Statistical Analysis An Introduction to MRI Physics and Analysis Michael Jay Schillaci, PhD Monday, April 7 th, 2007 Outline Statistical Concepts Standard Analysis of fMRI Data Voxel-based analysis Statistical Parametric Mapping Cluster Analysis Methods ROI Analysis Methods 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 Simple Hypothesis-Driven Analyses t-test across conditions Time point analysis (i.e., t-test) Correlation Fourier analysis 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 Suppose that we have two correlated regressors. R1: Motor? R2: Visual? Value of R1 (at each point in time) Value of R2 (at each point in time) Because of their correlation, the design is inefficient at distinguishing the contributions of R1 and R2 to the activation of a voxel. X = Y Lets now make the regressors anti-correlated. Value of R1 (at each point in time) Value of R2 (at each point in time) Now, the design allows us to separate the contributions of each regressor, but cannot look at their common effect. X = -Y Value of R1 (at each point in time) Value of R2 (at each point in time) This makes the activation uncorrelated, but doesnt efficiently use the space. We can shift our block design in time, so that the regressors are off-set. X = -Y X = Y And, we can make the regressors uncorrelated with each other through randomization. Value of R1 (at each point in time) Value of R2 (at each point in time) Now, we get more of a cloud arrangement of the time points. (Squareness and lack of evenness is caused by my simulation approach) 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 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 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. The Problem of Multiple Comparisons P < (32 voxels)P < 0.01 (364 voxels)P < 0.05 (1682 voxels) fMRI Analysis Individual voxel time series not efficient or quantitative SNR and Age An Example Spatial mean over 426 non- activated voxels Spatial mean over 426 activated voxels Average Signal for Multiple Stimulations Huettel et al. (2001) Two studies report that the BOLD signal has reduced signal-noise ratio (SNR) in elderly adults. DEsposito et al. (1999) YEE/Y fMRI study Predicted Model Statistical Parametric Mapping (SPM)K. J. Friston, UCL, UK Data Preprocessing Smoothing (): Convolution with Gaussian kernel Reduced effects of noise General Linear Model (GLM) GLM matrices Correlation maps fMRI study Cluster Analyses Assumptions Assumption I: Areas of true fMRI 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) How many foci of activation? Data from motor/visual event-related task (used in laboratory) 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 activation size Data from Forman et al., 1995 False Discovery Rate Controls the expected proportion of false positive values among suprathreshold values Genovese, Lazar, and Nichols (2002, NeuroImage) 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 Genovese, et al., 2002 (sum) 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 Voxel and ROI analyses are similar, in concept