Gene Set Enrichment AnalysisMicroarray Classification

STAT115

Jun S. Liu and Xiole Shirley Liu

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

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

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

2.79995.0005.0200

005.020080

)1(

pnp

npxz

Evaluate Differentially Expressed Genes

Whole genome Up genesGO term X 100 80Total 20K 200• Chi sq test:

Up !Up TotalGO: 80 (1) 20 (99) 100!GO: 120 (199) 20K-120 (19701) 20K-

100Total: 200 20K-200 20K

– Check Chi-sq table

i i

ii

E

EO 22 )(

GO Tools for Microarray Analysis

• 40 tools

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?

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

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?

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

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:

||

)(

X

Xz

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

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

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)

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 – v2 is 2nd projection direction, ui2d2 is 2nd

principal component, so on

• Captured variances by the first m principal components

p

jj

m

ii dd

11

5.0000

0200

0030

0005

PCA

N

P

× P

P

= N

P

× P

P

Original data Projection dir Projected value scale

X11V11 + X12V21 + X13V31 + …= X11’ = U11 D11

X21V11 + X22V21 + X23V31 + …= X21’ = U21 D11

X11V12 + X12V22 + X13V32 + …= X12’ = U12 D22

X21V12 + X22V22 + X23V32 + …= X22’ = U22 D22

1st Principal Component

2nd PrincipalComponent

PCA

v1v2

v1v2

v1

v2

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

PCA ExampleVariance in data explained by the first n principle

components

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 v2 v3 v4

Microarray Classificationprobe set Normal m412aNormal m414aNormal m416aNormal m426aNormal m430aMM m282 MM m331aMM m332aMM m333aMM m334aMM m353aMM m408aMM m423aMM m424a39089_at 89.31 143.37 111.61 134.78 121.57 104.02 101.11 105.16 121.21 176.72 117.16 137.19 109.5 109.0635862_at 95.05 107.04 71.06 100.63 117.58 103.96 95.2 114.35 95.03 90.32 93.13 88.61 90.87 112.9541777_at 22.76 20.05 21.37 25.55 30.8 20.75 21.95 28.82 30.85 28.81 22.65 18.91 22.58 21.6538250_at 53.55 62.89 29.36 62.74 36.14 60.07 37.46 42.85 27.86 41.48 116.4 46.39 38.9 29.11656_at 177.69 177.65 167.15 166.04 155.07 180.4 136.47 200.4 201.8 138.38 165.92 176.25 162.85 156.17332_at 128.5 98.29 130.58 111.49 103.56 115.47 121.01 134.5 118.85 88.71 105.08 93.28 113.18 140.1339185_at 107.86 114.02 104.08 108.89 112.75 113.61 120.9 120.1 113.82 102.72 109.81 104.86 104.4 95.53514_at 69.21 51.43 92.43 69.21 55.46 58.43 73.9 74.58 88.07 57.01 79.11 53.63 53.43 69.6235010_at 65.34 42 48.14 52.85 59.07 49.62 62.59 68.39 55.57 47.92 46.97 49.73 44.7 55.7334793_s_at 9.95 9.12 10.45 14.65 21.91 13.2 14.02 17.15 9.05 10.66 8.24 13.43 17.17 15.9733277_at 153.21 120.52 136.7 113.79 110.23 140.96 153.44 149.59 119.14 98.57 156.85 101.86 117.28 104.7234788_at 167.66 172.86 142.6 199.39 195.34 156.66 173.96 159.16 207.34 154.18 158.59 151.91 171.65 246.112053_at 91.76 111.82 99.57 95.58 87.17 123.15 82.24 93.92 97.76 114.66 80.33 107.65 89.78 85.4133465_at 63.37 45.24 54.72 56.74 58.16 59.55 63.43 71.55 55.76 46.63 49.78 40.49 44.5 69.3341097_at 145.34 148.08 171.78 151.96 128.26 138.98 148.45 160.25 169.47 133.5 166.24 135.37 159.2 129.9632394_s_at 449.9 1190.09 429.93 1034.13 196.52 214.51 220.81 331.66 652.66 488.37 699.41 1903.88 843.79 575.161969_s_at 30.03 34.58 59.76 32.84 46.98 51.34 40.4 41.75 31.8 36.74 62.42 40.4 36.37 26.0639225_at 43.19 82.15 97.56 78.3 57.23 65.29 75.14 54.5 58.35 62.47 124.64 56.42 90.55 57.2836919_r_at 36.45 26.84 37.94 35.79 38.86 33.99 28.94 32.57 39.61 32.08 31.37 36.58 44.33 36.9933574_at 16.14 12.58 10.93 14.65 29.64 19.38 14.65 15.29 16.14 19.72 11.23 12.6 18.2 24.0436271_at 41.71 25.8 39.79 49.71 52.64 33.5 48.33 41.15 48.74 45.12 36.5 38.58 55.99 29.73490_g_at 83.48 103.93 121.57 80.05 73.81 115.47 106.57 96.19 101.49 78.5 86.13 71.87 83.73 93.641654_at 78.63 82.7 93.15 73.96 73.82 104.4 100.39 91.78 82.26 63.21 76.23 56.97 76.2 73.0441207_at 100.27 80.62 84.98 75.44 74.26 95.56 96.83 100.36 85.12 71.34 81.04 75.81 70.77 70.8140080_at 172.83 106.63 122.03 118.12 131.15 153.53 150.19 161.04 123 101.64 142.03 110.02 113.58 117.1838699_at 69.1 67.16 62.73 67.46 74.03 61.16 75.27 75.7 63.2 68.12 57.25 65.42 70.71 75.81698_f_at 21.36 43.88 30.5 65.43 35.73 44.05 32.34 35.17 33.89 62.61 34.72 42.49 32.13 37.5136036_at 105.59 71.45 88.72 79.84 75.78 95.13 115.07 100.81 84.13 69.87 76.51 71.58 72.16 73.8540720_at 104.84 175.9 186.87 65.58 64 204.55 89.48 110.87 99 59.84 138.3 59.43 197.43 118.3232194_at 34.01 165.32 153.91 59.4 43.4 98.5 59.53 43.28 47.98 63.09 217.29 127.38 79.38 82.0431499_s_at 42.66 36.26 47.61 43.35 48.55 40.87 52.57 53.86 41.41 40.08 44.22 35.6 43.32 41.4841685_at 25.07 14.68 22.41 22.98 19.79 22.21 21.85 25.12 20.27 18.44 20.37 12.85 22.02 25.9131788_at 115.87 151.38 103.33 144.45 138.01 125.9 132.74 121.06 113.56 114.21 149.88 199.76 121.17 96.031719_at 15.65 18.26 16.74 21.49 15.16 11.49 17.52 21.35 19.36 20.6 15.13 14.3 18.77 18.49973_at 169.15 142.44 164.57 129 151.38 189.15 171.12 169.57 139.02 140.37 145.62 145.17 130.23 132.35

?

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)

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

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

STAT115 03/18/2008

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

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

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

class

classPclassP ))((log)( 2

class

classP 2))((1

18.1022

14

22

8122

22

78.19

1

9

819

13

13113

222

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

Support Vector Machine

• SVM– Which hyperplane is the best?

Support Vector Machine

• SVM finds the hyperplane that maximizes the margin

• Margin determined by support vectors (samples lie on the class

edge), others irrelevant

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)

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

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)

UCSC Genome Browser

• Can display custom tracks

Entrez: Main NCBI Search Engine

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

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

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