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Intersubject Heterogeneity in fMRI RFX Analysis

Intersubject Heterogeneity in fMRI RFX Analysis. Morning Workshop, OHBM 2005 Organizers Thomas Nichols, Stephen Smith & Jean-Baptist Poline Speakers Thomas Nichols, Jean-Baptist Poline, Christian Beckmann. Distribution of each subject’s estimated effect. Fixed vs. Random Effects in fMRI.

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Intersubject Heterogeneity in fMRI RFX Analysis

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  1. Intersubject Heterogeneity in fMRI RFX Analysis Morning Workshop, OHBM 2005 OrganizersThomas Nichols, Stephen Smith &Jean-Baptist Poline Speakers Thomas Nichols, Jean-Baptist Poline, Christian Beckmann

  2. Distribution of each subject’s estimated effect Fixed vs.RandomEffects in fMRI 2FFX Subj. 1 Subj. 2 • Fixed Effects • Intra-subject variation suggests all these subjects different from zero • Random Effects • Intersubject variation suggests population not very different from zero Subj. 3 Subj. 4 Subj. 5 Subj. 6 0 2RFX Distribution of population effect

  3. Multisubject fMRI Analyses • Fixed Effects Analyses • Compare effect magnitude to scan-to-scan variation, measurement error • Inferences only suitable for that cohort • Random Effects (RFX) analyses • Compare effect magnitude to combination of scan-to-scan & subject-to-subject • Inferences can be generalized to the population sampled(Assuming you have a random sample from the population of interest!)

  4. RFX Analyses Assumptions • 2nd level parametric models make more assumptions! • 1st level: Measurement error Normal • 2nd level: True subject responses Normal • Normality needed for... • Optimally precise estimates • Accurate P-values & thresholds

  5. Normality means... • Symmetric • No skew • Unimodal • No mixtureof populations • Thin tails • No outliers

  6. But Non-Normality may be interesting! • Bimodality • In controls, two populations of responses could be explained by behavior differences • In patients, could point to disease sub-groups • Outliers • Exceptional individuals could be performing task in completely different manner • All different aspects of heterogeneity ...

  7. Purpose of Workshop • Raise awareness of heterogeneity in group analyses • Talk 1: Traditional assumption checking Thomas Nichols, University of Michigan • Talk 2: Finding unusual subjects, multivariately Jean-Baptist Poline, CEA- SHFJ • Talk 3: Finding multivariate structure without models Christian Beckmann, Oxford University

  8. Massively UnivariateModel Diagnosis forGroup fMRI Data Thomas Nichols Department of Biostatistics, University of Michigan joint withHui Zhang, University of Michigan Wen-Lin Luo, Merck & Co, Inc http://www.sph.umich.edu/~nichols OHBM Morning Workshop June 14, 2005

  9. Statistical Commandments • But its not easy with imaging data! • 100,000 voxels, 1,000 scans, 20 subjects • Look at all 2 billion data points!? • Check all 100,000 models? • Thou shalt look at your data • Thou shalt check your assumptions

  10. Our Solution • Decompose data into signal & noise Y = X +  and explore each, using... • Model and scan summaries • Each sensitive to different violations of assumptions • Dynamic graphical tool • Explore many summaries simultaneously • Efficiently jump from summary to raw or residual data • End Result • Swiftly localize and understand problems

  11. Linear model fit at each voxel Assumptions on errors  Data = TrueFit + RandomError = EstimatedFit + Residuals X y = X +  = + e Plot e vs X, X, anything Methods: Model Checked with residuals e Mean 0, Constant Var.E(i)=0, Var(i)=2 UncorrelatedCov(i,j)=0 Plot ei vs ei+1, spectrum NormalityP(i  x) = (x) QQ plot, e(i) vs. E(z(i))

  12. Methods: Model Summaries • Create images of diagnostic statistics

  13. Methods:Scan Summaries • No spatial model explicitly fit • But several ad hoc measures useful

  14. Scan Summaries • Parallel time series w/ cursor Scan Summaries Scan Summaries Model Summaries Model Summaries • Model Summaries • Orthogonal Slice Viewers, MIPs • Model Detail • Raw data, fitted & residualtime series, and diagnostic plots Scan Detail • Scan Detail • Series of standardized residualimages Model Detail Model Detail Scan Detail Methods: Graphical Tool

  15. Methods: General Strategies • Scan Summaries • One bad subject? Several? • Model Summaries • Explore noise & signal • Assess assumptions w/ diagnostics • Find problem voxels • Model Detail • For a problem voxel, find which subjects involved • Model Detail • For a problem subject, assess spatial extent of problem

  16. Data: FIAC Data • Acquisition • 3 TE Bruker Magnet • For each subject:2 (block design) sessions, 195 EPI images each • TR=2.5s, TE=35ms, 646430 volumes, 334mm vx. • Experiment (Block Design only) • Passive sentence listening • 22 Factorial Design • Sentence Effect: Same sentence repeated vs different • Speaker Effect: Same speaker vs. different • Analysis • Slice time correction, motion correction, sptl. norm. • 555 mm FWHM Gaussian smoothing • Box-car convolved w/ canonical HRF • Drift fit with DCT, 1/128Hz

  17. Look at the Data! • With small n, really can do it! • Start with anatomical • Alignment OK? • Yup • Any horrible anatomical anomalies? • Nope

  18. Look at the Data! • Mean & Standard Deviationalso useful • Variancelowest inwhite matter • Highest around ventricles

  19. Look at the Data! • Then the functionals • Set same intensity window for all [-10 10] • Last 6 subjects good • Some variability in occipital cortex

  20. Feel the Void! • Compare functional with anatomical to assess extent of signal voids

  21. Check Scan Summaries • Not so interesting but... • Note subject 9 (FIAC8) has 1% outliers

  22. Check Model Summaries Tstat Con. • Expected signal • Auditory cortex in both T& con • Unexpected structure • Stdev shows visual cortex,MCA variability Stdev Norm.Test Out-liers

  23. Check Model Detail • Visual cortex variable, especially in subj 2, 8, 9, 10

  24. Check Model Detail • Normality test big in cingulate • Subject 9 again!

  25. Check Scan Detail • Standardized residuals confirm subject 9 is weird • Ant/Superior Cingulate deactivated(in addition to V1)

  26. Conclusions • Group data should be explored • To understand anomalies • To generate new hypotheses • Assumptions must be checked • For unbiased and optimal estimates • For valid p-values • Assumptions in group fMRI can be checked efficiently • Model and scan diagnostic summaries • Explore with dynamic visualization software • Localize and understand artifacts • Software: Statistical Parametric Mapping Diagnosis • http://www.sph.umich.edu/~nichols/SPMd • Luo & Nichols, NeuroImage, 2003, 19(3):1014-1032

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