Bioequivalence and Bioavailability Forum

Dear Helmut,

❝ from untransformed data of Xovers I always calculated \(CV_{intra} = \sqrt{MSE}/\bar{x}_R\).

Me too.

❝ Does anybody know a reference supporting my – maybe too naïve – assumption?

What are the deeper reasons behind your question?

As far as I have understood: This CV (call it CV_intra or whatsoever, Chow and Liu use simply CV f.i. on page 153 in their book and Hauschke, Steinijans and Pigeot use occasionally CV_R, page 108 of their book) is defined according to your formula as a useful term in calculating a confidence interval for the ratio T/R starting from the formula for a CI of the difference T-R:

meanT - meanR + tval*sqrt(mse)*sqrt(2/N)
divide by meanR and add 1 will give the ratio
(meanT-meanR)/meanR + 1 + tval*(sqrt(mse)/meanR))*sqrt(2/N)
now define CV=sqrt(mse)/meanR
(meanT-meanR)/meanR + 1 + tval*CV(whatever)*sqrt(2/N)

Don't ask me what is more useful with this last formula using CV and the means compared to to the ones with mse and means. IMHO its more or less a matter of taste.

Dear Helmut

❝ Does anybody know a reference supporting my – maybe too naïve – assumption?

I would say this is the definition rather than an assumption; (to me) CV is always given by sigma/mu. The nice thing for a log-normally distributed random variable is that in this case sigma/mu equals sqrt(exp(sigma^2)-1). So, I agree with you that it makes sense to present it as well.

Best,
Ben