = R T2 = R: ⇒ 95% CI

Clearly needs an adjustment because of the simultaneous tests and both T1 and T2 will be marketed.

I'm not quite sure if you are right here.
Consider the analogy with the "simultaneous" tests of AUC and Cmax.
I haven't seen any alpha correction for that case .
The IUT (intersection union test) principle protects us.
But can be very conservative.

IMHO we don't need an alpha correction for your case above, if we combine the tests with 'and'.

If we combine with 'or', e.g. any of the test products T1 or T2 is choosen for further development or for approval, than we have to split the familywise level of alpha = 0.05 and the two individual null hypotheses have to be tested at a comparisonwise type I error which is a fraction of alpha, e.g. according to the Bonferroni procedure. Means 95% CIs instead of 90% CIs in case of T1, T2 and R.

Reference (wording of my post partly copied from that Reference):
Hauschke D., Steinijans V.W., Pigeot I.
Bioequivalence Studies in Drug Development: Methods and Applications.
New York: Wiley; 2007.
Chapter 7 Designs with more than two formulations / 7.4 Multiplicity

Seems a case for sims if we don't trust in the Reference. Isn't it?
Eventually we can miss-use power.2TOST() if we consider for simplicity two simultaneous test of AUC_T1R and AUC_T2R as the two metrics, which are usually interpreted as two different metrics, e.g. AUC and Cmax, respectively.
Then of course the question of the correlation parameter rho arises. How to choose?

Regards,

Detlew