## On CI calculation, untransformed metrics [General Statistics]

Hi all,

I never did much work on untransformed metrics for BE calculation, but I am facing a situation where it is mandated by an authority, and what I need is the CI for the ratio (not per se the difference). I'd like to be well prepared.

A relevant publication, at least for sample size, is Hauschke et al. from 1999.

The ratio of two normal distributions is not itself a normal distribution. How is the calculation of the CI

I think Hauschke's paper is silent on the matter, as is Chow & Liu.

Note also that powerTOST's nomenclature seems to differ a bit (?) from Hauschke's in that it uses theta1 and theta2 where Hauscke would use f1 and f2. In powerTOST theta1 defaults to 0.8 when the limit for the ratio is actually 0.8*mu

Anyhow, the important part of this post is how the CI for the ratio is actually derived.

I never did much work on untransformed metrics for BE calculation, but I am facing a situation where it is mandated by an authority, and what I need is the CI for the ratio (not per se the difference). I'd like to be well prepared.

A relevant publication, at least for sample size, is Hauschke et al. from 1999.

The ratio of two normal distributions is not itself a normal distribution. How is the calculation of the CI

*for the ratio*actually done when the upper and lower limits are percentages of mu_{(R)}?I think Hauschke's paper is silent on the matter, as is Chow & Liu.

Note also that powerTOST's nomenclature seems to differ a bit (?) from Hauschke's in that it uses theta1 and theta2 where Hauscke would use f1 and f2. In powerTOST theta1 defaults to 0.8 when the limit for the ratio is actually 0.8*mu

_{(R)}, or so I am reading it. I may be quite wrong?!?Anyhow, the important part of this post is how the CI for the ratio is actually derived.

—

I could be wrong, but...

Best regards,

ElMaestro

I could be wrong, but...

Best regards,

ElMaestro

### Complete thread:

- On CI calculation, untransformed metricsElMaestro 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 interval ElMaestro 2019-11-30 05:11
- power.TOST with logscale=FALSE d_labes 2019-11-30 14:01

- Fieller’s (‘fiducial’) confidence interval ElMaestro 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