Bioequivalence and Bioavailability Forum

Dear Detlew!

❝ That's worth a paper.

Who’s going to write one?

❝ I think their approach was driven by […]

Agree. Maybe their choice was (partly?) strategic. Since Pocock’s 0.0294 has a tradition of decades of accepted use in phase III, they opted for a smooth introduction: “We used it for such a long time and it seems to work here as well…” In Section 5 they wrote: “It is our under­stand­ing that the FDA has accepted studies with designs like those considered here.” If I recall it correctly they were refer­ring to an NDA (bonus question: Guess the α!). Donald Schuir­mann wrote the bio­statis­tical as­sess­ment based on simulations he performed and accepted the study. I have to dig out the reference.

❝ As they have done later in method D and Montague’s paper.

Yep – but not consequently enough. Their maximum inflation of 0.0518 is the largest one of all papers published so far. Again I assume they tried to keep it simple: “We have shown in our first paper that for a T/R of 0.95 D’s 0.0280 is more conservative than C’s 0.0294. Let’s give it a try with a T/R of 0.9. Hey, <0.052 – let’s publish.”



Method D: Empiric type I error; Mont = Montague’s 0.0280, HB = homebrew’s 0.0270 (runtime one hour).

           12             24             36             48             60     
CV     Mont   HB      Mont   HB      Mont   HB      Mont   HB      Mont   HB 
0.1  0.0498 0.0494  0.0501 0.0496  0.0504 0.0499  0.0503 0.0498  0.0498 0.0497
0.2  0.0518 0.0500  0.0475 0.0463  0.0477 0.0469  0.0499 0.0494  0.0498 0.0497
0.3  0.0414 0.0396  0.0506 0.0490  0.0489 0.0473  0.0470 0.0451  0.0449 0.0439
0.4  0.0322 0.0307  0.0414 0.0395  0.0502 0.0483  0.0500 0.0484  0.0492 0.0469
0.5  0.0293 0.0283  0.0316 0.0304  0.0401 0.0382  0.0484 0.0465  0.0509 0.0487
0.6  0.0286 0.0277  0.0292 0.0282  0.0313 0.0296  0.0381 0.0360  0.0462 0.0441
0.7  0.0286 0.0273  0.0281 0.0276  0.0288 0.0275  0.0307 0.0292  0.0358 0.0340
0.8  0.0280 0.0273  0.0283 0.0273  0.0287 0.0271  0.0284 0.0273  0.0301 0.0286
0.9  0.0281 0.0271  0.0281 0.0275  0.0282 0.0270  0.0281 0.0271  0.0285 0.0273
1.0  0.0282 0.0271  0.0282 0.0273  0.0282 0.0271  0.0282 0.0270  0.0279 0.0273

No significant inflation with 0.0270. Largest observed 0.049994 (at 12/0.2; same location as reported by Montague).

❝ IMHO using a different but fixed seed or a single fixed seed doesn't make a big difference if we simulate with 1E6 sims.

❝ Setting setseed=FALSE in Power2Stage would have the drawback of differing results even for one scenario (CV, n1) if run again.

Agree.

❝ BTW: What is Anders algo?

The linear regression of type I errors vs. α_adj in order to find α_adj leading to TIE 0.05 (imple­mented in the second step of my code). I borrowed the idea from his 2011 paper you quoted. I’m afraid regu­la­tors likely will not accept his method of data-driven adjusting α in the interim step (EMA: “The plan to use a two-stage approach must be pre-specified in the protocol along with the ad­justed signi­fi­cance levels to be used for each of the analyses”).

❝ His C programs?

I have just a few of them. Given your last improvements Power2Stage is almost as fast as his com­piled stuff.

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