4/17/09 CSCI1950‐Z Computa4onal Methods for Biology Lecture 18 Ben Raphael April 8, 2009 hIp://cs.brown.edu/courses/csci1950‐z/ Classifica4on Binary classifica,on Given a set of examples (xi, yi), where yi = +‐ 1, from unknown distribu4on D. Design func4on f: Rn  {‐1,+1} that op+mally assigns addi4onal samples xi to one of two classes. Supervised learning (xi, yi) training data xi(j): feature. Rn: feature space. 1 4/17/09 Dimensionality Reduc4on Genomic data (e.g. gene expression) o[en high‐
dimensional (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 4/17/09 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 4/17/09 Feature Selec4on •  Selec4ng l << n features that are informa(ve for classifica4on. •  Gene expression: subset of genes. Feature Selec4on Informa4ve features: Use a measure of associa4on between xi and yi. •  Correla4on: rxi yi =
!m
i
k=1 (xk
− xi )(yki − y i )
(m − 1)sxi syi
•  Chi‐square (con4ngency table) F (xi ) =
•  Fischer criterion: |(xi )+ − (xi )− |2
s2(xi )+ + s2(xi )−
(xi)+ are elements in + class. •  t‐test sta4s4c •  Mutual informa4on •  TNoM score (previous lecture) [Whiteboard] 4 4/17/09 Feature Selec4on Results Colon Leukemia Feature Selec4on Results Top scoring genes (TNoM < 14) in colon dataset. 5 4/17/09 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 4/17/09 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 4/17/09 Predictors of Breast Cancer Prognosis Step 1: Clustering n = 25000 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(xi, yi) Between each gene and prognosis. Choose 231 genes with |ρ(xi, yi)| > 0.3. Rank genes by ρ(xi, yi). 8 4/17/09 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(xi, yi) Between each gene and prognosis. Choose 231 genes with |ρ(xi, yi)| > 0.3. Rank genes by ρ(xi, yi). 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(xR+), xR) and ρ(μ(xR‐), xR), where μ(xR+) is mean vector of genes in + class in R . Assign to best class. Add 5 genes to R un4l performance does not improve. 9 4/17/09 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 4/17/09 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. 7129 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 4/17/09 TNoM Results (ben‐Dor, Friedman, Yakhini, 2001) % survival years 40 pa4ents 24 pa4ents with low clinical risk. 12