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

Hi Rocco,

» I see people will typically enter sample sd / sample mean of the single formulation, but I feel this is incorrect.

You are right. PK metrics like AUC and C

If you plan for a parallel design you should use the geometric CV.

$$\overline{x}_{log}=\frac{\sum (log(x_i))}{n}$$ $$\overline{x}_{geo}=\sqrt[n]{x_1x_2\ldots x_n}=e^{\overline{x}_{log}}$$ $$s_{log}^{2}=\frac{\sum (log(x_i-\overline{x}_{log}))}{n-1}$$ $$CV_{log}=\sqrt{e^{s_{log}^{2}}-1}$$ Only if you don’t have access to the raw data, you would need simulations.

» I see people will typically enter sample sd / sample mean of the single formulation, but I feel this is incorrect.

You are right. PK metrics like AUC and C

_{max}follow a*lognormal*distribution and hence, arithmetic means and their SDs / CVs are wrong (*i.e.*, are positively biased).If you plan for a parallel design you should use the geometric CV.

$$\overline{x}_{log}=\frac{\sum (log(x_i))}{n}$$ $$\overline{x}_{geo}=\sqrt[n]{x_1x_2\ldots x_n}=e^{\overline{x}_{log}}$$ $$s_{log}^{2}=\frac{\sum (log(x_i-\overline{x}_{log}))}{n-1}$$ $$CV_{log}=\sqrt{e^{s_{log}^{2}}-1}$$ Only if you don’t have access to the raw data, you would need simulations.

—

Helmut Schütz

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

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*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 [Power / Sample Size]
- Geometric mean and CVHelmut 2019-09-05 14:05
- Geometric mean and CV Rocco_M 2019-09-05 23:49
- Geometric mean and CV Helmut 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 CV Helmut 2019-09-06 00:15

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

- Geometric mean and CVHelmut 2019-09-05 14:05