FMRI data analysis – t-tests and correlations.. Hypotheses vs. Data Hypothesis-driven Examples:...
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Transcript of FMRI data analysis – t-tests and correlations.. Hypotheses vs. Data Hypothesis-driven Examples:...
Hypotheses vs. DataHypothesis-drivenExamples: 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-drivenIndependent 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
• 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
Simple vs complex finger tapping sequences
• head coil• 19 quasi-axial slices• volume time = 4 sec• 3 x 3 x 6 voxels
• 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
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sequential tapping alternating tapping
Statistical Analyses: T-testT-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
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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
simple shift of function to
accommodate HRF
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T-test: Stats
Repeat this process 49,152 more times (64x64x12), once for each voxel in the volume obtained.
To look for Complex vs. Simple tapping activation, for a given voxel:
Measure average MR signal and SD for each volume in which simple tapping was performed (10 volumes)
simple
Measure average MR signal and SD for each volume in which complex tapping was performed (2 epochs x 5 volumes/epoch = 10 volumes)
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Notice a problem yet?… With a probability of .001 and 49,152 voxels, 49152*.001 = 49 voxels could be significant purely by chance
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)
C>SS>C
complex simple
To look for Simple > Complex tapping activation, look at the negative tail of the comparison
T-test: MapsFor each voxel in the brain, we can now color code a map based on the computed t and p values:
And we can also do this for the negative tail (Simple > Complex tapping)Blue = low significanceGreen = high significance
We can do this for the positive tail (Complex > Simple tapping)Orange = low significanceYellow = high significance
Schmutz or ESP voxels?
T-test: SurfingWe can surf the significant voxels to see what their time courses look like
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Creating event related averages.• sync activation to same starting point• average across epochs (determine variance)• compare activation in a given area
Correcting for linear trendsWe can surf the significant voxels to see what their time courses look like
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
1) If it is correlated with our paradigm, it could give us false positives or false rejections
2) It adds extra variability to our statistical computations and makes it less likely to reach significance
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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)/baselineusually 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 peaksignal peaks 4-6 sec after stimulus begins
post stimulus undershootsignal suppressed after stimulation ends
Correlations: Incorporating the HRFWe can model the expected curve of the data by convolving our predictor with the hemodynamic response function.
To find a region responsive to complex tapping AND simple tapping, we can correlate the convolved model predictor with each voxel time course
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standard box-car function
Statistical Analyses: Basic CorrelationCorrelation 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)
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%
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Problems with t-tests and correlations
Design Matrix
1) 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?
If this predictor is significant, we won’t know if it’s because complex>simple OR because complex>rest
Stay tuned next week for the solution: General Linear Model
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Two approaches: ROI
Source: Tootell et al., 1995
A. ROI approach
1. Do (a) localizer run(s) to find a region (e.g., show moving rings to find MT)2. Extract time course information from that region in separate independent runs3. 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
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)
Example study: Tootell et al, 1995, Motion Aftereffect
MT
Two Approaches: Whole Brain Stats
Source: Tootell et al., 1995
B. Whole volume statistical approach
1. Make predictions about what differences you should see if your hypotheses are correct2. Decide on statistical measures to test for predicted differences (e.g., t-tests, correlations,
GLMs)3. Determine appropriate statistical threshold4. See if statistical estimates are significant
Statistics available1. t-test2. correlation3. Fourier modelling (not discussed here – popular in the Stanford group – see brief description
in Buxton Ch 18)4. General Linear Model
-overarching statistical model that lets you perform many types of statistical analyses (including correlations, ANOVAs)
Comparing the two approaches
Source: Tootell et al., 1995
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.
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