## Geometric mean and CV [Power / Sample Size]

Hi Rocco,

» […] is it even reasonable to use the geometric CV for the reference? Isn’t the CV you want to input into a sample calculation the CV corresponding to the difference of the Test and Reference? Since you do not have the Test group here, I am a bit confused as to what using the geometric CV of only the reference tells you. In your slides, you have a lone that says “if you have only mean and sd of the reference, a pilot study is unavoidable.”

»

» What am I missing?

Oh dear, my slides always give only half of the picture (my is missing)…

Let’s start from a 2×2×2 crossover. We have the within-subject variabilities of T and R (CV

Similar in a parallel design. You can

If you are cautious: Pilot study or a Two-Stage-Design.

» […] is it even reasonable to use the geometric CV for the reference? Isn’t the CV you want to input into a sample calculation the CV corresponding to the difference of the Test and Reference? Since you do not have the Test group here, I am a bit confused as to what using the geometric CV of only the reference tells you. In your slides, you have a lone that says “if you have only mean and sd of the reference, a pilot study is unavoidable.”

»

» What am I missing?

Oh dear, my slides always give only half of the picture (my is missing)…

Let’s start from a 2×2×2 crossover. We have the within-subject variabilities of T and R (CV

_{wT}and CV_{wR}). Since this is not a replicate design, they are not accessible and pooled into the common CV_{w}.^{1}One of the assumptions in ANOVA are identical variances. If they are not truly equal (say CV_{wT}< CV_{wR}) the CI is inflated: The “good” T is punished by the “bad” R.Similar in a parallel design. You can

*assume*that CV_{wT}= CV_{wR}and CV_{bT}= CV_{bR}and therefore, use the (pooled, total) CV_{p}of your FIM study. Here it is the other way ’round (you have the CV_{p}of R). If the CV of T is higher, bad luck, power compromised. If both are ~ equal, fine. If it is lower, you gain power. There is no free lunch.If you are cautious: Pilot study or a Two-Stage-Design.

^{2}For the latter I recommend the function`power.tsd.p()`

of package `Power2Stage`

for . A reasonable stage 1 sample size is ~80% of what you estimate with `sampleN.TOST(alpha=0.05...)`

of package `PowerTOST`

and the CV_{p}of your FIM.- Of course, the same holds for between-subject variabilities: CV
_{bT}and CV_{bR}pooled to CV_{b}.

- Fuglsang A.
*Sequential Bioequivalence Approaches for Parallel Design.*AAPS J. 2014; 16(3):373–8. doi:10.1208/s1224801495711. Open access.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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### Complete thread:

- Input for CV when small first-in-man has been run Rocco_M 2019-09-03 18:45
- Geometric mean and CV Helmut 2019-09-05 14:05
- Geometric mean and CV Rocco_M 2019-09-05 23:49
- Geometric mean and CVHelmut 2019-09-06 00:15
- Geometric mean and CV Rocco_M 2019-09-06 17:49
- Geometric mean and CV Helmut 2019-09-06 18:15
- Geometric mean and CV ElMaestro 2019-09-06 19:03
- Geometric mean and CV Helmut 2019-09-07 09:57
- Geometric mean and CV Rocco_M 2019-09-09 13:31
- Assumptions… Helmut 2019-09-09 14:09
- Assumptions… Rocco_M 2019-09-09 16:35
- Assumptions… Helmut 2019-09-09 17:19
- Assumptions… Rocco_M 2019-09-13 21:28
- t-test & Welch-test Helmut 2019-09-14 00:16
- sampleN.TOST and CI.BE Rocco_M 2019-09-17 22:02
- assumptions vs. realizations Helmut 2019-09-18 11:04

- sampleN.TOST and CI.BE Rocco_M 2019-09-17 22:02

- t-test & Welch-test Helmut 2019-09-14 00:16

- Assumptions… Rocco_M 2019-09-13 21:28

- Assumptions… Helmut 2019-09-09 17:19

- Assumptions… Rocco_M 2019-09-09 16:35

- Assumptions… Helmut 2019-09-09 14:09

- Geometric mean and CV Rocco_M 2019-09-09 13:31

- Geometric mean and CV Helmut 2019-09-07 09:57

- Geometric mean and CV ElMaestro 2019-09-06 19:03

- Geometric mean and CV Helmut 2019-09-06 18:15

- Geometric mean and CV Rocco_M 2019-09-06 17:49

- Geometric mean and CVHelmut 2019-09-06 00:15

- Geometric mean and CV Rocco_M 2019-09-05 23:49

- Geometric mean and CV Helmut 2019-09-05 14:05