Bioequivalence and Bioavailability Forum

Dear Helmut!

❝ ... Sample size re-estimation based on PE and CV? Since we don’t assess BE in the first stage (that would be similar to Potvin’s “internal pilot” Method A – which they dropped due to α-inflation) we have to introduce a futility rule. Sample size estimation if the PE is not within the acceptance range simply doesn’t work.

That and your scheme reminds me on an idea I had some times ago but was not able to elaborate due to missing spare time.

Dropping all the Spanish bells and whistles no one is aware of its foundations, but retaining the sample size adaption based on PE and CV and the PE futility rule leads to a modification of Potvin B (with implicit power) according to:



Other settings of alpha₁, alpha₂ are imaginable.
For instance alpha₁=0 (resulting in CIs at stage 1 -Inf ... +Inf, i.e. BE test always "BE not proven") and alpha₂=0.05 .

I think this scheme is worth of exploration.

If the overall alpha <= 0.05 is satisfied for this decision scheme it would overcome the drawback of Potvin's decision schemes that even if the stage 1 point estimate is "jenseits von gut und böse" (beyond the pale) we are forced to go to stage 2, but with a sample size based on a 'true' ratio of 0.95. With that we definitely don't reach BE.

Here some preliminary results of simulations (10E5 sims only) with the Pocock alphas (alpha₁, alpha₂=0.0294):
             empirical
CV    n1   alpha   power
------------------------
15 %   8   0.045   0.918
      12   0.042   0.964
      16   0.039   0.982
20 %   8   0.044   0.811
      12   0.045   0.897
      16   0.043   0.939
      20   0.043   0.959
      24   0.041   0.974
25 %   8   0.039   0.703
      12   0.043   0.812
      16   0.045   0.873
      20   0.045   0.913
      24   0.042   0.937
      28   0.042   0.953
      32   0.041   0.964

No sign of an alpha-inflation. Power ok, except for the very small first stage with n₁=8. Seems promising.

BTW: The futility rule "PE outside 0.85...1/0.85~1.18" was used by Charles Bon, 2007 AAPS Annual Meeting. Unfortunately his presentation "Interim and Sequential Analyses" is no longer found on the Indernett.