Mediation Analysis in Neuroimaging Studies Yi Zhao Department of - - PowerPoint PPT Presentation

Mediation Analysis in Neuroimaging Studies

Yi Zhao

Department of Biostatistics Johns Hopkins Bloomberg School of Public Health

January 15, 2019

Overview

Introduction Functional mediation analysis High-dimensional mediation analysis Multimodal neuroimaging data integration Discussion

2 / 35

Mediation analysis

Treatment (X) Mediator (M) Outcome (Y ) α β γ

• Quantifies the intermediate effect of the mediator

3 / 35

Mediation analysis

Treatment (X) Mediator (M) Outcome (Y ) α β γ

• Quantifies the intermediate effect of the mediator
• Helps clarify the underlying causal mechanism

3 / 35

Mediation analysis

Treatment (X) Mediator (M) Outcome (Y ) α β γ

• Quantifies the intermediate effect of the mediator
• Helps clarify the underlying causal mechanism
• Popular approach: structural equation modeling (SEM)

M = Xα + ǫ1 Y = Xγ + Mβ + ǫ2

• αβ: indirect (mediation) effect
• γ: direct effect

3 / 35

Neuroimaging studies

• Non-invasive techniques
• e.g. structural/diffusion/functional MRI, PET, MEG/EEG
• Functional MRI (fMRI)
• brain activity: changes in brain

hemodynamics

• resting-state and task-based fMRI

Credit: NSF 4 / 35

Neuroimaging studies

• Non-invasive techniques
• e.g. structural/diffusion/functional MRI, PET, MEG/EEG
• Functional MRI (fMRI)
• brain activity: changes in brain

hemodynamics

• resting-state and task-based fMRI

Credit: NSF

Objective

• Resting-state fMRI
• brain co-activation (functional connectivity)
• impact on cognitive behaviors

4 / 35

Neuroimaging studies

• Non-invasive techniques
• e.g. structural/diffusion/functional MRI, PET, MEG/EEG
• Functional MRI (fMRI)
• brain activity: changes in brain

hemodynamics

• resting-state and task-based fMRI

Credit: NSF

Objective

• Resting-state fMRI
• brain co-activation (functional connectivity)
• impact on cognitive behaviors
• Task-based fMRI
• causal effect of stimulus on brain activity
• brain connectivity (effective connectivity)

4 / 35

Challenges

• Large n with hierarchically nested data structure
• participants (→ sessions) → tasks/trials
• population level inference
• Large p
• 105 ∼ 106 uniformly spaced voxels
• > 100 putative functional/anatomical regions
• high-dimensional problem
• Complex data output
• time series
• functional data

5 / 35

Challenges

• Large n with hierarchically nested data structure
• participants (→ sessions) → tasks/trials
• population level inference
• Large p
• 105 ∼ 106 uniformly spaced voxels
• > 100 putative functional/anatomical regions
• high-dimensional problem
• Complex data output
• time series
• functional data

5 / 35

Motivating example: response conflict task

• Response conflict task
• “GO” trial: button press
• “STOP” trial: withhold pressing
• Brain regions of interest
• primary motor cortex (M1):

responsible for movement

• presupplementary motor area

(preSMA): primary region for motor response prohibition

• Objective: quantify causal effects
• stimulus → preSMA, stimulus → M1
• preSMA → M1 (Obeso et al., 2013)

6 / 35

Motivating example: response conflict task

• Response conflict task
• “GO” trial: button press
• “STOP” trial: withhold pressing
• Brain regions of interest
• primary motor cortex (M1):

responsible for movement

• presupplementary motor area

(preSMA): primary region for motor response prohibition

• Objective: quantify causal effects
• stimulus → preSMA, stimulus → M1
• preSMA → M1 (Obeso et al., 2013)

6 / 35

Motivating example: response conflict task

• Response conflict task
• “GO” trial: button press
• “STOP” trial: withhold pressing
• Brain regions of interest
• primary motor cortex (M1):

responsible for movement

• presupplementary motor area

(preSMA): primary region for motor response prohibition

• Objective: quantify causal effects
• stimulus → preSMA, stimulus → M1
• preSMA → M1 (Obeso et al., 2013)

6 / 35

Mediation analysis

Treatment X(t) Mediator M(t) Outcome Y (t)

• Conflict response task: STOP/GO
• Mediator region: preSMA, outcome region: M1
• Mediation model on functional measures
• Dynamic causal effects

7 / 35

Functional mediation model

Treatment X(t) Mediator M(t) Outcome Y (t)

For ∀ t ∈ [0, T],

• Concurrent model

M(t) = X(t)α(t) + ǫ1(t) Y (t) = X(t)γ(t) + M(t)β(t) + ǫ2(t)

• Historical influence model

M(t) =

• Ω1

t

X(s)α(s, t) ds + ǫ1(t) Y (t) =

• Ω2

t

X(s)γ(s, t) ds +

• Ω3

t

M(s)β(s, t) ds + ǫ2(t)

• Ωk

t = [(t − δk) ∨ 0, t], δk ∈ (0, +∞], k = 1, 2, 3

• if δk ∈ [T, +∞]: whole history

8 / 35

• Concurrent model

DE(t) = E Y (t; {x(s), m(s)}Ht) − Y (t; {x′(s), m(s)}Ht) =

• x(t) − x′(t)

γ(t) IE(t) = E Y (t; {x(s), m(s; {x(u)}Hs)}Ht) − Y (t; {x(s), m(s; {x′(u)}Hs)}Ht) =

• x(t) − x′(t)

α(t)β(t)

• Historical influence model

DE(t) = E Y (t; {x(s), m(s)}Ht) − Y (t; {x′(s), m(s)}Ht) =

• Ω2

t

• x(s) − x′(s)

γ(s, t) ds IE(t) = E Y (t; {x(s), m(s; {x(u)}Hs)}Ht) − Y (t; {x(s), m(s; {x′(u)}Hs)}Ht) =

• Ω3

t

• Ω1

s

(x(u) − x′(u))α(u, s) du

• β(s, t) ds
• {x(s)}Ht : history of variable x, Ht = [0, t]
• M(t; {x(s)}Ht ): potential outcome of M at time t if X has the history {x(s)}Ht
• Y (t; {x(s), m(s)}Ht ): potential outcome of Y at time t when the history X and M at level {x(s)}Ht

and {m(s)}Ht 9 / 35

• Historical influence model

Direct effect (DE)

s

(x(s) − x′(s))γ(s, t) t t − δ

DE(t) = t

t−δ∨0(x(s) − x′(s))γ(s, t) ds

Indirect effect (IE)

u s

t − δ t t − 2δ t − δ t (x(u) − x′(u))α(u, s)β(s, t) IE(t) = t

t−δ∨0

s

s−δ∨0(x(u) − x′(u))α(u, s)β(s, t) duds

• δ1 = δ2 = δ3 = δ, δ small

10 / 35

• Historical influence model

Direct effect (DE)

s

(x(s) − x′(s))γ(s, t) t

DE(t) = t

0 (x(s) − x′(s))γ(s, t) ds

Indirect effect (IE)

u s

t t (x(u) − x′(u))α(u, s)β(s, t) IE(t) = t s

0 (x(u) − x′(u))α(u, s)β(s, t) duds

• δ1 = δ2 = δ3 = δ, δ ∈ [T, +∞]

10 / 35

Response conflict task fMRI study1

• N = 121 right-handed healthy participants
• randomized STOP/GO trials: 90 GO trials and 32 STOP trials
• mediator region: preSMA-post (MNI: (-4,-8,60))
• outcome region: M1 (MNI: (-41,-20,62))
• TR = 2 s, 184 time points
• X(t): convolution of event onsets and canonical HRF
• M(t) and Y (t): BOLD signals after motion correction

1OpenfMRI ds000030 11 / 35

• Concurrent model

M(t) = X(t)α(t) + ǫ1(t) Y (t) = X(t)γ(t) + M(t)β(t) + ǫ2(t)

• Historical influence model

M(t) =

• Ω1

t

X(s)α(s, t) ds + ǫ1(t) Y (t) =

• Ω2

t

X(s)γ(s, t) ds +

• Ω3

t

M(s)β(s, t) ds + ǫ2(t)

• Ωk

t = [(t − δk) ∨ 0, t], δk ∈ (0, +∞], k = 1, 2, 3

• if δk ∈ [T, +∞]: whole history
• δ = 2, 4, 6, 10, 20, 30, ∞ (seconds)

12 / 35

Model selection

• mean squared error: θi observed Mi or Yi

MSE(ˆ θ) = 1 N

N

• i=1

T

(ˆ θi(t) − θi(t))2 dt

Historical Historical (∼ X) Concurrent (∼ M) δ = 2 δ = 4 δ = 6 δ = 10 δ = 20 δ = 30 δ = ∞ M 353.460 352.645 352.244 351.988 351.652 351.179 351.272 357.396 δ = 2 212.331 212.308 211.960 212.333 212.378 212.130 212.343 δ = 4 211.324 211.227 211.062 211.064 211.124 211.070 211.572 δ = 6 211.883 211.663 211.541 211.546 211.592 211.575 212.110 δ = 10 214.277 214.035 213.909 213.953 213.989 213.971 214.510 δ = 20 218.383 218.098 217.878 217.928 218.312 218.247 218.765 δ = 30 221.183 220.915 220.666 220.685 221.041 221.266 221.727 Y 220.203 δ = ∞ 295.291 294.938 294.904 294.695 294.820 294.742 301.385 13 / 35

Mediator: preSMA-post (MNI: (−4, −8, 60))

• STOP trial: δMX = 20, δY X = 6, δY M = 4

14 / 35

Challenges

• Large n with hierarchically nested data structure
• participants (→ sessions) → tasks/trials
• population level inference
• Large p
• 105 ∼ 106 uniformly spaced voxels
• > 100 putative functional/anatomical regions
• high-dimensional problem
• Complex data output
• time series
• functional data

15 / 35

Single modality

Treatment (X) Mediator 1 (M1) Mediator 2 (M2) . . . Mediator p (Mp) Outcome (Y ) c a1 a2 ap b1 b2 bp

16 / 35

Single modality

Treatment (X) Mediator 1 (M1) Mediator 2 (M2) . . . Mediator p (Mp) Outcome (Y ) c a1 a2 ap d12 d1p d2p b1 b2 bp

16 / 35

Single modality

Treatment (X) Mediator 1 (M1) Mediator 2 (M2) . . . Mediator p (Mp) Outcome (Y ) c a1 a2 ap d12 d1p d2p b1 b2 bp

Objective

• Identify significant brain regions (mediators)
• Estimate mediation effects

16 / 35

Single modality

Treatment (X) Mediator 1 (M1) Mediator 2 (M2) . . . Mediator p (Mp) Outcome (Y ) c a1 a2 ap d12 d1p d2p b1 b2 bp

Challenges

• Ordering of the mediators unknown
• Large number of mediators (> number of observations)

16 / 35

Zhao and Luo (2016)

Full model

X M1 M2

. . .

Mp Y

ǫ11 ǫ12 ǫ1p ǫ2 c a1 a2 ap d12 d1p d2p b1 b2 bp

Reduced model

X M1 M2

. . .

Mp Y

η11 η12 η1p η2 γ α1 α2 αp β1 β2 βp

M1 = Xa1 + ǫ11 M2 = Xa2 + M1d12 + ǫ12 . . . Mp = Xap + M1d1p + · · · + Mp−1dp−1,p + ǫ1p Y = Xc + M1b1 + · · · + Mpbp + ǫ2 M1 = Xα1 + η11 M2 = Xα2 + η12 . . . Mp = XαK + η1p Y = Xγ + M1β1 + · · · + Mpβp + η2

17 / 35

Zhao and Luo (2016)

Full model

X M1 M2

. . .

Mp Y

ǫ11 ǫ12 ǫ1p ǫ2 c a1 a2 ap d12 d1p d2p b1 b2 bp

Reduced model

X M1 M2

. . .

Mp Y

η11 η12 η1p η2 γ α1 α2 αp β1 β2 βp

M1 = Xa1 + ǫ11 M2 = Xa2 + M1d12 + ǫ12 . . . Mp = Xap + M1d1p + · · · + Mp−1dp−1,p + ǫ1p Y = Xc + M1b1 + · · · + Mpbp + ǫ2 M1 = Xα1 + η11 M2 = Xα2 + η12 . . . Mp = XαK + η1p Y = Xγ + M1β1 + · · · + Mpβp + η2

17 / 35

Zhao and Luo (2016)

Full model

X M1 M2

. . .

Mp Y

ǫ11 ǫ12 ǫ1p ǫ2 c a1 a2 ap d12 d1p d2p b1 b2 bp

Reduced model

X M1 M2

. . .

Mp Y

η11 η12 η1p η2 γ α1 α2 αp β1 β2 βp

M1 = Xa1 + ǫ11 M2 = Xa2 + M1d12 + ǫ12 . . . Mp = Xap + M1d1p + · · · + Mp−1dp−1,p + ǫ1p Y = Xc + M1b1 + · · · + Mpbp + ǫ2 M1 = Xα1 + η11 M2 = Xα2 + η12 . . . Mp = XαK + η1p Y = Xγ + M1β1 + · · · + Mpβp + η2

17 / 35

• adjacency matrix of mediators:

∆ =

          

d12 d13 · · · d1p d23 · · · d2p ... ... . . . ... dp−1,p

          

p×p

• influence matrix: (Ip − ∆)−1

Full Model

X M1 M2 . . . Mp Y ǫ11 ǫ12 ǫ1p ǫ2 c a1 a2 ap d12 d1p d2p b1 b2 bp

• γ = c, β1 = b1, . . . , βp = bp
• α1

· · · αp

• =
• a1

· · · ap

• (Ip − ∆)−1
• η11

· · · η1p

• =
• ǫ11

· · · ǫ1p

• (Ip − ∆)−1

Reduced Model

X M1 M2 . . . Mp Y η11 η12 η1p η2 γ α1 α2 αp β1 β2 βp

18 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a1 a2 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a1 a2 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a1 a2 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a1 a2 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a2 a1 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a1 a2 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

Example with 3 mediators

X M1 M2 M3 Y

ǫ11 ǫ12 ǫ13 ǫ2

Full Model

c a1 a2 a3 d12 d13 d23 b1 b2 b3

X M1 M2 M3 Y

η11 η12 η13 η2

Reduced Model

γ α1 α2 α3 β1 β2 β3

∆ =

     

d12 d13 d23

     

, (I3 − ∆)−1 =

     

1 d12 d13 + d12d23 1 d23 1

     

• α1

α2 α3

• =
• a1

a2 a3

• (I3 − ∆)−1

=

• a1

a1d12 + a2 a1(d13 + d12d23) + a2d23 + a3

• 19 / 35

• η11

· · · η1p

• reduced model

=

• ǫ11

· · · ǫ1p

• full model

(Ip − ∆)−1

• Sequential ignorability of mediators (sequentially conditionally

independent)

Cov [vec(ǫ1)] = Ω ⊗ In = diag{ω2

1, . . . , ω2 p} ⊗ In

• Cov [vec(η1)] =

Ip − ∆⊤−1Ω Ip − ∆ −1 ⊗ In = Σ1 ⊗ In

• Σ1 diagonal matrix ⇔ ∆ = 0 (mediators causally independent)
• Ip − ∆⊤−1Ω

Ip − ∆ −1 LDL decomposition of Σ1

• Σ1 positive-definite, decomposition unique
• p > n, ˆ

Σ1 not of full rank

• decomposition not unique
• require knowledge of ordering of the mediators

20 / 35

Full Model

X M1 M2 . . . Mp Y ǫ11 ǫ12 ǫ1p ǫ2 c a1 a2 ap d12 d1p d2p b1 b2 bp

Reduced Model

X M1 M2 . . . Mp Y η11 η12 η1p η2 γ α1 α2 αp β1 β2 βp

• αj: total effect of X on Mj (e.g., α2 = a1d12 + a2)
• αjβj: Mj mediation effect as the last mediator in pathway to Y
• dependency in Mj’s → correlation in η1j’s (e.g., η12 = η11d12 + ǫ12)

21 / 35

Pathway Lasso

min 1 2ℓ+λ

 

p

• j=1
• |αjβj| + φj(α2

j + β2 j )

• + |γ|

 

• P1:pathway lasso penalty

+ω

p

• j=1

(|αj| + |βj|)

• P2:lasso penalty
• loss function

ℓ = tr W1(M − Xα)⊤(M − Xα) + w2(Y − Xγ − Mβ)⊤(Y − Xγ − Mβ)

• λ ≥ 0, φj > 1/2, ω ≥ 0 tuning parameters
• λ = 0: lasso penalty
• ω = 0: pathway lasso

22 / 35

Multimodal neuroimaging

(Liu et al. 2015) 23 / 35

Structural and functional imaging

Exposure Outcome

• Hypothesis: structural → functional
• Objective: integrating DTI and fMRI through mediation analysis

24 / 35

X M11 M12 ... M1p1 M21 M22 ... M2p2 Y

α1 α2 αp1 γ1 γ2 γp2 δ φ12 φ1p1 φ2p1 ω11 ω12 ω1p2 ω21 ω22 ω2p2 ωp11 ωp12 ωp1p2 θ1 θ2 θp1 ψ12 ψ1p2 ψ2p2

π1 π2 πp2

• Two blocks of mediators: {M11, . . . , M1p1} and {M21, . . . , M2p2}
• Within block, ordering unknown

25 / 35

Full model

X M11 M12 ... M1p1 M21 M22 ... M2p2 Y

α1 α2 αp1 γ1 γ2 γp2 δ φ12 φ1p1 φ2p1 ω11 ω12 ω1p2 ω21 ω22 ω2p2 ωp11 ωp12 ωp1p2 θ1 θ2 θp1 ψ12 ψ1p2 ψ2p2

π1 π2 πp2

Reduced model

X M11 M12 ... M1p1 M21 M22 ... M2p2 Y

β1 β2 βp1 ζ1 ζ2 ζp2 δ λ11 λ12 λ1p2 λ21 λ22 λ2p2 λp11 λp12 λp1p2 θ1 θ2 θp1

π1 π2 πp2

• Full model
• M1

M2 Y

• =
• X

M1 M2

• 

  

α γ δ Φ Ω θ Ψ π

    +

• ǫ

η ξ

• Reduced model
• M1

M2 Y

• =
• X

M1 M2

• 

  

β ζ δ Λ θ π

    +

• ε

ϑ ξ

• β = α(I − Φ)−1, ζ = γ(I − Ψ)−1, Λ = Ω(I − Ψ)−1

26 / 35

Full model

X M11 M12 ... M1p1 M21 M22 ... M2p2 Y

α1 α2 αp1 γ1 γ2 γp2 δ φ12 φ1p1 φ2p1 ω11 ω12 ω1p2 ω21 ω22 ω2p2 ωp11 ωp12 ωp1p2 θ1 θ2 θp1 ψ12 ψ1p2 ψ2p2

π1 π2 πp2

Reduced model

X M11 M12 ... M1p1 M21 M22 ... M2p2 Y

β1 β2 βp1 ζ1 ζ2 ζp2 δ λ11 λ12 λ1p2 λ21 λ22 λ2p2 λp11 λp12 λp1p2 θ1 θ2 θp1

π1 π2 πp2

• βjθj: indirect effect of M1j not through either M1s’s (for s > j) or M2’s
• ζkπk: indirect effect of M2k not through either M1’s or M2t’s (for t > k)
• βjλjkπk: indirect effect through M1j and M2k but not through either M1s’s

(for s > j) or (M1t for t > k)

• dependency in M1j’s → correlation in ε1j’s
• dependency in M2k’s → correlation in ϑ2k’s

27 / 35

min tr W1(M1 − Xβ)⊤(M1 − Xβ) + tr W2(M2 − Xζ − M1Λ)⊤(M2 − Xζ − M1Λ) + w (Y − Xδ − M1θ − M2π)⊤ (Y − Xδ − M1θ − M2π) such that

p1

• j=1

|βjθj| ≤ t1,

p2

• k=1

|ζkπk| ≤ t2,

p1

• j=1

p2

• k=1

|βjλjkπk| ≤ t3, |δ| ≤ t4

⇐

p1

• j=1
• |βjθj| + ν1(β2

j + θ2 j )

≤ r1,

p2

• k=1
• |ζkπk| + ν2(ζ2

k + π2 k)

≤ r2,

p1

• j=1

p2

• k=1

|λjk| ≤ r3, |δ| ≤ t4

• ν1, ν2 ≥ 1/2
• r1 ≤ t1, r2 ≤ t2, r3 ≤ t3
• ν1ν2/r1r2

28 / 35

A multimodal neuroimaging study

• N = 30 primary progressive aphasia (PPA) patients
• semantic (7): fluent speech, impaired word comprehension
• nonfluent (9): difficulty producing grammatical sentences and/or

motor speech impairment (apraxia of speech)

• logopenic (14): word-finding difficulties and disproportionately

impaired sentence repetition

• X = 1 if semantic, X = 0 otherwise
• Outcome (Y ): word naming accuracy
• total effect: -24.28 (p-value= 0.018)
• Imaging modalities: DTI (M1) and resting-state fMRI (M2)
• Baseline covariates: age, sex, year of onset, language severity
• Study interest: brain structural and functional pathways on

word naming accuracy comparing semantic vs. non-semantic

29 / 35

• DTI: FA value of p1 = 12 fiber tracks
• UNC (uncinate fasciculus)
• ILF (inferior longitudinal fasciculus)
• IFO (inferior fronto-occipital fasciculus)
• SLF (superior longitudinal fasciculus): FP

(fronto-parietal), FT (fronto-temporal), PT (parietal-temporal)

• both left and right

(Dick and Tremblay, 2012)

• fMRI: functional connectivity of 19 regions (p2 = 171)
• 13 language areas

IFG_opercularis IFG_orbitalis IFG_triangularis SMG FuG STG STG_pole MTG MTG_pole ITG

• 6 DMN

MFG_DPFC AG PCC

30 / 35

Single-modality result

• DTI: 4.01% effect mediated

X UNC_L Y

• fMRI: 25.02% effect mediated

X IFG_opercularis_L−STG_L_pole IFG_opercularis_R−SMG_L IFG_orbitalis_R−PCC_R IFG_triangularis_L−STG_L_pole IFG_triangularis_R−SMG_L SMG_L−MTG_L SMG_L−MFG_DPFC_R MTG_L−MTG_L_pole MTG_L−MFG_DPFC_R MTG_L−AG_R ITG_L−MFG_DPFC_R Y

31 / 35

Single-modality result

• DTI: 4.01% effect mediated
• fMRI: 25.02% effect mediated

31 / 35

Two-modality result

• X → DTI → fmri → Y : 4.19% effect mediated

X SLF_PT_L UNC_L ILF_L IFG_opercularis_L−IFG_orbitalis_R IFG_opercularis_L−STG_L IFG_opercularis_L−MTG_L_pole IFG_triangularis_L−AG_R SMG_L−STG_L SMG_L−MTG_L SMG_L−AG_R SMG_L−PCC_R STG_L−MTG_L STG_L−MTG_L_pole STG_L−AG_L STG_L−PCC_L STG_L_pole−AG_R MTG_L−MTG_L_pole MTG_L_pole−MFG_DPFC_R Y

32 / 35

Two-modality result

• X → DTI → fmri → Y : 4.19% effect mediated

32 / 35

Two-modality result

• X → DTI → fmri → Y : 4.19% effect mediated

(Petrides, 2014)

32 / 35

Discussion

• Mediation analysis in neuroimaging applications
• Functional mediation analysis
• dynamic effective connectivity
• limitations and future directions
• unmeasured confounding, sensitivity analysis
• covariates: scalar and functional
• dense/sparse functional data
• High-dimensional mediation analysis
• ordering of the mediators
• simultaneous mediator selection and mediation effect estimation
• multimodal/multiview data integration: imaging and omics
• R packages: macc, gma, cfma, spcma (github)

33 / 35

Acknowledgements

• Brown University

Xi (Rossi) Luo, PhD Department of Biostatistics Joseph Hogan, ScD Department of Biostatistics Yen-Tsung Huang, MD, ScD Departments of Epidemiology and Biostatistics Jerome Sanes, PhD Department of Neuroscience Eli Upfal, PhD Department of Computer Science

• Johns Hopkins University
• UC Berkeley

Brian Caffo, PhD Department of Biostatistics Martin Lindquist, PhD Department of Biostatistics Kyrana Tsapkini, PhD Department of Neurology Lexin Li, PhD Department of Biostatistics and Epidemiology

• R01 DC014475 by the National Institutes of Health (National Institute of Deafness

and Communication Disorders)

34 / 35

Thank you!

35 / 35