Statistical analysis of PET data using FMRISTAT

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Statistical analysis of PET data using FMRISTAT
(!)

• Keith Worsley
• Department of Mathematics and Statistics,
  McConnell Brain Imaging Centre, McGill University

2
CBF non kinetic

• Unnormalized data (z -6 mm)

base
3
CBF non-kinetic

• Normalized thresh at ½ max, average, divide

base
4
Correlation models
Independent scans
Autocorrelation AR(1)
All correlations
Autocorrelation AR(2)
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
FMRISTAT smoothing instead of
poolingEffective df depends on FWHMsd

• dfeff dfresidual(2 1)

FWHMsd2 3/2 FWHMdata2
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
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FMRISTAT smooth sd by FWHM 4.4 mm, df 100
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CBF non kinetic (z 57 mm)
T statistic SD Voxel Smooth Pooled
DF 51 100 infinite
Effect is always same
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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
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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
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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 gt 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)
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10
5
0
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CMRO kinetic

• Unnormalized, z -6 mm

base
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CMRO kinetic

• Unnormalized, smoothed 16mm FWHM

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Is pooling sd valid?Is sd constant across the
brain?Unsmoothed sd assuming independent scans,
48 df
Pooled Sd 12.7
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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
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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
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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)
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Effective FWHM
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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)
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10
0