## Sample size estimation for parallel design with more than 2 treatments [Power / Sample Size]

Hello BEQool!

When we refer to EMA BE guideline, the BE estimation shall be considered for the concerned treatment and the rest of the treatment shall be separated from calculation purpose.

So if there are more than two treatments, why can't the sample size be considered separately and then take a overall decision?
Consider below case.

Case 1:
Desired Power 80%
r (note: nT*r=nR) 1
a 5%
Total CV 40.00%
Expected mT/mR Ratio 95.00%
Lower Equivalence Limit 80.0%
Upper Equivalence Limit 125.0%

Required Sample Size 65 (nA)+65 (nB)=130 (Total)

Case 2:
Desired Power 80%
r (note: nT*r=nR) 1
a 5%
Total CV 40.00%
Expected mT/mR Ratio 90.00%
Lower Equivalence Limit 80.0%
Upper Equivalence Limit 125.0%
1-b 0.800076232

Required Sample Size 133 (nA)+133 (nB)=266 (Total)

Desired Power 80%
r (note: nT*r=nR) 1
a 5%
Total CV 20.00%
Expected mT/mR Ratio 95.00%
Lower Equivalence Limit 80.0%
Upper Equivalence Limit 125.0%

Required Sample Size 18 (nA)+18 (nB)=36 (Total)

And for 4 arm--> sample size is 72.

But why the assumption are same? what is the purpose of additional arm, if the expected ratio is same?

Regards,
Divyen  Ing. Helmut Schütz 