Bioequivalence and Bioavailability Forum

Hello Joy!

Since we are interested only in the upper limit of CV – if CV in the main study is lower than predicted, we are only gaining power – it may be better to apply a one-side approach instead:
df = n1+n2-2 (n1/n2 = number of subjects in sequences 1/2, or in the balanced case df = sample size-2)
alpha = 0.05 (95% confidence interval)
chi2 = chi2(1-alpha,df)
U  = SS-intra/chi2
U% = sqrt(exp(U)-1)

Unfortunately the function is a little bit nasty (depending on the sample size and the CV). The upper 95% confidence is given on the z-axis as a percentage of the CV (x-axis: sample size, and y-axis: CV found in pilot study).

A numerical example:
n1 = n2 = 8 (pilot study's sample size 16)
df = 14
CV = 15.0% (MS-intra 0.0222506, SS-intra 0.0311509)
chi2 = 6.5706
U  = 0.0474092
U% = 22.03% (147% of the CV found in the pilot study)

Therefore the one-sided 95% confidence limit of the 15% intra-subject CV from your pilot study is about 22%; if your pilot study has a sample size of 12, the 95% CL of the CV is 24.1% (161% of pilot study), and 36.5% (243%) for n=6...

Bottom line: the smaller the sample size of you pilot study is, the higher is the uncertainty of the estimated CV.