Logical Analysis of Diffuse Large B Cell Lymphoma

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Logical Analysis of Diffuse Large B Cell
Lymphoma

• Gabriela Alexe1, Sorin Alexe1, David Axelrod2,
  Peter Hammer1, and David Weissmann3
• of RUTCOR(1) and Department of Genetics(2),
  Rutgers University and Robert Wood Johnson
  Medical School(3)

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This Talk

• Lymphoma
• Gene Expression Level Analysis
• cDNA Microarray
• Applied to Diffuse Large B-Cell Lymphoma
• Logical Analysis of Data
• Discretization/Binarization
• Support Sets
• Pattern Generation
• Theories and Models
• Prediction

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Lymphoma
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Lymphoma

• Cancer of lymphoid cells
• Clonal
• Uncontrolled growth
• Metastasis
• Lymphoma
• Diagnosis
• Grade

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Diffuse Large B Cell Lymphoma (DLBCL)

• 31 of non-Hodgkin lymphoma cases
• 50 long-term, disease-free survival
• Clinical variability
• Prognosis therapy
• IPI
• Morphology
• Gene expression

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Diffuse Large B Cell Lymphoma
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Spleen with Diffuse Large B Cell Lymphoma
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Gene Expression Level Analysis
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DNA-RNA Hybridization
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Gene Expression Profiling
cDNA microarray analysis
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DLBCL cDNA Microarray Analysis

• Distinct types of diffuse large B-cell lymphoma
  identified by gene expression profiling,Alizadeh
  et al., Nature, Vol 403, pp 503-511
• cDNA microarray data -gt unsupervised hierarchical
  agglomerative clustering
• Germinal center signature 76 survival at 5
  years
• Activated B cell signature 16 at 5 years

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DLBCL Clustering
Each case (patient) is a point in N-dimensional
space where N of genes
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DLBCL Survival by Type
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Supervised Learning Classification of DLBCL

• Diffuse large B-cell lymphoma prediction by
  gene-expression profiling and supervised machine
  learningShipp et al., Nature Medicine, vol 8, p
  68-74
• Prognosis of DLBCL
• Highly correlated genes -gt weighted voting
  algorithm

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Shipps 13 Gene Predictor
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Logical Analysis of Data
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Logical Analysis of Data (LAD)

• Non-statistical method based on
• Combinatorics
• Optimization
• Logic
• Based on dataset of cases/patients
• LAD learns patterns characteristic of classes
• Subsets of patients who are /- for a condition
• Collections of patterns are extensible
• Predictions

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The Problem Approximation of Hidden Function
Dataset
HiddenFunction
LAD Approximation
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Main Components of LAD

• Discretization/Binarization
• Support Sets
• Pattern Generation
• Theories and Models
• Prediction

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Discretization
Separating Cutpoints
Minimum Set of SeparatingCutpoints
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Cutpoints and Support Set

• Minimization is NP hard
• Numerous powerful methods
• Support set
• Cutpoints define a grid in which ideally no cell
  contains both and cases
• Cutpoints simplify data and decrease noise

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Patterns

• Examples
• Gene A gt 34 gene B lt 24 gene C lt 2
• Positive and negative patterns
• Pattern parameters
• Degree ( of conditions)
• Prevalence ( of /- cases that satisfy it)
• Homogeneity (proportion of /- cases among those
  it covers)
• Best low degree, large prevalence, high
  homogeneity
• Patterns are extensible!

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Pattern Generation

• Generate patterns based on learning set
• Stipulate control parameters. For example
• Degree 4
• - prevalences gt 70
• - homogeneities 100
• All 75 patterns in 1.2 seconds on Pentium IV 1 Gz
  PC
• Evaluate set
• Average of patterns covering each observation
• Accuracy applied to evaluation set

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Patterns Illustration
Negative Pattern
Positive Pattern
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Theories Approximations of the 2 Regions
A theory is a set of positive (or negative)
patterns such that every positive (or negative)
case is covered.
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Models

• A set of a positive and a negative theory
• A good model
• Small number of features (genes)
• Patterns are high quality
• Low degrees
• High prevalences
• High homogeneities
• Number of patterns is small
• Maximize their biologic interpretability

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Theories and Models
Unexplained Area
Positive Theory
Negative Theory
Model
Positive Area
Discordant Area
Negative Area
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LAD Prediction

• A new case a set of gene expression levels
• Satisfy some positive no negative?
• Satisfy some negative no positive ?
• Satisfy some of both?
• Which more?
• Does not satisfy any (rare)

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8 Gene Classification Model
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Accuracy of Prognosis
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Conclusion

•  
• Logical Analysis of Data (LAD ) a versatile new
  classification method here applied to diagnosis
  and prognosis of lymphoma.
• LAD genes differ almost entirely from those
  specified by other studies.
• Genes not individually correlated with diagnosis
  or prognosis but highly correlated in
  combinations of as few as two genes.
• Patterns suggest biologic pathways
• LAD provides highly accurate prognosis of DLBCL

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Contacts

• Gabriela Alexe galexe_at_us.ibm.com
• Soren Alexe salexe_at_rutcor.rutgers.edu
• David Axelrod axelrod_at_biology.rutgers.edu
• Peter Hammer hammer_at_rutcor.rutgers.edu
• David Weissmann weissmdj_at_umdnj.edu