• Predictive sub-typing of subjects

• Retrospective and prospective studies

• Exploration of clinico-genomic data

• Identify relevant gene expression patterns

Issues in Bayesian Tree Modeling of Clinical and Gene

Expression Data

Current Areas of Application

Breast Cancer

lymph node status

disease recurrence

Ovarian Cancer

tumor location

Lymph Node Involvement Is a Key Breast Cancer Risk Factor

But -- lymph node dissection also carriesmorbidity and inaccuracy

Identifying Metagenes Associated With Lymph Node Status

Tumor Sample

Gen

e

Metagenes/ Expression Signatures

• Dimension reduction: Signal improvement

• Clustering• Singular value decomposition• Empirical or model-based factor

analysis• Characterize patterns in data

Gene Clustering

Gene Clustering (cont’d)

Factor extraction (SVD)

Differential Gene Expression

Differential Gene Expression (Threshold 1)

Differential Gene Expression (Threshold 2)

Differential Gene Expression (Threshold 3)

Nonlinear Expression

Nonlinear Expression (Threshold 1)

Nonlinear Expression (Threshold 2)

Lymph Node Metastasis Metagenes

Ovarian Tumor Site Genes

Statistical Tree Models for Clinico-Genomic Prediction

• Regression trees: Non-linear, interactions

• Recursive partitioning • Retrospective studies• Many trees: Model uncertainty• Predictions average across trees

Binary Outcomes Retrospective Sampling

)|1(Pr 1 ppxxY

LN +LN +

Binary Outcomes: Prospective Inference from Retrospective

Model)τ,...,xτ|x(Yπ kk 111Pr

10Pr 111 , yy), |Yτ(x a y

10,|Pr 11222 , yy), Yx(x a y

0201

1211

0Pr

1Pr

1 ,,

,,

aa

aa

)(Y

)(Y

π

π

Binary Outcomes: Retrospective Model

• Model conditionals for predictors

• Nonparametric Bayes: Dirichlet model

• Modeling in x space – joint structure• Implies Beta priors on

y)Yτ,...,xτ|xF(x 1k1kk ,11

iya

Growing Binary Trees

Node split:• Each candidate predictor:threshold pair• 2x2 table: 2 Bernoulli’s, fixed columns

(Y=0/1)• Assess and select split, or stop• Conservative Bayesian tests

Multiple trees:• Multiple splits at any node

Inference with Many Binary Trees

Within-tree inference & prediction: • Sequences of beta posteriors for • Simulate: Impute Pr(Y=1|leaf)

Multiple trees:• Likelihood across trees• Average predictions across trees • Model (predictor:threshold)s

uncertainty• “Smoothing” classification boundaries

iya

Binary Outcome: Lymph Node Metastasis

Tumor Sample

Gen

e

Predictive trees:

• Nonparametric Bayes’

• Metagene expression

• Retrospective sampling

Lancet 2003 (Huang, West et Lancet 2003 (Huang, West et al)al)

Predicting Lymph Node Status With Metagenes

LN+ LN-

Pro

babi

lity

of L

N+

Out-of-sample cross validation

Sample

Forests of Clinico-Genomic Trees

Select from potential clinical and genomic predictor variables

multiple trees

variable combination – co-occurrence

multiple subtypes

… With Metagenes and Clinical Predictors

LN+ LN-

Pro

babi

lity

of L

N+

Out-of-sample cross validation

Sample

Lymph Node Clinico-Genomic Predictors

Predicting Ovarian Tumor Site

Omentum Ovary

Pro

babi

lity

of O

men

tum

Out-of-sample cross validation

Sample

Gene Identification

• Implicated metagenes – gene subsets

• Genes correlated with key metagenes

Breast Cancer – nodal metastasis:• Interferon pathway/inducible gene subset

• Interferons mediate anti-tumor response

Evidence of dysfunction of normal anti-tumor response?

Ovarian Cancer – tumor site:• Growth regulatory pathway/inducible gene subset

Evidence of dysfunction of normal cell growth?

Ongoing Research

• Stochastic search (sequential,annealing)

• Representation of tree ‘forest’• Metagene definition/ creation• Cluster implementation of tree models

Computational & Applied Genomics Program

Joseph Nevins Mike WestErich Huang Ed IversenHolly Dressman

Duke University

Koo Foundation-Sun Yat Sen Cancer Center

Andrew Huang, Skye Cheng, Mei-Hua Tsou

http://www.isds.duke.edu/~jennifer/

Department of Obstetrics and Gynecology

John LancasterAndrew Berchuck

Growing Binary Trees (2x2)

kk tx

kk tx

0Y 1Y

1N

0N00n 01n

10n 11n

N

)Yτ,x,τ|xP(x 1k1kkk 0,11

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