Bioequivalence and Bioavailability Forum

Hello Joy!

❝ Before proceeding with a full-scale BE, we do pilot or trial study to validate the bioanalytical method and optimize sampling time intervals. We would also want to assess the variability i.e. intra-subject that would help us determine the best sample size for the full-scale BE.

This is a very good idea!

❝ Can anyone suggest what should be the sample size for a pilot BE to obtain the above objectives.

Bad news
CV-estimates from pilot studies, or values from the literature have a high degree of uncertainty (in the actual study it is much more likely that you will be able to reproduce the point estimate, than the CV).

Good news
It is possible to calculate a Confidence Interval on CVs; therefore, if you want to be on the safe side, you can use the upper limit in sample size estimation.
Bad news
Such a CI is never published (at least I haven’t seen a single one).

Good news
Help is on the way; just use following formulas (according to Chow/Liu, Design and Analysis of Bioavailability and Bioequivalence Studies, Marcel Dekker 2000, p.193-6)

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)
chi²L = chi²(alpha/2,df)
chi²U = chi²(1-alpha/2,df)
L = SS-intra/chi²L
U = SS-intra/chi²L
L% = sqrt(exp(L)-1)
U% = sqrt(exp(U)-1)

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)
chi²L = 26.119
chi²U =  5.6287
L = 0.0119265
U = 0.0553427
L% = 10.95%
U% = 23.85%

Therefore, the upper 95% confidence limit of the 16% intra-subject CV from your pilot study is almost 24%; if your pilot study has a sample size of 12, the upper limit is 26.6% (and 44.9% for n=6…)
This echoes the trivial statement that the bigger your pilot study is, the higher will be your certainty about CV. According to my experience I would not recommend performing a pilot study with a sample of less then 16 subjects.

Important is also the expected deviation from the reference.
Another example: acceptance range 80%–125%, CV=20%, n=24.
You will have 90% power to demonstrate BE for an expected deviation of ca. 5%, but if the actual deviation is ca. 7%, power will drop to 80%…

Good luck!