Bioequivalence and Bioavailability Forum

Dear All,

although in the days of this thread no R-user need to deal with approximate power, I was interested in how good these approximations were.

Here my results for three 'typical' CV's with my very famous R-code.
Null ratio was set to 0.95 as usual, the BE limits were 0.8 ... 1.25. The design was the classical 2x2 crossover.

• black: exact power using Owen's Q function
  
• red: approximate power using non-central Student's t-distribution (discussed lastly here, Helmuts code, which is part of Bear)
  
• green: approximate power using 'shifted' central Student's t-distribution mentioned here, Part of PASS2008 - module for replicate crossover

Lesson learned: The approximations perform very well in the region we are usually interested in (power >0.7). In this region the power(s) are not only optically indistinguishable but also numerically.
Thus users who have no access to an implementation of the exact power can use safely the formulas relying on the non-central t-distribution if they have access to software containing it.
Or even use the formulas relying on the 'shifted' central Student's t-distribution which should be available in nearly all statistical software.
With respect to the sample size estimation (power usually ≥0.8) only negligible differences if any were expected. In my experimentation I hadn't found any up to now.

There is no need to state (cit. EM): "The non-central t dist is hereby dead and buried."