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Basics of fMRI Group Analysis Douglas N. Greve

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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

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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

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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?

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5 Functional Anatomy/Brain Mapping

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

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7 Block Design: 15s Off, 15s On

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

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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

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10 Contrasts and the Full Model

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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

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

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

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14 Group Analysis Does not have to be all positive!

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15 “Random Effects (RFx)” Analysis RFx

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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

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

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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)

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19 “Fixed Effects (FFx)” Analysis FFx RFx

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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.

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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.

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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

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23 Higher Level GLM Analysis = 1111111111 GG 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)

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24 Two Groups GLM Analysis = 1110011100 G1 G2 y = X * Data from one voxel Observations (Low-Level Contrasts) 0001100011

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25 Contrasts: Two Groups GLM Analysis 1. Does Group 1 by itself differ from 0? C = [1 0], Contrast = C* = G1 = 1110011100 G1 G2 0001100011 2. 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 #2 1 0 0 1 C =

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26 One Group, One Covariate (Age) = 1111111111 G Age y = X * Data from one voxel Observations (Low-Level Contrasts) 21 33 64 17 47 Intercept: G Slope: Age Contrast Age

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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) = 1111111111 G Age 21 33 64 17 47 2. Does Slope differ from 0? C = [0 1], Contrast = C* = Age Intercept: G Slope: Age Contrast Age

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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?

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

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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

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31 = 1110011100 G1 G2 Age y = X * Data from one voxel Observations (Low-Level Contrasts) 0001100011 21 33 64 17 47 Two Groups, One (Nuisance) Covariate One regressor for Age. Different Offset Same Slope (DOSS)

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32 = 1110011100 G1 G2 Age 0001100011 21 33 64 17 47 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)

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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 = 1110011100 G1 G2 Age 0001100011 21 33 64 17 47

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34 = 1110011100 G1 G2 Age 0001100011 21 33 64 17 47 4. 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

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

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36 = 1110011100 G1 G2 Age1 Age2 y = X * Data from one voxel Observations (Low-Level Contrasts) 0001100011 21 33 64 0 17 47 Group-by-Age Interaction Different Offset Different Slope (DODS) Group/Covariate Interaction

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37 1.Does Slope differ between groups? Is there an interaction between group and age? C = [0 0 1 -1], Contrast = C* = Age1 - Age1 Group/Covariate Interaction = 1110011100 G1 G2 Age1 Age2 0001100011 21 33 64 0 17 47

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38 Group/Covariate Interaction = 1110011100 G1 G2 Age1 Age2 0001100011 21 33 64 0 17 47 Does this contrast make sense? 2. Does Group 1 mean differ from Group 2 mean (after regressing out effect of age)? C = [1 -1 0 0], Contrast = C* = G1 - G2 Very tricky! This tests for difference at Age=0 What about Age = 12? What about Age = 20?

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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

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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

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

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

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

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44 Longitudinal Paired Analysis = 1111111111 VV 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

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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

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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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