What the Mass Univariate
Model Doesn’t Tell You
Thomas Nichols, PhD
Department of Statistics, Warwick Manufacturing Group
University of Warwick
Mass-Univariate Can’t
Capture Spatial Heterogeneity
•  Controls false positive risk!
–  e.g. pFWE < 0.05 è 95%
confident of no false positives
•  Interpretable?
–  “Result” is 100,000 Yes/No’s,
significance at each voxel
•  Sensitive?
–  Must blur data until effects co-align
Individual responses
No smoothing
Toy Illustration:
•  3 subjects’ data before
& after smoothing
•  “Activation” only found
where no one
activates!
Individual responses
With smoothing
Blue-sky inference:
What we’d like…
•  Don’t threshold,
model the signal!
–  Signal location?
θˆMag.
•  CI’s on
(x,y,z) location
–  Signal magnitude?
•  P-values & CI’s
on % change
–  Spatial extent?
θˆLoc.
•  P-values & CI’s on activation volume
•  Robust to choice of cluster definition
•  .
θˆExt.
space
Blue-sky inference:
…what we actually get
•  Don’t threshold,
model the signal!
–  Signal location?
θˆMag.
•  CI’s on
(x,y,z) location
–  Signal magnitude?
•  P-values & CI’s
on % change
–  Spatial extent?
•  .
θˆLoc.
θˆExt.
space
•  P-values & CI’s on activation volume
•  Robust to choice of cluster definition
To make spatial inferences,
need spatial modelling
Blue-sky inference:
What we need
•  Explicit spatial model
–  High-dimensional mixture modeling problem
–  Need realistic shapes, sparse representation
•  Initial work exists,
many limitations
–  Too slow
–  Not robust
–  No public software
o  Xu et al. (2009). Modeling Inter-Subject Variability in fMRI
Activation Location: A Bayesian Hierarchical Spatial Model.
Biometrics, 65(4), 1041-1051.
o  Weeda et al. (2009). Activated region fitting: a robust highpower method for fMRI analysis using parameterized regions
of activation. Human brain mapping, 30(8), 2595-605.
o  Thirion et al. (2010). Accurate definition of brain regions
position through the functional landmark approach. MICCAI,
13(Pt 2), 241-8.
o  Kim et al. (2010). A Bayesian mixture approach to modeling
spatial activation patterns in multisite fMRI data. IEEE TMI,
29(6), 1260-74.
o  Gershman et al. (2011). A topographic latent source model
for fMRI data. NeuroImage, 57(1), 89-100.
o  Kang et al. (2011). Meta Analysis of Functional
Neuroimaging Data via Bayesian Spatial Point Processes.
5 J
Am Stat Assoc, 106(493), 124-134.
Blue-sky inference:
What we need
•  Explicit spatial model
–  High-dimensional mixture modeling problem
–  Need realistic shapes, sparse representation
•  Initial work exists,
many limitations
–  Too slow
–  Not robust
–  No public software
o  Xu et al. (2009). Modeling Inter-Subject Variability in fMRI
Activation Location: A Bayesian Hierarchical Spatial Model.
Biometrics, 65(4), 1041-1051.
o  Weeda et al. (2009). Activated region fitting: a robust highpower method for fMRI analysis using parameterized regions
of activation. Human brain mapping, 30(8), 2595-605.
o  Thirion et al. (2010). Accurate definition of brain regions
position through the functional landmark approach. MICCAI,
13(Pt 2), 241-8.
o  Kim et al. (2010). A Bayesian mixture approach to modeling
spatial activation patterns in multisite fMRI data. IEEE TMI,
29(6), 1260-74.
o  Gershman et al. (2011). A topographic latent source model
for fMRI data. NeuroImage, 57(1), 89-100.
o  Kang et al. (2011). Meta Analysis of Functional
Neuroimaging Data via Bayesian Spatial Point Processes.
6
J Am Stat Assoc, 106(493), 124-134.
Imaging Meta-Analysis Methods
•  Coordinate-Based Meta-Analysis (CBMA)
–  Only use location of peaks of activation maps
–  Current standard approach
•  x,y,z peak locations collected
–  Manually from published papers
–  From BrainMap or other databases
Results Table
of Coordinates
Standard
reporting format
for a fMRI
publication
x, y, z
atlas
coordinates
Multi-Level Kernel Density Analysis
Kober et al, 2008
3-Level Spatial
Hierarchy
“Population
Centers”
Level 1:
Population
Centres
Features
Some foci may
not “cluster”,
i.e. don’t
belong to any
centre
“Activation
Centers”
Some studies
report only one
focus per
cluster; some
multiple
Level 2:
Study
Activation
Centres
Population Center
Study Center
Study Foci Reported in paper
Kang et al., (2011), JASA 106:124-134. Level 3:
Study
Foci
Some studies
may not have
any foci from a
population
centre
CBMA Data
•  Neuroimaging Studies of Emotion
–  164 studies
–  Avg. n is 12 (4 ≤ n ≤ 40)
–  2350 peaks in total
–  Emotions studied: sad, happy, angry, fear,
disgust, surprise, affective and mixed
•  Goal
–  Find regions of consistent emotion-induced
activations
Example of
CBMA Data
•  x,y,z coord. in
MNI
(standard
atlas) space)
•  Each study
has multiple
points
Foci from 1 study
Foci from all 164 studies
Axial View
Coronal View
(from atop head)
(from behind head)
Example of
CBMA Data
•  x,y,z coord. in
MNI
(standard
atlas) space)
•  Each study
has multiple
points
•  We focus on
amygdala
Foci from 1 study
Foci from all 164 studies
Axial View
Coronal View
(from atop head)
(from behind head)
Posterior Fit & Comparison
Posterior Fit & Comparison
Activation Center Intensity
Where are foci in
a randomly
selected study?
(And how many!)
Population Center Intensity
Where is
there
evidence for
a population
center?
Posterior Fit
•  95% credible ellipses
–  Study-level centres (blue)
–  Population centres (yellow)
–  Amygdala voxels shown in red (Harvard-Oxford atlas)
Allows clear distinction between
Estimation of inter-study spread of loci, and
Inference on location of population centre
Comparison Between
Positive & Negative Emotions
P(DistLeft > 2mm) > 0.983
P(DistLeft > 4mm) > 0.704
P(DistRight > 2mm) > 0.999
P(DistRight > 4mm) > 0.932
Meta-Analysis Study Classification
•  Fit Bayesian model separately 5 times
•  Note, data very sparse
Foci per
Study
7.7
4.9
6.4
5.4
7.7
–  This is a challenge, but
–  Total counts informative of study type
•  Can then predict one new (held-out) study
LOOCV Classification Accuracy
•  Our model
–  83% avg.
–  69% worst
•  GNB with
MKDA
–  45% avg.
–  0% worst
•  Accurate
model
Chance Accuracy = 1/5 = 0.20
Conclusions: Meta Analysis
•  Intensity-Based Mega Analysis (IBMA)
–  Always preferred to use the original data
•  CBMA with ALE/(M)KDA, etc
–  Suffers from all limits of mass-univariate
modelling
•  CBMA & detailed spatial hierarchical
model
–  Much more interpretable model
Bayesian Model Selection Under Spatial
Uncertainty for Functional Imaging Studies
Alexis Roche
CIBM-Siemens, Ecole Polytechnique Fédérale (EPFL),
Lausanne, Switzerland
Bayesian Spatial Point Process Modeling of
Neuroimaging Data
Timothy D. Johnson
Department of Biostatistics, University of Michigan, Ann Arbor,
USA
New Tools for Tracking the Dynamics of Mental
Representations
Sam Gershman
Department of Psychology, Princeton University, Princeton, USA