Bioequivalence and Bioavailability Forum

Dear Mathews!

❝ I want the intra CV value of some drugs for sample size calculation.

You are not alone…

The only collection of CVs I know is rather outdated:

Steinijans VW, Sauter R, Hauschke D, Diletti E, Schall R, Luus HG, Elze E, Blume H, Hoffmann C, Franke G, and W Siegmund
Reference tables for the intrasubject coefficient of variation in bioequivalence studies
Int J Clin Pharm Therap 33(8), 427–30 (1995)

❝ In case if no pilot study is conducted what can i do?

❝ (I think in most of the BE studies CV is calculated fom literature).

You are right!

❝ Is there any web site giving information about drugs CV and all?

I don’t think so.

❝ From one of your post I understood that we can easily calculate the CV from the MSE of the ANOVA table.

Sometimes (though rarely!) the entire ANOVA-table is published; in such a case the calculation is straightforward:

\(CV=\sqrt{e^{MSE}-1}\); also see this post.

❝ From the paper "On Sample Size Calculation in Bioequivalence Trials" by Chow and Wang,…

Caution: This paper contains a lot of typographic errors. Please get the corrections also:

S-C Chow and H Wang
On Sample Size Calculation in Bioequivalence Trials (Errata)
J Pharmacokin Pharmacodyn 29(2), 101–2 (2002)

❝ … they give two type formulas for calculation of S.S., one formula for raw data and one for log transformed data. what is the difference between the value of "sigma" in both case?

There’s a lot of confusion in terminology. Some authors use the term CV_pooled instead of CV_total.

1. From a parallel design, we only get the total variability: of course variability between subjects (which generally is ≫ within), but also within subjects (the variability exists, the fact that we have obtained data just from one occasion does not eliminate it).
   
2. From a cross-over design we get total, between (inter), and within (intra).
   
3. From a replicate design additionally to #2 we get the variability of treatment(s).

For details please see

Midha KK, Ormsby ED, Hubbard JW, McKay G, Hawes EM, Gavalas L, and IJ McGilveray
Logarithmic Transformation in Bioequivalence: Application with Two Formulations of Perphenazine
J Pharm Sci 82(2), 138–44 (1993)

For the multiplicative model (cross-over)

\(CV=\sqrt{e^{MSE}-1}\)

For the additive model (cross-over)

\(CV=\sqrt{MSE}/\bar{x}_R\)

❝ Usually we use intra CV for the calculation of sample size.

If you mean by “usually” non-replicate cross-over designs, yes.

❝ Is there any formula for calculating sample size using inter subject CV?

This does not make sense. You get CV_inter only from a cross-over study (as said above a parallel design will give you CV_total). If you have CV_inter, most likely you also will have CV_intra; if there are no PK/clinical reasons to perform a parallel study, I would always go with a cross-over study, which is more powerful.

❝ please give some reference for sample size calculation in BE studies

OK, you know Chow and Wang’s paper already. Please see two responses:

• D Hauschke
  A Note on Sample Size Calculation in Bioequivalence Trials
  J Pharmacokin Pharmacodyn 29(1), 89–94 (2002)
  
• P Blood
  Sample Size Calculation in Bioequivalence Trials
  J Pharmacokin Pharmacodyn 29(1), 95–7 (2002)

Approximations for the multiplicative cross-over model:
Hauschke D, Steinijans VW, Diletti E and M Burke
Sample Size Determination for Bioequivalence Assessment Using a Multiplicative Model
J Pharmacokin Biopharm 20(5), 557–61 (1992)

Exact sample size tables for the multiplicative cross-over model:
Diletti E, Hauschke D and VW Steinijans
Sample size determination for bioequivalence assessment by means of confidence intervals
Int J Clin Pharm Ther Toxicol. 29(1), 1–8 (1991)
Diletti E, Hauschke D and VW Steinijans
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 30/Suppl.1, S59–62 (1992)

Exact sample size tables for the additive cross-over model:
KF Phillips
Pharmacometrics. Power of the Two One-Sides Tests
J Pharmacokin Biopharm 18(2), 137–44 (1990)