FMRI Group Analysis - FSLfsl.fmrib.ox.ac.uk/fslcourse/lectures/feat2_part1.pdfFMRI Group Analysis GLM Design matrix Effect size subject-series Voxel-wise group analysis Group effect

FMRI Group Analysis

GLM

Design matrix

Effect size subject-series

Voxel-wise group analysis

Groupeffect sizestatistics

Subjectgroupings

111111000000

000000111111

Standard-spacebrain atlas

subjects

Single-subject effect sizestatistics




subjects

Registersubjects intoa standardspace

Effect sizestatistics

Statistic ImageSignificant

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 the

Multi-Level FMRI analysis

Group 2

HannaJosephine 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

Group



0 effect size

A simple example

Group



0 effect size

A simple example

Group


Yk = Xk�k + ⇥k

First-level GLMon Mark’s 4D FMRIdata set


0 effect size

A simple example

Group


Yk = Xk�k + ⇥k

Mark’s effect size


0 effect size

A simple example

Group


Yk = Xk�k + ⇥k

Mark’s within-subject

variance


0 effect size

A simple example

Group


All first-level GLMson 6 FMRI data set

YK = XK�K + ⇥K


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

Group


Do these exact 6 subjects activate on average?

Fixed-Effects Analysis

Group


0 effect size

�g =16

6�

k=1

�k

estimate group effect size as straight-forward mean

across lower-level estimates



Group


0 effect size

YK = XK�K + ⇥K

�K = Xg�g

�g =16

6�

k=1

�kXg =

�

⇧⇧⇧⇧⇧⇧⇤

111111

⇥

⌃⌃⌃⌃⌃⌃⌅Group mean


• Consider only these 6 subjects• estimate the mean across these subject• only variance is within-subject variance


Group


YK = XK�K + ⇥K

�K = Xg�g

Fixed Effects Analysis:


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

Group

Mark Steve Karl Keith Tom Andrew

0 effect size

Does the population activate on average?

Mixed-Effects Analysis

Group


0 effect size

YK = XK�K + ⇥K

�g�k

Consider the distribution over the population from which our 6 subjects were sampled:

�2g• is the between-subject variance

�g



Group


YK = XK�K + ⇥K

0 effect size�g�k

�g�K = Xg�g + ⇥g

Xg =

�

⇧⇧⇧⇧⇧⇧⇤

111111

⇥

⌃⌃⌃⌃⌃⌃⌅Population

mean

between-subject

variation


• Consider the 6 subjects as samples from a wider population• estimate the mean across the population• between-subject variance accounts for random sampling


Group


YK = XK�K + ⇥K

Mixed-Effects Analysis:

�K = Xg�g + ⇥g

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 acquired

Group 2

HannaJosephine Anna Sebastian Lydia Elisabeth

Group 1


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

• At each level:

• Inputs are summary stats from levels below (or FMRI data at the lowest level)

• Outputs are summary stats or statistic maps for inference

• Need to ensure formal equivalence between different approaches!

In FEAT estimate levels one stage at a time

Group

Subject

Session

Groupdifference

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 approach

FMRIB’s Local Analysis of Mixed Effects

Group

Subject

Session

Groupdifference

COPESVARCOPES

DOFs

Z-Stats

COPESVARCOPES

DOFs

COPESVARCOPES

DOFs

FLAME Inference

• Default is:

• FLAME1: fast approximation for all voxels (using marginal variance MAP estimates)

• Optional slower, slightly more accurate approach:

• FLAME1+2:

• FLAME1 for all voxels, FLAME2 for voxels close to threshold

• FLAME2: MCMC sampling technique

Choosing 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

Use at top level: slow but even more accurate

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’ problem

0 effect size

pat ctl

GroupSubjectSession

< <

...

FLAME vs. OLS

• Two ways in which FLAME can give different Z-stats compared to OLS:

• higher Z due to increased efficiency from using lower-level variance heterogeneity

OLS

FLA

ME

FLAME vs. OLS

• Two ways in which FLAME can give different Z-stats compared to OLS:

• Lower Z due to higher-level variance being constrained to be positive (i.e. solve the implied negative variance problem)

OLS

FLA

ME

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 group

0 effect size

pat ctl

valid invalid

Examples

Single Group Average

• We have 8 subjects - all in one group - and want the mean group average:


• estimate mean

• estimate std-error(FE or ME)

• test significance of mean > 0

>0?

0

subj

ect

effect size



0

subj

ect

effect size



Unpaired Two-Group Difference• We have two groups (e.g. 9 patients, 7

controls) with different between-subject variance

Is there a significant group difference?

• estimate means

• estimate std-errors(FE or ME)

• test significance of difference in means

>0?0

subj

ect

effect size

Unpaired Two-Group Difference


0

subj

ect

effect size



0

subj

ect

effect size



Paired T-Test• 8 subjects scanned under 2 conditions (A,B)

Is there a significant difference between conditions?

0

subj

ect

effect size

>0?

Paired T-Test• 8 subjects scanned under 2 conditions (A,B)


0

subj

ect

effect size

try non-paired t-test

• 8 subjects scanned under 2 conditions (A,B)


de-meaned data

0su

bjec

teffect size

data

0

subj

ect

effect size

Paired T-Test

subject mean accounts for large prop.of the overall variance

• 8 subjects scanned under 2 conditions (A,B)


de-meaned data

0su

bjec

teffect size

data

0

subj

ect

effect size

Paired T-Test

>0?subject mean

accounts for large prop.of the overall variance

subj

ect

effect size00

Paired T-Test


subj

ect

effect size00

Paired T-Test


Paired T-Test


EV1models the A-B paired difference; EVs

2-9 are confounds which model out each

subject’s mean

Paired T-Test


Multi-Session & Multi-Subject• 5 subjects each have three sessions.


• Use three levels: in the second level we model the within-subject repeated measure

Multi-Session & Multi-Subject• 5 subjects each have three sessions.


• Use three levels: in the third level we model the between-subjects variance

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 measure typically using fixed effects(!) as #sessions are small

• in the third level we model the between subjects variance using fixed or mixed effects

Reducing variance


mean effect size smallrelative to std error

mean effect size largerelative to std error

0

subj

ect

effect size

>0?

0

subj

ect

effect size

>0?


Reducing variance



0

subj

ect

effect size

>0?

0

subj

ect

effect size

>0?

• We have 7 subjects - all in one group. We also have additional measurements (e.g. age; disability score; behavioural measures like reaction times):


• use covariates to ‘explain’ variation

• estimate mean


0

subj

ect

effect size

Single Group Average & Covariates




• estimate mean


0

subj

ect

effect size


fastRTslow




• estimate mean


0

subj

ect

effect size


fastRTslow




• estimate mean


0

subj

ect

effect size


fastRTslow




• estimate mean


0

subj

ect

effect size


fastRTslow



• need to de-mean additional covariates!


• Run FEAT on raw FMRI data to get first-level .feat directories, 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

FEAT Group Analysis

• Run second-level FEAT to get one .gfeat directory

• Inputs can be lower-level .feat dirs or lower-level COPEs

• the second-level GLM analysis is run separately for each first-level COPE

• each lower-level COPE generates its own .feat directory inside the .gfeat dir

That’s all folks

Appendix:

Group F-tests• 3 groups of subjects

Is any of the groups activating on average?

ANOVA: 1-factor 4-levels• 8 subjects, 1 factor at 4 levels

Is there any effect?

• EV1 fits cond. D, EV2 fits cond A relative to D etc.

• F-test shows any difference between levels

ANOVA: 2-factor 2-levels• 8 subjects, 2 factor at 2 levels. FE Anova: 3 F-tests give

standard results for factor A, B and interaction

• If both factors are random effects then Fa=fstat1/fstat3, Fb=fstat2/fstat3ME

• ME: if fixed fact. is A, Fa=fstat1/fstat3

ANOVA: 3-factor 2-levels• 16 subjects, 3 factor at 2 levels.

• Fixed-Effects ANOVA:

• For random/mixed effects need different Fs.

Understanding FEAT dirs

• First-level analysis:

Understanding FEAT dirs

• Second-level analysis:

That’s all folks

FMRI Group Analysis - FSLfsl.fmrib.ox.ac.uk/fslcourse/lectures/feat2_part1.pdfFMRI Group Analysis GLM Design matrix Effect size subject-series Voxel-wise group analysis Group effect

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