1. 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 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 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
Task
Unnormalized data (z = -6 mm)
base

3. 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
Task
Normalized: thresh at ½ max, average, divide
base

4. 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?

5. 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

6. FMRISTAT: smoothing instead of pooling Effective df depends on FWHMsd:
dfeff = dfresidual( )
FWHMsd /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

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

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

9. Stat_summary task 4 – base
CLUSTERS:
clus vol resel Pval (one)
( 0)
( 0)
(0.001)
( 0.01)
(0.015)
( 0.06)
Effective FWHM: 15
PEAKS:
clus peak Pval (one) Qval (i j k) ( x y z )
( 0) ( ) ( )
( 0) ( ) ( )
( 0) ( ) ( )
( 0) ( ) ( )
( 0) ( ) ( )
(0.001) ( ) ( )
(0.001) ( ) ( )
(0.001) ( ) ( )
(0.002) ( ) ( )
(0.004) ( ) ( )
(0.005) ( ) ( )
(0.007) ( ) ( )
(0.008) ( ) ( )
( 0.01) ( ) ( ) 10 5

10. CBF kinetic Unnormalized, z= -6 mm base 10 20 30 40 50 60 70 8010 20 30 40 50 60 70 80
c:/keith/fMRI/manou/cbf kin/bach allan -h1 sumpetkinetic tal 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
Task
Unnormalized, z= -6 mm
base

11. 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

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

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

14. Stat_summary task 4 – base
(search region is where
CBF non kinetic T > 5)
CLUSTERS:
clus vol resel Pval (one)
(0.002)
(0.043)
Effective FWHM:
PEAKS:
clus peak Pval (one) Qval (i j k) ( x y z )
( 0) ( ) ( )
( 0) ( ) ( )
(0.001) ( ) ( )
(0.003) ( ) ( )
(0.009) ( ) ( )
(0.015) ( ) ( )
(0.015) ( ) ( )
(0.021) ( ) ( )
(0.023) ( ) ( )
(0.049) ( ) ( )
(0.099) ( ) ( )
(0.135) ( ) ( )
(0.143) ( ) ( )
(0.175) ( ) ( )
(0.214) ( ) ( )
(0.313) ( ) ( ) 15 10 5

15. CMRO kinetic Unnormalized, z = -6 mm base 50 100 150 200 250 30050
100
150
200
250
300
c:/keith/fMRI/manou/cmro kin/bach allan -o1 sumpetkinetic tal 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
Task
Unnormalized, z = -6 mm
base

16. CMRO kinetic
Unnormalized, smoothed 16mm FWHM

17. 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

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

19. CMRO kinetic smoothed 16 mm, “safe” analysis of task 3 - base10 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

20. Stat_summary task 3 – base
CLUSTERS:
clus vol resel Pval (one)
(0.121)
(0.409)
(0.485)
(0.498) 40
Effective FWHM: 30
PEAKS:
clus peak Pval (one) Qval (i j k) ( x y z )
(0.034) ( ) ( )
(0.036) ( ) ( )
(0.036) ( ) ( )
(0.041) ( ) ( )
(0.047) ( ) ( ) .
( 0.54) ( ) ( )
(0.549) ( ) ( ) 20 10