## Simulating the Null [RSABE / ABEL]

Hi Pjs,

» Have gone through some of the post related to alpha correction incase of SABE approach in the forum. In the simulations done most extreme GMR of 1.25 is assumed for the simulation and calculation of possible alpha inflation.

Not exactly. In order to simulate the type I error we assume that the Null Hypothesis (of bio­in­equivalence) is true. In SCABE (ABEL: expanded limits, RSABE: implied limits) only if CVwR ≤30% the GMR of the Null is at 1.25 (or 0.8). Therefore, with higher CVs we have to simulate at higher GMRs as well.
Note that in ABE the Null is always at the borders of the acceptance range (0.8 and 1.25). Hence, here we don’t need simulations but can directly calculate the power (i.e., chance of passing BE = falsely rejecting the Null):

library(PowerTOST) power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=40) # [1] 0.05

Of course, we can simulate the TIE as well:

power.TOST.sim(CV=0.3, theta0=1.25, design="2x2x4", n=40, nsims=1e6) # [1] 0.05004

TOST (or the CI inclusion method) is not the most powerful test. If the sample size is very low, the TIE will be ≤5%:

power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=12) # [1] 0.04977286

On the other hand, a very high sample size would still preserve the nominal level:

power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=1200) # [1] 0.05

That’s a comforting property.

In SCABE the scaled limits (and hence the GMR which we use in simulating the Null) depend on the CVwR. Example for CVwR 40%:

 scABEL(CV=0.4, regulator="EMA") #    lower    upper # 0.746177 1.340165 scABEL(CV=0.4, regulator="FDA") #     lower     upper # 0.7090232 1.4103911

» I would like to understand as the actual alpha adjustment would be based on actual Swr observed in the study and number of subjects, what could be the rationale of doing adjustment of alpha based on the calculation which is done on extreme GMR while for the actual study conducted T/R ratio could be very much close to unity (let's say 0.95 or 0.97).

The observed GMR is only an estimate. We don’t know where the population’s true GMR lies. Think about the 90% CI. There is a 5% chance at each CL that the true GMR is outside. Imagine in ABE you observe a GMR of 1 with a 90% CI of 0.8–1.25. What is the TIE?

» I do understand the most deviated GMR would lead to maximum probability for the alpha inflation …

Correct.

» … but applying this extreme case and alpha adjustment in each and every study is required?

That’s maybe the best we have so far. OK, we could go even further (suggested by Molins et al.)* Simulating the Null at the scaled limits still assumes that the CVwR estimated in the study is the true value – which might not be correct. If one wants to get the most conservative adjusted α one should simulate at CVwR 30% – irrespective of what we observe (since this is the location of the maximum TIE both in ABEL and RSABE). However, there is no free lunch. Either power will be compromised or 20–25% more subjects are needed to preserve the desired power.

• Molins E, Cobo E, Ocaña J. Two‐stage designs versus European scaled average designs in bioequivalence studies for highly variable drugs: Which to choose? Stat Med. 2017;36(30):4777–88. doi:10.1002/sim.7452.

Dif-tor heh smusma 🖖
Helmut Schütz

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