Basics of fMRI Group Analysis Douglas N. Greve

2 fMRI Analysis Overview Higher Level GLM First Level GLM Analysis First Level GLM Analysis Subject 3 First Level GLM Analysis Subject 4 First Level GLM Analysis Subject 1 Subject 2 CX CX CX CX Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Raw Data CX

3 Overview Population vs Sample First-Level (Time-Series) Analysis Review Types of Group Analysis –Random Effects, Mixed Effects, Fixed Effects Multi-Level General Linear Model (GLM) Examples (One Group, Two Groups, Covariates) Longitudinal

4 Population vs Sample Group Population (All members) Hundreds? Thousands? Billions? Sample 18 Subjects Do you want to draw inferences beyond your sample? Does sample represent entire population? Random Draw?

5 Functional Anatomy/Brain Mapping

6 Visual/Auditory/Motor Activation Paradigm 15 sec ‘ON’, 15 sec ‘OFF’ Flickering Checkerboard Auditory Tone Finger Tapping

7 Block Design: 15s Off, 15s On

8 Contrasts and Inference p = , sig=-log10(p) =11 p =.10, sig=-log10(p) =1 Note: z, t, F monotonic with p

9 Matrix Model y = X *   Task  base Data from one voxel Design Matrix Regressors = Vector of Regression Coefficients (“Betas”) Design Matrix Observations Contrast Matrix: C = [1 0] Contrast = C*  =  Task

10 Contrasts and the Full Model

11 Statistical Parametric Map (SPM) +3% 0% -3% Contrast Amplitude CON, COPE, CES Contrast Amplitude Variance (Error Bars) VARCOPE, CESVAR Significance t-Map (p,z,F) (Thresholded p<.01) sig=-log10(p) “Massive Univariate Analysis” -- Analyze each voxel separately

12 Is Pattern Repeatable Across Subject? Subject 1Subject 2Subject 3Subject 4Subject 5

13 Spatial Normalization Subject 1 Subject 2 Subject 1 Subject 2 MNI305 Native SpaceMNI305 Space Affine (12 DOF) Registration

14 Group Analysis Does not have to be all positive!

15 “Random Effects (RFx)” Analysis RFx

16 “Random Effects (RFx)” Analysis RFx Model Subjects as a Random Effect Variance comes from a single source: variance across subjects –Mean at the population mean –Variance of the population variance Does not take first-level noise into account (assumes 0) “Ordinary” Least Squares (OLS) Usually less activation than individuals Sometimes more

17 “Mixed Effects (MFx)” Analysis MFx RFx Down-weight each subject based on variance. Weighted Least Squares vs (“Ordinary” LS)

18 “Mixed Effects (MFx)” Analysis MFx Down-weight each subject based on variance. Weighted Least Squares vs (“Ordinary” LS) Protects against unequal variances across group or groups (“heteroskedasticity”) May increase or decrease significance with respect to simple Random Effects More complicated to compute “Pseudo-MFx” – simply weight by first-level variance (easy to compute)

19 “Fixed Effects (FFx)” Analysis FFx RFx

20 “Fixed Effects (FFx)” Analysis FFx As if all subjects treated as a single subject (fixed effect) Small error bars (with respect to RFx) Large DOF Same mean as RFx Huge areas of activation Not generalizable beyond sample.

21 Multi-Level Analysis First Level (Time-Series) GLM Design Matrix (X) Contrast Matrix (C) Contrast Size ( Signed) Contrast Variance p/t/F/z Raw Data at a Voxel Visualize Higher Level ROI Volume Not recommended. Noisy.

22 Higher Level GLM First Level C Contrast Size 1 Subject 1 First Level C Contrast Size 2 Subject 2 First Level C Contrast Size 3 Subject 3 First Level C Contrast Size 4 Subject 4 Multi-Level Analysis

23 Higher Level GLM Analysis = GG y = X *  Data from one voxel Design Matrix (Regressors) Vector of Regression Coefficients (“Betas”) Observations (Low-Level Contrasts) Contrast Matrix: C = [1] Contrast = C*  =  G One-Sample Group Mean (OSGM)

24 Two Groups GLM Analysis =  G1  G2 y = X *  Data from one voxel Observations (Low-Level Contrasts)

25 Contrasts: Two Groups GLM Analysis 1. Does Group 1 by itself differ from 0? C = [1 0], Contrast = C*  =  G1 =  G1  G Does Group 2 by itself differ from 0? C = [0 1], Contrast = C*  =  G2 3. Does Group 1 differ from Group 2? C = [1 -1], Contrast = C*  =  G1 -  G2 4. Does either Group 1 or Group 2 differ from 0? C has two rows: F-test (vs t-test) Concatenation of contrasts #1 and # C =

26 One Group, One Covariate (Age) =  G  Age y = X *  Data from one voxel Observations (Low-Level Contrasts) Intercept:  G Slope:  Age Contrast Age

27 Contrasts: One Group, One Covariate 1.Does Group offset/intercept differ from 0? Does Group mean differ from 0 regressing out age? C = [1 0], Contrast = C*  =  G (Treat age as nuisance) =  G  Age Does Slope differ from 0? C = [0 1], Contrast = C*  =  Age Intercept:  G Slope:  Age Contrast Age

28 Two Groups, One Covariate Somewhat more complicated design Slopes may differ between the groups What are you interested in? Differences between intercepts? Ie, treat covariate as a nuisance? Differences between slopes? Ie, an interaction between group and covariate?

29 Two Groups, One (Nuisance) Covariate Is there a difference between the group means? Synthetic Data

30 Raw DataEffect of Age Means After Age “Regressed Out” (Intercept, Age=0) No difference between groups Groups are not well matched for age No group effect after accounting for age Age is a “nuisance” variable (but important!) Slope with respect to Age is same across groups Two Groups, One (Nuisance) Covariate

31 =  G1  G2  Age y = X *  Data from one voxel Observations (Low-Level Contrasts) Two Groups, One (Nuisance) Covariate One regressor for Age. Different Offset Same Slope (DOSS)

32 =  G1  G2  Age Two Groups, One (Nuisance) Covariate One regressor for Age indicates that groups have same slope – makes difference between group means/intercepts independent of age. Different Offset Same Slope (DOSS)

33 Contrasts: Two Groups + Covariate 1. Does Group 1 mean differ from 0 (after regressing out effect of age)? C = [1 0 0], Contrast = C*  =  G1 2. Does Group 2 mean differ from 0 (after regressing out effect of age)? C = [0 1 0], Contrast = C*  =  G2 3. Does Group 1 mean differ from Group 2 mean (after regressing out effect of age)? C = [1 -1 0], Contrast = C*  =  G1 -  G2 =  G1  G2  Age

34 =  G1  G2  Age Does Slope differ from 0 (after regressing out the effect of group)? Does not have to be a “nuisance”! C = [0 0 1], Contrast = C*  =  Age Contrasts: Two Groups + Covariate

35 Slope with respect to Age differs between groups Interaction between Group and Age Intercept different as well Group/Covariate Interaction

36 =  G1  G2  Age1  Age2 y = X *  Data from one voxel Observations (Low-Level Contrasts) Group-by-Age Interaction Different Offset Different Slope (DODS) Group/Covariate Interaction

37 1.Does Slope differ between groups? Is there an interaction between group and age? C = [ ], Contrast = C*  =  Age1 -  Age1 Group/Covariate Interaction =  G1  G2  Age1  Age

38 Group/Covariate Interaction =  G1  G2  Age1  Age Does this contrast make sense? 2. Does Group 1 mean differ from Group 2 mean (after regressing out effect of age)? C = [ ], Contrast = C*  =  G1 -  G2 Very tricky! This tests for difference at Age=0 What about Age = 12? What about Age = 20?

39 Group/Covariate Interaction If you are interested in the difference between the means but you are concerned there could be a difference (interaction) in the slopes: 1.Analyze with interaction model (DODS) 2.Test for a difference in slopes 3.If there is no difference, re-analyze with single regressor model (DOSS) 4.If there is a difference, proceed with caution

40 Interaction between Condition and Group Example: Two First-Level Conditions: Angry and Neutral Faces Two Groups: Healthy and Schizophrenia Desired Contrast = (Neutral-Angry) Sch - (Neutral-Angry) Healthy Two-level approach 1.Create First Level Contrast (Neutral-Angry) 2.Second Level: Create Design with Two Groups Test for a Group Difference

41 Longitudinal Visit 1 Visit 2 Subject 1Subject 2Subject 3Subject 4Subject 5

42 Longitudinal Did something change between visits? Drug or Behavioral Intervention? Training? Disease Progression? Aging? Injury? Scanner Upgrade?

43 Longitudinal Paired Differences Between Subjects Subject 1, Visit 1 Subject 1, Visit 2

44 Longitudinal Paired Analysis = VV y = X *  Paired Diffs from one voxel Design Matrix (Regressors) Observations (V1-V2 Differences in Low-Level Contrasts) Contrast Matrix: C = [1] Contrast = C*  =   V One-Sample Group Mean (OSGM): Paired t-Test

45 fMRI Analysis Overview Higher Level GLM First Level GLM Analysis First Level GLM Analysis Subject 3 First Level GLM Analysis Subject 4 First Level GLM Analysis Subject 1 Subject 2 CX CX CX CX Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Raw Data CX

46 Summary Higher Level uses Lower Level Results –Contrast and Variance of Contrast Variance Models –Random Effects –Mixed Effects – protects against heteroskedasticity –Fixed Effects – cannot generalize beyond sample Groups and Covariates (Intercepts and Slopes) Covariate/Group Interactions Longitudinal – Paired Differences

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