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

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

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Power Review: 1 Test Power: The probability of rejecting H 0 when H A is true Specify your null distribution –Mean=0, variance=σ 2 Specify the effect size (Δ), which leads to alternative distribution Specify the false positive rate, α 02468-4-2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 α Power Null Distribution Alternative Distribution Δ/σΔ/σ

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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?

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Qualitative Power Exploration Simplified power setting –Not voxel-wise; instead largish (>1000 voxel) VOIs –Large VOIs: Assuming σ within << σ between 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

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

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

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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

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

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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 σ WiN is no help

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

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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

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Why Doesn’t Bonf. Hurt More? H 0 True H 0 False Reject H 0 Type I Error α Power Accept H 0 Correct Type II Error Truth (unobserved) Test Result (observed) 1000 950 50 100 50 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

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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 σ 2 : The variance of Δ –Has a complicated structure with very little intuition –Depends on many things …

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

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Level 1 Y k : T k -vector timeseries for subject k X k : T k p design matrix β k : p-vector of parameters ε k : T k -vector error term, Cov(ε k )=σ 2 k V k = β k0 β k1 β k2 β k3 + Y k = X k β K + ε k

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Level 2 cβ k X g : N p g design matrix β g : p g -vector of parameters ε g : N-vector error term –Cov(ε g ) = V g = diag { c(X T k V k -1 X k ) -1 σ k 2 c T } + σ B 2 I N ^ β cont ^ = β g1 β g2 + =XgXg βgβg + εgεg Within subject variability Between subject variability

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Alternative distribution For a specific H A :c g β g =Δ t is distributed T n-pg, ncp –ncp= Δ/c g (X g T V g -1 X g )c g T NαΔσ2σ2 cgcg XgXg σ2WVσ2WVσ2Bσ2B cXkXk σ2kσ2k V k (σ WN,σ AR,ρ) # subjFPREffect Mag.2 nd Level Model known guessed Effect SD W/in Subj SDBtw Subj SD 1 st Level ModelNoise Mag.Noise Autocorrelation

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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

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

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

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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

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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

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Multivariate Classification: Classification of Subjects ICA Components appear to distinguish NC 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

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Multivariate Classification: Classification of Subjects ICA Components appear to distinguish NC 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

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Multivariate Classification Even very simple method can give very good performance –Define average IC grp for each group –Label subj k with group that has minimum Euclidian distance (btw IC k & IC grp )

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Multivariate Classification: Prediction Time Series

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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 Pittsburgh Brain Activity Interpretation Competition

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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 1 st 2 sessions Inferring Cognition R 2 =.79 17 minutes

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Very different methods gave similar scores (based on pre- and post- processing) Similar methods (e.g., support vector machines) gave very different results. Arousal Valence Hits SearchPeople SearchWeapons SearchFruit Instructions Dog Faces FruitsVegetables WeaponsTools InteriorExterior Velocity -.20.2.4.6.81 1 st place Correlation Surprisingly accurate results

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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 tuning per feature to be predicted Subject14 visual cortex Use for “Interior Exterior” Subject13 auditory cortex Use for “Dog”

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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

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