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
We don't know rho, the correlation berween both PK metrics, so lets look at the extremes.
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]
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
Regards,
Detlew
Complete thread:
- Two PK metrics: Inflation of the Type I Error Helmut 2017-11-12 11:57 [Two-Stage / GS Designs]
- Two PK metrics: Inflation of the Type I Error?d_labes 2017-11-12 17:46
- A place to start ElMaestro 2017-11-12 21:43
- A place to start? d_labes 2017-11-13 16:02
- A place to start? Helmut 2017-11-13 16:51
- Scientific gut feeling d_labes 2017-11-15 10:34
- Five minutes gone - power.tsd.2m() arose d_labes 2017-11-15 13:15
- Scientific gut feeling d_labes 2017-11-15 10:34
- A better place to start. ElMaestro 2017-11-14 00:04
- Nope Helmut 2017-11-14 00:21
- Nope nobody 2017-11-14 08:11
- I've meditated hard ElMaestro 2017-11-14 12:41
- Nope Helmut 2017-11-14 00:21
- A place to start? Helmut 2017-11-13 16:51
- A place to start? d_labes 2017-11-13 16:02