Dear FSLers
After reading some recent posts about repeated measures ANOVAs may I clarify if the hypothetical approaches below are valid as I sense that they may not be given answers to some questions regarding inflated statistics and confounding within- and between- subject errors:
1. Study 1:
20 subjects who at a single visit view 3 types of pictures: T1, T2 and T3 [latter as low-level baseline] in 2 runs.
The 2 runs for each subject are first combined for each contrast at 1st level by fixed effects.
At the group level I then wish to determine extent of activation for the following contrasts: (T1 or T2) > T3 and T1>T2.
Can I combine this in a single 2nd level mixed effects GLM as follows:
Input EV1 EV2 EV3 EV4 ……….EV21
PictType subj1subj2subj3 subj20
Subj1-T1>T3 1 1 0 0 0
Subj2-T1>T3 1 0 1 0 0
Subj3-T1>T3 1 0 0 1 0
etc.
Sub20-T1>T3 1 0 0 0 1
Subj1-T2>T3 -1 1 0 0 0
Subj2-T2>T3 -1 0 1 0 0
Subj3-T2>T3 -1 0 0 1 0
etc.
Subj20-T2>T3 -1 0 0 0 1
Contrasts
C1 T1>T2 1 0 0 0 0
C2 T2>T1 -1 0 0 0 0
C3 group mean 0 1 1 1 1
for (T1 or T2)>T3
2. Study 2:
20 subjects who at 2 different visits (receiving Drug A or placebo P) view 3 types of pictures: T1, T2 and T3 [latter as low-level baseline] in 2 runs.
The 2 runs for each subject are first combined for each contrast at 1st level by fixed effects at each visit.
At the 2nd level I then wish to determine the effect of drug A (>P) on activation to pictures (T1 or T2) > T3 and if there is a differential effect on picture type T1 compared to T2 ie a 2-factor 2-level repeated measures ANOVA: drug [A and P] and picture type [T1 and T2].
Can I combine this into a single 2nd level mixed effects GLM as follows:
Input EV1 EV2 EV3 EV4 EV5 EV6 ……….EV23
PictType Drug Inter subj1subj2subj3 subj20
Subj1-A-T1>T3 1 1 1 1 0 0 0
Subj2-A-T1>T3 1 1 1 0 1 0 0
Subj3-A-T1>T3 1 1 1 0 0 1 0
etc.
Subj20-A-T1>T3 1 1 1 0 0 0 1
Subj1-A-T2>T3 -1 1 -1 1 0 0 0
Subj2-A-T2>T3 -1 1 -1 0 1 0 0
Subj3-A-T2>T3 -1 1 -1 0 0 1 0
etc.
Subj20-A-T2>T3 -1 1 -1 0 0 0 1
Subj1-P-T1>T3 1 -1 -1 1 0 0 0
Subj2-P-T1>T3 1 -1 -1 0 1 0 0
Subj3-P-T1>T3 1 -1 -1 0 0 1 0
etc.
Subj20-P-T1>T3 1 -1 -1 0 0 0 1
Subj1-P-T2>T3 -1 -1 -1 1 0 0 0
Subj2-P-T2>T3 -1 -1 -1 0 1 0 0
Subj3-P-T2>T3 -1 -1 -1 0 0 1 0
etc.
Subj20-P-T2>T3 -1 -1 -1 0 0 0 1
Contrasts
C1 T1>T2 1 0 0 0 0 0 0
independent of drug
C2 T2>T1 -1 0 0 0 0 0 0
independent of drug
C3 Drug A>Placebo 0 1 0 0 0 0 0
for (T1 or T2)>T3
C4 Placebo>Drug A 0 1 0 0 0 0 0
for (T1 or T2)>T3
C5 Effect of drug A 0 0 1 0 0 0 0
is greater on T1 than T2
3. Study 3
Subjects also attend for a third visit when they receive drug B.
If I wish to compare the effects of drug A and drug B on activation to picture type contrast (T1 or T2) > T3 (i.e. I do not care whether there is an interaction between either drug and picture type) can I combine them in a single mixed effects triple t-test by including EVs mapping the drug as per the GLM on FSL FEAT tutorial as follows:
Input EV1 EV2 EV3 EV4 EV5 EV6 ……….EV23
PictType subj1subj2subj3 subj20
Subj1-A-T1>T3 1 1 1 1 0 0 0
Subj2-A-T1>T3 1 1 1 0 1 0 0
Subj3-A-T1>T3 1 1 1 0 0 1 0
etc.
Subj20-A-T1>T3 1 1 1 0 0 0 1
Subj1-A-T2>T3 -1 1 1 1 0 0 0
Subj2-A-T2>T3 -1 1 1 0 1 0 0
Subj3-A-T2>T3 -1 1 1 0 0 1 0
etc.
Subj20-A-T2>T3 -1 1 1 0 0 0 1
Subj1-B-T1>T3 1 -1 0 1 0 0 0
Subj2-B-T1>T3 1 -1 0 0 1 0 0
Subj3-B-T1>T3 1 -1 0 0 0 1 0
etc.
Subj20-B-T1>T3 1 -1 0 0 0 0 1
Subj1-B-T2>T3 -1 -1 0 1 0 0 0
Subj2-B-T2>T3 -1 -1 0 0 1 0 0
Subj3-B-T2>T3 -1 -1 0 0 0 1 0
etc.
Subj20-B-T2>T3 -1 -1 0 0 0 0 1
Subj1-P-T1>T3 1 0 -1 1 0 0 0
Subj2-P-T1>T3 1 0 -1 0 1 0 0
Subj3-P-T1>T3 1 0 -1 0 0 1 0
etc.
Subj20-P-T1>T3 1 0 -1 0 0 0 1
Subj1-P-T2>T3 -1 0 -1 1 0 0 0
Subj2-P-T2>T3 -1 0 -1 0 1 0 0
Subj3-P-T2>T3 -1 0 -1 0 0 1 0
etc.
Subj20-P-T2>T3 -1 0 -1 0 0 0 1
Contrasts
C1 T1>T2 1 0 0 0 0 0 0
independent of drug
C2 T2>T1 -1 0 0 0 0 0 0
independent of drug
C3 Drug A>Placebo 0 1 2 0 0 0 0
for (T1 or T2)>T3
C4 Drug B>Placebo 0 -1 1 0 0 0 0
for (T1 or T2)>T3
C5 Drug A>Drug B 0 2 1 0 0 0 0
for (T1 or T2)>T3
Many thanks for your expert help.
Dr Tony Goldstone
MRC Clinical Sciences Centre
Imperial College London, UK
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