Transcript Spatial correlation - Vanderbilt University School of Medicine

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 Contamination
Elevation
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
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ADC: apparent diffusion coefficient
Ktrans: tumor perfusion and permeability
kep: efflux rate constant
ve: extravascular extracellular volume fraction
vp: blood plasma volume fraction
MRI-derived Parameters
ADC
Ktrans
kep
ve
vp
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 R is high, then remove Xj
• We can also use backward elimination,
2
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
vs. mean = 0.284
Penalized Regression
•LASSO: L penalty
1
•Ridge: L penalty
2
•Elastic Net: L + L penalty
1
2
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 t2
MRI t1
1st NAC
NACs
Surgery
MRI t3
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.
Responder
Non-Responder
Correction for Overfitting
• Bootstrap based overfitting penalization
• Overfitting-corrected AUC = AUC (apparent) – optimism
(using bootstrap)
Results
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