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Survival-Time Classification of Breast Cancer Patients and ChemotherapyISMP-2003Copenhagen August 18-22, 2003: 

Survival-Time Classification of Breast Cancer Patients and Chemotherapy ISMP-2003 Copenhagen August 18-22, 2003 Y.-J. Lee, O. L. Mangasarian & W.H. Wolberg Data Mining Institute University of Wisconsin - Madison

 Breast Cancer Estimates American Cancer Society & World Health Organization: 

Breast Cancer Estimates American Cancer Society & World Health Organization Breast cancer is the most common cancer among women in the United States. 212,600 new cases of breast cancer will be diagnosed in the United States in 2003: 211,300 in women, 1,300 in men 40,200 deaths will occur from breast cancer in the United States in 2003: 39,800 in women, 400 in men WHO estimates: More than 1.2 million people worldwide were diagnosed with breast cancer in 2001 and 0.5 million died from breast cancer in 2000.

Key Objective: 

Key Objective Identify breast cancer patients for whom chemotherapy prolongs survival time Similar patients must be treated similarly Good group does not need chemotherapy Intermediate group benefits from chemotherapy Poor group not likely to benefit from chemotherapy

Outline: 

Outline Tools used Support vector machines (Linear & Nonlinear SVMs) Feature selection & classification Clustering (k-Median algorithm not k-Means) Cluster into chemo & no-chemo groups Cluster chemo patients into 2 groups: good & poor Cluster no-chemo patients into 2 groups: good & poor Merge into three final classes Good (No-chemo) Poor (Chemo) Intermediate : Remaining patients (chemo & no-chemo) Generate survival curves for three classes Use SSVM to classify new patients into one of above three classes Data description

Cell Nuclei of a Fine Needle Aspirate: 

Cell Nuclei of a Fine Needle Aspirate

Thirty Cytological FeaturesCollected at Diagnosis Time: 

Thirty Cytological Features Collected at Diagnosis Time

Two Histological Features Collected at Surgery Time: 

Two Histological Features Collected at Surgery Time

Slide8: 

Features Selected by Support Vector Machine

1- Norm Support Vector MachinesMaximize the Margin between Bounding Planes: 

1- Norm Support Vector Machines Maximize the Margin between Bounding Planes A+ A-

Support Vector MachineAlgebra of 2-Category Linearly Separable Case: 

Support Vector Machine Algebra of 2-Category Linearly Separable Case

Feature SelectionUsing 1-Norm Linear SVM Classification Based on Lymph Node Status: 

Feature Selection Using 1-Norm Linear SVM Classification Based on Lymph Node Status Features selected: 6 out of 31 by above SVM: Tumor size from surgery

Nonlinear SVM for Classifying New Patients: 

Nonlinear SVM for Classifying New Patients

The Nonlinear Classifier: 

The Nonlinear Classifier Where K is a nonlinear kernel, e.g.:

Clustering in Data Mining: 

Clustering in Data Mining General Objective Given: A dataset of m points in n-dimensional real space Problem: Extract hidden distinct properties by clustering the dataset into k clusters

Concave Minimization Formulationof 1-Norm Clustering Problem (k-Median): 

Concave Minimization Formulation of 1-Norm Clustering Problem (k-Median)

Clustering via Finite Concave Minimization: 

Clustering via Finite Concave Minimization

K-Median Clustering AlgorithmFinite Termination at Local Solution: 

K-Median Clustering Algorithm Finite Termination at Local Solution

Feature Selection & Initial Cluster Centers: 

Feature Selection & Initial Cluster Centers Perform k-Median algorithm in 6-dimensional input space Initial cluster centers used: Medians of Good1 & Poor1 Good1: Patients with Lymph = 0 AND Tumor < 2 Typical indicator for chemotherapy

Overall Clustering Process: 

Overall Clustering Process 253 Patients (113 NoChemo, 140 Chemo)

Survival Curves forGood, Intermediate & Poor Groups(Classified by Nonlinear SSVM): 

Survival Curves for Good, Intermediate & Poor Groups (Classified by Nonlinear SSVM)

Survival Curves for Intermediate Group:Split by Chemo & NoChemo: 

Survival Curves for Intermediate Group: Split by Chemo & NoChemo

Survival Curves for Overall Patients:With & Without Chemotherapy: 

Survival Curves for Overall Patients: With & Without Chemotherapy

Survival Curves for Intermediate GroupSplit by Lymph Node & Chemotherapy: 

Survival Curves for Intermediate Group Split by Lymph Node & Chemotherapy

Survival Curves for Overall PatientsSplit by Lymph Node Positive & Negative: 

Survival Curves for Overall Patients Split by Lymph Node Positive & Negative

Conclusion: 

Conclusion Good – No chemotherapy recommended Intermediate – Chemotherapy likely to prolong survival Poor – Chemotherapy may or may not enhance survival 3 groups have very distinct survival curves

Talk & Paper Available on Web: 

Talk & Paper Available on Web www.cs.wisc.edu/~olvi Y.-J. Lee, O. L. Mangasarian & W. H. Wolberg: “Computational Optimization and Applications” Volume 25, 2003, pages 151-166”