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

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

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

Correlation models bias variance Independent scans Autocorrelation 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?

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

FMRISTAT: smoothing instead of pooling Effective df depends on FWHMsd: dfeff = dfresidual(2 + 1) FWHMsd2 3/2 FWHMdata2 5 10 50 100 5 10 Infinity 50 100 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

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

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

Stat_summary task 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

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

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

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

T stat, smoothed sd, 100 df CBF non kinetic vs. kinetic

Stat_summary task 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

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

CMRO kinetic Unnormalized, smoothed 16mm FWHM

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

SD: Voxel Smooth Pooled SD: Voxel Smooth Pooled 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

CMRO kinetic smoothed 16 mm, “safe” analysis of task 3 - base 10 20 30 Sd 2 1 8 16 24 32 40 48 56 64 72 CMRO kinetic smoothed 16 mm, “safe” analysis of task 3 - base -2 2 4 6 T statistics 3 1 8 16 24 32 40 48 56 64 72 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

Stat_summary task 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