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Basics of fMRI Group Analysis

Basics of fMRI Group Analysis. Douglas N. Greve. fMRI Analysis Overview. Subject 1. Preprocessing MC, STC, B0 Smoothing Normalization. Preprocessing MC, STC, B0 Smoothing Normalization. Preprocessing MC, STC, B0 Smoothing Normalization. Preprocessing MC, STC, B0 Smoothing

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Basics of fMRI Group Analysis

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  1. Basics of fMRI Group Analysis Douglas N. Greve

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

  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. Sample 18 Subjects Population vs Sample Group Population (All members) Hundreds? Thousands? Billions? • 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 Note: z, t, F monotonic with p p = 10-11, sig=-log10(p) =11 p = .10, sig=-log10(p) =1

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

  10. Contrasts and the Full Model

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

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

  13. Spatial Normalization Native Space MNI305 Space Subject 1 Subject 1 MNI305 Subject 2 Subject 2 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 Raw Data at a Voxel Contrast Size (Signed) First Level (Time-Series) GLM Higher Level Contrast Variance ROI Volume p/t/F/z Contrast Matrix (C) Not recommended. Noisy. Visualize Design Matrix (X)

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

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

  24. Two Groups GLM Analysis bG1 bG2 y = X * b 1 1 1 0 0 0 0 0 1 1 = Observations (Low-Level Contrasts) Data from one voxel

  25. Contrasts: Two Groups GLM Analysis bG1 bG2 1 1 1 0 0 0 0 0 1 1 = 1 0 0 1 C = 1. Does Group 1 by itself differ from 0? C = [1 0], Contrast = C*b = bG1 2. Does Group 2 by itself differ from 0? C = [0 1], Contrast = C*b = bG2 3. Does Group 1 differ from Group 2? C = [1 -1], Contrast = C*b = bG1-bG2 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

  26. One Group, One Covariate (Age) Intercept: bG Contrast bG bAge Slope: bAge Age y = X * b 1 1 1 1 1 21 33 64 17 47 = Observations (Low-Level Contrasts) Data from one voxel

  27. Contrasts: One Group, One Covariate Intercept: bG Contrast bG bAge 1 1 1 1 1 21 33 64 17 47 Slope: bAge = Age • Does Group offset/intercept differ from 0? • Does Group mean differ from 0 regressing out age? • C = [1 0], Contrast = C*b = bG • (Treat age as nuisance) 2. Does Slope differ from 0? C = [0 1], Contrast = C*b = bAge

  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. Two Groups, One (Nuisance) Covariate Means After Age “Regressed Out” (Intercept, Age=0) Raw Data Effect of Age • 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

  31. Two Groups, One (Nuisance) Covariate y = X * b bG1 bG2 bAge 1 1 1 0 0 0 0 0 1 1 21 33 64 17 47 = Observations (Low-Level Contrasts) One regressor for Age. Data from one voxel Different Offset Same Slope (DOSS)

  32. Two Groups, One (Nuisance) Covariate One regressor for Age indicates that groups have same slope – makes difference between group means/intercepts independent of age. bG1 bG2 bAge 1 1 1 0 0 0 0 0 1 1 21 33 64 17 47 = Different Offset Same Slope (DOSS)

  33. Contrasts: Two Groups + Covariate bG1 bG2 bAge 1 1 1 0 0 0 0 0 1 1 21 33 64 17 47 = 1. Does Group 1 mean differ from 0 (after regressing out effect of age)? C = [1 0 0], Contrast = C*b = bG1 2. Does Group 2 mean differ from 0 (after regressing out effect of age)? C = [0 1 0], Contrast = C*b = bG2 3. Does Group 1 mean differ from Group 2 mean (after regressing out effect of age)? C = [1 -1 0], Contrast = C*b = bG1-bG2

  34. Contrasts: Two Groups + Covariate bG1 bG2 bAge 1 1 1 0 0 0 0 0 1 1 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*b = bAge

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

  36. Group/Covariate Interaction y = X * b bG1 bG2 bAge1 bAge2 1 1 1 0 0 0 0 0 1 1 21 33 64 0 0 0 0 0 17 47 = Observations (Low-Level Contrasts) Group-by-Age Interaction Data from one voxel Different Offset Different Slope (DODS)

  37. Group/Covariate Interaction 1 1 1 0 0 0 0 0 1 1 21 33 64 0 0 0 0 0 17 47 bG1 bG2 bAge1 bAge2 = • Does Slope differ between groups? • Is there an interaction between group and age? • C = [0 0 1 -1], Contrast = C*b = bAge1-bAge1

  38. Group/Covariate Interaction 1 1 1 0 0 0 0 0 1 1 21 33 64 0 0 0 0 0 17 47 bG1 bG2 bAge1 bAge2 = 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*b = bG1-bG2 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: • Analyze with interaction model (DODS) • Test for a difference in slopes • If there is no difference, re-analyze with single regressor model (DOSS) • 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 • Create First Level Contrast (Neutral-Angry) • Second Level: • Create Design with Two Groups • Test for a Group Difference

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

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

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

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

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

  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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