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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
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
Table of Contents•Spatial & Temporal Correlation
•Motivation
•DW- & DCE-MRI
•Spatial Information
•Redundancy Analysis & Penalized Regression
•Data Analysis
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....
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
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
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.
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
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
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
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
How to use the given spatial information?
1. Variable selection + penalization
2. Ridge
3. LASSO (Least Absolute Shrinkage and Selection Operator)
1. Elastic Net
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
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
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)
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
Description of Data•33 patients with grade II/III breast
cancer
•Three MRI examinations
MRI t1
1st NAC NACs MRI t3
MRI t2
Surgery
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.
Correction for Overfitting
•Bootstrap based overfitting penalization
•Overfitting-corrected AUC = AUC (apparent) – optimism (using bootstrap)
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
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