Classifica4on. CSCI1950 Z Computa4onal Methods for Biology Lecture 18. Ben Raphael April 8, hip://cs.brown.edu/courses/csci1950 z/

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1 CSCI1950 Z Computa4onal Methods for Biology Lecture 18 Ben Raphael April 8, 2009 hip://cs.brown.edu/courses/csci1950 z/ Binary classifica,on Given a set of examples (x i, y i ), where y i = + 1, from unknown distribu4on D. Design func4on f: R n { 1,+1} that op+mally assigns addi4onal samples x i to one of two classes. Supervised learning (x i, y i ) training data x i (j): feature. R n : feature space. Classifica4on 1

2 Dimensionality Reduc4on Genomic data (e.g. gene expression) o[en highdimensional (n > 5000), but rela4vely few samples available. Reduce dimensionality of data (lower dimensional subspace) to improve performance of the classifier by: Removing features that do not contribute to the classifica4on and may introduce noise. Reducing opportuni4es for overfi]ng. Improving 4me/memory efficiency in algorithms for learning and classifica4on. Feature Construc4on n features l features Linear/nonlinear transforma4on Common method: Principal components analysis. [Whiteboard] 2

3 PCA and Clustering Yeast gene expression data (477 genes) clustered into 7 clusters. First two principal components contain 89% of varia4on in data. Yeung and Ruzzo (Bioinforma4cs 2001) PCA and Clustering Exon and junc4on microarrays detect widespread mouse strain and sex bias expression differences. (Su et al. BMC Genomics 2008) 3

4 Selec4ng l << n features that are informa(ve for classifica4on. Gene expression: subset of genes. Feature Selec4on Feature Selec4on Informa4ve features: Use a measure of associa4on between x i and y i. m r Correla4on: x i y i = k=1 (xi k xi )(yk i yi ) (m 1)s x is y i Chi square (con4ngency table) F (x i )= (xi ) + (x i ) 2 Fischer criterion: s 2 (x i ) + s 2 + (x i ) (x i ) + are elements in + class. t test sta4s4c Mutual informa4on TNoM score (previous lecture) [Whiteboard] 4

5 Feature Selec4on Results Colon Leukemia Feature Selec4on Results Top scoring genes (TNoM < 14) in colon dataset. 5

6 Assessing Performance Feature Selec4on (e.g. TNoM) Build Classifier Test WRONG Cross valida4on Assessing Performance Feature Selec4on (e.g. TNoM) Build Classifier Test Cross valida4on Must assess performance of both steps together! 6

7 Gene Selec4on Results Predictors of Breast Cancer Prognosis 70 gene signature to predict breast cancer pa4ents with metastasis within 5 years (van de Vijver et al. NEJM 2002, van t Veer et al. Nature 2002) Now an FDA approved test: Mammaprint 7

8 Predictors of Breast Cancer Prognosis Step 1: Clustering n = genes 98 tumors. >2 fold change (and p<0.01) in >4 tumors n = 5000 differen+ally expressed genes Hierarchical clustering: genes and samples Predictors of Breast Cancer Prognosis Step 2: Classifica4on n = 5000 genes differen4ally expressed genes in 78 (sporadic lymph node nega4ve) tumors. Compute correla4on coefficient ρ(x i, y i ) Between each gene and prognosis. Choose 231 genes with ρ(x i, y i ) > 0.3. Rank genes by ρ(x i, y i ). 8

9 Predictors of Breast Cancer Prognosis Step 2: Classifica4on n = 5000 genes differen4ally expressed genes in 78 (sporadic lymph node nega4ve) tumors. Compute correla4on coefficient ρ(x i, y i ) Between each gene and prognosis. Choose 231 genes with ρ(x i, y i ) > 0.3. Rank genes by ρ(x i, y i ). Predictors of Breast Cancer Prognosis Step 3: Build a classifier Leave out one sample x. Let R = top 5 genes in list of 231. Compute correla4on coefficients ρ(μ(x R+ ), x R ) and ρ(μ(x R ), x R ), where μ(x R+ ) is mean vector of genes in + class in R. Assign to best class. Add 5 genes to R un4l performance does not improve. 9

10 Predictors of Breast Cancer Prognosis 70 gene classifier 65/78 (83%) of pa4ents predicted correctly. 5 poor and 8 good incorrectly assigned. Changing threshold gave 3 poor and 12 good incorrectly assigned. Discussion Cross valida4on done a[er feature selec4on! Also fixed this problem. Resul4ng 70 gene signature is not unique (Ein Dor et. al 2005: see notes) Drawing biological conclusions from the output of a black box predic4on algorithm is not wise. Correla4on vs. causality. 10

11 Results: Class Discovery with TNoM (ben Dor, Friedman, Yakhini, 2001) Find op4mal labeling L. Solu4on: use heuris4c search Find mul4ple (subop4mal) labelings Solu4on: Peeling: remove previously used genes from set. Results: Class Discovery with TNoM (ben Dor, Friedman, Yakhini, 2001) Leukemia (Golub et al. 1999): 72 expression profiles. 25 AML, 47 ALL genes Lymphoma (Alizadeh et al.): 96 expression profiles, 46 Diffuse large B cell lymphoma (DLBCL) 50 from 8 different 4ssues. Lymphoma DLBCL: subset of 46 of above. 11

12 TNoM Results (ben Dor, Friedman, Yakhini, 2001) % survival 40 pa4ents years 24 pa4ents with low clinical risk. 12