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Statistical analysis of PET data using FMRISTAT (!)

This paper presents a statistical analysis of PET data using FMRISTAT software. The analysis includes correlation models, independent scans, autocorrelation, and contrast calculations. The effects of smoothing and pooling on effective degrees of freedom are also discussed. The results of the analysis for CBF non-kinetic and CBF kinetic data are presented and compared.

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Statistical analysis of PET data using FMRISTAT (!)

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  1. Statistical analysis of PET data using FMRISTAT (!) Keith Worsley Department of Mathematics and Statistics, McConnell Brain Imaging Centre, McGill University

  2. c:/keith/fMRI/manou/cbf non kin/bach allan -h1 tal 200008161003.mnc, slice 21 4 x 10 4 1 6 11 16 21 25 30 35 40 45 50 55 60 65 3.5 2 7 12 17 22 26 31 36 41 46 51 56 61 66 3 4 3 2 1 Task 2.5 3 8 13 18 23 27 32 37 42 47 52 57 62 67 2 4 9 14 19 24 28 33 38 43 48 53 58 63 68 1.5 1 5 10 15 20 29 34 39 44 49 54 59 64 69 0.5 0 Subjects CBF non kinetic • Unnormalized data (z = -6 mm) base

  3. c:/keith/fMRI/manou/cbf non kin/normalized, slice 21 1.5 1 6 11 16 21 25 30 35 40 45 50 55 60 65 2 7 12 17 22 26 31 36 41 46 51 56 61 66 4 3 2 1 Task 1 3 8 13 18 23 27 32 37 42 47 52 57 62 67 4 9 14 19 24 28 33 38 43 48 53 58 63 68 0.5 5 10 15 20 29 34 39 44 49 54 59 64 69 0 Subjects CBF non-kinetic • Normalized: thresh at ½ max, average, divide base

  4. Correlation models Independent scans Autocorrelation AR(1) Autocorrelation AR(2) All correlations DF: (#subj-1) × (#scans-1) = 51 Depends on correlations, contrast (#subj-1) = 13 Standard error of contrasts: bias variance Safest: DOT, FMRISTAT boost df by pooling/smoothing SPM?

  5. Is pooling sd valid?Is sd constant across the brain?Unsmoothed sd assuming independent scans, 51 df: Pooled Sd = 0.027

  6. 100 100 50 50 0 0 0 0 5 5 10 10 Infinity FMRISTAT: smoothing instead of poolingEffective df depends on FWHMsd: FWHMsd2 3/2 FWHMdata2 dfeff = dfresidual(2 + 1) e.g. FWHMdata = 8.3 mm: Infinity pooled sd, dfeff = infinity Target = 100 df dfeff independent no smoothing, dfeff = 51 dfeff = 13 all correlations FWHM = 10.0 mm FWHMsd FWHM = 4.4 mm

  7. FMRISTAT: smooth sd by FWHM = 4.4 mm, df = 100

  8. CBF non kinetic (z = 57 mm) T statistic SD: Voxel Smooth Pooled DF: 51 100 infinite Effect is always same

  9. Stat_summarytask 4 – base CLUSTERS: clus vol resel Pval (one) 1 4688 10.92 0 ( 0) 2 7067 10.58 0 ( 0) 3 947 1.6 0.033 (0.001) 4 543 0.88 0.22 ( 0.01) 5 415 0.75 0.323 (0.015) 6 169 0.39 0.788 ( 0.06) Effective FWHM: 15 PEAKS: clus peak Pval (one) Qval (i j k) ( x y z ) 2 8.03 0 ( 0) 0 ( 35 62 64) (-38.9 -19.4 58.5) 1 6.8 0 ( 0) 0 ( 81 40 13) ( 22.8 -57.3 -18) 1 6.58 0 ( 0) 0 ( 76 43 11) ( 16.1 -52.1 -21) 2 6.34 0 ( 0) 0 ( 39 59 67) (-33.5 -24.6 63) 2 6.33 0 ( 0) 0 ( 42 64 70) (-29.5 -16 67.5) 1 5.41 0.019 (0.001) 0 ( 70 42 12) ( 8 -53.8 -19.5) 1 5.4 0.02 (0.001) 0 ( 68 41 13) ( 5.4 -55.6 -18) 1 5.38 0.021 (0.001) 0 ( 69 42 13) ( 6.7 -53.8 -18) 2 5.25 0.037 (0.002) 0 ( 30 57 63) (-45.6 -28 57) 3 5.08 0.076 (0.004) 0.001 ( 17 76 42) ( -63 4.6 25.5) 2 5 0.104 (0.005) 0.001 ( 31 59 64) (-44.2 -24.6 58.5) 9 4.9 0.155 (0.007) 0.001 ( 14 67 12) ( -67 -10.8 -19.5) 3 4.85 0.191 (0.008) 0.001 ( 16 75 42) (-64.3 2.9 25.5) 5 4.81 0.223 ( 0.01) 0.001 ( 65 77 61) ( 1.3 6.4 54) 10 5 0

  10. c:/keith/fMRI/manou/cbf kin/bach allan -h1 sumpetkinetic tal 200008161003.mnc, slice 21 80 1 6 11 19 24 29 34 39 44 49 54 59 64 70 2 7 12 20 25 30 35 40 45 50 55 60 65 60 4 3 2 1 Task 50 3 8 13 16 21 26 31 36 41 46 51 56 61 66 40 4 9 14 17 22 27 32 37 42 47 52 57 62 67 30 20 5 10 15 18 23 28 33 38 43 48 53 58 63 68 10 0 Subjects CBF kinetic • Unnormalized, z= -6 mm base

  11. Is pooling sd valid?Is sd constant across the brain?Unsmoothed sd assuming independent scans, 51 df: Pooled Sd = 7.2

  12. CBF kinetic (z = 57 mm) T statistic SD: Voxel Smooth Pooled DF: 51 100 infinite Effect is always same

  13. T stat, smoothed sd, 100 dfCBF non kinetic vs. kinetic

  14. Stat_summarytask 4 – base (search region is where CBF non kinetic T > 5) CLUSTERS: clus vol resel Pval (one) 1 1338 3.11 0 (0.002) 2 363 1 0.008 (0.043) Effective FWHM: PEAKS: clus peak Pval (one) Qval (i j k) ( x y z ) 1 6.24 0 ( 0) 0 (33 63 61) (-41.5 -17.7 54) 1 5.32 0 ( 0) 0 (32 62 63) (-42.9 -19.4 57) 1 5.14 0 (0.001) 0 (35 63 60) (-38.9 -17.7 52.5) 2 4.82 0.001 (0.003) 0 (79 43 11) ( 20.1 -52.1 -21) 2 4.48 0.003 (0.009) 0 (78 44 12) ( 18.8 -50.4 -19.5) 2 4.32 0.005 (0.015) 0 (81 42 11) ( 22.8 -53.8 -21) 1 4.3 0.005 (0.015) 0 (41 62 70) (-30.8 -19.4 67.5) 1 4.19 0.007 (0.021) 0 (40 61 69) (-32.2 -21.2 66) 1 4.16 0.007 (0.023) 0 (32 60 66) (-42.9 -22.9 61.5) 6 3.91 0.016 (0.049) 0.001 (31 59 64) (-44.2 -24.6 58.5) 2 3.64 0.034 (0.099) 0.001 (81 41 10) ( 22.8 -55.6 -22.5) 2 3.52 0.047 (0.135) 0.002 (82 41 11) ( 24.1 -55.6 -21) 1 3.5 0.05 (0.143) 0.002 (39 58 69) (-33.5 -26.3 66) 3 3.42 0.062 (0.175) 0.002 (30 58 64) (-45.6 -26.3 58.5) 1 3.33 0.077 (0.214) 0.002 (38 65 68) (-34.8 -14.3 64.5) 2 3.16 0.116 (0.313) 0.003 (82 38 10) ( 24.1 -60.7 -22.5) 15 10 5 0

  15. c:/keith/fMRI/manou/cmro kin/bach allan -o1 sumpetkinetic tal 200008161158.mnc, slice 21 300 1 6 11 16 21 26 31 36 45 50 55 60 65 250 2 7 12 17 22 27 32 37 41 46 51 56 61 66 4 3 2 1 Task 200 3 8 13 18 23 28 33 38 42 47 52 57 62 67 150 4 9 14 19 24 29 34 39 43 48 53 58 63 68 100 5 10 15 20 25 30 35 40 44 49 54 59 64 69 50 0 Subjects CMRO kinetic • Unnormalized, z = -6 mm base

  16. CMRO kinetic • Unnormalized, smoothed 16mm FWHM

  17. Is pooling sd valid?Is sd constant across the brain?Unsmoothed sd assuming independent scans, 48 df: Pooled Sd = 12.7

  18. CMRO kinetic T statistic, z = 57 mm SD: Voxel Smooth Pooled DF: 48 100 infinite T statistic, z = -6 mm SD: Voxel Smooth Pooled DF: 48 100 infinite

  19. Sd 30 0 1 8 1 16 1 24 1 32 1 40 1 48 1 56 1 64 1 72 1 20 0 2 8 2 16 2 24 2 32 2 40 2 48 2 56 2 64 2 72 2 10 0 T statistics 6 0 1 8 1 16 1 24 1 32 1 40 1 48 1 56 1 64 1 72 1 4 0 2 8 2 16 2 24 2 32 2 40 2 48 2 56 2 64 2 72 2 2 0 0 3 8 3 16 3 24 3 32 3 40 3 48 3 56 3 64 3 72 3 -2 CMRO kinetic smoothed 16 mm,“safe” analysis of task 3 - base Unsmoothed sd, 12 df Sd smoothed 26 mm, 100 df Unsmoothed sd, 12 df T = 6.79 Sd smoothed 26 mm, 100 df T = 4.14 Pooled sd, infinite df T = 3.93

  20. Stat_summarytask 3 – base CLUSTERS: clus vol resel Pval (one) 1 927 0.25 0.179 (0.121) 2 211 0.06 0.485 (0.409) 3 138 0.05 0.545 (0.485) 4 266 0.04 0.554 (0.498) 40 Effective FWHM: 30 PEAKS: clus peak Pval (one) Qval (i j k) ( x y z ) 1 4.42 0.065 (0.034) 0.651 (37 107 40) (-36.2 58 22.5) 1 4.41 0.068 (0.036) 0.651 (35 106 39) (-38.9 56.2 21) 1 4.41 0.068 (0.036) 0.651 (36 106 40) (-37.5 56.2 22.5) 1 4.37 0.077 (0.041) 0.651 (37 106 42) (-36.2 56.2 25.5) 1 4.32 0.089 (0.047) 0.651 (36 107 38) (-37.5 58 19.5) . . . 4 3.44 1.072 ( 0.54) 1.003 (83 75 21) ( 25.5 2.9 -6) 4 3.44 1.091 (0.549) 1.003 (82 75 22) ( 24.1 2.9 -4.5) 20 10 0

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