## Saturday, July 05, 2008

### Geometric Statistics, geometric CV, intra-subject variation

In bioavailability and bioequivalence studies, the pharmacokinetic parameters (AUC, Cmax) are often assumed to follow the log normal distribution. Further about log-normal distribution.

The common technique is to calculate the geometric statistics (geometric mean, geometric CV and geometric SD). Notice that the geometric CV is independent of the geometric mean (unlike the arithmetic CV which is dependent on the arithmetic mean) and the geometric CV is used in the sample size calculation. When calculating the geometric statistics, the data in original scale is log-transformed, then anti-log to transform back.

In crossover design, the geometric CV can be estimated from the mixed model and is used to gauge the intra-subject variation. Geometric CV = sqrt(exp(std^2)-1) or CV=sqrt(exp(variance)-1) where the std^2 is estimated by the MSE. Variance is from ODS ‘CovParms’ table of SAS PROC MIXEd. Another variation is inter-subject CV and the std^2 is estimated by the variance estimate for the random subject effect from the proc mixed procedure.

It should be cautioned that Geometric CV sometimes is just being called CV or intra-subject variability. I heard that some large pharmaceutical companies include 'intra-subject variability' in the standard data presentation for pharmacokinetic parameters.

The topic about the CV, geometric CV was discussed in Boomer.org (http://www.boomer.org/pkin/PK06/PK2006512.html), a discussion mailing list on bioavailability and bioequivalences. Boomer.org used to be a great resource for PK-related discussion. However, recently the discussion group was dominated by a lot of the junkies posted by Indian guys. I guess it is because of the booming generic drug development industry in India.

Seeji said...

Hi Dr. Deng,

I have a doubt on calculating intrasubject variabilty. Can you help me in this?

I'm wondering which is the proper approach for an assessment of intrasubject variabilty.

I have a series of patients of whom I have taken a parameter (contineous variable x) on 4 different days. How to check for the intrasubject variability?

What additionally complicates the matter is, by the virtue of experimental design, I already expect a uniform trend between the 4 readings. For example Expt1, 2, 3 and 4 should show a steady decrease of the variable x. The results are haywire now and what I expect is the increased intrasubject variabilty is causing this. How to find it out?

Seeji

Anonymous said...

How about the geo CV if the base of log-transform is 10?

Anonymous said...

with the base of log 10, the formula will remain the same. You would use log10 instead of ln and you would use 10^() instead of exp().

PJL said...

Sorry, but that's wrong. The formula only works with base e. If you have raw data on a log_10 scale, convert it to base e by multiplying the sd (or the raw values) by log_e(10).