## Fieller’s (‘fiducial’) confidence interval [General Statistics]

Dear d_labes,

you left me baffled.

» » For such cases we are setting

»

» Correct in so far if we use the approximation that the estimate of µ

Please explain then what exactly it is that power.TOST calculates when I use logscale=F.

Does it calculate power for a hypothesis based on a difference or for a ratio?

Which difference? Which ratio?

» But this has than nothing to do with Fieller’s (‘fiducial’) confidence interval, a more correct method for deriving a confidence interval for the ratio of untransformed PK metrics.

The mention of Fieller was not mine. I am quite confused now, what it is power.TOST tries to calculate when I do logscale=F.

I am convinced the assuming theta1=-0.2 by default when logscale=F is a misnomer. theta1 is elsewhere understood as an equivalence margin expressed as a ratio and that can't realistically be negative. If powerTOST tries to emulate Hauschke's paper then -.2 is f1, not a theta.

We need to be careful here about f, delta and theta.

you left me baffled.

» » For such cases we are setting

`logscale`

to False, right?»

» Correct in so far if we use the approximation that the estimate of µ

_{R}is (statistically) greater than zero. A very reasonable assumption for the usual metrics AUC and Cmax IMHO.Please explain then what exactly it is that power.TOST calculates when I use logscale=F.

Does it calculate power for a hypothesis based on a difference or for a ratio?

Which difference? Which ratio?

» But this has than nothing to do with Fieller’s (‘fiducial’) confidence interval, a more correct method for deriving a confidence interval for the ratio of untransformed PK metrics.

The mention of Fieller was not mine. I am quite confused now, what it is power.TOST tries to calculate when I do logscale=F.

I am convinced the assuming theta1=-0.2 by default when logscale=F is a misnomer. theta1 is elsewhere understood as an equivalence margin expressed as a ratio and that can't realistically be negative. If powerTOST tries to emulate Hauschke's paper then -.2 is f1, not a theta.

We need to be careful here about f, delta and theta.

—

I could be wrong, but...

Best regards,

ElMaestro

I could be wrong, but...

Best regards,

ElMaestro

### Complete thread:

- On CI calculation, untransformed metrics ElMaestro 2019-11-29 03:40 [General Statistics]
- Fieller’s (‘fiducial’) confidence interval Helmut 2019-11-29 10:03
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-29 15:53
- Fieller’s (‘fiducial’) confidence interval d_labes 2019-11-29 17:20
- Fieller’s (‘fiducial’) confidence intervalElMaestro 2019-11-30 05:11
- power.TOST with logscale=FALSE d_labes 2019-11-30 14:01

- Fieller’s (‘fiducial’) confidence intervalElMaestro 2019-11-30 05:11

- Fieller’s (‘fiducial’) confidence interval d_labes 2019-11-29 17:20

- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-29 15:53
- On CI calculation, untransformed metrics PharmCat 2019-11-29 12:05

- Fieller’s (‘fiducial’) confidence interval Helmut 2019-11-29 10:03