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SnPM: Statistical nonParametric Mapping A Permutation Test for PET & Second Level fMRI Thomas Nichols, University of Michigan Andrew Holmes, University.

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Presentation on theme: "SnPM: Statistical nonParametric Mapping A Permutation Test for PET & Second Level fMRI Thomas Nichols, University of Michigan Andrew Holmes, University."— Presentation transcript:

1 SnPM: Statistical nonParametric Mapping A Permutation Test for PET & Second Level fMRI Thomas Nichols, University of Michigan Andrew Holmes, University of Glasgow

2 BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA BBBBBBAAAAAA t-statisticvariancemean difference  = randomise 12 subjects 6 BA… 6 AB…6 AB… difference V5 PET activation experiment… ii 11 22 33 44 55 66 77 88 99  10  11  12

3 …example…example H 0 : scan would have been same whatever the condition H 0 : scan would have been same whatever the condition –labelling as active or baseline arbitrary –re-label scans  equally likely statistic image consider all possible relabellings (exchangability)consider all possible relabellings (exchangability) Üpermutation distribution of each voxel statistic ?of each voxel statistic ? of maximal voxel statisticof maximal voxel statistic H 0 : scan would have been same whatever the condition H 0 : scan would have been same whatever the condition –labelling as active or baseline arbitrary –re-label scans  equally likely statistic image consider all possible relabellings (exchangability)consider all possible relabellings (exchangability) Üpermutation distribution of each voxel statistic ?of each voxel statistic ? of maximal voxel statisticof maximal voxel statistic

4 mean difference smoothed variance t-statistic “pseudo” t-statistic variance mean difference

5 SnPM with “pseudo” t-statistic SPM with standard t-statisic permutation distribution SnPM with standard t-statisic? – similar!

6 SnPMSnPM SnPM:SnPM: +minimal assumptions guaranteed validguaranteed valid +intuitive, flexible, powerful +any statistic: voxel / summary +any summary statistic maximum pseudo t – restricted volume – cluster size / height / mass – omnibus testsmaximum pseudo t – restricted volume – cluster size / height / mass – omnibus tests –computational burden –need sufficient relabellings UsesUses low dflow df dodgy parametricdodgy parametric no parametric resultsno parametric results SnPM:SnPM: +minimal assumptions guaranteed validguaranteed valid +intuitive, flexible, powerful +any statistic: voxel / summary +any summary statistic maximum pseudo t – restricted volume – cluster size / height / mass – omnibus testsmaximum pseudo t – restricted volume – cluster size / height / mass – omnibus tests –computational burden –need sufficient relabellings UsesUses low dflow df dodgy parametricdodgy parametric no parametric resultsno parametric results

7 Non-parametric tests in fNI… Classic testsClassic tests Wilcoxon rank sum testWilcoxon rank sum test Kolmogorov-Smirnov testKolmogorov-Smirnov test Permutation testsPermutation tests Holmes, Arndt (PET)Holmes, Arndt (PET) Bullmore, Locascio (fMRI) noise whitening, permutationBullmore, Locascio (fMRI) noise whitening, permutation Nichols & Holmes (fMRI) label (re)-randomisationNichols & Holmes (fMRI) label (re)-randomisation Classic testsClassic tests Wilcoxon rank sum testWilcoxon rank sum test Kolmogorov-Smirnov testKolmogorov-Smirnov test Permutation testsPermutation tests Holmes, Arndt (PET)Holmes, Arndt (PET) Bullmore, Locascio (fMRI) noise whitening, permutationBullmore, Locascio (fMRI) noise whitening, permutation Nichols & Holmes (fMRI) label (re)-randomisationNichols & Holmes (fMRI) label (re)-randomisation 3 weak distributional assumptions Ô don’t assume normality ä replace data by ranks Ô lose information ä exchangeability  independence – fMRI  3 minimal assumptions Ô exchangeability 3 valid often exact 3 multiple comparisons Ü via maximal statistics 3 flexible ¢ computational burden ¢ sufficient permutations 3 additional power at low d.f. Ü via “pseudo” t-statistics

8 SnPM (standard t) 12 scans12 scans 2 12 permutations2 12 permutations All 2048/2 computedAll 2048/2 computed p=1/2048p=1/2048  = 0.05 critical threshold: u  = 7.9248  = 0.05 critical threshold: u  = 7.9248 Bonferoni critical threshold: u  = 9.0717Bonferoni critical threshold: u  = 9.0717 30 min on Sparc Ultra 1030 min on Sparc Ultra 10 12 scans12 scans 2 12 permutations2 12 permutations All 2048/2 computedAll 2048/2 computed p=1/2048p=1/2048  = 0.05 critical threshold: u  = 7.9248  = 0.05 critical threshold: u  = 7.9248 Bonferoni critical threshold: u  = 9.0717Bonferoni critical threshold: u  = 9.0717 30 min on Sparc Ultra 1030 min on Sparc Ultra 10

9 SnPM (pseudo t) 12 scans12 scans 2 12 permutations2 12 permutations All 2048/2 computedAll 2048/2 computed p = 1/2048p = 1/2048  = 0.05 critical threshold: u  = 5.120  = 0.05 critical threshold: u  = 5.120 40 min on a Sparc Ultra1040 min on a Sparc Ultra10 12 scans12 scans 2 12 permutations2 12 permutations All 2048/2 computedAll 2048/2 computed p = 1/2048p = 1/2048  = 0.05 critical threshold: u  = 5.120  = 0.05 critical threshold: u  = 5.120 40 min on a Sparc Ultra1040 min on a Sparc Ultra10

10 SnPM vs Parametric RF Corrected Significance of Threshold Permutation RT Theory

11 Holmes AP, Blair RC, Watson JDG, Ford I (1996) “Non-Parametric Analysis of Statistic Images from Functional Mapping Experiments” Journal of Cerebral Blood Flow and Metabolism 16:7-22 Arndt S, Cizadlo T, Andreasen NC, Heckel D, Gold S, O'Leary DS (1996) “Tests for comparing images based on randomization and permutation methods” Journal of Cerebral Blood Flow and Metabolism 16:1271-1279 Nichols TE, Holmes AP (2002) “Nonparametric permutation tests for functional neuroimaging experiments: A primer with examples” Human Brain Mapping 15:1-25 Bullmore ET, Brammer M, Williams SCR, Rabe-Hesketh S, Janot N, David A, Mellers J, Howard R, Sham P (1995) “Statistical Methods of Estimation and Inference for Functional MR Image Analysis” Magnetic Resonance in Medicine 35:261-277 Locascio JJ, Jennings PJ, Moore CI, Corkin S (1997) “Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging” Human Brain Mapping 5:168-193 Raz J, Zheng H, Turetsky B (1999) “Statistical Tests for fMRI based on experimental randomisation” (ENAR Conference Proceedings) Marchini JL, Ripley BD (2000) “A new statistical approach to detecting significant activation in functional MRI” NeuroImage Holmes AP, Blair RC, Watson JDG, Ford I (1996) “Non-Parametric Analysis of Statistic Images from Functional Mapping Experiments” Journal of Cerebral Blood Flow and Metabolism 16:7-22 Arndt S, Cizadlo T, Andreasen NC, Heckel D, Gold S, O'Leary DS (1996) “Tests for comparing images based on randomization and permutation methods” Journal of Cerebral Blood Flow and Metabolism 16:1271-1279 Nichols TE, Holmes AP (2002) “Nonparametric permutation tests for functional neuroimaging experiments: A primer with examples” Human Brain Mapping 15:1-25 Bullmore ET, Brammer M, Williams SCR, Rabe-Hesketh S, Janot N, David A, Mellers J, Howard R, Sham P (1995) “Statistical Methods of Estimation and Inference for Functional MR Image Analysis” Magnetic Resonance in Medicine 35:261-277 Locascio JJ, Jennings PJ, Moore CI, Corkin S (1997) “Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging” Human Brain Mapping 5:168-193 Raz J, Zheng H, Turetsky B (1999) “Statistical Tests for fMRI based on experimental randomisation” (ENAR Conference Proceedings) Marchini JL, Ripley BD (2000) “A new statistical approach to detecting significant activation in functional MRI” NeuroImage Nonparametric approaches…

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