Bioequivalence and Bioavailability Forum

Dear All!

This should read in connection with my previous post in this thread.
Helmut, I have posted to you because I otherwise had to post to myself.

After touting the anti-conservatism of the all-fixed-effects-approach of the Liu ANOVA and noticing the fact that omitting SxF results in the classical model, hopefully with SxF incorporated in the error term.
I was interested in going the Bear way for replicate designs because meanwhile I hazard a guess that EMA is expecting this from us.

Some little evidence:

• EMA comments, page 139: Q: "What is the suggested statistical model for crossover designs with more than 2 periods in BE studies?
  EMA comment: "The model is the same for designs with more than 2 periods."
  
• 3x3 and 4x4 cross-over curiosity in the guidance (extract common 2x2 studies)
  
• EMA comments, page 185: Q: "How to evaluate a replicate design in an average BE approach?"
  EMA comment: "... it is standard statistical analysis."
  
• Mixed model curiosity (Nothing other then common ANOVA, ANOVA, ANOVA ...)
  
• The Old s.. story.

But then I remembered a paper coming under my eyes some times ago:

S.A. Willavize, E.A. Morgenthin
Comparison of models for average bioequivalence in replicate cross-over designs
Pharm. Stat. Volume 5 Issue 3, Pages 201 - 211 (2006)
Published Online: 24 May 2006

The authors have simulated data of a TRTR/RTRT design distributed exactly according to the models underlying the evaluation methods, namely according to the classical model without any SxF interaction and some variants of including such an interaction. Various values of the involved variabilities were employed. For each setting 1500 datasets were simulated with 24 subjects.
These data were then evaluated with each evaluation method.

Here is a part of the results of evaluations with the classical model, also Proc Mixed was employed instead of Proc GLM (the Bear way):
  Probability of concluding BE at T/R = 0.8 (=alpha)
Data model1       0.041 ... 0.054
Data model2       0.047 ... 0.174  sic! 
Data model3       0.047 ... 0.129
model1=classical model
model2=FDA model with SxF
model3=Ekbohm-Melander (very similar to the Liu ANOVA)

Although not mentioned exactly in the paper I suppose that the greatest anti-conservatism / alpha-inflation occurred with drastic values of the SxF interaction.
Seems the SxF component can not always incorporated into the error term of the simple classical evaluation.

Of course the impact of these results depend on the belief if the SxF is a real phenomenon in bioequivalence studies. For instance in

Endrenyi, Tothfalusi
Subject-by-formulation interaction in determination of individual bioequivalence: Bias and prevalence
Pharm. Res. 16 (1999), 186-190

and others it is strongly argued against it in showing that the datasets used by FDA during evaluation of IBE are compatible with a SxF=0.