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RegisterHeteroscedasticity: TRT|RTR rulez! [RSABE / ABEL]
Dear Helmut! Dear All!
Thanks for the praise in advance. Let's see if I'm worth the "Vorschuss-Lorbeeren".
Going the long walk and simulating ABE type I error for the 3-period design with the sequences TRT and RTR via subject data sims (1 value after ~24 h!) I was more and more frustrated: No alpha-inflation, no too conservative alphas far and wide! Although the Oracle Chow&Liu had forecasted their certain occurrence!
But finally arriving in the green realms of FDA/ISC I got the following, resorting to heavy imbalance (forgot my Schützomycin dose
):
There is no hint of an alpha-inflation or too conservative alpha values if one uses the EMA recommended evaluation (same ANOVA as for the classical 2x2x2 crossover), regardless of grade of heteroscedasticity and unbalancedness analyzed!
The evaluation via intra-subject contrasts also do not show noticeable deviations from the nominal level 0.05 as long as the design is balanced or only slightly unbalanced.
Alpha-inflation or too conservative type I error values are only observed if the sequence groups are strongly unbalanced.
Thus this design is much more ‘friendly’ in respect to heteroscedasticity than the 2x3x3 design in the EMA evaluation. See this post of mine.
Some simulations of power of scaled ABE show that even for heavy unbalanced designs the influence of this observed behaviour is only small.
Conclusion 1: TRT|RTR rulez!
Conclusion 2: Expect an update of PowerTOST in the near future.
❝ ❝ Meanwhile I have some sims underway which (hopefully) will underpin my criticism of the TRT/RTR design.
❝
❝ Kudos for your pioneering work on exploring heteroscedasticity.
Thanks for the praise in advance. Let's see if I'm worth the "Vorschuss-Lorbeeren".
Going the long walk and simulating ABE type I error for the 3-period design with the sequences TRT and RTR via subject data sims (1 value after ~24 h!) I was more and more frustrated: No alpha-inflation, no too conservative alphas far and wide! Although the Oracle Chow&Liu had forecasted their certain occurrence!
But finally arriving in the green realms of FDA/ISC I got the following, resorting to heavy imbalance (forgot my Schützomycin dose
):CVwT CVwR n1 n2 EMA FDA
ANOVA ISC
---------------------------------------
0.5 0.2 18 18 0.0509 0.0496*
21 15 0.0509 0.0559*
15 21 0.0507 0.0430*
24 24 0.0505
---------------------------------------
0.5 0.3 18 18 0.0503 0.0502
19 17 0.0516
21 15 0.0502 0.0541
15 21 0.0503 0.0459
---------------------------------------
0.2 0.5 18 18 0.0509
21 15 0.0511
15 21 0.0506
24 24 0.0505
---------------------------------------
0.3 0.5 18 18 0.0505 0.0504
19 17 0.0490
21 15 0.0505 0.0469
15 21 0.0503 0.0542
---------------------------------------
n1 = n(TRT), n2 = n(RTR)
1E6 sims, *1E5 sims onlyThere is no hint of an alpha-inflation or too conservative alpha values if one uses the EMA recommended evaluation (same ANOVA as for the classical 2x2x2 crossover), regardless of grade of heteroscedasticity and unbalancedness analyzed!
The evaluation via intra-subject contrasts also do not show noticeable deviations from the nominal level 0.05 as long as the design is balanced or only slightly unbalanced.
Alpha-inflation or too conservative type I error values are only observed if the sequence groups are strongly unbalanced.
Thus this design is much more ‘friendly’ in respect to heteroscedasticity than the 2x3x3 design in the EMA evaluation. See this post of mine.
Some simulations of power of scaled ABE show that even for heavy unbalanced designs the influence of this observed behaviour is only small.
Conclusion 1: TRT|RTR rulez!
Conclusion 2: Expect an update of PowerTOST in the near future.
—
Regards,
Detlew
Regards,
Detlew
Complete thread:
- 3-per, 2-trt designs and estimation of intra-subj. variance ElMaestro 2013-08-12 19:54
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- 3-per, 2-trt designs and estimation of intra-subj. variance Dr_Dan 2013-08-13 10:11
- 3-per, 2-trt designs and estimation of intra-subj. variance ElMaestro 2013-08-13 15:00
- TRT|RTR rulez! Helmut 2013-08-13 18:23
- TRT|RTR rulez? Really? d_labes 2013-08-14 08:16
- TRT|RTR rulez? Really? Yes. ElMaestro 2013-08-14 11:29
- TRT|RTR rulez? Really? No. d_labes 2013-08-14 13:34
- TRT|RTR rulez? Really? No. ElMaestro 2013-08-14 14:25
- TRT|RTR Lost in formulas. d_labes 2013-08-14 16:35
- TRT|RTR rulez? Really? No. ElMaestro 2013-08-14 14:25
- TRT|RTR rulez? Really? No. d_labes 2013-08-14 13:34
- TRT|RTR rulez? References Helmut 2013-08-14 13:44
- References László & László d_labes 2013-08-14 19:12
- Heteroscedasticity Helmut 2013-08-17 17:33
- Heteroscedasticity: TRT|RTR rulez!d_labes 2013-08-29 16:45
- Heteroscedasticity: TRT|RTR rulez! ElMaestro 2013-08-29 17:50
- Sims & evaluation d_labes 2013-08-30 09:16
- Sims & evaluation ElMaestro 2013-08-31 14:11
- Evaluation subtleties d_labes 2013-08-31 17:20
- Sims & evaluation ElMaestro 2013-08-31 14:11
- Sims & evaluation d_labes 2013-08-30 09:16
- Heteroscedasticity: TRT|RTR rulez! ElMaestro 2013-08-29 17:50
- Heteroscedasticity: TRT|RTR rulez!d_labes 2013-08-29 16:45
- Heteroscedasticity Helmut 2013-08-17 17:33
- References László & László d_labes 2013-08-14 19:12
- TRT|RTR rulez? Really? Yes. ElMaestro 2013-08-14 11:29
- TRT|RTR rulez? Really? d_labes 2013-08-14 08:16
- TRT|RTR rulez! Helmut 2013-08-13 18:23
- 3-per, 2-trt designs and estimation of intra-subj. variance ElMaestro 2013-08-13 15:00
- 3-per, 2-trt designs and estimation of intra-subj. variance Dr_Dan 2013-08-13 10:11
Ing. Helmut Schütz