Logical Analysis of Logical Analysis of Diffuse Large B Cell LymphomaDiffuse Large B Cell Lymphoma

Gabriela AlexeGabriela Alexe11, Sorin Alexe, Sorin Alexe11, David Axelrod, David Axelrod22, , Peter HammerPeter Hammer11, and David Weissmann, and David Weissmann33

of RUTCOR(1) and Department of Genetics(2), Rutgers of RUTCOR(1) and Department of Genetics(2), Rutgers University; and Robert Wood Johnson Medical School(3)University; and Robert Wood Johnson Medical School(3)

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This Talk

• LymphomaLymphoma• Gene Expression Level AnalysisGene Expression Level Analysis

• cDNA MicroarraycDNA Microarray• Applied to Diffuse Large B-Cell LymphomaApplied to Diffuse Large B-Cell Lymphoma

• Logical Analysis of DatLogical Analysis of Data• Discretization/BinarizationDiscretization/Binarization• Support SetsSupport Sets• Pattern GenerationPattern Generation• Theories and ModelsTheories and Models• PredictionPrediction

LymphomaLymphoma

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Lymphoma

• Cancer of lymphoid cellsCancer of lymphoid cells• ClonalClonal

• Uncontrolled growthUncontrolled growth

• MetastasisMetastasis

• LymphomaLymphoma• DiagnosisDiagnosis

• GradeGrade

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Diffuse Large B Cell Lymphoma (DLBCL)

• 31% of non-Hodgkin lymphoma cases31% of non-Hodgkin lymphoma cases

• 50% long-term, disease-free survival50% long-term, disease-free survival

• Clinical variabilityClinical variability

• Prognosis & therapyPrognosis & therapy

• IPIIPI

• MorphologyMorphology

• Gene expressionGene expression

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Diffuse Large B Cell Lymphoma

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Spleen with Diffuse Large B Cell Lymphoma

Gene Expression Level AnalysisGene Expression Level Analysis

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DNA-RNA Hybridization

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Gene Expression Profiling

cDNA microarray analysis

Tumor Standard

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DLBCL & cDNA Microarray Analysis

• Distinct types of diffuse large B-cell Distinct types of diffuse large B-cell lymphoma identified by gene lymphoma identified by gene expression profiling,expression profiling,Alizadeh et al., Nature, Vol 403, pp 503-511Alizadeh et al., Nature, Vol 403, pp 503-511

• cDNA microarray data -> cDNA microarray data -> unsupervised hierarchical unsupervised hierarchical agglomerative clusteringagglomerative clustering• Germinal center signature: 76% survival Germinal center signature: 76% survival

at 5 yearsat 5 years• Activated B cell signature: 16% at 5 Activated B cell signature: 16% at 5

yearsyears

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DLBCL Clustering

Each case (patient) is a point in N-dimensional space where N = # of genes Germinal

center genes

Activated B cell genes

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DLBCL Survival by Type

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Supervised Learning Classification of DLBCL

• Diffuse large B-cell lymphoma prediction Diffuse large B-cell lymphoma prediction

by gene-expression profiling and by gene-expression profiling and

supervised machine learningsupervised machine learningShipp et al., Nature Medicine, vol 8, p 68-74Shipp et al., Nature Medicine, vol 8, p 68-74

• Prognosis of DLBCLPrognosis of DLBCL

• Highly correlated genes -> weighted Highly correlated genes -> weighted

voting algorithmvoting algorithm

Logical Analysis of DataLogical Analysis of Data

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Logical Analysis of Data (LAD)

• Non-statistical method based on:Non-statistical method based on:• CombinatoricsCombinatorics

• OptimizationOptimization

• LogicLogic

• Based on dataset of cases/patientsBased on dataset of cases/patients

• LAD learns patterns characteristic of LAD learns patterns characteristic of classesclasses• Subsets of patients who are +/- for a conditionSubsets of patients who are +/- for a condition

• Collections of patterns are extensibleCollections of patterns are extensible• PredictionsPredictions

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The Problem : The Problem : Approximation of Hidden FunctionApproximation of Hidden Function

HiddenHiddenFunctionFunction

LAD LAD ApproximatioApproximationn

DatasetDataset

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Main Components of LADMain Components of LAD

• Discretization/BinarizationDiscretization/Binarization

• Support SetsSupport Sets

• Pattern GenerationPattern Generation

• Theories and ModelsTheories and Models

• PredictionPrediction

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DiscretizationDiscretization

Separating Separating CutpointsCutpoints

Minimum Set of Minimum Set of SeparatingSeparatingCutpointsCutpoints

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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 > 34 & gene B < 24 & gene C < 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 >= 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: IllustrationPatterns: Illustration

Positive PatternPositive Pattern Negative PatternNegative Pattern

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Positive TheoryPositive Theory Negative TheoryNegative Theory

Theories: Approximations of the 2 RegionsTheories: 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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Positive TheoryPositive Theory Negative TheoryNegative Theory

ModelModel

Theories and ModelsTheories and Models

Positive AreaPositive Area

Negative AreaNegative Area

Unexplained AreaUnexplained Area

Discordant AreaDiscordant Area

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LAD Prediction

• A new case: a set of gene expression A new case: a set of gene expression

levelslevels

• Satisfy some positive & no negative?Satisfy some positive & no negative?

• Satisfy some negative & no positive ?Satisfy some negative & no positive ?

• Satisfy some of both?Satisfy some of both?

• Which more?Which more?

• Does not satisfy any (rare) Does not satisfy any (rare)

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8 Gene Classification Model

Gene index 6642 6992 3890 5383 3674 2004 1692 2280

Description Butyrophilin (BTF1) mRNADystrobrevin-alpha mRNAP120E4F transcription factor mRNAMitogen induced nuclear orphan receptor (MINOR) mRNASM15 gene (human interferon-related protein SM15 (U09585); final exon similar to partial sequence of human EST R48415, but would require alternative splice) extracted from Human cosmid LUCA14Neurotrophin-3 (NT-3) geneLecithin-cholesterol acyltransferase mRNA, with 5' and 3' flanking DNA sequencesBETA-1,4 N-ACETYLGALACTOSAMINYLTRANSFERASE

Accession # U90543_at U46744_at U87269_at U12767_at U73167_cds5_atM37763_at M12625_at M83651_at

Pattern Positive Negative Positive NegativeP1 >0.49 0. >0.3 72.22 0.00 62.50 30.00

P2 >0.48 >0.46 0.40 72.22 0.00 50.00 20.00

P3 >0.48 >0.46 0.36 72.22 0.00 62.50 10.00

P4 >0.48 >0.47 >0.0 72.22 0.00 50.00 20.00

P5 0.3 >0.1 >0.6 61.11 0.00 62.50 20.00

P6 >0.46 0.30 61.11 0.00 50.00 10.00

P7 >0.63 >0.46 55.56 0.00 25.00 0.00

P8 >0.8 >0.8 55.56 0.00 50.00 20.00

P9 >0.49 >0. 55.56 0.00 50.00 30.00

N1 0.60 0.69 0.6 0.00 72.73 12.50 70.00

N2 0.3 0.69 0.7 0.00 68.18 12.50 50.00

N3 0.3 0.69 0. 0.00 63.64 12.50 40.00

N4 0.60 >0.10.6 0.00 63.64 50.00 70.00

N5 0.3 0.69 >0.10.69 0.00 63.64 0.00 50.00

N6 0.3 0. 0.00 59.09 0.00 40.00

Prevalence (%)

Training set Test set

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Accuracy of Prognosis

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Conclusion  

• Logical Analysis of Data (LAD ): a versatile new Logical Analysis of Data (LAD ): a versatile new classification method here applied to diagnosis classification method here applied to diagnosis and prognosis of lymphoma.and prognosis of lymphoma.

• LAD genes differ almost entirely from those LAD genes differ almost entirely from those specified by other studies.specified by other studies.

• Genes not individually correlated with diagnosis Genes not individually correlated with diagnosis or prognosis but highly correlated in or prognosis but highly correlated in combinations of as few as two genes. combinations of as few as two genes.

• Patterns suggest biologic pathwaysPatterns suggest biologic pathways

• LAD provides highly accurateLAD provides highly accurate pprognosis of DLBCL

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Contacts

• Gabriela Alexe: galexe@us.ibm.com

• Soren Alexe: salexe@rutcor.rutgers.edu

• David Axelrod:

axelrod@biology.rutgers.edu

• Peter Hammer:

hammer@rutcor.rutgers.edu

• David Weissmann: weissmdj@umdnj.edu