Carlo Colantuoni – ccolantu@jhsph

1. Summer Inst. Of Epidemiology and Biostatistics, 2008:Gene Expression Data Analysis8:30am-12:30pm in Room W2017 Carlo Colantuoni – ccolantu@jhsph.edu http://www.biostat.jhsph.edu/GenomeCAFE/GeneExpressionAnalysis/GEA2008.htm

2. Class Outline • Basic Biology & Gene Expression Analysis Technology • Data Preprocessing, Normalization, & QC • Measures of Differential Expression • Multiple Comparison Problem • Clustering and Classification • The R Statistical Language and Bioconductor • GRADES – independent project with Affymetrix data. http://www.biostat.jhsph.edu/GenomeCAFE/GeneExpressionAnalysis/GEA2008.htm

3. Class Outline - Detailed • Basic Biology & Gene Expression Analysis Technology • The Biology of Our Genome & Transcriptome • Genome and Transcriptome Structure & Databases • Gene Expression & Microarray Technology • Data Preprocessing, Normalization, & QC • Intensity Comparison & Ratio vs. Intensity Plots (log transformation) • Background correction (PM-MM, RMA, GCRMA) • Global Mean Normalization • Loess Normalization • Quantile Normalization (RMA & GCRMA) • Quality Control: Batches, plates, pins, hybs, washes, and other artifacts • Quality Control: PCA and MDS for dimension reduction • Measures of Differential Expression • Basic Statistical Concepts • T-tests and Associated Problems • Significance analysis in microarrays (SAM) [ & Empirical Bayes] • Complex ANOVA’s (limma package in R) • Multiple Comparison Problem • Bonferroni • False Discovery Rate Analysis (FDR) • Differential Expression of Functional Gene Groups • Functional Annotation of the Genome • Hypergeometric test?, Χ2, KS, pDens, Wilcoxon Rank Sum • Gene Set Enrichment Analysis (GSEA) • Parametric Analysis of Gene Set Enrichment (PAGE) • geneSetTest • Notes on Experimental Design • Clustering and Classification • Hierarchical clustering • K-means • Classification • LDA (PAM), kNN, Random Forests • Cross-Validation • Additional Topics • The R Statistical Language • Bioconductor • Affymetrix data processing example!

4. DAY #4: Clustering Classification R and Bioconductor! Affymetrix Example

5. Clustering and Classification In Gene Expression Data Carlo Colantuoni ccolantu@jhsph.edu Slide Acknowledgements: Elizabeth Garrett-Mayer, Rafael Irizarry, Giovanni Parmigiani, David Madigan, Kevin Coombs, Richard Simon, Ingo Ruczinski. Classification based in part on Chapter 10 of Hand, Manilla, & Smyth and Chapter 7 of Han and Kamber

6. Data from Garber et al. PNAS (98), 2001.

8. Clustering • Clustering is an exploratory tool to see who's running with who: Genes and Samples. • “Unsupervized” • NOT for classification of samples. • NOT for identification of differentially expressed genes.

9. Clustering • Clustering organizes things that are close into groups. • What does it mean for two genes to be close? • What does it mean for two samples to be close? • Once we know this, how do we define groups? • Hierarchical and K-Means Clustering

10. Distance • We need a mathematical definition of distance between two points • What are points? • If each gene is a point, what is the mathematical definition of a point?

11. Points 1 2 . . . . . . . N 1 2 . . . . . . . . G • Gene1= (E11, E12, …, E1N)’ • Gene2= (E21, E22, …, E2N)’ • Sample1= (E11, E21, …, EG1)’ • Sample2= (E12, E22, …, EG2)’ • Egi=expression gene g, sample i DATA MATRIX

12. Most Famous Distance • Euclidean distance • Example distance between gene 1 and 2: • Sqrt of Sum of (E1i -E2i)2, i=1,…,N • When N is 2, this is distance as we know it: Remember Highschool? Pythagorean Theorum Baltimore Distance DC When N is 20,000 you have to think abstractly

13. Correlation can also be used to compute distance • Pearson Correlation (r) • Spearman Correlation • Uncentered Correlation • Absolute Value of Correlation (or r2)

14. The difference is that, if you have two vectors X and Y with identical shape, but which are offset relative to each other by a fixed value, they will have a standard Pearson correlation (centered correlation) of 1 but will not have an uncentered correlation of 1.

15. The similarity/distance matrices 1 2 ………………………………...G 1 2 ……….N 1 2 . . . . . . . . G 1 2 . . . . . . . . G GENE SIMILARITY MATRIX DATA MATRIX

16. The similarity/distance matrices 1 2 ……….N 1 2 …………..N 1 2 . . . N 1 2 . . . . . . . . G SAMPLE SIMILARITY MATRIX DATA MATRIX

17. Gene and Sample Selection • Do you want all genes included? • What to do about replicates from the same individual/tumor? • Genes that contribute noise will affect your results. • Including all genes: dendrogram can’t all be seen at the same time. • Perhaps screen the genes?

18. Two commonly seen clustering approaches in gene expression data analysis • Hierarchical clustering • Dendrogram (red-green picture) • Allows us to cluster both genes and samples in one picture and see whole dataset “organized” • K-means/K-medoids • Partitioning method • Requires user to define K = # of clusters a priori • No picture to (over)interpret

19. Hierarchical Clustering • The most overused statistical method in gene expression analysis • Gives us pretty red-green picture with patterns • But, pretty picture tends to be pretty unstable. • Many different ways to perform hierarchical clustering • Tend to be sensitive to small changes in the data • Provided with clusters of every size: where to “cut” the dendrogram is user-determined

20. Choose clustering direction • Agglomerative clustering (bottom-up) • Starts with as each gene in its own cluster • Joins the two most similar clusters • Then, joins next two most similar clusters • Continues until all genes are in one cluster • Divisive clustering (top-down) • Starts with all genes in one cluster • Choose split so that genes in the two clusters are most similar (maximize “distance” between clusters) • Find next split in same manner • Continue until all genes are in single gene clusters

21. Choose linkage method (if bottom-up) • Single Linkage: join clusters whose distance between closest genes is smallest (elliptical) • Complete Linkage: join clusters whose distance between furthest genes is smallest (spherical) • Average Linkage: join clusters whose average distance is the smallest.

22. Dendrogram Creation + Interpretation

23. Dendrogram Creation + Interpretation

24. Dendrogram Creation + Interpretation

25. Cluster Assignment

26. Simulated Data with 4 clusters: 1-10, 11-20, 21-30, 31-40 450 relevant genes + 450 “noise” genes. 450 relevant genes.

27. K-means and K-medoids • Partitioning Method • Don’t get pretty picture • MUST choose number of clusters K a priori • More of a “black box” because output is most commonly looked at purely as assignments • Each object (gene or sample) gets assigned to a cluster • Begin with initial partition • Iterate so that objects within clusters are most similar

28. K-means (continued) • Euclidean distance most often used • Spherical clusters. • Can be hard to choose or figure out K. • Not unique solution: clustering can depend on initial partition • No pretty figure to (over)interpret

29. K-means Algorithm 1. Choose K centroids at random 2. Make initial partition of objects into k clusters by assigning objects to closest centroid • Calculate the centroid (mean) of each of the k clusters. • a. For object i, calculate its distance to each of the centroids. b. Allocate object i to cluster with closest centroid. c. If object was reallocated, recalculate centroids based on new clusters. 4. Repeat 3 for object i = 1,….N. • Repeat 3 and 4 until no reallocations occur. • Assess cluster structure for fit and stability

30. We start with some data Interpretation: We are showing expression for two samples for 14 genes We are showing expression for two genes for 14 samples This is with 2 genes. K-means Iteration = 0

31. Choose K centroids These are starting values that the user picks. There are some data driven ways to do it K-means Iteration = 0

32. Make first partition by finding the closest centroid for each point This is where distance is used K-means Iteration = 1

33. Now re-compute the centroids by taking the middle of each cluster K-means Iteration = 2

34. Repeat until the centroids stop moving or until you get tired of waiting K-means Iteration = 3

35. K-means Limitations • Final results depend on starting values • How do we chose K? There are methods but not much theory saying what is best. • Where are the pretty pictures?

36. Assessing cluster fit and stability • Most often ignored. • Cluster structure is treated as reliable and precise • Can be VERY sensitive to noise and to outliers • Homogeneity and Separation • Cluster Silhouettes: how similar genes within a cluster are to genes in other clusters (Rousseeuw Journal of Computation and Applied Mathematics, 1987)

37. Silhouettes • Silhouette of gene i is defined as: • ai = average distance of gene i to other gene in same cluster • bi = average distance of gene i to genes in its nearest neighbor cluster

38. Add perturbations to original data Calculate the number of paired samples that cluster together in the original cluster that didn’t in the perturbed Repeat for every cutoff (i.e. for each k) Do iteratively Estimate for each k the proportion of discrepant pairs. WADP: Weighted Average Discrepancy Pairs

39. Different levels of noise have been added By Bittner’s recommendation, 1.0 is appropriate for our dataset But, not well-justified. External information would help determine level of noise for perturbation We look for largest k before WADP gets big. WADP

41. Classification • Diagnostic tests are good examples of classifiers • A patient has a given disease or not • The classifier is a machine that accepts some clinical parameters as input, and spits out an prediction for the patient • D • Not-D • Classes must be mutually exclusive and exhaustive

42. Components of Class Prediction • Select features (genes) • Which genes will be included in the model • Select type of classifier • E.g. (D)LDA, SVM, k-Nearest-Neighbor, … • Fit parameters for model (train the classifier) • Quantify predictive accuracy: Cross-Validation

43. Feature Selection • Goal is to identify a small subset of genes which together give accurate predictions. • Methods will vary depending on nature of classification problem • Choose genes with significant t-statistics to distinguish between two simple classes e.g.

44. Classifier Selection • In microarray classification, the number of features is (almost) always much greater than the number of samples. • Overfitting is a distinct risk, and increases with more complicated methods.

45. How microarrays differ from the rest of the world • Complex classification algorithms such as neural networks that perform better elsewhere don’t do as well as simpler methods for expression data. • Comparative studies have shown that simpler methods work as well or better for microarray problems because the number of candidate predictors exceeds the number of samples by orders of magnitude. (Dudoit, Fridlyand and Speed JASA 2001)

46. Statistical Methods Appropriate for Class Comparison may not be Appropriate for Class Prediction • Demonstrating statistical significance of prognostic factors is not the same as demonstrating predictive accuracy. • Demonstrating goodness of fit of a model to the data used to develop it is not a demonstration of predictive accuracy. • Most statistical methods were not developed for p>>n prediction problems

47. Many Classification Algorithms have been Applied to and Modified for Expression Analysis • LDA, QDA, DLDA, Weighted Gene Voting, kNN, SVM, Random Forests, CART, Logistic Regression, Bayesian Classifiers, very simple gene combination rules, very complex algorithms.

48. Linear discriminant analysis • If there are K classes, simply draw lines (planes) to divide the space of expression profiles into K regions, one for each class. • If profile X falls in region K, predict class K.

49. LDA QDA

50. Nearest Neighbor Classification • To classify a new observation X, measure the distance d(X,Xi) between X and every sample Xi in training set • Assign to X the class label of its “nearest neighbor” in the training set.