Gene Expression Based Gene Expression Based Tumor Classification Tumor Classification Using Biologically Using Biologically Informed ModelsInformed Models

ISI 2003 Berlin

Claudio Lottaz und Rainer Spang

Computational Diagnostics Group

Max Planck Institute for Molecular Genetics, Berlin

Tumor Diagnosis/Prognosis with expression profiles

Data:

Tens of thousands of genes

Tens to hundreds of patients

Patients are labeled

E.g. Disease (D) / Control (C)

Problem:

Predict the label of a new patient given his/her expression profile

Patients

Gen

es

D C

Statistical Context: Learning TheoryHigh dimensional models overfitting problems

Additional constraints Regularized Multivariate Models

What are these constraints?

-A small maximal number of genes allowed in the model

(Variable Selection, Sparse Models)

- Likelihood penalties,

- Informative priors,

- Large Margins,

Frustrations

• Falsely predicted patients

• Questionable Labels

• Genes that make no sense in the context

• Secondary and tertiary effects are more prominent then causal molecular mechanisms

The patient groups are seen as molecular homogenous groups

Genes are anonymous variables:

x1,…,xn

Implicit assumptions of standard approaches

Our approach:

1. Sub-class finding instead of global class prediction

2. Use of functional annotations of genes

Molecular Symptoms

Global class prediction vs. Subclass finding

D

C D‘ D\D‘

C

Global class prediction:

Find a molecular signature that separates D from C and generalizes to new patients

Subclass finding:

Find a Subclass D‘ D and a molecular signature that separates D‘ from C

We call this signature a molecular symptom associated to D

Molecular symptoms

• High specificity and sub-optimal sensitivity

• partially supervised

• Molecular properties that are (almost) unique to the disease group, but do not need to be present in all patients having the disease

• Novel stratification of patients

• Hidden molecular sub-entities

• There are in general many molecular symptoms associated to a disease

• One patient can have several molecular symptoms

Exploiting functional annotations of genes

A posteriori use of functional annotations

A priori use of functional annotations

( suggested here )

Data Functional Annotations

StatisticalAnalysis

Data

Functional Annotations

StatisticalAnalysis

What are we looking for?

C

D‘1

D‘2

D‘3

D‘4 D‘4

DNA Repair

Apoptosis

Cell Proliferation

HOX Genes

Functional grouping of genes using Gene Ontologies (GO)

n GO is a database of terms for genesn Known genes are annotated to the termsn Terms are connected as a directed acyclic graphn Levels represent specifity of the terms

The whole thing at a glance

GO contains three different sub-ontologies:

–Molecular function–Biological process–Cellular component

The Annotation

Gene 1023

Gene 12975

Gene 22666

Gene 13

Gene 17945

Gene 19999

Gene 311

Gene 314

Gene 22666

Gene 6702

Gene 12744

Gene 22669

Genes are annotated to both leave and inner nodes

Genes can have multiple annotations

Gene 1023

Gene 12975

Gene 22666

Gene 1023

Gene 12975

Gene 22666

Augmented Ontology

Structured Analysis of Microarrays (StAM)

- Claudio Lottaz -

Modular Grid of three components

1. Classification in Leave Nodes

2. Diagnosis Propagation

3. Regularization:

Gene 1023

Gene 12975

Gene 22666

Gene 311

Gene 314

Gene 22666

1. Classification in the leave nodes by Shrunken centroid classification: PAM (Tibshirani et al 2002)

DLDA-like Discrimination

Discriminant function via the distance to the shrunken class centroids d(C), d(D)

Regularization:

Variable selection via centroid shrinkage

Class Probabilities:

2. Propagation of Diagnosis by weighted averages

w1

w2

w3

C1 C3C2

Pa

Weights are proportional to CV-Performance measured by a weighted deviance

The weight is used to enforce high specificity and relaxed sensitivity. Typically: =0.95

3. Regularization by graph shrinkageTo get rid of uninformative branches of the Gene Ontology, we shrink the weights in the progression step by a constant

is chosen by crossvalidation

Redundancy of a shrunken graph

For two nodes we define the distance:

... which reflects the probability of an inconsistent diagnosisFor a single node we define its redundancy after shrinkage:

... where K is the set of all remaining nodes in the graph after shrinkage

For a shrunken GO graph, we define its redundancy:

Expression data from a leukemia study

Study on acute lymphoblastic leukaemia (ALL) 327 patients12625 genes (Affymetrix HG-U95Av2)

Yeoh et al., Cancer Cell 2002

My focus in this talk:

MLL – ( ) vs. Others

Objective: Diagnosis ofcytogenetic subtypesof ALLs:

20 MLL - ( )27 E2A-PBX115 BCR-ABL79 TEL-AML187 Hyperdiploid7 Hypodiploid29 Pseudodiploid18 nomal (B-cell

ALL)43 T-ALL

Training and TestDisease group: ( MLL positive ALL )

Control group : ( other types of ALL )

Trainings – Test data (2/3 – 1/3 of both Disease and Control cases, randomly split)

All model selection steps are part of the training !!!

They are performed using CV of only the trainings data.

- Centroid shrinkage in the leave nodes

- Deviances for the propagation weights

- Graph shrinkage

Error Rate

Redundancy

The GO graph before and after shrinkage

AfterBefore

The results on the next slides show the performance of the fully shrinked model on the test data

Rows: GO-Nodes

Columns: 7 MLL-Patients (Testset)

Color: MLL-Score

Selectivity/Specificity

Molecular Symptom III

Molecular Symptom I

Molecular Symptom II

Spermatogenesis???

Cyclin A1

Even Skipped Homolog

Transcription Factor like 5

Cell Cycle

Oncogenesis

Cell Proliferation

Molecular Symptom I

Apoptosis

Lectin

Protein Tyrosin Phosphotase

Molecular Symptom I

Phosphorylation

Molecular Symptom II

Cell-Cell Signalling

Molecular Symptom III

Almost Global Nodes

Signal Transduction

The Root

Claudio Lottaz

R-code

StAM

Structured Analysis of Microarrays

Julie Floch

Java Application

for browsing StAM output

Summary

Data

Functional Annotations

StatisticalAnalysis

D‘ D\D‘

C

a prori use of functional annotations

gene ontologies

StAM

1. Classification in Leave Nodes

2. Diagnosis Propagation

3. Regularization:

subclass finding

Molecular Symptoms