An Overview, Challenges, and Future Directions - SAMSI

Experiments Models Connectivity Prediction Summary 

Statistical Modeling of Neuroimaging Data: An 

Overview, Challenges, and Future Directions 

F. DuBois Bowman 

Department of Biostatistics and Bioinformatics 

Center for Biomedical Imaging Statistics 

Emory University, Atlanta, GA, 30322 

Neuroimaging Data Analysis 

SAMSI 

Research Triangle Park, NC 

June 6, 2013 

F. D. Bowman (Emory University) SAMSI: NDA RTP, NC 1 / 77


Outline 

1 fMRI Experiments 

2 Modeling of fMRI Data: Neuroactivation Studies 

3 Connectivity 

4 Prediction 

5 Summary 



Hemodynamic Response Function 

HRF 

Typical BOLD response to an impulse stimulation 



fMRI Study Designs 

Block Designs 

Dominant in the early years of fMRI studies 

Multiple stimuli of the same condition are grouped together in blocks 

[f ∗ g] (t) = ∫ ∞ 

−∞ 

f (τ)g(t − τ)dτ 




Block Designs 

Advantages: 

Relatively simplified data analysis 

Increased statistical power 

More robust results 

Often yields relatively large BOLD signal changes. 

Disadvantage: 

Many potential confounds 

Habituation 

Anticipation 

Other strategy effects. 




Event-related Designs 

Allow different stimuli to be presented in arbitrary sequences. 

Permits randomization of conditions. 

Two types of event-related designs: 

Spaced event-related designs 

Rapid event-related designs 




Event-related Designs 

Advantages: 

Detect transient variations in hemodynamic responses. 

Allow the temporal characterization of BOLD signal changes: the HRF. 

Reduce potential confounds. 

Disadvantages: 

Reduced statistical power to detect BOLD differences between different 

conditions. 

Lower SNR. 

More complex design and analysis. (Dale, 1999) 




Resting-state fMRI Studies 

Rapid growth in resting-state studies 

Acquire scans while subjects are left to think for themselves. 

May reflect a natural and more common mode of neural processing. 




Resting-state fMRI Studies 

Common analytic objectives: 

Resting-state connectivity 

Correlations (associations) in neural activity between distinct brain 

locations. 

Default mode network 

Raises numerous analytical challenges 

Lower SNR. 

More complex design and analysis. 

Mode of neural processing is inconsistent across subjects. 

Unable to make relative comparisons reflecting changes in localized 

neural processing. 

I.e., unable to determine average brain activity changes at each voxel. 



Data Example 

Working Memory in Schizophrenia Patients 

N=28 subjects: 15 schizophrenia patients and 13 healthy controls 

fMRI Tasks: Serial Item Recognition Paradigm (SIRP) 

Encoding set: Subjects asked to memorize 1, 3, or 5 target digits. 

Probing set: Subjects sequentially shown single digit probes and asked 

to press a button: 

with their index finger, if the probe matched 

with their middle finger, if not. 

6 runs per subject: (177 scans per run for each subject) 

3 runs of working memory tasks on each of 2 days 

Objective: Compare working memory-related brain activity between 

patients and controls 

Data from the Biomedical Informatics Research Network (BIRN) [1]: Potkin et al. (2002), Proc. 41st Annu. Meeting Am. 

College Neuropsychopharm. 



Notable fMRI Data Characteristics 

Massive Data Sets 

Roughly 300,000 brain voxels for each scan at time of analysis 

S = 177 scans per run 

6 runs (sessions) per subject 

T=1062 scans total per subject 

Over 300 million spatio-temporal data points per subject! Over 5 

billion for all subjects!! 

Temporal correlations 

Scan to scan correlations 

Between session correlations 

Complex spatial correlations 

Correlations between neighboring voxels 

Long-range correlations between different brain regions 

Roughly 45 billion voxel pairs 



Common Analysis Framework 

Two-stage Model 

First, fit a linear model separately for each subject (at each voxel) 

Temporal correlations between scans: AR models (+ white noise) 

Pre-coloring/temporal smoothing [Worsley and Friston, 1995] 

Pre-whitening [Bullmore et al, 1996; Purdon and Weisskoff, 1998] 

Linear covariance structure 

Alternative structures available for PET [Bowman and Kilts, 2003] 

Second, fit linear model that combines subject-specific estimates 

A two-stage (random effects) model 

Simplifies computations* 

Sacrifices efficiency 

For Inference: Compute t-statistics at each voxel and threshold 

Consider a multiple testing adjustment (Bonferonni-type, FDR, RFT) 



Common Analysis Framework 

Properties 

Two-stage (random effects) model 

Simplifies computations 

Sacrifices efficiency 

Assumes independence between different brain locations 

Targets activation analyses, disregarding functional connectivity 



Statistical Modeling 

General Linear Model: Stage I 

Y ig (v) = X igv β ig (v) + H iv γ ig (v) + ε ig (v) 

Y ig (v) S × 1 serial brain (BOLD) activity at voxel v. 

X igv S × q design matrix containing independent variables. 

β ig (v) q × 1 parameter vector linking experimental tasks. 

ε ig (v) S × 1 random error about ith subject’s mean. 

H iv S × m contains other covariates, e.g. high-pass filtering. 

ε ig (v) ∼ Normal(0, τgv 2 V). 




General Linear Model: Stage II 

β ig (v) = µ g (v) + d ig (v) 

β ig (v) regression coefficients from stage I. 

µ g (v) group-level mean for all effects. 

d ig (v) 

random error. 

d ig (v) ∼ Normal(0, ω 2 (v)R). 

*Examine contrasts, e.g. A = [PostTx − PreTx] patients − [FU − BL] controls 




General Linear Model: Test Statistic 

t(v) = 

Cˆµ g (v) 

ŝe(Cˆµ g (v)) 

C is a user-specified contrast matrix (or vector). 

A threshold is applied to the test statistic t(v) for every voxel, 

v = 1, . . . , V . 

Adjustments are made for multiplicity 

Bonferroni-type corrections: divide significance level by the number of 

tests performed. 

Random field theory: account for spatial dependence, as captured by 

the maximum distribution. 

False discovery rate: expected proportion of erroneous rejections, 

among all rejections. 




Mixed Model Equivalent 

Y ig (v) = X igv β ig (v) + H iv γ ig (v) + ε ig (v) 

β ig (v) = µ g (v) + d ig (v) 

=⇒ Y ig (v) = X igv µ g (v) + X igv d ig (v) + H iv γ ig (v) + ε ig (v) 

X igv µ g (v) 

X igv d ig (v) 

fixed effects (group-level). 

random effects (subject-specific effects). 




Assumptions 

BOLD signals follow a Gaussian 

distribution. 

The same effects are present for each 

voxel. 

Relationship between independent 

variables and the BOLD response are 

captured by the general linear model. 

Estimation at one voxel is unrelated to 

estimation at other voxels, i.e. no 

spatial correlations. 

Stage II model does not always 

address correlations between multiple 

effects estimated for each individual. 

Quadratic Linear 




Other Considerations 

How well does my model fit? For which voxel? 

Do I have sufficient power? For which voxel? 

Multiplicity: Are you really conducting hundreds of thousands of 

tests? 

Largely addressed by random field theory. 

How do I best portray the uncertainty in my images of estimates? 

Confidence intervals for images. 



Spatial Correlations 

Distances 

Functional 

Physical (Geometric) 

Anatomical 

(a) Functional 

(b) Geometric 

The complex 

neuroanatomy and 

neurophysiology make 

basic assumptions of 

many spatial methods 

questionable for 

neuroimaging 

Figure: Alternative measures of 

distance. 

Bowman (2007), JASA. 



Spatial Modeling Framework 

Bayesian Spatial Model for Activation and Connectivity (BSMac): 

Stage I: Individual level - addresses temporal correlations. 

Stage II: Group level 

Define brain regions using 

neuroanatomic parcellation (e.g. 

Brodmann or AAL) 

Spatial correlations 

Within regions 

Between regions 

Inferences 

Voxel-level 

Regional 

Bowman et al. (2008), NeuroImage 

Zhang et al. (2011), Journal of Neuroscience Methods 



BSMac 

Stage II: Bayesian Spatial Model for Activation and Connectivity (BSMac): 

Y igj | µ gj , α igj , σ 2 gj ∼ Normal(µ gj + 1α igj , σ 2 gjI) 

µ gj | λ 2 gj ∼ Normal(1µ 0gj , λ 2 gjI) 

σ −2 

gj 

∼ Gamma(a 0 , b 0 ) 

α ij | Γ j ∼ Normal(0, Γ j ) 

λ −2 

gj 

∼ Gamma(c 0 , d 0 ) 

Γ −1 

j 

∼ Wishart { (h 0 H 0j ) −1 } 

, h 0 

Y igj = (Y igj1 , . . . , Y igjVg ) ′ , µ gj = (µ gj1 , . . . , µ gjVg ) ′ , and 

α ij = (α i1j , . . . , α iGj ) ′ 

Bowman et al. (2008), NeuroImage 

Zhang et al. (2011), Journal of Neuroscience Methods 



BSMac MATLAB Toolbox 

GUI Interface: Available at www.sph.emory.edu/bios/CBIS/ 




Interactive Activation Maps 




Task-Related Connectivity Maps: Schizophrenia Patients, WM Load 5 




Task-Related Connectivity Maps: Healthy Controls, WM Load 5 



BSMac Properties 

BSMac framework 

Considers activation objectives and task-related FC 

Models spatial correlations in brain activity 

Within and between defined neuroanatomic regions 

Yields easily interpretable posterior probabilities of activation 

Permits voxel-level and region-level inferences 

Can apply FDR-like concepts 

Limitations 

Does not account for temporal dependence between multiple sessions 

Fairly simple intra-regional correlation model 



Extensions: Spatial Modeling 

Between session correlations: (a) captures correlations between 

multiple scanning sessions (e.g. days or treatment periods), (b) does 

NOT model between-region spatial correlations 

[Derado et al. (2010), Biometrics] 

Model correlations between scanning sessions, between-regions, and 

locally within regions* 

Use imaging data to predict future neural responses 

[Derado et al. (2012), Statistical Methods in Medical Research] 

Model spatial correlations: Between AAL regions (unstructured 

covariance matrix), borrow strength between subregions within each 

AAL region (CAR model), between voxels within each subregion 

(exchangeable structure) 



Other Extensions 

Unspecified onsets of stimuli: meditation or pain tolerance. 

[Robinson et al. (2010), NeuroImage] 

Spectral modeling: Fourier coefficients are approximately uncorrelated 

across frequencies; wavelets have decorrelating properties. 

[Kang et al. (2012), JASA; Ombao et al. (2008), Statistica Sinica] 

Rician regression model to characterize noise contributions in fMRI 

along with associated estimation and diagnostic procedures. 

[Zhu et al. (2009), JASA] 



Brain Connectivity 

Determine functional and anatomical 

organization of the brain 

Anatomical 

Structural links between regions (axonal 

fiber tracts) 

Millions of axonal connections 

Functional 

Functional Connectivity: Correlations in 

brain activity between regions 

Task-induced 

Resting state 

Effective Connectivity: Influence that one 

region exerts on another 



Structural Connectivity 

Structural linkages through white-matter. 

Humans have estimated 86 billion neurons. 

Axons are neuron fibers that form bundles 

and serve as lines of transmission in the CNS 

Millions of fiber bundles in the white-matter 

These bundles directly link some brain 

structures 

Association bundles joining cortical areas 

within the same hemisphere 

Commissural bundles linking cortical areas 

in separate hemispheres 

Projection fibers uniting areas in the 

cerebral cortex to various subcortical 

structures 




Diffusion Tensor Imaging 

Identifies major white matter (axonal) 

fiber tracts in the brain 

Reflects white matter integrity by 

measuring restricted water diffusion in 

tissue 

Diffuse more quickly in the direction of 

fibers than in a perpendicular direction 

White matter fiber bundles (axons) are 

tracked from tensor field information 

combined across voxels. 

Reconstruct 3-D fibers (colors indicate 

direction): Red: Left-Right, Green: 

Ant.-Post., Blue: Inferior-Superior. 




Diffusion Tensor Imaging 

The tensor 

Represented by matrix D 

D xx , D yy , D zz reflect molecular 

mobility along x, y, z axes. 

D xy , D xz , D yz reflect correlations 

between molecular displacements in 

perpendicular directions. 

Eigenvalues λ 1 , λ 2 , λ 3 indicate 

main diffusion direction 

⎡ 

D = ⎣ 

D xx D xy D xz 

⎤ 

D xy D yy D yz 

⎦ 



Functional Connectivity 

Functional Specialization (Localization): 

Specific mental processes link to particular 

brain regions [Gall, 1796; Broca, 1861; 

Brodmann, 1909] 

Functional Integration: 

Interactions between specialised neuronal 

populations 




Functional Specialization (Localization): 

Specific mental processes link to particular 

brain regions [Gall, 1796; Broca, 1861; 

Brodmann, 1909] 

Functional Integration: 

Interactions between specialised neuronal 

populations 

=⇒ Functional connectivity 




Seed Voxel (or Region) Approaches 

Calculate the correlation (or partial 

correlation) between a selected voxel 

(region) and all other voxels (regions). 

ρ ij = min 

u∈U ρ ij(u) 

∑ T −u 

= min { t=1 [y i(t + u) − ȳ i ][y j (t) − ȳ j ] 

} 

u∈U ˆσ i ˆσ j 

Should be strongly hypothesis driven 

May miss important associations due to 

limited number of voxels (regions) assessed 




Whole-Brain Region to Region Approaches 

Calculate the correlation (or partial 

correlation) between a all pairs of regions). 

∑ T −u 

ρ ij = min { t=1 [y i(t + u) − ȳ i ][y j (t) − ȳ j ] 

} 

u∈U ˆσ i ˆσ j 

Requires parcellation of the brain into 

regions OR selection of a subset of regions. 

May miss important associations due to this 

selection process 

May select finer or coarser map of regions 

depending on objectives 

Finer map may prompt the assessment of 

whole brain topological properties (graph 

methods) 




Partitioning Approaches: Independent Components Analysis (ICA) 

Y = × . + 

Goal: Decompose observed fMRI data into a linear combination of 

spatio-temporal source signals. 

Y(T × V ): observed fMRI measurements 

A(T × q): mixing matrix (columns contain latent time series for ICs) 

S(q × V ): statistically independent spatial signals (in rows) 

E(T × V ): noise or variability not explained by the ICs, e v ∼MVN 




Partitioning Approaches: ICA 

Goal: Decompose observed fMRI data into a linear combination of 

spatio-temporal source signals. 





A Zen meditation study 

Zen meditation involves disciplined regulation of attention and bodily 

posture 

24 subjects: Zen meditation group (n=12) and control group (n=12). 

fMRI scans acquired at 520 time points. 

There was a meditative condition interspersed with a lexical decision 

task 

Mediative condition: Subjects were instructed to focus on breathing 

and to refocus attention to breathing when distracted by a lexical task. 

Lexical task: Subjects were randomly shown word or nonword letter 

strings and instructed to press a button indicating whether a word 

appeared, ”yes” (index finger) or ”no“” (middle finger). 

Objective: whether training in Zen meditation modifies the neural 

activity underlying attentional control and behavior switching. 

Pagnoni et al., 2008, PLoS ONE 





A Zen meditation study 




Partitioning Approaches: Cluster Analysis 

Goal is to partition the brain into 

clusters of regions, which exhibit 

similar patterns of brain function 

within. 

Each region begins as a single cluster 

Calculate functional distances between 

all brain regions, e.g. d ij = 1 − ρ ij 

Iteratively join most similar regions 

(clusters) until a single cluster remains 

Examine each stage of clustering tree 

to determine the optimal number of 

clusters, e.g. assess within and 

between cluster variability 

Motor 

Visual: 

Auditory 



Multimodal Connectivity 

Anatomically-weighted Functional Connectivity (awFC) 

[Bowman et al., 2012, NeuroImage] 

Functional connectivity relies on signaling along structural white 

matter pathways. 

Our main objective is to reliably detect networks of functionally 

connected regions 

We leverage supplementary information from the SC strength between 

brain regions 

SC does not imply FC 

Absence of SC does not preclude FC 

Indirect SC (e.g. via a remote third brain region) 

Potential Advantages: 

Help determine FC in the presence of fMRI noise 

Defaults to standard clustering techniques when no structural 

weighting is considered 

Provides additional information about connectivity relationships 



Subregion Selections and Summaries 

Whole-brain analysis with subregions 

for each AAL region 

For fMRI, 

Resting-state subregions selected in 

GM to be representative of larger 

regions 

Task-based subregions selected 

according to other criterion, e.g. 

centered on maximally activated 

voxel in region (across all tasks) 

Generate summary temporal signal 

for each subregion 

For DTI, 

Subregions centered in WM proximal 

to GM regions 

Probabilistic tractography used to 

summarize region-to-region SC 

fMRI 

DTI 



Determining Functional Networks 

Functional Clustering with DTI-based Anatomical Weighting: 



Anatomically Weighted Functional Distance 

( 

d ij = 

1 − π ij 

λ 

) 

f ij 

f ij is a measure of functional dissimilarity between regions i and j 

E.g. 1 − ρ ij 

We allow lag-u associations, u ∈ [−2, 2] 

π ij is the probability of structural connectivity 

π ij ∈ [0, 1) 

We consider second-order connections 

Adjust for physical distances between regions 

λ is a parameter used to potentially attenuate the impact of 

anatomical weighting 

λ determined empirically 

λ ∈ [1, ∞) 

d ij → f ij , as λ → ∞ 



awFC 

Anatomically weighted Functional Connectivity (awFC): 

Perform subject-specific clustering using average linkage method 

applied to distances d ij 

Empirically optimize λ using objective function based solely on the 

functional data 

h(λ, G) = log 

( 

FCwi 

FC tot 

) 

Generate group cluster solution from subject-specific networks 

Conduct hypothesis testing to determine the statistical significance of 

the correlation between each pair of regions within the identified 

networks 



awFC 

(a) 

(b) 

6 

0.16 

0.14 

G=9 

0.12 

5.5 

λ=7.5 

0.1 

Σ i 

∆ i 

(λ) 

5 

∆(G) 

0.08 

0.06 

0.04 

0.02 

4.5 

10 20 30 40 50 60 70 80 90 100 

λ 

0 

0 5 10 15 20 25 30 35 

G (lag 1) 

(a) Empirical optimization of the attenuation parameter λ 

(b) Determination of the number of cluster, G, for subject 1 



Data Example 

Auditory Task Study 

N=17 healthy female subjects 

3 fMRI runs (483 scans total for each subject) 

fMRI Auditory Task 

Cue: Hear an auditory tone (2000 Hz) in one ear. 

Target: Subsequently hear a target tone (1000 Hz) in either ear. 

Instructed to click a button with right (a) index finger if the target is 

from the left earphone OR (b) middle finger if from right earphone. 

50% of the trials have the cue and target tones in the same ear. 

Subjects fixated at a cross throughout the entire scanning session. 

DTI data also collected 

Objective: Study had a broad set of objectives (Mayer et al., 2009). 

We consider an analysis that identifies different functional networks. 



awFC: Analysis of Task Data 

Motor Motor Visual 

Visual 

Auditory 



awFC Results: Auditory Data 

(a) 

(b) 

1 

0.9 

Network Correlations median 

In−network 

Cross−network 

1 

0.9 

Network SC Proportion 

In−network 


0.8 

0.8 

0.7 

0.7 

Median Correlation 

0.6 

0.5 

0.4 

Proportion Connected 

0.6 

0.5 

0.4 

0.3 

0.3 

0.2 

0.2 

0.1 

0.1 

0 

0 5 10 15 20 

subject 

0 

0 5 10 15 20 

subject 

(a) Median correlations within-networks and between-networks 

(b) Proportion of region pairs exhibiting SC, i.e. Pr(SC) > 0.5, 

within-networks and between-networks 




Regional Time-series from 90 Brain Regions (Subject 2) 

5 

4 

3 

2 

1 

0 

−1 

−2 

−3 

−4 

0 10 20 30 40 50 60 70 80 90 




Time-series for awFC Networks (Subject 2) 



awFC: Analysis of Resting-state Data 



awFC Results: Resting-state Data 

(a) 

(b) 

1 

0.9 

Network Correlations 

In−network 


1 

0.9 

Network SC 

In−network 


0.8 

0.8 

0.7 

0.7 

Median Correlation 

0.6 

0.5 

0.4 

Proportion Connected 

0.6 

0.5 

0.4 

0.3 

0.3 

0.2 

0.2 

0.1 

0.1 

0 

1 2 3 4 5 6 

subject 

0 

1 2 3 4 5 6 

subject 

(a) Median correlations within-networks and between-networks 

(b) Proportion of region pairs exhibiting SC, i.e. Pr(SC) > 0.5, 

within-networks and between-networks 



Comparative Analysis 

Simulation Results: awFC versus Standard (Unweighted) Clustering 

Table: Percent accuracies and standard errors (in parentheses). G=13 clusters 

used for all results, and σ 2 set using the experimental data. 

Noise-level Accuracy awFC Unweighted 

σ 2 Overall 97.35 (1.02) 94.61 (1.59) 

In-network 89.74 (4.61) 76.82 (7.78) 

Cross-network 98.70 (0.58) 97.78 (0.72) 

1.25σ 2 Overall 96.72 (1.15) 93.28 (1.73) 

In-network 87.01 (5.46) 70.60 (8.48) 

Cross-network 98.46 (0.61) 97.32 (0.80) 

1.50σ 2 Overall 96.13 (1.29) 92.33 (1.77) 

In-network 84.38 (6.01) 66.28 (8.52) 

Cross-network 98.23 (0.67) 96.97 (0.84) 



Other Connectivity Methods 

Model-based methods (Bayesian): 

Chen et al., 2013, submitted. 

Xue and Bowman, 2013, submitted. 

Patel et al., 2006a, Human Brain Mapping. 

Patel et al., 2006b, Human Brain Mapping. 

Whole-brain complex networks (graph theoretic methods) 

Simpson et al., 2013, Statistics Surveys. 

Effective Connectivity 

Granger causality 

Structural equation modeling 

Dynamic causal modeling 



Prediction Studies 

Emerging direction in neuroimaging 

Increase clinical applicability 

Use imaging data to predict clinical outcomes (e.g. to distinguish 

treatment responders and non-responders) 

We address intermediate objective of predicting neural responses 

Forecast neural representations of disease progression 

Predict neural responses to various treatments 

We develop a spatial modeling framework within this prediction 

context 



Motivating Data Example 

From the Alzheimer’s Disease Neuroimaging Initiative (ADNI) 

database http://www.loni.ucla.edu/ADNI/. 

Goal of ADNI: to develop biomarkers of AD in elderly subjects. 

Study participants receive PET scans at: baseline, 6 months, 12 

months and 24 months. 

In our analysis, we used 

Baseline and month 6 scans. 

Subjects classified as: AD patients or healthy controls (HC). 

Training data set: 40 AD and 40 HC subjects; Testing data set: 33 AD 

and 33 HC subjects. 



Bayesian spatial hierarchical model 

[Derado et al., 2012, Statistical Methods in Medical Research]. 

Notation 

We developed a Bayesian spatial hierarchical model for predicting 

follow-up neural activity based on baseline functional neuroimaging 

data and other patient characteristics. 

Model borrows strength from spatial correlations present in the data. 

Let i = 1, . . . , n denote subjects, v = 1, . . . , V voxels, g = 1, . . . , G 

regions. 

Let Y (v) denote the regional cerebral blood flow (rCBF) (a proxy for 

brain activity) at voxel v. 

( 

) T 

Let Y ig (v) = Y ig (v) (1) , Y ig (v) (2) , (1)=baseline, (2)=follow-up. 



Spatial dependence: 3D neighborhood 

For each voxel in the analysis, we define a 3D neighborhood as the 26 

immediate neighboring voxels. 

Borrow strength locally. 

We consider only within-region neighbors. 

This information is saved in a connectivity matrix W. 



Model 

Y ig (v)|β g , φ g , α ig , γ gv , Ω g ∼ N(β g (v) + φ g (v) + α ig + X ig γ g , Ω g ) 

φ g (v)|φ g (v ′ ), v ≠ v ′ , ρ, Σ ∼ N ( ρ ∑ w vv ′ 

w v+ 

φ g (v ′ 1 

), 

w v+ 

Σ ) ( MCAR(ρ, Σ) ) 

β gj (v)|λ 2 gj ∼ N(β 0gj , λ 2 gj) (λ vgj = λ gj , ∀v ∈ region g) 

Ω −1 

g ∼ Wishart ( (c 1 Z 1 ) −1 ) 

, c 1 

Σ −1 ∼ Wishart ( (c 2 Z 2 ) −1 , c 2 

) 

α ij |Γ j ∼ N(0, Γ j ) 

(α ij = α (j) 

i 

Γ −1 

j 

∼ Wishart((h j H j ) −1 , h j ) j = 1, 2 

λ −2 

gj 

∼ Gamma(a j , b j ) 

γ gjq |τ 2 gjq ∼ N(0, τ 2 gjq) 

τ −2 

gjq ∼ Gamma(e 0, f 0 ) 

= (α (j) 

i1 , . . . , α(j) iG )′ ) 

q = 1, . . . , Q (covariates) 



Estimation and Prediction 

Estimation is performed using MCMC methods (Gibbs) 

Prediction: 

For region g, we can write 

Y g = (Y T g,1 , YT g,2 )T ∼ N ( (µ T g,1 , µT g,2 )T , Ψ g 

) 

, where Ψg = Σ g ⊗ I Vg . 

Then E(Y i ∗ g,2|Y i ∗ g,1) = b i ∗ g , where 

b i ∗ g = µ i ∗ g,2 + Ψ T g,12Ψ −1 

g,11 (Y i ∗ g,1 − µ i ∗ g,1) 

and µ i ∗ g = β g + φ g + 1 Vg ⊗ α i ∗ g + 1 Vg ⊗ X i ∗ gv γ gv . 

Estimated conditional mean ˆb i ∗ g obtained from inputting the posterior 

means of the corresponding parameters 

The follow-up brain activity Y i ∗ g,2 is predicted using the estimated 

conditional mean ˆb i ∗ g . 



Figure: Individualized observed and predicted 6 month follow-up rCBF 

measurements for a test subject in the AD group (axial slice 40). 

F. D. Bowman (Emory University) SAMSI: NDA RTP, NC 63 / 77 

Results: Prediction for PET study of AD 

Subject 1: observed Y (2) Subject 1: predicted Y (2)


Figure: Individualized observed and predicted 6 month follow-up rCBF 

measurements for a test subject in the AD group (axial slice 40). 

F. D. Bowman (Emory University) SAMSI: NDA RTP, NC 64 / 77 

Results cont. 

Subject 19: observed Y (2) Subject 19: predicted Y (2)


Prediction Error 

We evaluate the prediction error using a scale-free (squared error) loss 

function, which adjusts for local magnitude of brain activity 

√ 

1 

∑ 

(2) ) N 

(v)}, {Ŷ i (v)} = 

N i=1 [Ŷ (2) (2) 

i (v) − Y 

stPMSE ( {Y (2) 

i 

1 

N 

∑ N 

i=1 Y (2) 

i 

(v) 

i 

(v)] 2 



Comparative Analyses 

Model BSPM BSMac GLM 

Aver. error 0.083 0.154 (85.5% increase) 0.157 (89.2% increase) 



Simulation Study 

We simulated 100 data sets for 15 subjects. 

Selected 5 AAL regions with sizes ranging from 234 to 4,655 voxels. 

Specified the true values for β g , φ g , α i , and γ g . 

The rest of the (hyper)parameters drawn from their prior distributions. 

Param. 

Region 

1 2 3 4 5 

True Est. True Est. True Est. True Est. True Est. 

Ω g,11 323.26 321.09 160.61 159.99 11.46 11.46 3.44 3.44 3.57 3.57 

Ω g,22 120.75 120.46 45.30 45.11 37.24 37.19 10.45 10.45 3.38 3.38 

Ω g,12 -41.95 -41.25 -33.70 -33.40 16.32 16.30 4.08 4.08 2.40 2.40 

Table: Summary of the simulation results for the parameters in the covariance 

matrix Ω g . 



NIH Parkinson’s Disease Biomarker Program 



Parkinson’s Disease 

PD is a chronic, progressive movement disorder affecting at least one 

half million patients in the U.S. 

No diagnostic test to validate PD determination 

Diagnosis: medical history, neurological exam, and treatment response 

Brain scans and lab tests possibly used to rule out other diseases 

Symptoms 

Tremor, rigidity, bradykinesia (slowness of movement), and impaired 

balance and coordination 

With progression, patients may have difficulty walking, talking, or 

completing other simple tasks 

Non-motor symptoms: cognition, mood, sleep, and autonomic function 

PD usually affects people over 50 years of age 

Drug (e.g. levodopa combined with carbidopa) and surgical (DBS) 

treatments available, but none halt progression 



Parkinson’s Disease Biomarkers 

Motivation 

The optimal window for 

neuroprotecion in PD is during 

the premotor period before 

most neuronal death occurs. 

Neurology 2009;72(Suppl 2):S21-S26. 



Multimodal PD biomarker detection 

Suggested links between PD and single 

genetic, imaging, and biologic factors. 

Many of these are non-specific or 

insensitive. 

Single modality biomarkers may not fully 

address the complexity of PD. 

We regard PD as a complex, systems-level, 

multi-dimensional disorder with discrete, but 

functionally integrated manifestations. 

We are developing methods to define 

multimodal PD biomarkers from a massive 

number of hypothesis driven and exploratory 

candidate markers. 



Data 

Multimodal Parkinson’s Disease Imaging Studies 

The data will include 81 subjects 

across three studies 

38 Parkinson’s disease patients 

32 Healthy control subjects 

11 Alzheimers disease patients 

Potential Biomarkers 

Imaging (MRI, fMRI, DTI, 

NM-MRI, CSI) 

Genetic 

Neurocognitive Testing 

Questionnaire-Derived Scores 

Clinical 

CSF Neuroinflammation 

CSF Catecholamine Metabolites 



Methods 

High-dimensional Data Methods 

Develop statistical models, which pool predictive strength across 

multiple data modalities 

Proposed statistical techniques 

Penalized likelihood approaches: 

l p (β, λ) = −l(β) + ∑ k λ kP k (β k ) 

l(β) = ∑ i [y ilogπ i + (1 − y i )log(1 − π i ] 

Variable selection or shrinkage 

Novel joint multimodal probability models 

Model development, training, testing, and validation 



Bayesian Spatial Prediction Model 

We blindly classify subjects as either PD or HC 

from multimodal imaging data (and other patient 

information) 

Two-level parcellation: AAL Regions → Subregions 

Spatial correlations: 

Between AAL regions: Unstructured covariance 

matrix 

Borrow strength between subregions within each 

AAL region: CAR model 

Between voxels within each subregion: 

Exchangeable structure 



Bayesian Spatial Prediction Model 

Example of modelling framework using ALFF and VBM data 

Let D i ∈ {0, 1} represent disease status (e.g. 1=PD, 0=HC) 

Let X ilg (v) and Z ilg (v) respectively denote the ALFF and VBM for 

subject i at voxel v in subregion l (in region g), and 

B i = [X ilg (v), Z ilg (v)] 

Construct a Bayesian joint (multimodal) probability model 

f (X ilg (v), Z ilg (v)|D i ) ∝ f 1 (X ilg (v)|Zilg(v), D i ) × f 2 (Z ilg (v)|D i ) 

Generate predictions for a new subject n + 1 based on 

Pr(D n+1 = k|B n+1 , {B i , D i } n i=1 ) 



Summary 

Statistical methods play important roles in the analysis of 

neuroimaging data 

identify biomarkers of disease and treatment response. 

detect disease- or treatment-related alterations in brain function 

determine brain networks 

Multimodal analyses may yield more accurate and robust results than 

single genetic, imaging, biological, or clinical markers. 

Leveraging available information in the data (e.g. borrowing strength 

across brain areas) may yield more precise estimates. 



Acknowledgements 

Research Team 

Lijun Zhang, PhD, Emory, Biostatistics and Bioinformatics 

Jian Kang, PhD, Emory, Biostatistics and Bioinformatics 

Ying Guo, PhD, Emory, Biostatistics and Bioinformatics 

Gordana Derado, PhD, CDC 

Shuo Chen, PhD, Univ. of Maryland, Epidemiology and Biostatistics 

Daniel Huddleston, MD, Kaiser Permanente Georgia 

Xiaoping Hu, PhD, Emory/GA Tech, Biomedical Engineering 

Helen Mayberg, MD, Emory, Psychiatry and Behavioral Sciences 

Doctoral Students: 

Wenqiong Xue, MS, Emory, Biostatistics and Bioinformatics 

Anthony Pileggi, Emory, Biostatistics and Bioinformatics 

Phebe L. Brenne, Emory, Biostatistics and Bioinformatics 

Qing He, Emory, Biostatistics and Bioinformatics 

Yize Zhao, Emory, Biostatistics and Bioinformatics 

NINDS U18 NS082143-01 (Bowman) and the PDBP 

NIMH R01-MH079251 (Bowman)

An Overview, Challenges, and Future Directions - SAMSI

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