## 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 Cmax 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.

Dif-tor heh smusma 🖖
Helmut Schütz

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