Geometric mean and CV [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2019-09-05 14:05 (549 d 18:46 ago) – Posting: # 20543
Views: 4,132

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
[image]

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

Complete thread:

Activity
 Admin contact
21,371 posts in 4,463 threads, 1,496 registered users;
online 6 (0 registered, 6 guests [including 6 identified bots]).
Forum time: Monday 07:51 CET (Europe/Vienna)

When puzzled, it never hurts to read the primary documents 
a rather simple and self-evident principle that has, nonetheless,
completely disappeared from large sectors
of the American experience.    Stephen Jay Gould

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5