## Power of two combined TOST [General Sta­tis­tics]

Dear Louis,

❝ Can anyone direct me towards a thread where it is discussed/presented how to deal with alpha adjustment and power in case of multiplicity (AUC and Cmax considered at the same time)? Both CO and Parallel designs.

have a loook at this post or this one.
As our ElMaestro already said: According to the intersection-union principle there is no need for adjusting alpha if you combine two TOST with AND. As long as the two combined test on their own have size alpha.

Power is another pair of shoes.
If the correlation is zero, the overall power is the product of the powers of the individual tests, i.e. may be considerable lower then the targeted power.
If the correlation is one, the overall power is the minimum of the powers of the individual tests. This is the foundation why we make a sample size calculation for both metrics and choose the resulting higher sample size.

But no one knows, at least not me, to what number the correlation should be set in practice.
The authors team of the R package PowerTOST is currently discussing that theme. May be we came out with some aid in the near future.

Be aware: It is not the correlation of the two PK metrics itself. To cite from the man page of function power.2TOST():
"rho: Correlation between the two PK metrics (e.g. AUC and Cmax) under consideration. This is defined as correlation between the estimator of the treatment difference of PK metric one and the estimator of the treatment difference of PK metric two."

Be further aware: The functions for power and sample size for the combination of 2 TOST are currently under revision since the implemented versions in V1.4-6 came out as statistical flawed. You need the development version of PowerTOST to get reliable values for the power of 2 TOST. See this thread how to get it.

Reference to look into:
Phillips KF.
Power for Testing Multiple Instances of the Two One-Sided Tests Procedure
Int J Biostat. 2009;5(1):Article 15. doi:10.2202/1557-4679.1169

Regards,

Detlew