N sufficiently large‽ [Two-Stage / GS Designs]
❝ Two-sided or not two-sided, that is the question!
Yessir!
❝ 2*(1-pnorm(rep(mean(bds2.poc$upper.bounds),2)))
❝ simsalabim, Pocock's natural constant!
mean(bds2.poc$upper.bounds)
[1] 2.17897
[1] 0.02933386 0.02933386
rep(2*(1-pnorm(2.178)), 2)
[1] 0.02940604 0.02940604
‘Exact’
library(mvtnorm)
mu <- c(0, 0)
sigma <- diag(2); sigma[sigma == 0] <- 1/sqrt(2)
C <- qmvnorm(1-0.05, tail="both.tails", mean=mu,
sigma=sigma)$quantile
C
[1] 2.178273
rep(2*(1-pnorm(C)), 2)
[1] 0.0293857 0.0293857
rep(1-pnorm(1.875), 2)
[1] 0.03039636 0.03039636
C <- qmvnorm(1-2*0.05, tail="both.tails", mean=mu,
sigma=sigma)$quantile
C
[1] 1.875424
rep(1-pnorm(C), 2)
[1] 0.03036722 0.03036722
library(ldbounds)
C <- mean(bounds(t=c(0.5, 1), iuse=c(2, 2), alpha=rep(0.05, 2))$upper.bounds)
C
[1] 1.875529
rep(1-pnorm(C), 2)
[1] 0.03035998 0.03035998
In chapter 12 Jones/Kenward (in the context of blinded sample re-estimation) report an inflation of the TIE. The degree of inflation depends on the timing of the interim (the earlier, the worse). They state:
“In the presence of Type I error rate inflation, the value of α used in the TOST must be reduced, so that the achieved Type I error rate is no larger than 0.05.”
(my emphasis)They recommend an iterative algorithm [sic] by Golkowski et al3 and conclude:
“[…] before using any of the methods […], their operating characteristics should be evaluated for a range of values of n1, CV and true ratio of means that are of interest, in order to decide if the Type I error rate is controlled, the power is adequate and the potential maximum total sample size is not too great.”
Given all that, I’m not sure whether the discussion of proofs, exact values, etc. does make sense at all. This wonderful stuff is based solely on normal theory and I’m getting bored by reading the phrase “when N is sufficiently large” below a series of fancy formulas. Unless someone comes up with a proof for small samples (many tried, all failed so far) I rather stick to simulations.
- Jennison C, Turnbull BW. Group sequential methods with applications to clinical trials. Boca Raton: Chapman & Hall/CRC; 1999.
- Jones B, Kenward MG. Design and analysis of cross-over trials. Boca Raton: Chapman & Hall/CRC; 3rd ed 2014.
- Golkowski D, Friede T, Kieser M. Blinded sample size reestimation in crossover bioequivalence trials. Pharm Stat. 2014;13(3):157–62. doi 10.1002/pst.1617
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:
- Adaptive TSD vs. “classical” GSD Helmut 2015-11-27 19:05 [Two-Stage / GS Designs]
- Adaptive TSD vs. “classical” GSD ElMaestro 2015-11-27 19:54
- “classical” GSD - E[n] d_labes 2015-11-30 11:15
- Apples are pears by comparing the weight Helmut 2015-12-01 16:35
- Apples are pears by comparing the weight d_labes 2015-12-03 09:16
- Apples are pears by comparing the weight Helmut 2015-12-03 13:10
- Oranges d_labes 2015-12-03 13:56
- Apples are pears by comparing the weight Helmut 2015-12-03 13:10
- Apples are pears by comparing the weight d_labes 2015-12-03 09:16
- Apples are pears by comparing the weight Helmut 2015-12-01 16:35
- Adaptive TSD vs. “classical” GSD Ben 2015-12-02 19:27
- Adaptive TSD vs. “classical” GSD Helmut 2015-12-03 03:11
- “classical” GSD alpha's d_labes 2015-12-03 09:47
- N sufficiently large‽Helmut 2015-12-03 14:56
- An other one with 0.0304 d_labes 2015-12-03 16:15
- An other one with 0.0304 Helmut 2015-12-03 16:26
- An other one with 0.0304 d_labes 2015-12-03 16:15
- N sufficiently large‽Helmut 2015-12-03 14:56
- Adaptive TSD vs. “classical” GSD Ben 2016-01-10 12:43
- “classical” GSD alpha's d_labes 2015-12-03 09:47
- Adaptive TSD vs. “classical” GSD Helmut 2015-12-03 03:11