## Inflation type one error [RSABE / ABEL]

Hi Mikalai,

» I may be wrong but I cannot see how we can get a true within-subject CV of any drug.

Of course, you are right. The true CVwR is unknown. But reference-scaling should be done for true HVD(P)s, i.e., where the population’s CVwR >30%. However, $$s_{wR}$$ is the best unbiased estimate of $$\sigma_{wR}$$. The former is used in the expansion formula, i.e., treating $$s_{wR}$$ as a true value.

» I may be wrong, but even with simulations (I suppose with simulations some assumptions regarding variance should be made), it is very difficult or even impossible.

There are essentially two options:
1. Our ad hoc solution1 by simulating under the assumption $$s_{wR}=\sigma_{wR}$$ to iteratively adjust $$\alpha$$. That’s in the “spirit of the guideline” where the observed CVwR is used for expanding the limits.
2. Muñoz et al.2 suggested to “assume the worst” and – since the true value is unknown – adjust $$\alpha$$ always as if CVwR = 30%. That’s in any case the most conservative approach but might negatively impact power in case of high CVs (were the upper cap of scaling and the GMR-restriction already effectively controls the TIE). For examples see there.
Note that in both approaches the GMR of the Null is specified according to the expanded limits.

Still: The expansion is based on the observed CVwR. We once had the crazy idea of using a very conservative (99.9%) CI instead. Doesn’t work because then we would practically never be allowed to scale…

» […] what regulators say on this subject?

Nothing. I raised this issue at numerous conferences. Dead silence. Armin Koch (co-author of one of the papers3 noting the inflated TIE) is a member of the EMA’s Biostatistical Working Party. Sent him an e-mail in 2016. No answer.

» I do not remember any reflection on this matter in official documents (EMA, FDA)?

EMA = zero. At the 2nd GBHI conference (Sep 2016, Rockville) László Endrenyi gave a presentation “Features, Constraints, and Extensions of the Scaling Approach” where he showed examples of the TIE, both for the EMA’s and the FDA’s approaches. Donald Schuirmann said “There is a recent paper in Pharm Res. showing how to deal with the inflation of the type I error. This is an excellent and applicable approach.” and told me in a coffee-break “… if this is correct, we have to modify our method”. Didn’t happen. Will ask him again next month at the 4th GBHI in Bethesda.

1. Labes D, Schütz H. Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control. Pharm Res. 2016: 33(11); 2805–14. doi:10.1007/s11095-016-2006-1.
2. Muñoz J, Alcaide D, Ocaña J. Consumer’s risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs. Stat Med. 2016: 35(12); 1933–43. doi:10.1002/sim.6834.
3. Wonnemann M, Frömke C, Koch A. Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs. Pharm Res. 2015: 32(1); 135–43. doi:10.1007/s11095-014-1450-z.

Cheers,
Helmut Schütz

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