Bioequivalence and Bioavailability Forum

Dear Detlew!

❝ Thanks for sharing this code!

My pleasure! I think that we still need some improvements:

1. In my example the largest inflation was seen at 48/0.45 with 0.05410 and the second largest at 12/0.20 with 0.05408. However, in step 3 the largest inflation showed up at 12/0.20. It might well be that the result of step 1 was an artifact due to only 10⁵ sim’s performed. With 10⁶ I got for 12/0.20 0.054605 (↑) and for 48/0.45 0.05374 (↓), confirming the location of the maximum picked by my code was due to chance.
   
2. In most methods (except Karalis/Macheras) the “ridge” of the “type I error-surface” follows rough­ly the diagonal of the grid – from low n₁/low CV to high n₁/high CV (see the contour-plots of Potvin’s Methods B and C to the right).
   Maybe it would make sense to split the first step:
   1. Get preliminary estimates for all combos obtained from 10⁵ sim’s like before.*
      
   2. Repeat for the largest inflation observed in each column (i.e., the n₁); this time with 10⁶ sim’s. Should be closer to the “true” maximum and avoid the trap mentioned above.
3. If I repeat the second step at 12/0.20 I get an adjusted α of 0.0268 – which is substantially smaller than 0.0274 (and identical to what I got for “Method C”, which is counter­intu­itive, IMHO).
   
   
   Overall α (step 3) for this combo decreases from 0.051255 to 0.049795… If we follow this track I expect lower alphas than in any of the published papers. Does that make sense?

❝ How is your experience in regulatory acceptance of Potvin's 'acceptable' alpha-inflation of 0.052?

Mixed. Some European (!) regulators don’t like (‼) TSDs at all, but accept them if following “Me­thod B” (quote: “according to the guideline…”). In one case Austria’s AGES asked for a pos­te­ri­ori confirmation of “lacking inflation” of “Method C” based on the actual sample size and CV in the study (was 0.0494 with a 95% CI of 0.0490–0.0498). Duno what might have happened if 0.05 <α ≤0.052. According to Chinese whis­pers ≤0.051 is considered acceptable. Why? Duno. The maxi­mum inflation in Potvin’s paper for “Method B” is 0.0485 and for “Method C” 0.051. Maybe someone read the wrong column.

❝ If I remember correctly there was some rumour that even a smaller value of the empirical alpha has to be seen as inflation.

If I recall correctly that’s the personal opinion of the Austrian member or EMA’s Biostatistics Working Party. Recently a member of the PKWP told me how he made peace with TSDs – after years of lurking doubt: “The in­fla­tion would be relevant only if the CI in the study covers exactly 80–125%. Since in real life the CI is narrower, the actual patient’s risk – even if there would be a small inflation due to the method – likely is ≪5%. So I don’t bother any more.” Pragmatic approach.

❝ That would mean that we had to down weight the adj. alpha to some extent.

By throwing away all published papers and increasing the downloads of Power2Stage? Of course PQRI’s Sequential Design Working Group’s “negligible inflation” (≤0.052) is arbitrary – as are many other rules we have to observe in BE. BTW, only Montague’s “Method D” scratches 0.052. Results of the publications:

                   αadj     αmax  sign. >0.05?
Potvin 2008 B     0.0294  0.0485   
Potvin 2008 C     0.0294  0.0510   yes
Montague 2011 D   0.0280  0.0518   yes
Fuglsang 2013 B   0.0284  0.0501   no
Fuglsang 2013 D1  0.0274  0.0503   no
Fuglsang 2013 D2  0.0269  0.0501   no
Fuglsang 2014 B   0.0294  0.0478   no
Fuglsang 2014 C   0.0294  0.0506   yes

Unless the EMA makes a clear statement about their preferred maximum inflation (or at least some­one receives a deficiency letter and hopefully reports here) I would not change anything.

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• Running my original code with the setup of Potvin’s paper I “detect” a maximum inflation of 0.04882 at 36/0.40 (B) and 0.0513 at 12/0.20 (C) in the first step.
  Good news: These locations agree with the ones reported.
  Bad news: My guess of the upper limit for the regression is crap if there is only a small inflation with the α employed in the first step. I suggest this modi­fi­cation:
  UL <- alpha.max/2*1.1
if(UL <= alpha[1]) UL <- alpha[1]*1.1
  I got:
  
  Anders’ algo suggests ↑0.0304 for B and ↓0.0282 for C. Interesting. Validation under way.