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 carries morbidity and inaccuracy

Identifying Metagenes Associated With Lymph Node Status Tumor Sample Gene

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 LN +

Binary Outcomes: Prospective Inference from Retrospective Model

Binary Outcomes: Retrospective Model Model conditionals for predictors Nonparametric Bayes: Dirichlet model Modeling in x space – joint structure Implies Beta priors on

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

Binary Outcome: Lymph Node Metastasis Tumor Sample Gene Predictive trees: Nonparametric Bayes’ Metagene expression Retrospective sampling Lancet 2003 (Huang, West et al) Lancet 2003 (Huang, West et al)

Predicting Lymph Node Status With Metagenes LN+ LN- Probability of LN+ 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- Probability of LN+ Out-of-sample cross validation Sample

Lymph Node Clinico-Genomic Predictors

Predicting Ovarian Tumor Site Omentum Ovary Probability of Omentum 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 West Erich Huang Ed Iversen Holly Dressman Duke University Koo Foundation-Sun Yat Sen Cancer Center Andrew Huang, Skye Cheng, Mei-Hua Tsou Department of Obstetrics and Gynecology John Lancaster Andrew Berchuck

Growing Binary Trees (2x2) ?