fMRI data analysis – t-tests and correlations.

Hypotheses vs. Data Hypothesis-driven Data-driven Examples: t-tests, correlations, general linear model (GLM) a priori model of activation is suggested comparison between data and model is made most commonly used approach Data-driven Independent Component Analysis (ICA) no prior hypotheses are necessary – operates somewhat like factor analysis multivariate techniques determine the patterns in the data that account for the most variance across all voxels can be used to validate a model (see if the math comes up with the components you would’ve predicted) can be inspected to see if there are things happening in your data that you didn’t predict need a way to organize the many possible components new and upcoming

Why do we need statistics? MR Signal intensities are arbitrary -vary from magnet to magnet, coil to coil, within a coil (especially surface coil), day to day, even run to run -may also vary from area to area (some areas may be more metabolically active) We must always have a comparison condition within the same run (baseline or control contrasts) We need to know whether the “eyeball tests of significance” are real. Because we do so many comparisons, we need a way to compensate (e.g., Bonferroni, clusters, etc.).

Example Experiment Simple vs complex finger tapping sequences protocol experiment in patient SP – with large porencephalic syst Purpose: Can we identify regions responding to simple and complex motor tasks in remaining left hemisphere cortex 3 conditions – simple alternating tapping (tap index and middle fingers alternately for 20 seconds), complex tapping (tap fingers in sequences indicated on screen) and rest protocol images 1 21 41 % s i g n a l c h e 2 3 -1 head coil 19 quasi-axial slices volume time = 4 sec 3 x 3 x 6 voxels sequential tapping alternating tapping

Statistical Analyses: T-test simple, sometimes seems more reliable than fancy stuff compare the means and standard deviations between two conditions shift activation to compensate for hemodynamic lag (HDL) – assume a 4- 6 sec lag so with a 4 sec TR this would be a one or two volume shift (can’t do a one a half volume shift) given that only means are tested the shift for the HDL is not an accurate model of the function each voxel considered an ‘n’ – so Bonferroni correction is made for the number of voxels compared images 1 21 41 % s i g n a l c h e 2 3 -1 simple shift of function to accommodate HRF Kolmogorov-Smirnov non-parametric version of t-test – instead of comparing means of two populations, the cumulative distributions are compared sensitive to differences in variance as well as means – so could detect a difference between two populations with the same means but different SDs (t-test can’t do this) more conservative than t-tests

T-test: Stats e h c l a n g i s % images To look for Complex vs. Simple tapping activation, for a given voxel: Measure average MR signal and SD for each volume in which complex tapping was performed (2 epochs x 5 volumes/epoch = 10 volumes) images 1 21 41 % s i g n a l c h e 2 3 -1 Measure average MR signal and SD for each volume in which simple tapping was performed (10 volumes) complex simple To look for Simple > Complex tapping activation, look at the negative tail of the comparison S>C C>S MR Signal Determine if mean difference is statistically significant: Calculate t-value. Use t to look up p value for that number of degrees of freedom (df = 10 x 2 = 20). e.g., For ~20 df t >1.98  p <.05 (1/20 chance) t > 3.39  p < .001 (1/1000 chance) complex simple Notice a problem yet?… With a probability of .001 and 49,152 voxels, 49152*.001 = 49 voxels could be significant purely by chance Repeat this process 49,152 more times (64x64x12), once for each voxel in the volume obtained.

T-test: Maps For each voxel in the brain, we can now color code a map based on the computed t and p values: We can do this for the positive tail (Complex > Simple tapping) Orange = low significance Yellow = high significance Schmutz or ESP voxels? And we can also do this for the negative tail (Simple > Complex tapping) Blue = low significance Green = high significance

T-test: Surfing We can surf the significant voxels to see what their time courses look like s g l c h a n e 1 21 6.0 4.0 2.0 0.0 -2.0 % i 41 images 6 4 2 -1 1 3 5 % s i g n a l c h e images Creating event related averages. sync activation to same starting point average across epochs (determine variance) compare activation in a given area

Correcting for linear trends We can surf the significant voxels to see what their time courses look like 6.0 4.0 2.0 0.0 -2.0 % s i g n a l c h e 1 21 41 images Linear trend - could be due to magnet (e.g., warming up) or subject (e.g., head slowly settling) Bad paradigm design – linear confound Problematic for two reasons If it is correlated with our paradigm, it could give us false positives or false rejections It adds extra variability to our statistical computations and makes it less likely to reach significance

Linear Trend Removal After LTR, significance levels increase considerably.

Linear Trend Removal Because our statistics are now more reliable, we can bump up the threshold and get rid of some of the schmutz. We can also superimpose the stat map on top of the anatomical image to compare it to landmarks.

Hemodynamic Response Function % signal change = (point – baseline)/baseline usually 0.5-3% initial dip -more focal and potentially a better measure -somewhat elusive so far, not everyone can find it time to rise signal begins to rise soon after stimulus begins time to peak signal peaks 4-6 sec after stimulus begins post stimulus undershoot signal suppressed after stimulation ends

Correlations: Incorporating the HRF We can model the expected curve of the data by convolving our predictor with the hemodynamic response function. basic model standard box-car function convolved model To find a region responsive to complex tapping AND simple tapping, we can correlate the convolved model predictor with each voxel time course fMRI signal

Statistical Analyses: Basic Correlation Correlation analysis voxels with time course correlated with reference function can incorporate hemodynamic response function (HRF) to predict time course more accurately (compared with simple shifting of the function in t-tests) value of fMRI signal volumes For each voxel: Find the correlation between the predictor and the MR signal Extract the correlation (r value) and find the corresponding p value. Determine whether it is statistically significant In this example, similar in spirit to a t-test. Remember r2 is the proportion of variance accounted for by our predictor, e.g., if r = .7, r2 = .5 = 50%

Problems with t-tests and correlations How do we evaluate runs with different orders? Right now, we could average our two runs done in Order1 together, and also average our two runs done in Order2 together and then do stats on the two orders separately. There is no way to collapse between orders. If there is an artifact on part of one run, we have to exclude the whole run. 2) If we test more subjects, how can we evaluate the subjects together? As with the single subject runs, we could average all the subjects together (after morphing them into a common brain space) but that still means we have to run all of them in the same order. 2) We can get nice hemodynamic predictors for simple vs. complex finger tapping but how can we compare them accurately? convolved model If this predictor is significant, we won’t know if it’s because complex>simple OR because complex>rest Design Matrix Stay tuned next week for the solution: General Linear Model

Two approaches: ROI A. ROI approach MT Do (a) localizer run(s) to find a region (e.g., show moving rings to find MT) Extract time course information from that region in separate independent runs See if the trends in that region are statistically significant Because the runs that are used to generate the area are independent from those used to test the hypothesis, liberal statistics can be used Example study: Tootell et al, 1995, Motion Aftereffect Localize “motion area” MT in a run comparing moving vs. stationary rings Extract time courses from MT in subsequent runs while subjects see illusory motion (motion aftereffect) MT Source: Tootell et al., 1995

Two Approaches: Whole Brain Stats B. Whole volume statistical approach Make predictions about what differences you should see if your hypotheses are correct Decide on statistical measures to test for predicted differences (e.g., t-tests, correlations, GLMs) Determine appropriate statistical threshold See if statistical estimates are significant Statistics available t-test correlation Fourier modelling (not discussed here – popular in the Stanford group – see brief description in Buxton Ch 18) General Linear Model -overarching statistical model that lets you perform many types of statistical analyses (including correlations, ANOVAs) Source: Tootell et al., 1995

Comparing the two approaches Region of Interest (ROI) Analyses Gives you more statistical power because you do not have to correct for the number of comparisons Hypothesis-driven ROI is not smeared due to intersubject averaging Easy to analyze and interpret Neglects other areas which may play a fundamental role Popular in North America Whole Brain Analysis Requires no prior hypotheses about areas involved Includes entire brain Can lose spatial resolution with intersubject averaging Can produce meaningless “laundry lists of areas” that are difficult to interpret Depends highly on statistics and threshold selected Popular in Europe NOTE: Though different experimenters tend to prefer one method over the other, they are NOT mutually exclusive. You can check ROIs you predicted and then check the data for other areas. Source: Tootell et al., 1995