## Simulating the Null [RSABE / ABEL]

❝ 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 bio

**in**equivalence) is

*true*. In SCABE (ABEL: expanded limits, RSABE: implied limits) only if CV

_{wR}≤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

*simulate*the TIE as well:

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

# [1] 0.05004

`power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=12)`

# [1] 0.04977286

`power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=1200)`

# [1] 0.05

In SCABE the scaled limits (and hence the GMR which we use in simulating the Null) depend on the CV

_{wR}. Example for CV

_{wR}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 CV

_{wR}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 CV

_{wR}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*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- question of adjustment Yura 2017-04-25 15:14 [RSABE / ABEL]
- TIE depends on CVwR (and n) Helmut 2017-04-26 14:17
- TIE depends on CVwR (and n) Yura 2017-04-26 17:28
- TIE depends on CVwR (and n) Helmut 2017-04-26 18:00
- TIE depends on CVwR (and n) Yura 2017-04-26 18:55
- TIE depends on CVwR (and n) Yura 2017-04-28 11:13
- TIE = p(BE) at expanded limits Helmut 2017-04-28 19:16
- TIE = p(BE) at expanded limits Yura 2017-04-29 13:01

- TIE = p(BE) at expanded limits Helmut 2017-04-28 19:16

- TIE depends on CVwR (and n) Yura 2017-04-28 11:13

- TIE depends on CVwR (and n) Yura 2017-04-26 18:55

- TIE depends on CVwR (and n) Helmut 2017-04-26 18:00
- TIE depends on CVwR (and n) pjs 2018-02-28 14:33
- TIE depends on CVwR (and n) Helmut 2018-02-28 14:48
- TIE depends on CVwR (and n) pjs 2018-03-01 07:35
- Comparing methods for (S)ABE Helmut 2018-03-01 13:32
- Comparing methods for (S)ABE pjs 2018-03-05 14:50
- Simulating the NullHelmut 2018-03-05 17:40

- Comparing methods for (S)ABE pjs 2018-03-05 14:50

- Comparing methods for (S)ABE Helmut 2018-03-01 13:32

- TIE depends on CVwR (and n) pjs 2018-03-01 07:35
- Adjusting α Helmut 2018-03-07 16:21

- TIE depends on CVwR (and n) Helmut 2018-02-28 14:48

- TIE depends on CVwR (and n) Yura 2017-04-26 17:28

- TIE depends on CVwR (and n) Helmut 2017-04-26 14:17