TIE = p(BE) at expanded limits [RSABE / ABEL]
❝ Did I understand correctly, when constructing a confidence interval for T-R differences, use the adjusted alpha for R-R?
Exactly – now you got it!
In a nutshell, the Type I Error is the probability of falsely claiming BE. The TIE can be estimated by setting theta0 to one of the limits of the acceptance range. Easy for ABE (since an explicit solution exists).
library(PowerTOST)
CV <- 0.3
des <- "2x2x4"
n <- 34
U <- 1.25
power.TOST(CV=CV, n=n, theta0=U, design=des)
# [1] 0.05
power.TOST.sim(CV=CV, n=n, theta0=U, design=des, nsims=1e7)
# [1] 0.0500178
When it comes to reference-scaling no explicit formula for power exists. Hence, we need simulations. There is a complication: ABEL is a framework of decisions where the Null-hypothesis is constructed in face of the data. In other words we don’t know the expanded limits until we have calculated CVwR. Unlike in ABE the limits are random variables themselves.
CVwR <- 0.3
reg <- "EMA"
U <- scABEL(CV=CVwR, regulator=reg)[["upper"]]
power.scABEL(CV=CVwR, n=n, theta0=U, design=des,
regulator=reg, nsims=1e6)
# [1] 0.081626
PowerTOST
you can simulate subject data as well.power.scABEL.sdsims(CV=CVwR, n=n, theta0=U, design=des,
regulator=reg, nsims=1e6)
# [1] 0.081602
res <- scABEL.ad(CV=CVwR, n=n, design=des, regulator=reg, print=FALSE)
TIE0 <- res[["TIE.unadj"]]
adj <- res[["alpha.adj"]]
TIE1 <- res[["TIE.adj"]]
cat(TIE0, adj, TIE1, "\n")
# 0.081626 0.028572 0.05
round(100*CI.BE(alpha=0.05, pe=0.9, CV=CV, n=n, design=des), 2)
# lower upper
# 82.78 97.85
round(100*CI.BE(alpha=adj, pe=0.9, CV=CV, n=n, design=des), 2)
# lower upper
# 81.69 99.16
res <- sampleN.scABEL.ad(CV=CVwR, theta0=0.9, design=des,
regulator=reg, print=FALSE)
adj <- res[["alpha.adj"]]
n.a <- res[["Sample size"]]
cat(adj, n.a, "\n")
# 0.028311 42
round(100*CI.BE(alpha=adj, pe=0.9, CV=CV, n=n.a, design=des), 2)
# lower upper
# 82.49 98.20
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png)
Helmut Schütz
![[image]](https://static.bebac.at/img/CC by.png)
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 limitsHelmut 2017-04-28 19:16
- TIE = p(BE) at expanded limits Yura 2017-04-29 13:01
- TIE = p(BE) at expanded limitsHelmut 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 Null Helmut 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