Bioequivalence and Bioavailability Forum

Dear Ahmed,

since you have quoted ANVISA, have a look at the example given at page 9 of the document. You must apply an iterative method, in order to get a sample size estimate (because the t-dis­tri­bution depends on the degrees of freedom and therefore, on the sample size itself).
Anyhow, ANVISA’s example is derived from Chow and Liu’s textbook, which refers to a linear (addi­tive) model on untransformed data – which is useless in our case.

For sample size estimation of log-transformed data (multiplicative model), you may either use tables^1,2 or approximations.^3,4
Approximations may give slightly larger samples size in a few cases (generally give the same num­bers than exact values from tables), but give you the freedom of choosing any deviation of test from reference, whereas tables give only a step size of 5%.
Another option is software, e.g., StudySize, PASS, NQuery Advisor,…

---

1. Diletti E, Hauschke D, Steinijans VW. Sample size determination for bioequivalence assessment by means of confidence intervals. Int J Clin Pharm Ther Toxicol. 1991;29(1):1–8.
   
2. Diletti E, Hauschke D, Steinijans VW. Sample size determination: Extended tables for the multiplicative model and bioequivalence ranges of 0.9 to 1.11 and 0.7 to 1.43. Int J Clin Pharm Ther Toxicol. 1992;30/Suppl.1:S59–62.
   
3. Hauschke D, Steinijans VW, Diletti E, Burke M. Sample Size Determination for Bioequivalence Assessment Using a Multiplicative Model. J Pharmacokin Biopharm 1992;20(5):557–61.
   
4. Chow SC, Wang H. On Sample Size Calculation in Bioequivalence Trials. J Pharmacokin Pharmacodyn. 2001;28(2):155–69.
   Errata: J Pharmacokin Pharmacodyn. 2002;29(2):101–2.

Dear youri!

❝ ❝ Remark: even if the CV is not given, you can calculate it from the confidence limits and the sample size of a published study by means of a little bit of algebra

❝

❝ Can you please give some more details on the "little bit of algebra"?

No sorry, such calculations are part of my professional services.
Although I really love public discussions, such an information would go beyond one point – the one I’m making part of my living from.

❝ How exactly can I calculate the CV on the basis of a published CI and sample size?

If you solve the little ‘algebra’, and the study was balanced (equal number of subjects in both sequences), results are exact. The only limitation is the number of significant digits the confidence interval was reported, e.g., if the CI is given as 89.0–115% (n=24), you will get the CV also to three significant digits as 26.3%
If the CI was reported as 89–115%, I apply a conservative approach of using 88.5–115.4% instead (thus avoiding any potential rounding errors from the report), getting 27.3%.

If the study was imbalanced, calculations yield only an approximate result, but the deviation from exact values generally is not very large (however, conservative).
You can obtain an exact result if the number of subjects in each sequence is known – which is rarely stated in publications.
Example: (CI 89.0%-115%; going from balanced 12/12 to increased imbalance, keeping the total sample size at 24):

n1/n2 | CVintra
------+-------
12/12 | 26.29%
13/11 | 26.20%
14/10 | 25.91%
15/ 9 | 25.43%
16/ 8 | 24.74%

In other words if the study was extremely imbalanced (16/8 = CV 24.7%) and you assume a balanced design (12/12 = CV 26.3%), you are on the safe side.