FMRI Group Analysis GLM. Voxel-wise group analysis. Design matrix. Subject groupings. Group effect size. statistics. Effect size

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1 FMRI Group Analysis Voxel-wise group analysis Standard-space brain atlas Subject groupings Design matrix subjects Single-subject Single-subject effect size Single-subject effect statistics size Single-subject effect statistics size effect statistics size statistics Register subjects into a standard space Effect size subject-series subjects GLM Group effect size statistics Contrast Statistic Image Significant voxels/clusters Effect size statistics Thresholding

2 Multi-Level 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 First-level 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 within-subject 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 first-level 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? Fixed-Effects (FE) Analysis 2. The group mean for the population from which these 6 subjects were drawn? Mixed-Effects (ME) analysis

10 Fixed-Effects Analysis Do these exact 6 subjects activate on average? Group Mark Steve Karl Will Tom Andrew estimate group effect size as straight-forward mean across lower-level estimates effect size 6 g = 1 6 k=1 k

11 Fixed-Effects 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 Fixed-Effects 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 within-subject 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? Fixed-Effects (FE) Analysis 2. The group mean for the population from which these 6 subjects were drawn? Mixed-Effects (ME) analysis

14 Mixed-Effects 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 between-subject variance

15 Mixed-Effects 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 Mixed-Effects 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 Mixed-Effects Analysis: Consider the 6 subjects as samples from a wider population estimate the mean across the population between-subject variance accounts for random sampling

17 All-in-One 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 sub-questions 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 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 Z-Stats 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 within-level variances (e.g. patients vs. controls) pat ctl allow non-balanced designs (e.g. containing behavioural scores) effect size... allow un-equal group sizes solve the negative variance problem Session < < Subject Group

23 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 FLAME OLS

24 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) 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 non-zero 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 std-error (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 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 >? effect size

31 subject Unpaired Two-Group Difference Is there a significant group difference? effect size

32 subject Unpaired Two-Group Difference Is there a significant group difference? effect size

33 Unpaired Two-Group Difference Is there a significant group difference?

34 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? subject effect size

35 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? try non-paired t-test subject >? effect size

36 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? data de-meaned data subject subject effect size subject mean accounts for large prop. of the overall variance effect size

37 Paired T-Test 8 subjects scanned under 2 conditions (A,B) Is there a significant difference between conditions? data de-meaned data subject subject effect size subject mean accounts for large prop. of the overall variance >? effect size

38 Paired T-Test Is there a significant difference between conditions? subject effect size

39 Paired T-Test Is there a significant difference between conditions? subject effect size

40 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 subject s mean

41 Paired T-Test Is there a significant difference between conditions?

42 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

43 Multi-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 variance

44 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

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 std-error (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 std-error (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 std-error (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 std-error (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 std-error (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 de-mean additional covariates!

53 FEAT Group Analysis 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

54 FEAT Group Analysis Run second-level FEAT to get one.gfeat directory Inputs can be lowerlevel.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

55 That s all folks

56 Appendix:

57 3 groups of subjects Group F-tests Is any of the groups activating on average?

58 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

59 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

60 ANOVA: 3-factor 2-levels 16 subjects, 3 factor at 2 levels. Fixed-Effects ANOVA: For random/mixed effects need different Fs.

61 Understanding FEAT dirs First-level analysis:

62 Understanding FEAT dirs Second-level analysis:

63 That s all folks

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