Simulations [Regulatives / Guidelines]
❝ ❝ The idea behind the Group-by-Treatment interaction is that the T/R in one group is different from the other (i.e., we have collinearity with a “hidden” variable). Therefore, simulate a group of subjects with T/R 0.95 and another one with T/R 0.95–1 (CV ad libitum). Merge them to get a “study”. Run model 1 and check the p-value of the Group-by-Treatment interaction. With the simple model you should expect T/R 1.
❝
❝ seems to be reasonable, but I do not see why the power is low?
Good question. Next question?
I performed simulations (100,000 2×2×2 studies each for conditions a. and b. specified below). Two groups of 16 subjects each, CV 30%, no period and sequence effects. 32 subjects should give power 81.52% for T/R 1. If the Group-by-Treatment interaction is not significant (p ≥0.1) in model 1, the respective study is evaluated by model 2 (pooled data) or both groups by model 3 otherwise. All studies are evaluated by model 3 (pooled data). The listed PE is the geometric mean of passing studies’ PEs.
- T/R in group 1 0.95, T/R in group 2 0.95–1
(i.e., ‘true’ Group-by-Treatment interaction):
Model 1: p(G×T) <0.1 in 17.91% of studies.
Evaluation of studies with p(G×T) <0.1 (Groups):
passed model 3 (1) : 1.42% (of tested); PE 98.69%
range of PEs: 92.45% to 107.63%
passed model 3 (2) : 1.64% (of tested); PE 100.99%
range of PEs: 93.99% to 108.23%
passed model 3 (1 and 2): 0.00% (of tested)
Evaluation of studies with p(G×T) ≥0.1 (pooled):
passed model 2 : 66.47% (overall)
80.97% (of tested); PE 99.97%
range of PEs: 86.36% to 114.27%
Studies passing any of model 2 or 3: 67.02%
Criteria for simple model fulfilled:
passed model 3 : 80.95%; PE 99.98%
range of PEs: 86.36% to 114.68%
- T/R in both groups 1.00
(i.e., no Group-by-Treatment interaction):
Model 1: p(G×T) <0.1 in 9.79% of studies.
Evaluation of studies with p(G×T) <0.1 (Groups):
passed model 3 (1) : 1.86% (of tested); PE 100.28%
range of PEs: 93.09% to 108.40%
passed model 3 (2) : 1.87% (of tested); PE 100.01%
range of PEs: 92.18% to 108.41%
passed model 3 (1 and 2): 0.00% (of tested)
Evaluation of studies with p(G×T) ≥0.1 (pooled):
passed model 2 : 73.33% (overall)
81.28% (of tested); PE 99.98%
range of PEs: 86.36% to 114.68%
Studies passing any of model 2 or 3: 73.69%
Criteria for simple model fulfilled:
passed model 3 : 81.40%; PE 99.98%
range of PEs: 86.36% to 115.15%
Lessons learned:
If we test at the 10% level and there is no true Group-by-Treatment interaction we will find a significant effect at ~ the level of the test – as expected (b). Hurray, false positives!
On the other hand, if there is one, we will detect it (a).
The percentage of studies passing in models 2 and 3 are similar. Theoretically in model 2 it should be slightly lower than in model 3 (one degree of freedom of the treatment effect less). However, overall power is seriously compromised.
Slowly I get the impression that the evaluation of groups (by model 3) is not a good idea. If there is a true Group-by-Treatment interaction why the heck should the PE (say in the largest group) be unbiased? I would rather say that if one believes that a Group-by-Treatment interaction really exists (I don’t) and the test makes sense (I don’t) evaluation (of the largest group) by model 3 should not be performed. Consequently ~⅒ of (otherwise passing) studies would go into the waste bin. Didn’t I say that before?
The distribution of p-values should be uniform.
Looks good for b.
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000011 0.2517777 0.5002957 0.5008763 0.7508297 0.9999974
Interesting shape for a.
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000001 0.1562932 0.3991516 0.4306846 0.6868190 0.9999981
If you prefer more extreme stuff: T/R in group 1 0.90, T/R in group 2 0.90–1
Model 1: p(G×T) <0.1 in 40.35% of studies.
Evaluation of studies with p(G×T) <0.1 (Groups):
passed model 3 (1) : 1.09% (of tested); PE 98.76%
range of PEs: 91.69% to 105.97%
passed model 3 (2) : 1.06% (of tested); PE 101.40%
range of PEs: 94.58% to 108.34%
passed model 3 (1 and 2): 0.00% (of tested)
Evaluation of studies with p(G×T) ≥0.1 (pooled):
passed model 2 : 47.74% (overall)
80.03% (of tested); PE 99.98%
range of PEs: 87.24% to 114.13%
Studies passing any of model 2 or 3: 48.60%
Criteria for simple model fulfilled:
passed model 3 : 79.45%; PE 99.99%
range of PEs: 87.24% to 114.13%
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00000 0.03962 0.15648 0.26602 0.42742 0.99997
PS: The code seems to work – at least for the pooled model 3. Comparisons of powers
power.TOST(...) 0.815152
power.TOST.sim(..., nsims=1e5) 0.81437
power.TOST.sim(..., nsims=1e6) 0.815127
My code (nsims=1e5) 0.81402
My code (nsims=1e6) 0.81551
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:
- Russian «Экспертами» and their hobby Helmut 2017-04-29 00:46 [Regulatives / Guidelines]
- Low power of Group-by-Treatment interaction mittyri 2017-04-29 22:57
- Let’s forget the Group-by-Treatment interaction, please! Helmut 2017-04-30 13:54
- Let’s forget the Group-by-Treatment interaction, please! ElMaestro 2017-05-01 16:19
- Some answers Helmut 2017-05-02 01:10
- Some answers ElMaestro 2017-05-02 09:04
- Example Helmut 2017-05-02 12:35
- Sensitivity of term? mittyri 2017-05-02 18:29
- SimulationsHelmut 2017-05-05 14:38
- loosing specificity due to low sensitivity mittyri 2017-05-08 23:28
- loosing specificity due to low sensitivity Helmut 2017-05-09 00:55
- loosing specificity due to low sensitivity mittyri 2017-05-08 23:28
- Loss in power Helmut 2017-05-06 17:31
- Interval between groups Helmut 2017-05-08 19:02
- IMP handling mittyri 2017-05-08 23:40
- IMP handling Helmut 2017-05-09 01:08
- IMP handling mittyri 2017-05-08 23:40
- Loss in power Helmut 2017-05-14 17:22
- SimulationsHelmut 2017-05-05 14:38
- Some answers ElMaestro 2017-05-02 09:04
- No convergence in JMP and Phoenix WinNonlin Helmut 2017-05-25 15:26
- Ouch?!??? ElMaestro 2017-05-25 16:24
- Some answers Helmut 2017-05-02 01:10
- Let’s forget the Group-by-Treatment interaction, please! ElMaestro 2017-05-01 16:19
- Let’s forget the Group-by-Treatment interaction, please! Helmut 2017-04-30 13:54
- Russian «Экспертами» and their hobby Artem Gusev 2017-05-02 16:13
- be careful with mixed models mittyri 2017-05-02 17:53
- be careful with mixed models Artem Gusev 2017-05-03 11:02
- p-value(s) in model 2 Helmut 2017-05-05 14:48
- be careful with mixed models mittyri 2017-05-02 17:53
- Russian «Экспертами» following the EEU GLs Helmut 2017-05-24 20:17
- Russian «Экспертами» following the EEU GLs Beholder 2017-05-24 22:37
- Penalty for carelessness mittyri 2017-05-25 08:52
- Russian «Экспертами» following the EEU GLs Beholder 2017-05-25 10:43
- Russian «Экспертами» following the EEU GLs Mikalai 2018-01-04 10:43
- Belarus = member of the EEU Helmut 2018-01-04 13:08
- Belarus = member of the EEU Mikalai 2018-01-04 19:49
- Trying your model for EEU mittyri 2018-01-04 22:04
- Trying your model for EEU Helmut 2018-01-05 00:06
- help us to stop it, please... Astea 2018-01-10 12:09
- help us to stop it, please... Beholder 2018-01-10 12:49
- regulators convinced by science? d_labes 2018-01-10 15:15
- regulators convinced by science? Beholder 2018-01-10 17:14
- Чёрт побери! d_labes 2018-01-10 18:53
- regulators convinced by science? Astea 2018-01-10 19:10
- regulators convinced by science? Beholder 2018-01-10 17:14
- help us to stop it, please... Astea 2018-01-10 12:09
- Trying your model for EEU Helmut 2018-01-05 00:06
- Belarus = member of the EEU Helmut 2018-01-04 13:08
- Russian «Экспертами» following the EEU GLs Beholder 2017-05-24 22:37
- Low power of Group-by-Treatment interaction mittyri 2017-04-29 22:57