FMRI Group Analysis
GLM Design matrix
Effect size subject-series
Voxel-wise group analysis
Group effect size statistics Subject groupings 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 Standard-space brain atlas subjects Single-subject effect size statistics Single-subject effect size statistics Single-subject effect size statistics Single-subject effect size statistics subjects Register subjects into a standard space Effect size statistics Statistic Image Significant voxels/clusters Contrast Thresholding
•
uses GLM at both lower and higher levels•
typically need to infer across multiple subjects,sometimes multiple groups and/or multiple sessions
•
questions of interest involve comparisons at thehighest level
Multi-Level FMRI analysis
Group 2
Hanna
Josephine Anna Sebastian Lydia Elisabeth
Group 1
Mark Steve Karl Will Tom Andrew
session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 4 Difference?
Does the group activate on average?
A simple example
GroupDoes the group activate on average?
0 effect size
A simple example
GroupDoes the group activate on average?
0 effect size
A simple example
GroupMark Steve Karl Will Tom Andrew
Y
k
=
X
k k
+
⇥
k
First-level GLM
on Mark’s 4D FMRI data set
Does the group activate on average?
0 effect size
A simple example
GroupMark Steve Karl Will Tom Andrew
Y
k
=
X
k k
+
⇥
k
Mark’s effect size
Does the group activate on average?
0 effect size
A simple example
GroupMark Steve Karl Will Tom Andrew
Y
k
=
X
k k
+
⇥
k
Mark’s within-subject
Does the group activate on average?
0 effect size
A simple example
GroupMark Steve Karl Will Tom Andrew
All first-level GLMs on 6 FMRI data set
Does the group activate on average?
What group mean are we after? Is it:
1. The group mean for those exact 6 subjects?
Fixed-Effects (FE) Analysis
2. The group mean for the population from which these 6 subjects were drawn?
Mixed-Effects (ME) analysis
A simple example
GroupDo these exact 6 subjects activate on average?
Fixed-Effects Analysis
GroupMark Steve Karl Will Tom Andrew
0 effect size
g
=
1
6
6
k=1
k estimate group effect size as
straight-forward mean across lower-level estimates
Do these exact 6 subjects activate on average?
Fixed-Effects Analysis
GroupMark Steve Karl Will Tom Andrew
0 effect size
Y
K
=
X
K K
+
⇥
K
K
=
X
g gg
=
1
6
6 k=1 kXg =
⇧ ⇧ ⇧ ⇧ ⇧ ⇧ ⇤ 1 1 1 1 1 1 ⇥ ⌃ ⌃ ⌃ ⌃ ⌃ ⌃ ⌅ Group mean
Do these exact 6 subjects activate on average?
•
Consider only these 6 subjects•
estimate the mean across these subject•
only variance is within-subject varianceFixed-Effects Analysis
GroupMark Steve Karl Will Tom Andrew
YK = XK K + ⇥K
K = Xg g
Does the group activate on average?
What group mean are we after? Is it:
1. The group mean for those exact 6 subjects?
Fixed-Effects (FE) Analysis
2. The group mean for the population from which these 6 subjects were drawn?
Mixed-Effects (ME) analysis
A simple example
Group0 effect size
Does the population activate on average?
Mixed-Effects Analysis
GroupMark Steve Karl Keith Tom Andrew
0 effect size
Y
K
=
X
K K
+
⇥
K
g k
Consider the distribution over the population from which our 6
subjects were sampled:
2
g
•
is the between-subject varianceDoes the population activate on average?
Mixed-Effects Analysis
GroupMark Steve Karl Keith Tom Andrew
Y
K
=
X
K K
+
⇥
K
0 effect size
g k
g
K
=
X
g g+
⇥
gXg =
⇧ ⇧ ⇧ ⇧ ⇧ ⇧ ⇤ 1 1 1 1 1 1 ⇥ ⌃ ⌃ ⌃ ⌃ ⌃ ⌃ ⌅ Population mean between-subject variation
Does the population activate on average?
•
Consider the 6 subjects as samples from a wider population•
estimate the mean across the population•
between-subject variance accounts for random samplingMixed-Effects Analysis
GroupMark Steve Karl Keith Tom Andrew
YK = XK K + ⇥K
Mixed-Effects Analysis:
All-in-One Approach
•
Could use one (huge) GLM to infer group difference•
difficult to ask sub-questions in isolation•
computationally demanding•
need to process again when new data is acquiredGroup 2 Hanna
Josephine Anna Sebastian Lydia Elisabeth Group 1
Mark Steve Karl Will Tom Andrew
session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 1 session 2 session 3 session 4 session 1 session 2 session 3 session 4 Difference?
Summary Statistics Approach
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At each level:•
Inputs are summary stats from levelsbelow (or FMRI data at the lowest level)
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Outputs are summary stats orstatistic maps for inference
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Need to ensure formal equivalence between different approaches!In FEAT estimate levels one stage at a time
Group
Subject Session Group difference
FLAME
•
Fully Bayesian framework•
use non-central t-distributions:Input COPES, VARCOPES & DOFs from lower-level
•
estimate COPES, VARCOPES &DOFs at current level
•
pass these up•
Infer at top level•
Equivalent to All-in-One approachFMRIB’s Local Analysis of Mixed Effects
Group Subject Session Group difference COPES VARCOPES DOFs Z-Stats COPES VARCOPES DOFs COPES VARCOPES DOFs
FLAME Inference
•
Default is:•
FLAME1: fast approximation for all voxels (usingmarginal variance MAP estimates)
•
Optional slower, slightly more accurate approach:•
FLAME1+2:•
FLAME1 for all voxels, FLAME2 for voxels close to thresholdChoosing Inference Approach
1. Fixed Effects
Use for intermediate/top levels
2. Mixed Effects - OLS
Use at top level: quick and less accurate
3. Mixed Effects - FLAME 1
Use at top level: less quick but more accurate
4. Mixed Effects - FLAME 1+2
FLAME vs. OLS
•
allow different within-level variances (e.g. patients vs. controls)•
allow non-balanced designs (e.g. containing behavioural scores)•
allow un-equal group sizes•
solve the ‘negative variance’ problem0 effect size
pat ctl
Group Subject
Session
< < ...
FLAME vs. OLS
•
Two ways in which FLAME can give different Z-stats compared to OLS:•
higher Z due to increased efficiency from usinglower-level variance heterogeneity
OLS
FL
AM
FLAME vs. OLS
•
Two ways in which FLAME can give different Z-stats compared to OLS:•
Lower Z due to higher-level variance beingconstrained to be positive (i.e. solve the implied negative variance problem)
OLS
FL
AM
Multiple Group Variances
•
can deal with multiple group variances•
separate variance will be estimated for each variance group (be aware of #observations for each estimate, though!)•
design matrices need to be ‘separable’, i.e. EVs only have non-zero values for a single group0 effect size
pat ctl
Single Group Average
•
We have 8 subjects - all in one group - and want the mean group average:Does the group activate on average?
•
estimate mean•
estimate std-error (FE or ME)•
test significance of mean > 0>0?
0
su
bjec
t
Single Group Average
Does the group activate on average?
0
su
bjec
t
Single Group Average
Unpaired Two-Group Difference
•
We have two groups (e.g. 9 patients, 7 controls) with different between-subject varianceIs there a significant group difference?
•
estimate means•
estimate std-errors (FE or ME)•
test significance of difference in means>0?
0
su
bjec
t
Unpaired Two-Group Difference
Is there a significant group difference?
0
su
bjec
t
Unpaired Two-Group Difference
Is there a significant group difference?
0
su
bjec
t
Unpaired Two-Group Difference
Paired T-Test
•
8 subjects scanned under 2 conditions (A,B)Is there a significant difference between conditions?
0
su
bjec
t
>0?
Paired T-Test
•
8 subjects scanned under 2 conditions (A,B)Is there a significant difference between conditions?
0
su
bjec
t
effect size
•
8 subjects scanned under 2 conditions (A,B)Is there a significant difference between conditions?
de-meaned data
0
su
bjec
t
effect size
data
0
su
bjec
t
effect size
Paired T-Test
subject mean
accounts for large prop. of the overall variance
•
8 subjects scanned under 2 conditions (A,B)Is there a significant difference between conditions?
de-meaned data 0 su bjec t effect size data 0 su bjec t effect size
Paired T-Test
>0? subject meanaccounts for large prop. of the overall variance
su
bjec
t
effect size
00
Paired T-Test
su
bjec
t
effect size
00
Paired T-Test
Paired T-Test
Is there a significant difference between conditions?
EV1models the A-B paired difference; EVs
2-9 are confounds which model out each
Paired T-Test
Multi-Session & Multi-Subject
•
5 subjects each have three sessions.Does the group activate on average?
•
Use three levels: in the second level we model the within-subject repeated measureMulti-Session & Multi-Subject
•
5 subjects each have three sessions.Does the group activate on average?
•
Use three levels: in the third level we model the between-subjects varianceMulti-Session & Multi-Subject
•
5 subjects each have three sessions.•
Does the group activate on average?•
Use three levels:•
in the second level we model the within subjectrepeated measure typically using fixed effects(!)
as #sessions are small
•
in the third level we model the between subjectsReducing variance
Does the group activate on average?
mean effect size small relative to std error mean effect size large
relative to std error 0
su
bjec
t
effect size
>0?
0
su
bjec
t
effect size
mean effect size large relative to std error
Reducing variance
Does the group activate on average?
mean effect size large relative to std error 0
su
bjec
t
effect size
>0?
0
su
bjec
t
effect size
•
We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times):Does the group activate on average?
•
use covariates to ‘explain’ variation•
estimate mean•
estimate std-error (FE or ME)0
su
bjec
t
effect size
•
We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times):Does the group activate on average?
•
use covariates to ‘explain’ variation•
estimate mean•
estimate std-error (FE or ME)0
su
bjec
t
effect size
Single Group Average & Covariates
fast RT
•
We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times):Does the group activate on average?
•
use covariates to ‘explain’ variation•
estimate mean•
estimate std-error (FE or ME)0
su
bjec
t
effect size
Single Group Average & Covariates
fast RT
•
We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times):Does the group activate on average?
•
use covariates to ‘explain’ variation•
estimate mean•
estimate std-error (FE or ME)0
su
bjec
t
effect size
Single Group Average & Covariates
fast RT
•
We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times):Does the group activate on average?
•
use covariates to ‘explain’ variation•
estimate mean•
estimate std-error (FE or ME)0
su
bjec
t
effect size
Single Group Average & Covariates
fast RT
Does the group activate on average?
•
use covariates to ‘explain’ variation•
need to de-mean additional covariates!•
Run FEAT on raw FMRI data to get first-level .featdirectories, each one with several (consistent) COPEs
•
low-res copeN/varcopeN .feat/stats•
when higher-level FEAT is run, highres copeN/varcopeN .feat/reg_standard
FEAT Group Analysis
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Run second-level FEAT to get one .gfeat directory•
Inputs can belower-level .feat dirs or lower-level COPEs
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the second-level GLM analysis is run separatelyfor each first-level COPE
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each lower-level COPE generates its own .featGroup F-tests
•
3 groups of subjectsANOVA: 1-factor 4-levels
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8 subjects, 1 factor at 4 levelsIs there any effect?
