Bioequivalence and Bioavailability Forum

Dear Detlew & Martin!

❝ This behaviour is not unexpected. See the various power curves in:

❝

Hauschke, Steinijans, Pigeot

❝ "Bioequivalence Studies in Drug Development"

❝ Wiley, Chichester (2007)

❝ Chapter 10: Equivalence assessment for clinical endpoints /

❝ 10.3 Power and sample size calculation

They all show maximum power apart from ratio 1.

I see.

❝ This has only partly to do with the fact that we use the 'unsymmetrical' acceptance ranges [theta1=0.8, theta2=1/theta1=1.25] ('unsymmetrical' in the original domain):

Noticed that yesterday, but was too tired to explore it further.

1. Forget my idea. The acceptance range is asymmetrical in the original domain (θ₁, θ₂=1/θ₁).
   
2. Interesting the last sentence on page 284: “Additionally, it can be shown that, only for equivalence limits so defined, the maximum power stabilizes at the point of equality, i.e., μ_T∕μ_R=1, as the sample size increases.*”
   (my emphasis)

❝ ❝ […] is this behavior well known?

Yes – at least for equal variances. Martin, your sims show a similar behavior for heterogenous variances. Increase the sample size and see what’s happening.

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• Hauschke D, Kieser M, Diletti E, Burke M. Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Stat Med. 1999:18(1);93–105.
  doi 10.1002/(SICI)1097-0258(19990115)18:1<93::AID-SIM992>3.0.CO;2-8