Bioequivalence and Bioavailability Forum

Dear all,

since variants of Potvin’s “Method C” seem to be controversial (euphemism!) amongst European regulators I felt tempted to perform some simulations. In their original paper Potvin et al. used the same α_adj of 0.0294 (94.12% CI) for both Methods “B” and “C”. Maximum α_emp was 0.0485 (B) and 0.0510 (C). Therefore, B was slightly (!) more conservative though with a little less power. Some follow-up papers (other ratios and/or target power) reported results for variants of “Method C” (Montague et al. 2011, Fuglsang 2013). Interestingly Fuglsang* reported for T/R 0.95 and 90% power α_adj 0.0284 (B, max. α_emp 0.0501) and α_adj 0.0274 (C, max. α_emp 0.0503) demonstrating that one needs less adjustment in “Method B”. He reported also results for T/R 0.95 and 90% power (C only): α_adj 0.0269 and max. α_emp 0.0501.

Given all above I suspected that adjustments published for variants of “Method C” would lead to no/less inflation if applied to “Method B”. As a first step I explored Fuglsang’s 0.0269. Don’t ask me why I have chosen this range of sample sizes…



As usual for “Method B” in the area of high n₁ / low CV α_emp approaches α_adj since most studies stop already in the first stage and the full penalty has to be paid (“Method C” in this area would be close to nominal α; for examples see this presentation, slides 25 and 29). Maximum α_emp was 0.050106 (at n₁ 12, CV 20%; not significantly >0.05). Target power was well above 90% in most cases; >90% for all CVs if n₁ ≥50. Slightly below 90% if a study with high CV is started in a low sample size (deserved punishment for gambling).

To make a long story short: If you want to go with “Method B” – and only adjustments for “Method C” are published – you have two options.

1. Justify the approach by referring to Potvin’s paper showing that the same α_adj leads to less inflation in “Method B”. This is also supported by Fuglsang where a smaller adjustment could be used in “Method B” leading to essentially the same inflation as in “Method C”.
   In other words, applying “Method C’s” α_adj to “Method B” should be conservative.
   Don’t refer to this post, since it is just a not peer-reviewed kind of homebrew.
   
2. Perform your own simulations. Start with a little bit less adjustment as reported for “Method C” (i.e., higher α_adj). My recommendation for start values is the area of n₁ 12 and CV ~20%. I don’t know why but in many simulations I saw the maximum inflation there. Once you have found a suitable value, check all combinations of n₁/CV where the publication showed high inflation and adjust if necessary. Confirm the value over the whole grid. Be patient. Takes a while.
   

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• Fuglsang A. Sequential Bioequivalence Trial Designs with Increased Power and Controlled Type I Error Rates. AAPS J. 2013;15(3):659–61. doi 10.1208/s12248-013-9475-5

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PS: Though my sim’s are still running I don’t think that for “Method B” T/R 0.9, and 90% power α_adj larger than 0.0270 (≡ 94.60% CI) will ‘work’ if you want to stay below the significance limit of 0.05036. If you are of a more adventurous nature (aiming at Potvin’s ‘acceptable inflation’ of 0.052) and are willing to defend your approach answering deficiency letters you can expect to have more headroom (maybe up to 0.0278 ≡ 94.44% CI).
PPS: Don’t follow the bad example of Karalis’/Macheras’ papers and perform only 10⁵ simulations for speed reasons.* The convergence is slow and not by chance all others performed 10⁶ simulations (example in this post). If you want to speed things up go for only 10⁵ in simulating power. In my experience differences are only ~1–2% and not worth the additional efforts (unless you want to publish your results).

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• I received an e-mail from Βαγγέλης Καραλής where he pointed out that in all of their methods they also simulated 10⁶ studies for α. I’m sorry! Λυπάμαι!