From Potvin C to Inverse Normal: history (and outlook?) [Two-Stage / GS Designs]

posted by Helmut Homepage – Vienna, Austria, 2022-06-27 20:54 (159 d 15:57 ago) – Posting: # 23098
Views: 836

Hi Mittyri and all,

❝ ❝ Consider to avoid this stuff in the future. See this post and followings for better alternatives.


❝ there are zero papers I've seen by Russian experts regarding inverse normal method. I guess this is the reason why the sponsors do not want to have a risk with that invention. "Why should we care if everything works with Potvin?"


[image]Obviously it doesn’t work. Maybe it’s [image] time for a change.

In my studies I used only “Method C” and never received a single (‼) defici­ency letter. Why? Not sure. Only because all studies stopped for success in the first stage? Or because I was ‘famous’?1 Anyhow, later I faced defici­ency letters – even for “Method B”.2

Since this was an extremely unsatisfactory situation, I nudged my friends to de­ve­lop an exact method (i.e., with strict Type I Error control without relying on simulations). Not an easy job, took us two years.3,4 As an aside, only the 2×2×2 crossover design is covered, but we stated:

[…] the proposed adaptive design would allow to switch from a classical two-period design to a more complex replicate design if it turns out the reference product is highly vari­able and the within subject-variability has to be determined as well.

Currently science fiction.
Our posters were noticed and Byron Jones started working on the stuff together will a veteran of adap­tive designs, Willi Maurer. In December 2016 the method appeared in a book.5 Un­for­tu­nately the [image] code was crude, politely speaking. In February 2018 the paper6 – containing the analytical proof and ‘improved’ [image] code as supplementary information7 – was published. The method is extre­mely flexible when it comes to futility criteria (PE or CI not within certain limits, estimated total sample size above a limit), minimum stage 2 sample size protecting against drop­outs, and even sample size re-estimation based on the T/R-ratio observed in the first stage (i.e., fully adaptive). Since stages are evaluated separately, not only an ANOVA can be used but also a mixed-effects model, which is recommended by the FDA and Health Canada. It took Ben­ja­min Lang and Det­lew Labes almost half a year to implement the inverse-normal com­bi­nation method in Power2Stage.8 BTW, the method is acceptable for the FDA as well.9

I was told that Russian »эксперты« have altercations of the type:

“Helmut said …!” – “No, on the contrary! He said …”

and so on and so forth.
What I really said and keep saying:  Use the inverse-normal combination method! 

Regrettably a parallel design is another pot of tea. Taking unequal group sizes in the first stage and heterogenicity into account is not trivial. At the very bottom of our todo list.
In the meantime use the simulation-based method10 available in Power2Stage.


  1. Schütz H. Two-stage designs in bioequivalence trials. Eur J Clin Pharmacol. 2015; 71(3): 271–81. doi:10.1007/s00228-015-1806-2.
  2. Last year I had to deal with a deficiency letter of the Czech agency SÚKL. “Method B” pas­sed with flying colors in the first stage. The agency questioned the reliability of Potvin’s si­mu­lations ‘because the grid in the publication’s simulations was too sparse’. Bizarre. Of course, a narrow grid with a step size of 2 for n1 and 2% for the CV showed no inflated Type I Error as well (maxi­mum 0.048856 for n1 12 and CV 24%). Hurray, 1.116 billion simu­lated studies!
  3. König F, Wolfsegger M, Jaki T, Schütz H, Wassmer G. Adaptive two-stage bioequivalence trials with early stopping and sample size re-estimation. Vienna: 2014; 35th Annual Con­fe­rence of the International Society for Cli­ni­cal Biostatistics. Poster P1.2.88. doi:10.13140/RG.2.1.5190.0967.
  4. König F, Wolfsegger M, Jaki T, Schütz H, Wassmer G. Adaptive two-stage bioequivalence trials with early stopping and sample size re-estimation. Trials. 2015; 16(Suppl 2); P218. doi:10.1186/1745-6215-16-S2-P218.
  5. Patterson SD, Jones B. Bioequivalence and Statistics in Clinical Pharmacology. Boca Raton: CRC Press; 2nd edition 2017. ISBN 978-1-4665-8520-1. p. 141–187.
  6. Maurer W, Jones B, Chen Y. Controlling the type 1 error rate in two-stage sequential designs when testing for average bioequivalence. Stat Med. 2018; 37(10): 1–21. doi:10.1002/sim.7614.
  7. Maurer W, Jones B, Chen Y. Supplementary Information for ”Controlling the Type I error rate in two-stage sequential adaptive designs when testing for Average Bioequivalence”. [image] Open access.
  8. Labes D, Lang B. Schütz H. Power2Stage: Power and Sample-Size Distribution of 2-Stage Bio­equi­valence Studies. Package version 0.5-1. 2018-04-03. Current version on CRAN.
  9. Lee J, Feng K, Xu M, Gong X, Sun W, Kim J, Zhang Z, Wang M, Fang L, Zhao L. Appli­ca­tions of Adaptive Designs in Generic Drug Development. Clin Pharm Ther. 2020; 110(1): 32–5. doi:10.1002/cpt.2050.
  10. Fuglsang A. Sequential Bioequivalence Approaches for Parallel Designs. AAPS J. 2014; 16(3): 373–8. doi:10.1208/s12248-014-9571-1. [image] Free Full text.

Seems that this is a hot topic. 210 views in 3½ days. :-D

Dif-tor heh smusma 🖖🏼 Довге життя Україна! [image]
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