1 / 32

Estimating Power for fMRI & Classification Directions in fMRI

Estimating Power for fMRI & Classification Directions in fMRI. Thomas Nichols Clinical Imaging Centre GlaxoSmithKline. Overview. Power Exploration

saima
Download Presentation

Estimating Power for fMRI & Classification Directions in fMRI

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Estimating Power for fMRI&Classification Directions in fMRI Thomas Nichols Clinical Imaging Centre GlaxoSmithKline

  2. Overview • Power Exploration • ROIs (small/big, lots/few) ?GD Mitsis, GD Iannetti, TS Smart, I Tracey & R WiseRegions of interest analysis in pharmacological fMRI: How do the definition criteria influence the inferred result?Epub NeuroImage • Power Prediction • Classification

  3. Power Review: 1 Test Alternative Distribution Null Distribution • Power: The probability of rejecting H0 when HA is true • Specify your null distribution • Mean=0, variance=σ2 • Specify the effect size (Δ), which leads to alternative distribution • Specify the false positive rate, α 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 α Power 0 -4 -2 0 2 4 6 8 Δ/σ

  4. Power: 100,000 Tests? • Avoid Multiple Testing Problem if possible • Typically study will use well-characterized paradigm • Expected region of response should be known • But… • Variation in functional and structural anatomy • “Perfect” region never known • Should we use focal ROI? • Voxel-wise search in neighborhood? • Over whole brain anyway?

  5. Qualitative Power Exploration • Simplified power setting • Not voxel-wise; instead largish (>1000 voxel) VOIs • Large VOIs: Assuming σwithin << σbetween • Hence different sized VOI’s will have similar variance • Large VOIs: Assuming independence between VOIs • Consider impact of many vs. fewer VOI’s • Many VOIs • Better follows anatomy, possible shape of signal • Worse multiple testing correction • Fewer VOIs • Will dilute localized signal • Fewer tests to correct for

  6. Atlas 0 (AAL) k = 116 regions αFWE = 0.00043 (surrogate for correlatedvoxel-wise search) Atlas 3 k = 17 regions αFWE = 0.00294 Atlas 1 (AAL symmetric) k = 58 regions αFWE = 0.00086 Atlas 4 (Lobar AAL) k = 6 regions αFWE = 0.00833 Atlas 2 k = 28 regions αFWE = 0.00179 Atlas 5 (whole GM) k = 1 region αFWE =0.05000 AAL & Derived ROI Atlases

  7. Atlas 0 (AAL) k = 116 regions αFWE = 0.00043 Signal # VOIs = 1 Strength = 100% Atlas 3 k = 17 regions αFWE = 0.00294 Signal # VOIs = 1 Strength = 4.9% Atlas 1 (AAL symmetric) k = 58 regions αFWE = 0.00086 Signal # VOIs = 1 Strength = 47% Atlas 4 (Lobar AAL) k = 6 regions αFWE = 0.00833 Signal # VOIs = 1 Strength = 0.6% Atlas 2 k = 28 regions αFWE = 0.00179 Signal # VOIs = 1 Strength = 47% Atlas 5 (whole GM) k = 1 region αFWE =0.05000 Signal # VOIs = 1 Strength 0.1% L Amygdala

  8. Power: L Amygdala, True ROI • True ROI best(of course) • Rich ROI atlas (k=116) beats coarser atlases • Dilution more punishing than greater multiple testing

  9. Power: L Amygdala, Shifted ROI • True ROI best • Wrong (unshifted) ROI next • Rich ROI atlas still beats coarser atlases

  10. Power: ½ of Mid-Cingulate • Whole Mid-Cing ROI best • Again, huge (k=116) atlas next best • But we’ve assumed RFX • No precision gain for large ROI’s, as shrinking σWiN is no help

  11. Power: ½ of Mid-Cingulate: FFX • Whole Mid-Cing ROI best • Now Symmetric AAL atlas (k=58) best! • If σBTW small, precision increase with large ROIs has impact

  12. Power Exploration Conclusions • Compared Range of Scales • Whole Brain, Lobar (k=6),…, AAL (k=116) • Focal structures – Focal ROI’s best • More extended signals, with heterogeneity • Rich atlas best • Dilution of signal worse than Bonferroni • But whole-brain always less powerful than reduced volume • Suggests voxel-wise / “Multiple Endpoint” result preferred, constrained coarsely

  13. Example 1100 total voxels 100 voxels have β=Δ A test with 50% power on average will detect 50 of these voxels with true activation 1000 voxels have β=0 α=5% implies on average 50 null voxels will have false positives 1 Signal ROI 1 opportunity for a positive 100 Signal Voxels 100 opportunities for a positive Why Doesn’t Bonf. Hurt More? Truth (unobserved) Test Result (observed) 50 50 950 50 1000 100

  14. Formal Power analysis • N: Number of Subjects • Adjusted to achieve sufficient power • α: The size of the test you’d like to use • Commonly set to 0.05 (5% false positive rate) • Δ: The size of the effect you’re interested in detecting • Based on intuition or similar studies • σ2: The variance of Δ • Has a complicated structure with very little intuition • Depends on many things …

  15. Power for Group fMRI Temporal autocorr. Cov(Y)=σ2wV Time . . . . . . . . . . . . Subject 1 Subject 2 Subject N Between subject variability, σ2B http://www.fmripower.org J. Mumford & TE. Nichols. NeuroImage 39:261–268, 2008

  16. Yk : Tk-vector timeseries for subject k Xk : Tk  p design matrix βk : p-vector of parameters εk : Tk-vector error term, Cov(εk)=σ2kVk Yk = Xk βK + εk βk0 βk1 βk2 βk3 + = Level 1

  17. cβk Xg : N  pg design matrix βg : pg-vector of parameters εg : N-vector error term Cov(εg) = Vg = diag{c(XTkVk-1Xk)-1σk2cT} + σB2IN Level 2 ^ βcont = Xg βg + εg + βg1 βg2 = ^ Within subject variability Between subject variability

  18. Alternative distribution • For a specific HA:cgβg=Δ • t is distributed Tn-pg, ncp • ncp= Δ/cg(XgTVg-1Xg)cgT N α Δ σ2 cg Xg # subj FPR Effect Mag. Effect SD 2nd Level Model known σ2WV σ2B W/in Subj SD Btw Subj SD guessed c Xk σ2k Vk(σWN,σAR,ρ) 1st Level Model Noise Mag. Noise Autocorrelation

  19. Model • Block design 15s on 15s off • TR=3s • Hrf: Gamma, sd=3 • Parameters estimated from Block study • FIAC single subject data • Read 3 little pigs • Same/different speaker, same/different sentence • Looked at blocks with same sentence same speaker

  20. Assumes fixed maximal scanner time 21 Ss optimal Btw 23 and 18 subjects sufficient 17 subjects cannot obtain sufficient power Power as a function of run length and sample size

  21. More importantly….cost! • Cost to achieve 80% power • Cost=$300 per subject+$10 per each extra minute

  22. Power, Accounting for searching over space? S Hayasaka, AM Peiffer, CE Hugenschmidt, PJ Laurienti.Power and sample size calculation for neuroimaging studies by non-central random field theory. NeuroImage 37 (2007) 721–730

  23. Univariate vs. Multivariate • Mass Univariate Modelling • Model each voxel independently(account for dependence at inference stage) • Great for localization • Doesn’t acknowledge spatial structure • Multivariate Modelling • Model entire volume simultaneously • Explicitly uses spatial structure • Not as good for localization

  24. Multivariate Classification:Classification of Subjects • ICA Components appear to distinguishNC vs. SZ vs. BP • fMRI Experiment: Auditory oddball task • But no one voxel responsible VD Calhoun, PK Maciejewski, GD Pearlson, KA Kiehl. Temporal Lobe and ‘‘Default’’ Hemodynamic Brain Modes Discriminate Between Schizophrenia and Bipolar Disorder. Human Brain Mapping, Epub 2007 Sep 25

  25. Multivariate Classification:Classification of Subjects • ICA Components appear to distinguishNC vs. SZ vs. BP • fMRI Experiment: Auditory oddball task • But no one voxel responsible VD Calhoun, PK Maciejewski, GD Pearlson, KA Kiehl. Temporal Lobe and ‘‘Default’’ Hemodynamic Brain Modes Discriminate Between Schizophrenia and Bipolar Disorder. Human Brain Mapping, Epub 2007 Sep 25

  26. Multivariate Classification • Even very simple method can give very good performance • Define average ICgrp for each group • Label subj k with group that has minimum Euclidian distance (btw ICk & ICgrp)

  27. Multivariate Classification:Prediction Time Series

  28. Pittsburgh Brain Activity Interpretation Competition Inferring Experience Based Cognition from Virtual Reality fMRI Greg Siegle, Walter Schneider, Maureen McHugo, Melissa Thomas, Lori Koerbel, Lena Gemmer, Kate Fissell, Sudhir Pathak, Dan Jones, Kevin Jarbo University of Pittsburgh

  29. Inferring Cognition • Virtual Reality fMRI Paradigm • Subjects explore neighborhood, looking for fruit, guns, dogs • 11 features rated continuously • e.g. arousal, valance, movement, dog, cell phone, etc • 3 Sessions of fMRI data • Features only given for 1st 2 sessions R2=.79 17 minutes

  30. Surprisingly accurate results 1st place Arousal • Very different methods gave similar scores (based on pre- and post-processing) • Similar methods (e.g., support vector machines) gave very different results. Valence Hits SearchPeople SearchWeapons SearchFruit Instructions Dog Faces FruitsVegetables WeaponsTools InteriorExterior Velocity -.2 0 .2 .4 .6 .8 1 Correlation

  31. Lessons from Contest • Pre-processing mattered • Detrending details had big impact • Multivariate, but not un-informed • Winners used masks • Weighting salient voxels, ignoring uninformative ones • Post-processing clean up • In general, extensive tuningper feature to be predicted Subject14 visual cortex Use for “Interior Exterior” Subject13 auditory cortex Use for “Dog”

  32. Conclusions • Power for fMRI • Focused ROI’s, but not too focused • Exact power predictions possible • As always, based on guesses • Classification • Uses entire brain to predict subject identity or cognitive state • New direction, methods still evolving • e.g. Support Vector Machines work well, but never with out appreciable feature selection/tuning

More Related