spatial information in dw- and dce-mri parametric maps in breast cancer research hakmook kang...
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Spatial Information in DW- and DCE-MRI Parametric Maps in
Breast Cancer Research
Hakmook KangDepartment of Biostatistics
Center for Quantitative SciencesVanderbilt University
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Joint Work
•Allison Hainline in Biostatistics
•Xia (Lisa) Li Ph.D at VUIIS
•Lori Arlinghaus, Ph.D at VUIIS
•Tom Yankeelov, Ph.D at VUIIS
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Table of Contents•Spatial & Temporal Correlation
•Motivation
•DW- & DCE-MRI
•Spatial Information
•Redundancy Analysis & Penalized Regression
•Data Analysis
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Spatial & Temporal Correlation
•Temporal correlation: Any measure at a time point is correlated with measures from neighboring time points, e.g., longitudinal data
•Spatial correlation: Any measure at a voxel is correlated with measures from its neighbors, e.g., ADC, Ktrans....
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Spatial Correlation
Radioactive Contamination
Elevation
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Medical Imaging Data
•Structural & functional MRI data, e.g., brain fMRI, breast DW- & DCE-MRI
•CT scans, etc
•Imaging data consist of lots of measures at many pixels/voxels
•Not reasonable to assume independence
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Motivation•Intrinsic spatial correlation in
medical imaging data
•Ignoring the underlying dependence
•Oversimplifying the underlying dependence
•Overly optimistic if positive spatial/temporal correlation is ignored
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Mathematics•Cov(X, Y) = 2, positively correlated
•Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)
•Var(X+Y) = Var(X) + Var(Y) if assume X⊥Y, always smaller by 2Cov(X,Y)
•Variance is smaller than what it should be if correlations among voxels are ignored.
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Motivation
•DW- & DCE-MRI data from 33 patients with stage II/III breast cancer
•Typical ROI-level analysis: define one region of interest (ROI) per patient and take the average of values (e.g., ADC) within ROI
•Build models to predict who will response to NAC
•Need a tool to fully use the given information to improve prediction
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MRI – Derived Parameters
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DW- and DCE-MRI
•DW-MRI: water motion
•DCE-MRI: tumor-related physiological parameters
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MRI-derived Parameters
• ADC: apparent diffusion coefficient
• Ktrans: tumor perfusion and permeability
• kep: efflux rate constant
• ve: extravascular extracellular volume fraction
• vp: blood plasma volume fraction
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MRI-derived Parameters
ADC Ktrans kep ve vp
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Using Spatial Information
Radioactive Contamination
http://www.neimagazine.com/features/featuresoil-contamination-in-belarus-25-years-later/featuresoil-contamination-in-belarus-25-years-later-5.html
Kep & ADC
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Spatial Information
•Model change in mortality by looking at the average contamination over time
•Model Pr(pCR=1) using ROI-level Kep and/or ADC maps, pCR = pathological complete response
•Oversimplification
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How to use the given spatial information?
1. Variable selection + penalization
2. Ridge
3. LASSO (Least Absolute Shrinkage and Selection Operator)
1. Elastic Net
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Redundancy Analysis
•A method to select variables which are most unlikely to be predicted by other variables
•X1, X2, ..., X21
•Fit Xj ~ X(-j), if R2 is high, then remove Xj
•We can also use backward elimination,
Y ~ X1 + ... + X21 + e
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Redundancy Analysis
•First, compute 0,5,...,100 percentiles of Kep and ADC for each patient
•X1= min, X2=5 percentile,..., X20 = 95 percentile, and X21 = max
•Apply redundancy analysis: choose which percentiles uniquely define the distribution of Kep (or ADC)
•Apply backward elimination
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vs. mean = 0.284
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Penalized Regression
•LASSO: L1 penalty
•Ridge: L2 penalty
•Elastic Net: L1 + L2 penalty
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Penalized Regression
•The penalty terms control the amount of shrinkage
•The larger the amount of shrinkage, the greater the robustness to collinearity
•10-fold CV to estimate the penalty terms (default in R)
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Approaches
1) Var Selection + Penalization (ridge)
- Variable selection either by redundancy analysis or by backward elimination
- Combined with ridge logistic regression
2) Ridge (No variable selection)
3) Lasso
4) Elastic Net
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ModelsVoxel-Level
Voxel-Level + ROI + Clinical
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Conventional Method
•ROI-level analysis
•ROI + clinical variables (i.e., age and tumor grade)
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Data Analysis
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Description of Data•33 patients with grade II/III breast
cancer
•Three MRI examinations
MRI t1
1st NAC NACs MRI t3
MRI t2
Surgery
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Objective: Using MRI data (Kep & ADC only) at t1 and t2, we want to predict if a patient will response to the first cycle of NAC.
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Responder Non-Responder
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Correction for Overfitting
•Bootstrap based overfitting penalization
•Overfitting-corrected AUC = AUC (apparent) – optimism (using bootstrap)
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Results
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Results
•Penalizing overly optimistic results
•Redundancy + Ridge with clinical variables is better than the others
•AUC = 0.92, 5% improvement over ROI + clinical model
•ACC = 0.84, 10% improvement over ROI + clinical model
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Summary
•Compared to ROI-level analysis (i.e., average ADC & Kep), we are fully using available information (voxel-level information)
•We partially take into account the underlying spatial correlation
•Reliable & early prediction -> better treatment options before surgery
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Future Research:Spatial Correlation
•Modeling the underlying spatial correlation in imaging data
•Parametric function: 1) Exponential Cov function 2) Matern’s family
•Need to relax isotropic assumption