Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Voxel-wise and Cluster-based Heritability
Inference for fMRI Data
Xu Chen1 , Gabriëlla Blokland2,3 , Lachlan Strike2 , Thomas
Nichols1
2
1 Department of Statistics, University of Warwick, UK,
Genetic Epidemiology Laboratory, Queensland Institute of Medical Research,
Australia,
3 Centre for Advanced Imaging, University of Queensland, Australia
OHBM 2013
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Background
Voxel-wise Heritability Estimation
• Existing Methods
2
• Falconer’s Method: ĥF = 2 × (rMZ − rDZ )
Pros Simple, fast and easy to use
Cons Poor estimation accuracy
• SEM Method Implemented in Mx/OpenMx
Pros Has better estimation properties
Cons Time-consuming, can have convergence
problems, and requires R ←→ Nifti conversion
• Our LR-SD Method
• Based on squared differences of paired observations (Grimes
and Harvey, 1980)
• Fast, no iterations, no convergence issues
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Contributions
Outline
• Previous work
• Demonstrated validity and excellent bias-variance properties
• As good as or better than OpenMx
• Current work
• Power comparison of voxel-wise and cluster-based heritability
inference methods
• We demonstrate our method on a real dataset
• Spatial statistics: cluster size, cluster mass
• Non-parametric p-values: uncorrected, corrected
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Brief Method Description
• Linear Regression with Squared Differences (LR-SD)
• Relate squared differences of data pairs to variance
components A,C,E:
E (MZ1 − MZ2 )2 =
2E
2
E (DZ1 − DZ2 )
= A +
2E
2
E (I1 − I2 )
= 2A + 2C + 2E
• Modification of Grimes and Harvey’s method: n(n − 1)/2 obs.
→ (nMZ + nDZ )/2 obs. (50,721 vs. 141)
• Permutation Inference
• Under H0: h2 = 0, MZ and DZ twin pairs are exchangeable
•
(nMZ +nDZ )/2
nMZ /2
possible permutations
• Calculate FWE-corrected P-values from maximum distributions
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Simulation Setting
Simulation Setting
• 10,000 simulations
• Sample sizes: 10+10, 50+50
• 15 ACE parameter settings:
A
C
E
E
0
0
1
CE
0
0.2
0.8
A
C
E
0
0.3
0.7
ACE
0.2
0.2
0.6
0
0.5
0.5
0.3
0.2
0.5
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
0
0.7
0.3
0.2
0.3
0.5
AE
0.2
0
0.8
0.5
0.2
0.3
0.3
0
0.7
0.3
0.3
0.3
0.5
0
0.5
0.7
0
0.3
0.2
0.5
0.3
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
LR-SD vs. OpenMx
Simulations: MSE Comparison
Mean squared error comparison between LR-SD and OpenMx
MSE Comparison: LR−SD (blue) vs. OpenMx (red), nMZ=10, nDZ=10
0.2
0.15
0.1
0.05
0
Null (0,.2)(0,.3)(0,.5)(0,.7)(.2,0)(.3,0)(.5,0)(.7,0)(.2,.2)(.3,.2)(.2,.3)(.5,.2)(.3,.3)(.2,.5)
MSE Comparison: LR−SD (blue) vs. OpenMx (red), nMZ=50, nDZ=50
0.2
0.15
0.1
0.05
0
Null (0,.2)(0,.3)(0,.5)(0,.7)(.2,0)(.3,0)(.5,0)(.7,0)(.2,.2)(.3,.2)(.2,.3)(.5,.2)(.3,.3)(.2,.5)
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
LR-SD vs. OpenMx
Simulations: Power Comparison
Statistical power comparison between LR-SD and OpenMx
Power for LRT (100%): LR−SD (blue) vs. OpenMx (red), nMZ=10, nDZ=10
60
40
20
0
(.2,0) (.3,0) (.5,0) (.7,0) (.2,.2)(.3,.2)(.2,.3)(.5,.2)(.3,.3)(.2,.5)
Power for LRT (100%): LR−SD (blue) vs. OpenMx (red), nMZ=50, nDZ=50
60
40
20
0
(.2,0) (.3,0) (.5,0) (.7,0) (.2,.2)(.3,.2)(.2,.3)(.5,.2)(.3,.3)(.2,.5)
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
LR-SD vs. OpenMx
Simulations: Running Time Comparison
Overall running time comparison between LR-SD and OpenMx
→ On average, our LR-SD is around 300 times faster than OpenMx
Running Time Comparison: LR−SD (blue) vs. OpenMx (red), nMZ=10, nDZ=10
4000
2000
0
Null (0,.2)(0,.3)(0,.5)(0,.7)(.2,0)(.3,0)(.5,0)(.7,0)(.2,.2)(.3,.2)(.2,.3)(.5,.2)(.3,.3)(.2,.5)
Running Time Comparison: LR−SD (blue) vs. OpenMx (red), nMZ=50, nDZ=50
4000
2000
0
Null (0,.2)(0,.3)(0,.5)(0,.7)(.2,0)(.3,0)(.5,0)(.7,0)(.2,.2)(.3,.2)(.2,.3)(.5,.2)(.3,.3)(.2,.5)
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Simulation Setting
Power Simulations
• 1,000 simulations
• Sample sizes: 10+10, 50+50
• ACE parameter settings: [0.3 0 0.7], [0.5 0.2 0.3], [0.7 0 0.3]
• Signal shapes:
(1) Focal signal
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
(2) Distributed signal
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
ROC Curve Analysis
ROC Curve Comparison
ROC curves of voxel-wise and cluster-based methods for different
ACE settings for focal signal, sample size: 10+10
nMZ=10, nDZ=10, Focal Signal
0.05
Voxel, [.3,0,.7]
Voxel, [.5,.2,.3]
Voxel, [.7,0,.3]
Cluster, [.3,0,.7]
Cluster, [.5,.2,.3]
Cluster, [.7,0,.3]
Average true positive rate (TPR)
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Familywise false positive rate (FPR)
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
ROC Curve Analysis
ROC Curve Comparison
ROC curves of voxel-wise and cluster-based methods for different
ACE settings for focal signal, sample size: 50+50
nMZ=50, nDZ=50, Focal Signal
0.5
Voxel, [.3,0,.7]
Voxel, [.5,.2,.3]
Voxel, [.7,0,.3]
Cluster, [.3,0,.7]
Cluster, [.5,.2,.3]
Cluster, [.7,0,.3]
Average true positive rate (TPR)
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Familywise false positive rate (FPR)
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
ROC Curve Analysis
Area under the ROC Curves
Normalized area under the ROC curves (20 × AUC) for
FPR=0:0.05 for different ACE settings
Normalized AUC
nMZ=10, nDZ=10
0.2
0.1
Voxel − Focal
Voxel − Distributed
Cluster − Focal
Cluster − Distributed
0
[.3,0,.7]
[.5,.2,.3]
[.7,0,.3]
Normalized AUC
nMZ=50, nDZ=50
0.4
0.2
Voxel − Focal
Voxel − Distributed
Cluster − Focal
Cluster − Distributed
0
[.3,0,.7]
[.5,.2,.3]
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
[.7,0,.3]
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Real Data
Real Data Acquisition
An fMRI heritability study of working memory brain activation by
Blokland et al., 2011
• n = 319 young and healthy participants
• 75 MZ twin pairs, 66 DZ twin pairs and 37 singletons
• Age range: 20 - 28 (mean ± SD: 23.6 ± 1.8 years)
• 199 females and 120 males
• Performed an n-back (0- and 2-back) working memory task
• Task-related fMRI BOLD signals were acquired
• Age, gender and 2-back performance accuracy were included
as the covariates
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Real Data
Running Time
• On a MacPro with 12 physical CPUs (24 logical CPUs), using
the system at full capacity
• Only areas of expected activation were included in the mask
• Totally 14,627 in-mask voxels
• 1,000 permutations, 10 parallelized jobs, each with 100
permutations
• Running time for one permutation
• LR-SD: 6 mins
• Mx: around 2 days (= 2880 mins)
• Running time for 10 parallelized jobs
• LR-SD: 15.5 hours
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Real Data
Twin Correlations
(1) MZ twin correlation
(2) DZ twin correlation
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Voxel-wise vs. Cluster-based Methods
FWE P-value Images of Significance
(1) Voxel-wise significance image
(2) Cluster-based significance image
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Voxel-wise vs. Cluster-based Methods
Voxel-wise vs. Cluster-based Methods
• Voxel-wise Method
• Construct empirical distribution of maximum test statistic
• FWE P-value = 0.006 for voxel
• 3 significant voxels
• Cluster-based Method
• Construct empirical distributions of maximum suprathreshold
cluster size and cluster mass
• FWE P-value = 0.003 for cluster size
• FWE P-value = 0.002 for cluster mass
• 3 significant clusters (127, 201, 210)
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Conclusions
1
We have developed a fast, accurate, and non-iterative
heritability inference method, which makes permutation
feasible
2
Our LR-SD method is faster than SEM method in
Mx/OpenMx with comparable power and accuracy
3
For equivalent false positive rates, cluster-based method gives
higher sensitivity, and thus more statistical power
4
Demonstrate the need for permutation inference to take
advantage of cluster statistics
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Introduction
Methods
1D Simulation Results
2D Simulation Results
Real Data Results
Conclusions
Acknowledgements
Acknowledgements
• Dr Thomas Nichols (Supervisor)
Department of Statistics, University of Warwick, UK
• Dr Gabriëlla Blokland
Lachlan Strike
Dr Margie Wright
Genetic Epidemiology Laboratory, Queensland Institute of Medical
Research, Australia
School of Psychology, University of Queensland, Australia
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE
Thank You!
Voxel-wise and Cluster-based Heritability Inference for fMRI Data
Chen X, Blokland G, Strike L and Nichols TE