## Two PK metrics: Inflation of the Type I Error? [Two-Stage / GS Designs]

Dear Helmut!

Very good question.
Next question .

My gut feeling says: Don't worry, be happy .
What we had to do if we take two or more metrics into consideration is to combine the results of both metrics, i.e. some sort of inter-section-union test (IUT).
The IUT is known to be conservativ up to very conservative.
For illustration let's look at the results in a single stage design using Ben's function power.2TOST():
We don't know rho, the correlation berween both PK metrics, so lets look at the extremes.

library(PowerTOST) power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1., 1.25), rho=0) [1] 0.03784 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1), rho=0) [1] 0.04958 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1.25), rho=0) [1] 0.00244 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1., 1.25), rho=1) [1] 0.00416 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1), rho=1) [1] 0.04282 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1.25), rho=1) [1] 0.04977
green: conservative
red: very conservative

This behavior should protect against an additional alpha inflation due to combining the results of both metrics if you control the TIE (alpha) of each.

Ok. All this is only analogy and gut feeling.
We only know exactly what's going on, if we simulate.
But I doubt if time spent and effort of doing this pays off.

Edit: Values corrected after a bug-fix in PowerTOST v1.4-7 (see the “Details” section of the man-page. [Helmut]

Regards,

Detlew