Bioequivalence and Bioavailability Forum • For the tough ones

For the tough ones [Surveys]

posted by Helmut – Vienna, Austria, 2014-10-24 16:54 (3465 d 11:50 ago) – Posting: # 13801
Views: 10,425

Hi ElMaestro,

❝ to round this off, can it be mathematically proven that upper type 1 error asymptotes exist

Yes. At least this is what my stats friends told me. Note that Bonferroni is the most conservative method in adjusting for multiplicity.*
IMHO, you could gain a little solving the quadratic equation \(\small{1-(1-x)^2=\alpha}\), which leads for α 0.05 to \(\small{(2-\sqrt{4-4\alpha})/2=0.02532057\ldots}\)
Others (f.i. Holm, Hochberg) are less conservative but may lead to a CI which doesn’t include the PE any more. Counterintuitive, but my stats friends just smile about it. See also EMA’s 2012 workshop on multiplicity. If you – really! – have nothing better to do, watch the six (‼) hours of video.

❝ for any level of common alpha smaller than 1?

Smaller than one?

❝ I bet that should be possible, too. I'd love to see how. I imagine that to deliver the proof one would have to one way or another get aorund to Owen's Q and non-central t. So I am very certain that would improve yours truly's understanding of statistics for BE.

Yep. People are working on it (for three years now)…

Since I’m not gifted with enough knowledge to proof anything I can only offer extreme simulations:

library(Power2Stage) power.2stage.GS(alpha=rep(0.025, 2), n=c(10, 100000), CV=0.05, theta0=1.25, fCrit="PE", fClower=0, nsims=1e7) TSD with 2x2 crossover non-adaptive group sequential with alpha (s1/s2) = 0.025 0.025 No futility criterion BE acceptance range = 0.8 ... 1.25 CV= 0.05; n(s1, s2)= 10 1e+05 1e+07 sims at theta0 = 1.25 (p(BE) = TIE 'alpha'). p(BE) = 0.0493985 p(BE) s1 = 0.0250372 Studies in stage 2 = 97.5%

That’s pretty close to what we would expect from Bonferroni (0.049375).
The Japanese stuff gives me 0.0975317 (expected 0.0975).

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Complete thread:

Riddle Helmut 2014-10-23 20:11
- Riddle nobody 2014-10-23 20:37
  - Riddle Helmut 2014-10-23 20:58
- A wild guess ElMaestro 2014-10-23 22:47
  - Partly solved Helmut 2014-10-23 23:08
    - Partly solved ElMaestro 2014-10-23 23:19
      - Partly solved Helmut 2014-10-23 23:27
        
        Partly solved ElMaestro 2014-10-23 23:37
        
        Partly solved Helmut 2014-10-24 00:20
        
        Solved? d_labes 2014-10-24 13:13
        
        99 points! Helmut 2014-10-24 13:19
        
        For the tough ElMaestro 2014-10-24 14:19
        
        For the tough onesHelmut 2014-10-24 14:54
        
        99 points! nobody 2014-10-24 14:25
        
        99 points! Helmut 2014-10-24 15:01