FMRI Data Analysis I Basic Analyses and the

FMRI Data Analysis: I. Basic Analyses and the General Linear Model FMRI Graduate Course (NBIO 381, PSY 362) Dr. Scott Huettel, Course Director FMRI – Week 9 – Analysis I Scott Huettel, Duke University

When do we not need statistical analysis? Inter-ocular Trauma Test (Lockhead, personal communication) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Why use statistical analyses? • Replaces simple subtractive methods – Signal highly corrupted by noise • Typical SNRs: 0. 2 – 0. 5 – Sources of noise • Thermal variation (unstructured) • Physiological, task variability (structured) • Assesses quality of data – How reliable is an effect? – Allows distinction of weak, true effects from strong, noisy effects FMRI – Week 9 – Analysis I Scott Huettel, Duke University

What do our analyses generate? • Statistical Parametric Maps • Brain maps of statistical quality of measurement – Examples: correlation, regression approaches – Displays likelihood that the effect observed is due to chance factors – Typically expressed in probability (e. g. , p < 0. 001), or via t or z statistics FMRI – Week 9 – Analysis I Scott Huettel, Duke University

What are our statistics for? FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Key Concepts • Within-subjects analyses – Simple non-GLM approaches (older) – General Linear Model (GLM) • Across-subjects analyses – Fixed vs. Random effects • Correction for Multiple Comparisons • Displaying Data FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Simple Hypothesis-Driven Analyses • • t-test across conditions Time point analysis (i. e. , t-test) Correlation Fourier analysis FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Correlation Approaches (old-school) • How well does our data match an expected hemodynamic response? • Special case of General Linear Model • Limited by choice of HDR – Assumes particular correlation template – Does not model task-unrelated variability – Does not model interactions between events FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Fourier Analysis • Fourier transform: converts information in time domain to frequency domain – Used to change a raw time course to a power spectrum – Hypothesis: any repetitive/blocked task should have power at the task frequency • BIAC function: FFTMR – Calculates frequency and phase plots for time series data. • Equivalent to correlation in frequency domain • Subset of general linear model – Same as if used sine and cosine as regressors FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Power 12 s on, 12 s off FMRI – Week 9 – Analysis I Frequency (Hz) Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

The General Linear Model (GLM) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Basic Concepts of the GLM • GLM treats the data as a linear combination of model functions plus noise – Model functions have known shapes – Amplitude of functions are unknown – Assumes linearity of HDR; nonlinearities can be modeled explicitly • GLM analysis determines set of amplitude values that best account for data – Usual cost function: least-squares deviance of residual after modeling (noise) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Signal, noise, and the General Linear Model Amplitude (solve for) Measured Data Noise Design Model Cf. Boynton et al. , 1996 FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Form of the GLM FMRI – Week 9 – Analysis I Model Functions * Amplitudes + Noise N Time Points = Data N Time Points Model Functions Scott Huettel, Duke University

Design Matrices Images Model Parameters FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Regressors (How much of the variance in the data does each explain? ) Contrasts (Does one regressor explain more variance than another? ) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Task and Nuisance Regressors Task Regressors FMRI – Week 9 – Analysis I Nuisance (Motion) Regressors Scott Huettel, Duke University

Hemodynamic and Basis Functions Double Gamma Gaussian Gamma FMRI – Week 9 – Analysis I Scott Huettel, Duke University

The optimal relation between regressors depends on our research question FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Suppose that we have two correlated regressors. R 1: Motor? Because of their correlation, the design is inefficient at distinguishing the contributions of R 1 and R 2 to the activation of a voxel. Value of R 2 (at each point in time) R 2: Visual? X = Y Value of R 1 (at each point in time) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Now, the design allows us to separate the contributions of each regressor, but cannot look at their common effect. Value of R 2 (at each point in time) Let’s now make the regressors anti-correlated. X = -Y Value of R 1 (at each point in time) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

This makes the activation uncorrelated, but doesn’t efficiently use the space. Value of R 2 (at each point in time) We can shift our block design in time, so that the regressors are off-set. X X = = -Y Y Value of R 1 (at each point in time) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Now, we get more of a “cloud” arrangement of the time points. (Squareness and lack of evenness is caused by my simulation approach) Value of R 2 (at each point in time) And, we can make the regressors uncorrelated with each other through randomization. Value of R 1 (at each point in time) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Orthogonalization of Regressors Non. Orthogonal Cue Regressor Orthogonal FMRI – Week 9 – Analysis I Target Regressor (Orthogonalized) Scott Huettel, Duke University

Setting up Parametric Effects 1 2 3 Parametric Effect Constant Effect 4 FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Fixed and Random Effects Comparisons FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Fixed Effects • Fixed-effects Model – Assumes that effect is constant (“fixed”) in the population – Uses data from all subjects to construct statistical test – Examples • Averaging across subjects before a t-test • Taking all subjects’ data and then doing an ANOVA – Allows inference to subject sample FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Random Effects • Random-effects Model – – – Assumes that effect varies across the population Accounts for inter-subject variance in analyses Allows inferences to population from which subjects are drawn Especially important for group comparisons Required by many reviewers/journals FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Key Concepts of Random Effects • Assumes that activation parameters may vary across subjects – Since subjects are randomly chosen, activation parameters may vary within group – (Fixed-effects models assume that parameters are constant across individuals) • Calculates descriptive statistic for each subject – i. e. , parameter estimate from regression model • Uses all subjects’ statistics in a higher-level analysis – i. e. , group significance based on the distribution of subjects’ values. FMRI – Week 9 – Analysis I Scott Huettel, Duke University

The Problem of Multiple Comparisons P < 0. 05 (1682 voxels) FMRI – Week 9 – Analysis I P < 0. 01 (364 voxels) P < 0. 001 (32 voxels) Scott Huettel, Duke University

A t = 2. 10, p < 0. 05 (uncorrected) FMRI – Week 9 – Analysis I B C t = 3. 60, p < 0. 001 (uncorrected) t = 7. 15, p < 0. 05, Bonferroni Corrected Scott Huettel, Duke University

Options for Multiple Comparisons • Statistical Correction (e. g. , Bonferroni) – Family-wise Error Rate – False Discovery Rate (FDR) • Cluster Analyses • ROI Approaches FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Statistical Corrections • If more than one test is made, then the collective alpha value is greater than the single -test alpha – That is, overall Type I error increases • One option is to adjust the alpha value of the individual tests to maintain an overall alpha value at an acceptable level – This procedure controls for overall Type I error – Known as Bonferroni Correction FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Bonferroni Correction • Very severe correction – Results in very strict significance values – Typical brain may have up to ~30, 000 functional voxels • P(Type I error) ~ 1. 0 ; Corrected alpha ~ 0. 000003 • Greatly increases Type II error rate • Is not appropriate for correlated data – If data set contains correlated data points, then the effective number of statistical tests may be greatly reduced – Most f. MRI data has significant correlation FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Gaussian Field Theory • Approach developed by Worsley and colleagues to account for multiple comparisons • Provides false positive rate for f. MRI data based upon the smoothness of the data – If data are very smooth, then the chance of noise points passing threshold is reduced • Recommendation: Use a combination of voxel and cluster correction methods FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Cluster Analyses • Assumptions – Assumption I: Areas of true f. MRI activity will typically extend over multiple voxels – Assumption II: The probability of observing an activation of a given voxel extent can be calculated • Cluster size thresholds can be used to reject false positive activity – Forman et al. , Mag. Res. Med. (1995) – Xiong et al. , Hum. Brain Map. (1995) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

How many foci of activation? Data from motor/visual event-related task (used in laboratory) FMRI – Week 9 – Analysis I Scott Huettel, Duke University

How large should clusters be? • At typical alpha values, even small cluster sizes provide good correction – Spatially Uncorrelated Voxels • At alpha = 0. 001, cluster size 3 • Type 1 rate to << 0. 00001 per voxel – Highly correlated Voxels • Smoothing (FW = 0. 5 voxels) • Increases needed cluster size to 7 or more voxels • Efficacy of cluster analysis depends upon shape and size of f. MRI activity – Not as effective for non-convex regions – Power drops off rapidly if cluster size > activation size Data from Forman et al. , 1995 FMRI – Week 9 – Analysis I Scott Huettel, Duke University

False Discovery Rate • Controls the expected proportion of false positive values among suprathreshold values – Genovese, Lazar, and Nichols (2002, Neuro. Image) – Does not control for chance of any face positives • FDR threshold determined based upon observed distribution of activity – So, sensitivity increases because metric becomes more lenient as voxels become significant FMRI – Week 9 – Analysis I Scott Huettel, Duke University

(sum) Genovese, et al. , 2002 FMRI – Week 9 – Analysis I Scott Huettel, Duke University

ROI Comparisons • Changes basis of statistical tests – Voxels: ~16, 000 – ROIs : ~ 1 – 100 • Each ROI can be thought of as a very large volume element (e. g. , voxel) – Anatomically-based ROIs do not introduce bias • Potential problems with using functional ROIs – Functional ROIs result from statistical tests – Therefore, they cannot be used (in themselves) to reduce the number of comparisons FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Voxel and ROI analyses are similar, in concept FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Summary of Multiple Comparison Correction • Basic statistical corrections are often too severe for f. MRI data • What are the relative consequences of different error types? – Correction decreases Type I rate: fewer false positives – Correction increases Type II rate: more misses • Alternate approaches may be more appropriate for f. MRI – – Cluster analyses Region of interest approaches Smoothing and Gaussian Field Theory False Discovery Rate FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Displaying Data FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Never Mask! FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

FMRI – Week 9 – Analysis I Scott Huettel, Duke University

Summary of Basic Analysis Methods • Simple experimental designs – Blocked: t-test, Fourier analysis – Event-related: correlation, t-test at time points • Complex experimental designs – Regression approaches (GLM) • Critical problem: Minimization of Type I Error – Strict Bonferroni correction is too severe – Cluster analyses improve – Accounting for smoothness of data also helps • Use random-effects analyses to allow generalization to the population FMRI – Week 9 – Analysis I Scott Huettel, Duke University