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Multiple comparison correction Methods & models for fMRI data analysis 29 October 2008 Klaas Enno Stephan Branco Weiss Laboratory (BWL) Institute for Empirical.

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Presentation on theme: "Multiple comparison correction Methods & models for fMRI data analysis 29 October 2008 Klaas Enno Stephan Branco Weiss Laboratory (BWL) Institute for Empirical."— Presentation transcript:

1 Multiple comparison correction Methods & models for fMRI data analysis 29 October 2008 Klaas Enno Stephan Branco Weiss Laboratory (BWL) Institute for Empirical Research in Economics University of Zurich Functional Imaging Laboratory (FIL) Wellcome Trust Centre for Neuroimaging University College London With many thanks for slides & images to: FIL Methods group

2 Overview of SPM RealignmentSmoothing Normalisation General linear model Statistical parametric map (SPM) Image time-series Parameter estimates Design matrix Template Kernel Gaussian field theory p <0.05 Statisticalinference

3 Time BOLD signal Time single voxel time series single voxel time series Voxel-wise time series analysis model specification model specification parameter estimation parameter estimation hypothesis statistic SPM

4 Inference at a single voxel  = p(t > u | H 0 ) NULL hypothesis H 0 : activation is zero u t-distribution p-value: probability of getting a value of t at least as extreme as u. If  is small we reject the null hypothesis. We can choose u to ensure a voxel- wise significance level of . t = contrast of estimated parameters variance estimate

5 t-contrast: a simple example Q: activation during listening ? c T = [ 1 0 ] Null hypothesis: Passive word listening versus rest SPMresults: Height threshold T = 3.2057 {p<0.001} Design matrix 0.511.522.5 10 20 30 40 50 60 70 80 1 voxel-level p uncorrected T ( Z  ) mm mm mm 13.94 Inf0.000-63 -27 15 12.04 Inf0.000-48 -33 12 11.82 Inf0.000-66 -21 6 13.72 Inf0.000 57 -21 12 12.29 Inf0.000 63 -12 -3 9.89 7.830.000 57 -39 6 7.39 6.360.000 36 -30 -15 6.84 5.990.000 51 0 48 6.36 5.650.000-63 -54 -3 6.19 5.530.000-30 -33 -18 5.96 5.360.000 36 -27 9 5.84 5.270.000-45 42 9 5.44 4.970.000 48 27 24 5.32 4.870.000 36 -27 42

6 Inference on images Signal+Noise Noise

7 Using an ‘uncorrected’ p-value of 0.1 will lead us to conclude on average that 10% of voxels are active when they are not. This is clearly undesirable. To correct for this we can define a null hypothesis for images of statistics.

8 Family-wise null hypothesis FAMILY-WISE NULL HYPOTHESIS: Activation is zero everywhere. If we reject a voxel null hypothesis at any voxel, we reject the family-wise null hypothesis A false-positive anywhere in the image gives a Family Wise Error (FWE). Family-Wise Error (FWE) rate = ‘corrected’ p-value

9 Use of ‘uncorrected’ p-value,  =0.1 FWE Use of ‘corrected’ p-value,  =0.1

10 The Bonferroni correction The family-wise error rate (FWE), ,a family of N independent voxels is The family-wise error rate (FWE), , for a family of N independent voxels is α = Nv where v is the voxel-wise error rate. Therefore, to ensure a particular FWE set v = α / N BUT...

11 The Bonferroni correction Independent voxelsSpatially correlated voxels Bonferroni is too conservative for smooth brain images !

12 Smoothness intrinsic smoothness –some vascular effects have extended spatial support extrinsic smoothness –resampling during preprocessing –matched filter theorem  deliberate additional smoothing to increase SNR described in resolution elements: "resels" resel = size of image part that corresponds to the FWHM (full width half maximum) of the Gaussian convolution kernel that would have produced the observed image when applied to independent voxel values # resels is similar, but not identical to the number of independent observations can be computed from spatial derivatives of the residuals critical for corrected p-values based on Gaussian random field theory

13 Random Field Theory Consider a statistic image as a discretisation of a continuous underlying random field Use results from continuous random field theory Discretisation (“lattice approximation”)

14 Euler Characteristic (EC) Topological measure –threshold an image at u -EC = # blobs -at high u: p (blob) = E [EC] therefore FWE,  = E [EC]

15 Euler Characteristic (EC) R= number of resels Z T = Z value threshold We can determine that Z threshold for which E[EC] = 0.05. At this threshold, every remaining voxel represents a significant activation, corrected for multiple comparisons across the search volume.

16 Voxel level test: intensity of a voxel Cluster level test: spatial extent above u Set level test: number of clusters above u Sensitivity  Regional specificity  Voxel, cluster and set level tests

17 Small volume correction (SVC) When we have a good hypothesis about where an activation should be, we can reduce the search volume: –mask defined by (probabilistic) anatomical atlases –mask defined by functional localisers –mask defined by orthogonal contrasts –spherical search volume around known coordinates Computing EC is relatively insensitive to the shape of the search volume.

18 Thank you


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