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Registernon-central t is not the question [🇷 for BE/BA]
Dear ElMaestro,
don't waste your time in attempting to improve Al Gore's rhythms.
The inventors of them for the non-central t distri had already made every effort for its accuracy and reliability, I think.
Your time is better invested for NLYW (blonde downstairs) or for the Seven seas
.
The formula given in Julious is definitely approximate, albeit a good one for the usual power range ≥70% as the sample size calculations with that formula show.
The exact algo for the power of the equivalence test (two one sided tests aka TOST) in a 2x2 cross-over is ([1],[2]):
The t1 and t2 values are the t-variates of the two one-sided t-tests of bioequivalence.
(t1, t2) have according to Owen a bivariate non-central t-distribution and the power can be calculated as the difference of two definite integrals (Owen's Q functions dependent on df=degrees of freedom and with four arguments)
See [1] and [2] for that and for the formulas for d1, d2 and R.
So you need not a better algo for the non-central t but rather an algo for Owen's Q-functions
.
My SAS beast has these functions implemented (but not documented!).
And my sasophylistic answer to the your ElMaestrophylistic question "what the power in a 2,2,2-BE trial is at N=38, CV=65% and T/R=95%." given here, power=4.5%, is based on these Q-functions.
Implementing the Julious formulas (according to Helmut's R-code) in "The power to know" results in power=-0.027799235, same as Fartssie!
don't waste your time in attempting to improve Al Gore's rhythms.
The inventors of them for the non-central t distri had already made every effort for its accuracy and reliability, I think.
Your time is better invested for NLYW (blonde downstairs) or for the Seven seas
.The formula given in Julious is definitely approximate, albeit a good one for the usual power range ≥70% as the sample size calculations with that formula show.
The exact algo for the power of the equivalence test (two one sided tests aka TOST) in a 2x2 cross-over is ([1],[2]):
Power=Prob(t1≥t1-alpha,(n-2) and t2≤-t1-alpha,(n-2)|bioequivalence)
The t1 and t2 values are the t-variates of the two one-sided t-tests of bioequivalence.
(t1, t2) have according to Owen a bivariate non-central t-distribution and the power can be calculated as the difference of two definite integrals (Owen's Q functions dependent on df=degrees of freedom and with four arguments)
Power=Qdf(-t1-alpha,(n-2),d2,0,R)-Qdf(t1-alpha,(n-2),d1,0,R)
See [1] and [2] for that and for the formulas for d1, d2 and R.
So you need not a better algo for the non-central t but rather an algo for Owen's Q-functions
.My SAS beast has these functions implemented (but not documented!).
❝ In a previous thread I asked what the power in a 2,2,2-BE trial is at N=6, CV=65% and T/R=95%.
And my sasophylistic answer to the your ElMaestrophylistic question "what the power in a 2,2,2-BE trial is at N=38, CV=65% and T/R=95%." given here, power=4.5%, is based on these Q-functions.
Implementing the Julious formulas (according to Helmut's R-code) in "The power to know" results in power=-0.027799235, same as Fartssie!
[1] Diletti, E., Hauschke, D., and Steinijans, V.W. (1991),
"Sample Size Determination for Bioequivalence Assessment by Means of Confidence Intervals"
International Journal of Clinical Pharmacology, Therapy and Toxicology, Vol. 29, 1 -8.
[2] Hauschke, Steinijans, Pigeot
"Bioequivalence studies in drug development"
Wiley 2007, pages 120-121
—
Regards,
Detlew
Regards,
Detlew
Complete thread:
- non-central t, power, R: ElMaestro 2009-10-03 19:05 [🇷 for BE/BA]
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- non-central t, power, R: Helmut 2009-10-03 21:45
- non-central t, power, R: ElMaestro 2009-10-04 21:51
- non-central t, power, R: Helmut 2009-10-04 23:58
- non-central t, power, R: ElMaestro 2009-10-04 21:51
- non-central t is not the questiond_labes 2009-10-05 12:58
- SAS -> R -> SAS Helmut 2009-10-05 14:53
- Lost in translation d_labes 2009-10-06 14:31
- Lost in translation Helmut 2009-10-06 14:42
- Macacus cynocephalus d_labes 2009-10-06 15:14
- Lost in translation Helmut 2009-10-06 21:46
- Macacus cynocephalus d_labes 2009-10-06 15:14
- Lost in translation Helmut 2009-10-06 14:42
- Lost in translation d_labes 2009-10-06 14:31
- non-central t is not the question ElMaestro 2009-10-05 17:32
- Power of TOST in R d_labes 2009-10-06 16:45
- Power of TOST (R package MBESS) Helmut 2009-10-07 02:18
- Power of TOST (R package MBESS) d_labes 2009-10-07 08:46
- Power of TOST (R package MBESS) Helmut 2009-10-07 12:38
- Power of TOST (R package MBESS) d_labes 2009-10-07 08:46
- The Power at limits d_labes 2009-10-07 11:32
- Power at limits 2 d_labes 2009-10-07 15:15
- package MBESS Helmut 2009-10-07 22:36
- Package MBESS and Power curiosity d_labes 2009-10-15 14:57
- Package MBESS and Power curiosity ElMaestro 2009-10-17 12:26
- Apfelstrudel and EFG 2.01 Helmut 2009-10-17 13:44
- EFG and another power curiosity d_labes 2009-10-20 11:35
- EFG and another power curiosity ElMaestro 2009-11-23 19:03
- EFG and another power curiosity Helmut 2009-11-23 19:17
- EFG and another power curiosity ElMaestro 2009-11-23 19:03
- Package MBESS and Power curiosity ElMaestro 2009-10-17 12:26
- Package MBESS and Power curiosity d_labes 2009-10-15 14:57
- package MBESS Helmut 2009-10-07 22:36
- Power at limits 2 d_labes 2009-10-07 15:15
- Power of TOST (R package MBESS) Helmut 2009-10-07 02:18
- Power of TOST in R d_labes 2009-10-06 16:45
- SAS -> R -> SAS Helmut 2009-10-05 14:53
- non-central t, power, R: yjlee168 2009-10-07 00:08
- R code for power ElMaestro 2009-10-09 11:32
- Belgian beer ? Ohlbe 2009-10-09 11:50
- Another one - R code for power of TROST d_labes 2009-10-09 13:50
- non-central t, power, R: Helmut 2009-10-03 21:45
Ing. Helmut Schütz