Bioequivalence and Bioavailability Forum

Dear Sukimmm!

❝ I have to calculate a sample size for a parallel design with 1 test product and 3 references.

❝ We would like to know if the Test is Bioequivalent to the reference 1, then to the reference 2 and then to the reference 3 (not simulateneously of course !).

This sounds a little bit strange to me. I guess you will try to shoot three birds with a single bullet. Probably you want to run a BE study for a long half life drug to be submitted in different countries, each of them calling for their own reference. I would not recommend it, beacuse it's not possible to split the report accordingly. What if one of the T/R comparisons fails?

❝ Q1. Should I adjust for the multiplicity of tests error (i.e. as a Bonferroni adjustment to the alpha = alpha/number of planned comparisons)?

Tricky. If you plan to submit the package to different countries with their respective references, I wouldn't see the reason for a correction (the patient's risk of one population is independent from the others).

❝ Q2. Should I use the sample size calculations as in a 0ne-test one-treatment parallel design (as in Julious's Tutorial pp. 1969-70-71, Stat in Medicine) ?

Yes.
Just for other readers:

Julious SA. TUTORIAL IN BIOSTATISTICS. Sample sizes for clinical trials with Normal data.
Stat Med. 2004;23(12):1921–86. doi:10.1002/sim.1783.

❝ Q3. Or maybe I should work on a alpha=0.05 with an allocation ratio (r in the equation) of 1/4 ?

No. The allocation ratio r is the ratio of sample sizes within arms (n_R/n_T). For equal sample sizes n_R=n_T r=1.