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Spatial Information in DW- and DCE-MRI Parametric Maps in Breast Cancer Research Hakmook Kang Department of Biostatistics Center for Quantitative Sciences Vanderbilt 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 ContaminationElevation

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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 K trans : tumor perfusion and permeability k ep : efflux rate constant v e : extravascular extracellular volume fraction v p : blood plasma volume fraction

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MRI-derived Parameters ADC K trans k ep v e v p

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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 R 2 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: L 1 penalty Ridge: L 2 penalty Elastic Net: L 1 + L 2 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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Models Voxel-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 t11 st NACNACsMRI 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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ResponderNon-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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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

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