Gene Set Enrichment Analysis Microarray Classification

1. Gene Set Enrichment AnalysisMicroarray Classification STAT115 Jun S. Liu and Xiole Shirley Liu

2. Outline • Gene ontology • Check differential expression and clustering results • Gene set enrichment analysis • Unsupervised learning for classification • Clustering and KNN • PCA (dimension reduction) • Supervised learning for classification • CART, SVM • Expression and genome resources

3. GO • Relationships: • Subclass: Is_a • Membership: Part_of • Topological: adjacent_to; Derivation: derives_from • E.g. 5_prime_UTR is part_of a transcript, and mRNA is_a kind of transcript • Same term could be annotated at multiple branches • Directed acyclic graph

4. Evaluate Differentially Expressed Genes • NetAffx mapped GO terms for all probesets Whole genome Up genes GO term X 100 80 Total 20K 200 • Statistical significance? • Binomial proportional test • p = 100 / 20 K = 0.005 • Check z table

5. Evaluate Differentially Expressed Genes Whole genome Up genes GO term X 100 80 Total 20K 200 • Chi sq test: Up !Up Total GO: 80 (1) 20 (99) 100 !GO: 120 (199) 20K-120 (19701) 20K-100 Total: 200 20K-200 20K • Check Chi-sq table

6. GO Tools for Microarray Analysis • 40 tools

7. GO on Clustering • Evaluate and refine clustering • Check GO term for members in the cluster • Are GO term significantly enriched? • Can we summarize what this cluster of these genes do? • Are there conflicting members in the cluster? • Annotate unknown genes • After clustering, check GO term • Can we infer an unknown gene’s function based on the GO terms of cluster members?

8. Gene Set Enrichment Analysis • In some microarray experiments comparing two conditions, there might be no single gene significantly diff expressed, but a group of genes slightly diff expressed • Check a set of genes with similar annotation (e.g. GO) and see their expression values • Kolmogorov-Smirnov test • One sample z-test • GSEA at Broad Institute

9. Gene Set Enrichment Analysis • Kolmogorov-Smirnov test • Determine if two datasets differ significantly • Cumulative fraction function • What fraction of genes are below this fold change?

10. Gene Set Enrichment Analysis • Set of genes with specific annotation involved in coordinated down-regulation • Need to define the set before looking at the data • Can only see the significance by looking at the whole set

11. Gene Set Enrichment Analysis • Alternative to KS: one sample z-test • Population with all the genes follow normal ~ N(,2) • Avg of the genes (X) with a specific annotation:

12. Dimension Reduction • High dimensional data points are difficult to visualize • Always good to plot data in 2D • Easier to detect or confirm the relationship among data points • Catch stupid mistakes (e.g. in clustering) • Two ways to reduce: • By genes: some experiments are similar or have little information • By experiments: some genes are similar or have little information

13. Principal Component Analysis • Optimal linear transformation that chooses a new coordinate system for the data set that maximizes the variance by projecting the data on to new axes in order of the principal components • Components are orthogonal (mutually uncorrelated) • Few PCs may capture most variation in original data • E.g. reduce 2D into 1D data

14. Principal Component Analysis • Achieved by singular value decomposition (SVD): X = UDVT • X is the original N  p data • E.g. N genes, p experiments • V is p  p project directions • Orthogonal matrix: UTU = Ip • v1 is direction of the first projection • Linear combination (relative importance) of each experiment or (gene if PCA on samples)

15. PCA • U is N  p, relative projection of points • D is p  p scaling factor • Diagonal matrix, d1 d2 d3 …  dp 0 • ui1d1 is distance along v1 from origin (first principal components) • Expression value projected on v1 • v2is 2nd projection direction, ui2d2 is 2nd principal component, so on • Captured variances by the first m principal components

16. PCA P P P P = N × P N × P Original data Projection dir Projected value scale X11V11 + X12V21 + X13V31 + …= X11’ = U11 D11 X21V11 + X22V21 + X23V31 + …= X21’ = U21 D11 1st Principal Component 2nd Principal Component X11V12 + X12V22 + X13V32 + …= X12’ = U12 D22 X21V12 + X22V22 + X23V32 + …= X22’ = U22 D22

17. PCA v2 v2 v1 v1 v2 v1

18. PCA on Genes Example • Cell cycle genes, 13 time points, reduced to 2D • Genes: 1: G1; 4: S; 2: G2; 3: M

19. PCA Example Variance in data explained by the first n principle components

20. PCA Example • The weights of the first 8 principle directions • This is an example of PCA to reduce samples • Can do PCA to reduce the genes as well • Use first 2-3 PC to plot samples, give more weight to the more differentially expressed genes, can often see sample classification v1 v2v3 v4

21. Microarray Classification ?

22. Classification • Equivalent to machine learning methods • Task: assign object to class based on measurements on object • E.g. is sample normal or cancer based on expression profile? • Unsupervised learning • Ignore known class labels, e.g. cluster analysis or KNN • Sometimes can’t separate even the known classes • Supervised learning: • Extract useful features based on known class labels to best separate classes • Can over fit the data, so need to separate training and test set (e.g. cross-validation)

23. Clustering Classification • Which known samples does the unknown sample cluster with? • No guarantee that the known sample will cluster • Try different clustering methods (semi-supervised) • E.g. change linkage, use subset of genes

24. K Nearest Neighbor • Used in missing value estimation • For observation X with unknown label, find the K observations in the training data closest (e.g. correlation) to X • Predict the label of X based on majority vote by KNN • K can be determined by predictability of known samples, semi-supervised again! • Offer little insights into mechanism

25. Supervised Learning Performance Assessment • If error rate is estimated from whole learning data set, it will be over-optimistic (do well now, but poorly in future observations) • Divide observations into L1 and L2 • Build classifier using L1 • Compute classifier error rate using L2 • Requirement: L1 and L2 are iid (independent & identically-distributed) • N-fold cross validation • Divide data into N subsets (equal size), build classifier on (N-1) subsets, compute error rate on left out subset STAT115 03/18/2008

26. Classification And Regression Tree • Split data using set of binary (or multiple value) decisions • Root node (all data) has certain impurities, need to split the data to reduce impurities

27. CART • Measure of impurities • Entropy • Gini index impurity • Example with Gini: multiply impurity by number of samples in the node • Root node (e.g. 8 normal & 14 cancer) • Try split by gene xi (xi 0, 13 cancer; xi< 0, 1 cancer & 8 normal): • Split at gene with the biggest reduction in impurities

28. CART • Assume independence of partitions, same level may split on different gene • Stop splitting • When impurity is small enough • When number of node is small • Pruning to reduce over fit • Training set to split, test set for pruning • Split has cost, compared to gain at each split

29. Support Vector Machine • SVM • Which hyperplane is the best?

30. Support Vector Machine • SVM finds the hyperplane that maximizes the margin • Margin determined by support vectors (samples lie on the class edge), others irrelevant

31. Support Vector Machine • SVM finds the hyperplane that maximizes the margin • Margin determined by support vectors others irrelevant • Extensions: • Soft edge, support vectors diff weight • Non separable: slack var  > 0 Max (margin –  # bad)

32. Nonlinear SVM • Project the data through higher dimensional space with kernel function, so classes can be separated by hyperplane • A few implemented kernel functions available in Matlab & BioConductor, the choice is usually trial and error and personal experience K(x,y) = (xy)2

33. Most Widely Used Sequence IDs • GenBank: all submitted sequences • EST: Expressed Sequence Tags (mRNA), some redundancy, might have contaminations • UniGene: computationally derived gene-based transcribed sequence clusters • Entrez Gene: comprehensive catalog of genes and associated information, ~ traditional concept of “gene” • RefSeq: reference sequences mRNAs and proteins, individual transcript (splice variant)

34. UCSC Genome Browser • Can display custom tracks

35. Entrez: Main NCBI Search Engine

36. Public Microarray Databases • SMD: Stanford Microarray Database, most Stanford and collaborators’ cDNA arrays • GEO: Gene Expression Omnibus, a NCBI repository for gene expression and hybridization data, growing quickly. • Oncomine: Cancer Microarray Database • Published cancer related microarrays • Raw data all processed, nice interface

37. Outline • Gene ontology • Check diff expr and clustering, GSEA • Microarray clustering: • Unsupervised • Clustering, KNN, PCA • Supervised learning for classification • CART, SVM • Expression and genome resources

38. Acknowledgment • Kevin Coombes & Keith Baggerly • Darlene Goldstein • Mark Craven • George Gerber • Gabriel Eichler • Ying Xie • Terry Speed & Group • Larry Hunter • Wing Wong & Cheng Li • Ping Ma, Xin Lu, Pengyu Hong • Mark Reimers • Marco Ramoni • Jenia Semyonov