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

Spatial Correlation Radioactive ContaminationElevation

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

DW- and DCE-MRI DW-MRI: water motion DCE-MRI: tumor-related physiological parameters

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

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

Using Spatial Information Radioactive Contamination 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 R 2 is high, then remove Xj We can also use backward elimination, Y ~ X 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

vs. mean = 0.284

Penalized Regression LASSO: L 1 penalty Ridge: L 2 penalty Elastic Net: L 1 + L 2 penalty

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

Models Voxel-Level Voxel-Level + ROI + Clinical

Conventional Method ROI-level analysis ROI + clinical variables (i.e., age and tumor grade)

Data Analysis

Description of Data 33 patients with grade II/III breast cancer Three MRI examinations MRI t11 st NACNACsMRI 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.

ResponderNon-Responder

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

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