# Bioequivalence and Bioavailability Forum 05:11 CEST

## 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.

```power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1., 1.25), rho=0) [1] 0.03912574 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1), rho=0) [1] 0.04944888 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1.25), rho=0) [1] 0.003067528 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1., 1.25), rho=1) [1] 0.004008864 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1), rho=1) [1] 0.0434052 power.2TOST(CV=c(0.3,0.2), n=28, theta0=c(1.25, 1.25), rho=1) [1] 0.04995503```
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.

Regards,

Detlew

Bioequivalence and Bioavailability Forum |  Admin contact
18,698 posts in 3,983 threads, 1,237 registered users;
online 7 (0 registered, 7 guests [including 5 identified bots]).

When puzzled, it never hurts to read the primary documents –
a rather simple and self-evident principle that has, nonetheless,
completely disappeared from large sectors
of the American experience.    Stephen Jay Gould

The BIOEQUIVALENCE / BIOAVAILABILITY FORUM is hosted by
Ing. Helmut Schütz