Weighted Gene Co-Expression Network Analysis of

Multiple Independent Lung Cancer Data Sets

Steve Horvath

University of California, Los Angeles

Contents

• Mini review of weighted correlation network analysis (WGCNA)

• Module preservation statistics

• Application to multiple adenocarcinoma

Network=Adjacency Matrix

• A network can be represented by an adjacency matrix, A=[aij], that encodes whether/how a pair of nodes is connected.– A is a symmetric matrix with entries in [0,1] – For unweighted network, entries are 1 or 0

depending on whether or not 2 nodes are adjacent (connected)

– For weighted networks, the adjacency matrix reports the connection strength between node pairs

– Our convention: diagonal elements of A are all 1.

Connectivity (aka degree)

• Node connectivity = row sum of the adjacency matrix– For unweighted networks=number of direct

neighbors– For weighted networks= sum of connection

strengths to other nodes

iScaled connectivity=Kmax( )

i i ijj i

i

Connectivity k a

k

k

Density

• Density= mean adjacency• Highly related to mean connectivity

( )

( 1) 1

where is the number of network nodes.

iji j ia mean k

Densityn n n

n

How to construct a weighted gene co-expression

network?

Use power β for soft thresholding a correlation coefficient

Unsigned network, absolute value

| ( , ) |

Signed network preserves sign info

| 0.5 0.5 ( , ) |

ij i j

ij i j

a cor x x

a cor x x

Default values: β=6 for unsigned and β =12 for signed networks.Zhang et al SAGMB Vol. 4: No. 1, Article 17.

Comparing adjacency functions for transforming the correlation into a

measure of connection strength

Unsigned Network Signed Network

Advantages of soft thresholding with the power function

1. Robustness: Network results are highly robust with respect to the choice of the power β (Zhang et al 2005)

2. Calibrating different networks becomes straightforward, which facilitates consensus module analysis

3. Math reason: Geometric Interpretation of Gene Co-Expression Network Analysis. PloS Computational Biology. 4(8): e1000117

4. Module preservation statistics are particularly sensitive for measuring connectivity preservation in weighted networks

How to detect network modules?

Module Definition

• Numerous methods have been developed • We often use average linkage hierarchical

clustering coupled with the topological overlap dissimilarity measure.

• Once a dendrogram is obtained from a hierarchical clustering method, we choose a height cutoff to arrive at a clustering.

• Modules correspond to branches of the dendrogram

How to cut branches off a tree?

Langfelder P, Zhang B et al (2007) Defining clusters from a hierarchical cluster tree: the Dynamic Tree Cut library for R. Bioinformatics 2008 24(5):719-720

Module=branch of a cluster tree

Dynamic hybrid branch cutting method combinesadvantages of hierarchical clustering and pam clustering

Question: How does one summarize the expression profiles in a module?

Answer: This has been solved.Math answer: module eigengene= first principal componentNetwork answer: the most highly connected intramodular hub gene

Both turn out to be equivalent

brown

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brown

-0

.1

0.0

0.1

0.2

0.3

0.4

Module Eigengene= measure of over-expression=average redness

Rows,=genes, Columns=microarray

The brown module eigengenes across samples

Module eigengene is defined by the singular value decomposition of X• X=gene expression data of a module

gene expressions (rows) have been standardized across samples (columns)

1 2

1 2

1 2

1

( )

( )

(| |,| |, ,| |)

Message: is the module eigengene E

m

m

m

X UDV

U u u u

V v v v

D diag d d d

v

Module detection in very large data sets

• Large may mean >25k variables

R function blockwiseModules (in WGCNA library) implements 3 steps:

1. Variant of k-means to cluster variables into blocks

2. Hierarchical clustering and branch cutting in each block

3. Merge modules across blocks (based on correlations between module eigengenes)

Define 2 alternative measures of intramodular connectivity and

describe their relationship.

Intramodular Connectivity• Intramodular connectivity kIN with respect

to a given module (say the Blue module) is defined as the sum of adjacencies with the members of this module.– For unweighted networks=number of direct links

to intramodular nodes– For weighted networks= sum of connection

strengths to intramodular nodes

{ }

BlueModulei ijj BlueModule

kIN a

Eigengene based connectivity, also known as kME or module membership measure

( ) ( , )i ikME ModuleMembership i cor x ME

kME(i) is simply the correlation between the i-th gene expression profile and the module eigengene.

Very useful measure for annotating genes with regard to modules.

Module eigengene turns out to be the most highly connected gene

When dealing with a network comprised of module genes,

the scaled intramodular connectivity is determined by kME

kIM | ( , ) | | ( ) |m

" "

ax(kIM)

Group conform behavior leads to a lot of friends.

iicor x E kME i .

where | ( ) | measures group conform behavior

Derivation requires an unsigned weighted correlation network

PLoS Comput Biol 4(8): e1000117

kME i

Question

• How to measure relationships between different networks (e.g. how similar is the female liver network to the male network).

Networkof

cholesterol biosynthesis

genes

Message: female liver network (reference)Looks most similar to male liver network

Network concepts to measure relationships between networks

Numerous network concepts can be used to measure the preservation of network connectivity patterns between a reference network and a test network

• cor.k=cor(kref,ktest)

• cor(Aref,Atest)

• Cor(ClusterCoefref,ClusterCoeftest)

Is my network module preserved and reproducible?

Langfelder et al PloS Comp Biol. 7(1): e1001057.

Network module

Abstract definition of module=subset of nodes in a network.

Thus, a module forms a sub-network in a larger network

Example: module (set of genes or proteins) defined using external knowledge: KEGG pathway, GO ontology category

Example: modules defined as clusters resulting from clustering the nodes in a network

• Module preservation statistics can be used to evaluate whether a given module defined in one data set (reference network) can also be found in another data set (test network)

In general, studying module preservation is different from studying cluster preservation.

Many statistics for assessing cluster preservation e.g.Kapp AV, Tibshirani R (2007) Are clusters found in one dataset present in another dataset? Biostatistics (2007), 8, 1, pp. 9–31

But in general network modules are different from clusters (e.g. KEGG pathways may not correspond to clusters in the network).

However, many module preservation statistics lend themselves as cluster preservation statistics and vice versa

Module preservation is often an essential step in a network analysis

Construct a networkRationale: make use of interaction patterns between genes

Identify modulesRationale: module (pathway) based analysis

Relate modules to external informationArray Information: Clinical data, SNPs, proteomicsGene Information: gene ontology, EASE, IPARationale: find biologically interesting modules

Find the key drivers of interesting modulesRationale: experimental validation, therapeutics, biomarkers

Study Module Preservation across different data Rationale: • Same data: to check robustness of module definition• Different data: to find interesting modules

One can study module preservation in general networks specified by an adjacency matrix, e.g. protein-protein interaction networks.

However, particularly powerful statistics are available for correlation networks

weighted correlation networks are particularly useful for detecting subtle changes in connectivity patterns. But the methods are also applicable to unweighted networks (i.e. graphs)

Module preservation in different types of networks

Input: module assignment in reference data.

Adjacency matrices in reference Aref and test data Atest

Network preservation statistics assess preservation of

1. network density: Does the module remain densely connected in the test network?

2. connectivity: Is hub gene status preserved between reference and test networks?

3. separability of modules: Does the module remain distinct in the test data?

Network-based module preservation statistics

Several connectivity preservation statisticsFor general networks, i.e. input adjacency matrices

cor.kIM=cor(kIMref,kIMtest)

correlation of intramodular connectivity across module nodes

cor.ADJ=cor(Aref,Atest)

correlation of adjacency across module nodes

For correlation networks, i.e. input sets are variable measurements

cor.Cor=cor(corref,cortest)

cor.kME=cor(kMEref,kMEtest)

One can derive relationships among these statistics in case of weighted correlation network

Choosing thresholds for preservation statistics based on permutation test

For correlation networks, we study 4 density and 4 connectivity preservation statistics that take on values <= 1

Challenge: Thresholds could depend on many factors (number of genes, number

of samples, biology, expression platform, etc.)

Solution: Permutation test. Repeatedly permute the gene labels in the test

network to estimate the mean and standard deviation under the null hypothesis of

no preservation.

Next we calculate a Z statistic

Z=observed−mean permuted

sd permuted

Gene modules in AdiposePermutation test for estimating Z scores

For each preservation measure we report the observed value and the permutation Z score to measure significance.

Each Z score provides answer to “Is the module significantly better than a random sample of genes?”

Summarize the individual Z scores into a composite measure called Z.summary

Zsummary < 2 indicates no preservation, 2<Zsummary<10 weak to moderate evidence of preservation, Zsummary>10 strong evidence

Z=observed−mean permuted

sd permuted

Details are provided below and in the paper…

Module preservation statistics are often closely related

Red=density statistics

Blue: connectivity statistics

Green: separability statistics

Cross-tabulation based statistics

Message: it makes sense to aggregate the statistics into “composite preservation statistics”Clustering module preservation statistics based on correlations across modules

Composite statistic in correlation networks based on Z statistics

( )( ) ( )

. ( )

Permutation test allows one to estimate Z version of each statistic

. ( . | )

( . | )

Composite connectivity based statistics for correlation networks

qq q

cor Cor q

connect

cor Cor E cor Cor nullZ

Var cor Cor null

Z

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

. . . .( , , , )

Composite density based statistics for correlation networks

( , , , )

Composit

q q q q q

q q q q q

ivity cor Cor cor kME cor A cor kIM

density meanCor meanAdj propVarExpl meanKME

median Z Z Z Z

Z median Z Z Z Z

( ) ( )

( )

e statistic of density and connectivity preservation

2

q q

q connectivity densitysummary

Z ZZ

Gene modules in AdiposeAnalogously define composite statistic:

medianRank

Based on the ranks of the observed preservation statistics

Does not require a permutation test

Very fast calculation

Typically, it shows no dependence on the module size

Summary preservation• Standard cross-tabulation based statistics are intuitive

– Disadvantages: i) only applicable for modules defined via a module detection procedure, ii) ill suited for ruling out module preservation

• Network based preservation statistics measure different aspects of module preservation– Density-, connectivity-, separability preservation

• Two types of composite statistics: Zsummary and medianRank.• Composite statistic Zsummary based on a permutation test

– Advantages: thresholds can be defined, R function also calculates corresponding permutation test p-values

– Example: Zsummary<2 indicates that the module is *not* preserved– Disadvantages: i) Zsummary is computationally intensive since it is

based on a permutation test, ii) often depends on module size• Composite statistic medianRank

– Advantages: i) fast computation (no need for permutations), ii) no dependence on module size.

– Disadvantage: only applicable for ranking modules (i.e. relative preservation)

Application:Modules defined as KEGG pathways.Connectivity patterns (adjacency matrix) is defined as signed weighted co-expression network.Comparison of human brain (reference) versus

chimp brain (test) gene expression data.

Preservation of KEGG pathwaysmeasured using the composite preservation

statistics Zsummary and medianRank

• Humans versus chimp brain co-expression modules

Apoptosis module is least preserved according to both composite preservation statistics

Apoptosismodule has low valueof cor.kME=0.066

Visually inspect connectivity patterns of the apoptosis module in humans and chimpanzees

Weighted gene co-expression module. Red lines=positive correlations,Green lines=negative cor

Note that the connectivity patterns look very different.Preservation statistics are ideally suited to measure differences in connectivity preservation

Literature validation:Neuron apoptosis is known to differ between humans and chimpanzees

• It has been hypothesized that natural selection for increased cognitive ability in humans led to a reduced level of neuron apoptosis in the human brain:– Arora et al (2009) Did natural selection for increased cognitive

ability in humans lead to an elevated risk of cancer? Med Hypotheses 73: 453–456.

• Chimpanzee tumors are extremely rare and biologically different from human cancers

• A scan for positively selected genes in the genomes of humans and chimpanzees found that a large number of genes involved in apoptosis show strong evidence for positive selection (Nielsen et al 2005 PloS Biol).

Application:Studying the preservation of human brain co-expression modules in chimpanzee brain expression data.

Modules defined as clusters(branches of a cluster tree)

Data from Oldam et al 2006

Preservation of modules between human and chimpanzee brain networks

2 composite preservation statistics

Zsummary is above the threshold of 10 (green dashed line), i.e. all modules are preserved. Zsummary often shows a dependence on module size which may or may not be attractive (discussion in paper)In contrast, the median rank statistic is not dependent on module size.It indicates that the yellow module is most preserved

Application: Studying the preservation of a female mouse liver module in different

tissue/gender combinations. Module: genes of cholesterol biosynthesis pathway Network: signed weighted co-expression networkReference set: female mouse liverTest sets: other tissue/gender combinations

Data provided by Jake Lusis

Networkof

cholesterol biosynthesis

genes

Message: female liver network (reference)Looks most similar to male liver network

Note that Zsummaryis highest in the male liver network

Application:Modules defined as KEGG pathways.

Comparison of human brain (reference) versus

chimp brain (test) gene expression data.

Connectivity patterns (adjacency matrix) is defined as signed weighted co-expression network.

Preservation of KEGG pathwaysmeasured using the composite preservation

statistics Zsummary and medianRank

• Humans versus chimp brain co-expression modules

Apoptosis module is least preserved according to both composite preservation statistics

Publicly available microarray data from

lung adenocarcinoma patients

References of the array data sets

• Shedden et al (2008) Nat Med. 2008 Aug;14(8):822-7

• Tomida et al (2009) J Clin Oncol 2009 Jun 10;27(17):2793-9

• Bild et al (2006) Nature 2006 Jan 19;439(7074):353-7

• Takeuchi et al (2006) J Clin Oncol 2006 Apr 10;24(11):1679-88

• Roepman et al (2009) Clin Cancer Res. 2009 Jan 1;15(1):284-90

Array platforms 5 Affymetrix data sets

–Affy 133 A – Shedden et al ( HLM, Mich, MSKCC, DFCI)

–Affy 133 plus 2 – Bild et al

3 Agilent platforms:–21.6K custom array – Takeuchi et al–Whole Human Genome Microarray 4x44K –

Tomida et al– Whole Human Genome Oligo Microarray

G4112A – Roepman et al

Standard marginal analysisfor relating genes to survival time

(Prognostic) Gene Significance

• Roughly speaking: the correlation between gene expression and survival time.

• More accurately: relation to hazard of death (Cox regression model)

Weak relations between gene significances

Meta analysis across 8 data for select cancer stem cell related genes

Marker Gene High expression pValue High expressionpValueStemcell NANOG protective 4.3E-03 protective 3.81E-03Stemcell collagen IV protective 5.2E-03 Not Signif 3.07E-01Stemcell CD133 Not Signif 1.2E-01 protective 3.19E-02Stemcell "OCT4" Not Signif 1.5E-01 Not Signif 7.60E-01Stemcell SOX2 Not Signif 2.3E-01 Not Signif 2.58E-01Stemcell BMI1 Not Signif 3.3E-01 Not Signif 4.84E-01Stemcell CD34 Not Signif 6.2E-01 Not Signif NAStemcell N-cadherin Not Signif 8.4E-01 Not Signif 3.81E-01Stemcell CD44 Not Signif 6.5E-01 Not Signif 4.95E-01Stemcell vitronectin Not Signif 2.6E-01 Not Signif 8.50E-01Stemcell thrombospondin risk 3.5E-02 Not Signif 1.60E-01Stemcell vimentin risk 1.1E-02 Not Signif 5.73E-01Stemcell fibronectin risk 3.5E-04 Not Signif 1.24E-01TF SLUG risk 5.3E-02 risk 5.65E-02TF SIP1 risk 9.9E-05 Not Signif 2.76E-01

survival time recurrence time

Most genes are not associated with survival or recurrence

Preservation of co-expression relationships between select

cancer stem cell markers

Signed weighted co-expression network between select markers

Overall, very weak preservation. Some evidence for connectivity preservation in other Affy data

Gene co-expression module preservation

Modules found in the Shedden Michigan data set;

Zsummay

Adenocarcinoma:Network connectivity is correlated for

data from the same platform.

Affy

Agilent

Connectivity preservation often indicatesmodule preservation

Consensus module analysis

Steps for defining “consensus” modules that are shared across many networks

• Calibrate individual networks so that they become comparable– Often easier for weighted networks

• Define consensus network using quantile

• Define consensus dissimilarity based on consensus network• Define modules as clusters• Use WGCNA R function blockwiseConsensusModules or consensusDissTOMandTree

25.,...,,. 21 probAApquantileconsA ijijij

Cell cycle immune system

ProteinaceousExtracellular matrix

Consensus modules based on 8 adeno data sets

As expected, the cell cycle module eigengene is significantly (p=2E-6)

associated with survival timeCor, p-valueMeta Z, p

Cancer stem cell markers and TFs

Advantages of soft thresholding with the power function

1. Robustness: Network results are highly robust with respect to the choice of the power beta (Zhang et al 2005)

2. Calibrating different networks becomes straightforward, which facilitates consensus module analysis

3. Math reason: Geometric Interpretation of Gene Co-Expression Network Analysis. PloS Computational Biology. 4(8): e1000117

4. Module preservation statistics are particularly sensitive for measuring connectivity preservation in weighted networks

• General information on weighted correlation networks• Google search

– “WGCNA”– “weighted gene co-expression network”

R function modulePreservation is part of WGCNA package

Tutorials: preservation between human and chimp brains

www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation

Implementation and R software tutorials, WGCNA R library

Acknowledgement

(Former) Students and Postdocs: • Peter Langfelder first author & carried out lung cancer

analysis • Jason Aten, Chaochao (Ricky) Cai, Jun Dong, Tova Fuller, Ai Li,

Wen Lin, Michael Mason, Jeremy Miller, Mike Oldham, Anja Presson, Lin Song, Kellen Winden, Yafeng Zhang, Andy Yip, Bin Zhang

• Colleagues/Collaborators• Cancer: Paul Mischel, Stan Nelson• Neuroscience: Dan Geschwind, Giovanni

Coppola, Roel Ophoff• Mouse: Jake Lusis, Tom Drake

NCI: P50CA092131, P30CA16042