FMRI Group Analysis GLM. Voxelwise group analysis. Design matrix. Subject groupings. Group effect size. statistics. Effect size


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1 FMRI Group Analysis Voxelwise group analysis Standardspace brain atlas Subject groupings Design matrix subjects Singlesubject Singlesubject effect size Singlesubject effect statistics size Singlesubject effect statistics size effect statistics size statistics Register subjects into a standard space Effect size subjectseries subjects GLM Group effect size statistics Contrast Statistic Image Significant voxels/clusters Effect size statistics Thresholding
2 MultiLevel FMRI analysis uses GLM at both lower and higher levels typically need to infer across multiple subjects, sometimes multiple groups and/or multiple sessions Group 1 Difference? Group 2 Mark Steve Karl Will Tom Andrew Josephine Anna Hanna Sebastian Lydia Elisabeth session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 4 session 4 session 4 session 4 session 4 session 4 session 4 session 4 questions of interest involve comparisons at the highest level
3 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew
4 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew effect size
5 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y k = X k k + k Firstlevel GLM on Mark s 4D FMRI data set effect size
6 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y k = X k k + k Mark s effect size effect size
7 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y k = X k k + k Mark s withinsubject variance effect size
8 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew Y K = X K K + K All firstlevel GLMs on 6 FMRI data set effect size
9 A simple example Does the group activate on average? Group Mark Steve Karl Will Tom Andrew What group mean are we after? Is it: 1. The group mean for those exact 6 subjects? FixedEffects (FE) Analysis 2. The group mean for the population from which these 6 subjects were drawn? MixedEffects (ME) analysis
10 FixedEffects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew estimate group effect size as straightforward mean across lowerlevel estimates effect size 6 g = 1 6 k=1 k
11 FixedEffects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew Y K = X K K + K X g = K = X g g Group mean effect size g = k k=1
12 FixedEffects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew Y K = X K K + K K = X g Fixed Effects Analysis: Consider only these 6 subjects estimate the mean across these subject only variance is withinsubject variance g
13 A simple example Does the group activate on average? Group Mark Steve Karl Keith Tom Andrew What group mean are we after? Is it: 1. The group mean for those exact 6 subjects? FixedEffects (FE) Analysis 2. The group mean for the population from which these 6 subjects were drawn? MixedEffects (ME) analysis
14 MixedEffects Analysis Does the population activate on average? Group Mark Steve Karl Keith Tom Andrew Y K = X K K + K Consider the distribution over the population from which our 6 subjects were sampled: g effect size g k 2 g is the betweensubject variance
15 MixedEffects Analysis Does the population activate on average? Group Mark Steve Karl Keith Tom Andrew Y K = X K K + K X g = K = X g g + g Population mean betweensubject variation g effect size g k
16 MixedEffects Analysis Does the population activate on average? Group Mark Steve Karl Keith Tom Andrew Y K = X K K = X g K + K g + g MixedEffects Analysis: Consider the 6 subjects as samples from a wider population estimate the mean across the population betweensubject variance accounts for random sampling
17 AllinOne Approach Group 1 Difference? Group 2 Mark Steve Karl Will Tom Andrew Josephine Anna Hanna Sebastian Lydia Elisabeth session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 1 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 2 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 3 session 4 session 4 session 4 session 4 session 4 session 4 session 4 session 4 Could use one (huge) GLM to infer group difference difficult to ask subquestions in isolation computationally demanding need to process again when new data is acquired
18 Summary Statistics Approach In FEAT estimate levels one stage at a time 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! Group difference Group Subject Session
19 FLAME FMRIB s Local Analysis of Mixed Effects Fully Bayesian framework use noncentral tdistributions: Input COPES, VARCOPES & DOFs from lowerlevel estimate COPES, VARCOPES & DOFs at current level pass these up Infer at top level Equivalent to AllinOne approach ZStats Group difference COPES VARCOPES DOFs COPES VARCOPES DOFs COPES VARCOPES DOFs Group Subject Session
20 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
21 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
22 FLAME vs. OLS allow different withinlevel variances (e.g. patients vs. controls) pat ctl allow nonbalanced designs (e.g. containing behavioural scores) effect size... allow unequal group sizes solve the negative variance problem Session < < Subject Group
23 FLAME vs. OLS Two ways in which FLAME can give different Zstats compared to OLS: higher Z due to increased efficiency from using lowerlevel variance heterogeneity FLAME OLS
24 FLAME vs. OLS Two ways in which FLAME can give different Zstats compared to OLS: Lower Z due to higherlevel variance being constrained to be positive (i.e. solve the implied negative variance problem) FLAME OLS
25 Multiple Group Variances can deal with multiple variances separate variance will be estimated for each variance group (be aware of #observations for each estimate, though!) group effect size design matrices need to be separable, i.e. EVs only have nonzero values for a single group pat ctl valid invalid
26 Examples
27 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 stderror (FE or ME) test significance of mean > subject effect size >?
28 Single Group Average Does the group activate on average? subject effect size
29 Single Group Average Does the group activate on average?
30 subject Unpaired TwoGroup Difference We have two groups (e.g. 9 patients, 7 controls) with different betweensubject variance Is there a significant group difference? estimate means estimate stderrors (FE or ME) test significance of difference in means >? effect size
31 subject Unpaired TwoGroup Difference Is there a significant group difference? effect size
32 subject Unpaired TwoGroup Difference Is there a significant group difference? effect size
33 Unpaired TwoGroup Difference Is there a significant group difference?
34 Paired TTest 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? subject effect size
35 Paired TTest 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? try nonpaired ttest subject >? effect size
36 Paired TTest 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? data demeaned data subject subject effect size subject mean accounts for large prop. of the overall variance effect size
37 Paired TTest 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? data demeaned data subject subject effect size subject mean accounts for large prop. of the overall variance >? effect size
38 Paired TTest Is there a significant difference between conditions? subject effect size
39 Paired TTest Is there a significant difference between conditions? subject effect size
40 Paired TTest Is there a significant difference between conditions? EV1models the AB paired difference; EVs 29 are confounds which model out each subject s mean
41 Paired TTest Is there a significant difference between conditions?
42 MultiSession & MultiSubject 5 subjects each have three sessions. Does the group activate on average? Use three levels: in the second level we model the withinsubject repeated measure
43 MultiSession & MultiSubject 5 subjects each have three sessions. Does the group activate on average? Use three levels: in the third level we model the betweensubjects variance
44 MultiSession & MultiSubject 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
45 Reducing variance Does the group activate on average? subject subject >? effect size mean effect size large relative to std error >? mean effect size small relative to std error effect size
46 Reducing variance Does the group activate on average? subject subject >? effect size mean effect size large relative to std error >? mean effect size large relative to std error effect size
47 Single Group Average & Covariates 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 Does the group activate on average? estimate mean estimate stderror (FE or ME) subject effect size
48 Single Group Average & Covariates 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 Does the group activate on average? estimate mean estimate stderror (FE or ME) subject effect size slow RT fast
49 Single Group Average & Covariates 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 Does the group activate on average? estimate mean estimate stderror (FE or ME) subject effect size slow RT fast
50 Single Group Average & Covariates 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 Does the group activate on average? estimate mean estimate stderror (FE or ME) subject effect size slow RT fast
51 Single Group Average & Covariates 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 Does the group activate on average? estimate mean estimate stderror (FE or ME) subject effect size slow RT fast
52 Single Group Average & Covariates Does the group activate on average? use covariates to explain variation need to demean additional covariates!
53 FEAT Group Analysis Run FEAT on raw FMRI data to get firstlevel.feat directories, each one with several (consistent) COPEs lowres copen/varcopen.feat/stats when higherlevel FEAT is run, highres copen/ varcopen.feat/reg_standard
54 FEAT Group Analysis Run secondlevel FEAT to get one.gfeat directory Inputs can be lowerlevel.feat dirs or lowerlevel COPEs the secondlevel GLM analysis is run separately for each firstlevel COPE each lowerlevel COPE generates its own.feat directory inside the.gfeat dir
55 That s all folks
56 Appendix:
57 3 groups of subjects Group Ftests Is any of the groups activating on average?
58 ANOVA: 1factor 4levels 8 subjects, 1 factor at 4 levels Is there any effect? EV1 fits cond. D, EV2 fits cond A relative to D etc. Ftest shows any difference between levels
59 ANOVA: 2factor 2levels 8 subjects, 2 factor at 2 levels. FE Anova: 3 Ftests 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
60 ANOVA: 3factor 2levels 16 subjects, 3 factor at 2 levels. FixedEffects ANOVA: For random/mixed effects need different Fs.
61 Understanding FEAT dirs Firstlevel analysis:
62 Understanding FEAT dirs Secondlevel analysis:
63 That s all folks
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