Bioequivalence and Bioavailability Forum

HI GSD,

welcome to the club!

❝ For Potvin’s 2-stage adaptive design, does anyone know how to simulate for the overall type I error with EMA reference scaling (Full Replicate)?

You are aware that this framework is valid for (strictly speaking: balanced) 2×2×2 crossovers only?

❝ If there were no EMA reference scaling, then we can simulate random numbers from a normal distribution with mean centered on ln(0.8) to estimate the type I error.

Yep. If you want to be consistent with Potvin & Montague go with ln(1.25). Of course α_emp. will be the same, but regulators are a strange bunch.

❝ But what distribution should we simulate from to account for the random changing nature of the acceptance limits (EMA scaling)?

Courageous! EMA has some strange POVs concerning Potvin’s methods (see these posts). Leaving this aside, there are some more problems to solve:

• EMA’s crippled ‘models’ (both Methods A and B according to the Q&A-document) assume a common (equal!) variance of test and reference. Weird, because in many cases (pharmaceutical technology improves) and the variance of the reference is higher than the one of the test. In simulations you should account for that.
  
• The sample size estimation for stage 2 is not straightforward. This is actually the major obstacle. Assuming you already have a validated framework, you would run simulations like the two Lázlós did^*. But if you set up your own simulations in every run you would have to embed the same stuff – or simply use their tables, which have a too wide step size (CVs and GMRs 5%). I had the same idea a while ago and estimated the runtime on my machine with six years 24/7).
  
• How would you estimate power between stages? Well, EMA has some problems with this approach anyhow. Maybe you go with the ‘rumour method’ (see this post and followings), but definitely not with C/D.
  
• At last coming back to you question. Simulate as usual - but you have to employ a conventional ABE-model if CV<30%, ABEL above + the 50% cap + the GMR-restriction. At CV 30%, half of the studies have to assessed by ABE and the other half by ABEL.

If you consider the ‘table-approach’ I would suggest to recalculate the Lázlós’ tables for a least 10⁵ studies each. For my taste the given ten thousand sims are too ‘granular’. It should be enough to simulate GMRs of 0.95 (for 1–β_emp.) and 1.25 (for α_emp.) with a smaller step size of CVs (and probably for >80% as well).





BTW, the plots nicely reveal the impact of EMA’s 50% cap on the sample size. For GMR 0.95 and CV 75% according to EMA you would need 35 subjects but only 20 for the FDA…

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• László Endrényi, László Tóthfalusi
  Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs
  J Pharm Pharmaceut Sci 15(1), 73–84 (2011)
  online