Bioequivalence and Bioavailability Forum

Dear EM,

let's take a numerical example (again the OBF alpha's alpha₁=0.005, alpha₂=0.048):
Imagine after stage 1 with n=24 subjects we got CV1=0.2, PE=0.90.
The (1-2*alpha₁ CI) is 0.7660 ... 1.0574 if I don't make a mistake. Thus 'not BE' if we use the common acceptance range 0.8 ... 1.25.
We know the stage 1 size is higher than the necessary sample size for a one-stage design with alpha=0.05 (n=20 for this alpha, CV=0.2 and true ratio 0.95).

Using the famous R-package PowerTOST we obtain:
power.TOST(alpha=0.005, CV=0.2, theta0=0.95, n=24) -> 0.5489
power.TOST(alpha=0.048, CV=0.2, theta0=0.95, n=24) -> 0.8919

sampleN.TOST(alpha=0.005,CV=0.2,theta0=0.95) -> 36
sampleN.TOST(alpha=0.048,CV=0.2,theta0=0.95) -> 20

In my schemes (using alpha₂ for power check and/or sample size adaptation) you have to stop with stage 1. because the study is powered enough for the end alpha.
The choice to stay with the first BE evaluation with alpha1 will produce 'Not BE'. But for that alpha the power is <80%.
If you choose 'Evaluate BE with alpha2=0.048' the CI is 0.8148 ... 0.9941, i.e. 'BE shown' (except in Denmark ).

If you use alpha₁ in all steps except stage 2 BE evaluation you end in an study with n=36, highly overpowered.

If you use alpha1 only in the power check step you have to re-calculate the sample size because power < 80%, but come out with n_est=20 using alpha₂=0.048 although you have already 24 subjects in the study. This is contradictory.

To get rid of all these curiosities I had arrived at the decision schemes mentioned in the posts above.