meta analysis and differential network analysis with applications in mouse expression data steve...
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Meta Analysis and Differential Network Analysis with Applications in Mouse
Expression Data
Meta Analysis and Differential Network Analysis with Applications in Mouse
Expression DataSteve Horvath
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Outline
• Standard differential expression analysis
• Statistical power studies• Important network concepts• Single versus differential network
analysis• Differential network construction
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Standard (gene based) differential expression analysis
• Many software packages and R functions calculate T tests, p-values, false discovery rates, fold changes, etc.
• WGCNA R functions:– For a binary trait (e.g. case control status), use
standardScreeningBinaryTrait– For a numeric trait (e.g. body weight), use
standardScreeningNumericTrait– For a right censored time variable, use
standardScreeningCensoredTime
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metaAnalysis R function in the WGCNA R package
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helpfile metaAnalysis
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Stouffer Z statistics from metaAnalysis
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Ranking based metaAnalysis statistics
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Combine several gene rankings using the rankPvalue function
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Statistical Power Studies
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Statistical power calculations
According to google scholar, it was cited by 11708 (July 2013).
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Network concept=network statistics
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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.
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Motivational example I:Pair-wise relationships between genes across
different mouse tissues and genders
Challenge:Develop simple descriptive measures that describe the patterns.Solution: The following network concepts are useful: density, centralization,clustering coefficient, heterogeneity
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Motivational example (continued)
Challenge: Find a simple measure for describing the relationship between gene significance and connectivity
Solution: network concept called hub gene significance
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Backgrounds
• Network concepts are also known as network statistics or network indices– Examples: connectivity (degree), clustering
coefficient, topological overlap, etc• Network concepts underlie network
language and systems biological modeling.
• Dozens of potentially useful network concepts are known from graph theory.
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Review of some fundamental network concepts
which are defined for all networks (not just co-expression
networks)
Horvath 2011 Weighted Network Analysis. Springer Book. Hardcover ISBN: 978-1-4419-8818-8Dong Horvath 2007 Understanding network
concepts in modules BMC Syst BiolHorvath Dong (2008) Geometric Interpretation of Gene Co-expression network analysis. Plos Comp
Biol
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Connectivity
• 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
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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
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Centralization
Centralization = 1
because it has a star topology
Centralization = 0
because all nodes have the same connectivity of 2
max( ) max( )
2 1 1
n k kCentralization Density Density
n n n
= 1 if the network has a star topology
= 0 if all nodes have the same connectivity
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Heterogeneity
• Heterogeneity: coefficient of variation of the connectivity
• Highly heterogeneous networks exhibit hubs
( )
( )
variance kHeterogeneity
mean k
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Clustering CoefficientMeasures the cliquishness of a particular node« A node is cliquish if its neighbors know each other »
Clustering Coef of the black node = 0
Clustering Coef = 1
,
22
il lm mil i m i li
il ill i l i
a a aClusterCoef
a a
This generalizes directly to weightednetworks (Zhang and Horvath 2005)
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The topological overlap dissimilarity is used as input of hierarchical clustering
• Generalized in Zhang and Horvath (2005) to the case of weighted networks• Generalized in Li and Horvath (2006) to multiple nodes• Generalized in Yip and Horvath (2007) to higher order interactions
,
min( , ) 1
iu uj iju i j
iji j ij
a a a
TOMk k a
1ij ijDistTOM TOM
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Network Significance
• Defined as average gene significance• We often refer to the network significance
of a module network as module significance.
iGSNetworkSignif
n
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Maximum adjacency ratio
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Network concepts for comparing two networks
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Differential network concepts• Node specific statistics:
– Diff.ClusterCoef(i) = CC1(i) – CC2(i)
– Diff.Mar(i)= MAR1(i) – MAR2(i)
• Global statistics– Diff.MeanClusterCoef = Mean.CC1–Mean.CC2
– Diff.MeanConnectivity=Mean.k1 – mean.k2
– Diff.MeanMAR=Mean.MAR1 – mean.MAR2
– Diff.MeanKME=Mean.KME
– Diff.Density=Density1 – Density2
– can be calculated via the modulePreservation function
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Measuring the similarity between two networks
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R code for computing network concepts
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R code, help file
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Data analysis strategies
Single network analysis versus differential network
analysis
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Goals of Single Network Analysis
• Identifying genetic pathways (modules)
• Finding key drivers (hub genes)• Modeling the relationships
between:– Transcriptome– Clinical traits / Phenotypes– Genetic marker data
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Validation set 1 Validation set 2
Single Network WGCNA
1 gene co-expression networkMultiple data sets may be used for
validation
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Goals of Differential Network Analysis
• Uncover differences in modules and connectivity in different data sets– Ex: Human versus chimpanzee brains
(Oldham et al. 2006)
• Differing topology in multiple networks reveals genes/pathways that are wired differently in different sample populations
Fuller TF, Ghazalpour A, Aten JE, Drake TA, Lusis AJ, …(2007) "Weighted Gene Co-expression Network Analysis Strategies Applied to Mouse Weight", Mamm Genome. 18(6):463-472
Oldham MC, …Geschwind DH (2006) Conservation and evolution of gene coexpression networks in human and chimpanzee brains. Proc Natl Acad Sci U S A 103, 17973-17978.
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NETWORK 1
Differential Network WGCNA
2+ gene co-expression networksIdentify genes and pathways that are:
1. Differentially expressed2. Differentially wired
NETWORK 2
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• Single network analysis female BxH mice revealed a weight-related module (Ghazalpour et al. 2006)
• Samples: Constructed networks from mice from extrema of weight spectrum:– Network 1: 30 leanest mice– Network 2: 30 heaviest mice
• Transcripts: Used 3421 most connected and varying transcripts
BxH Mouse Data from AJ Lusis
Ghazalpour A, Doss S, Zhang B, Wang S, Plaisier C, Castellanos R, Brozell A, Schadt EE, Drake TA, Lusis AJ, Horvath S (2006) Integrating genetic and network analysis to characterize genes related to mouse weight. PLoS genetics 2, e130
NETWORK 1 NETWORK 2
135 FEMALES
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Methods
Compute Comparison MetricsCompute Comparison Metrics• Difference in expression: t-test statisticDifference in expression: t-test statistic• Compare difference in connectivity: Compare difference in connectivity: DiffKDiffK
Compute Comparison MetricsCompute Comparison Metrics• Difference in expression: t-test statisticDifference in expression: t-test statistic• Compare difference in connectivity: Compare difference in connectivity: DiffKDiffK
Identify significantly different genes/pathwaysIdentify significantly different genes/pathwaysPermutation testPermutation test
Identify significantly different genes/pathwaysIdentify significantly different genes/pathwaysPermutation testPermutation test
Functional analysis of significant genes/pathwaysFunctional analysis of significant genes/pathwaysDAVID databaseDAVID database
Primary literaturePrimary literature
Functional analysis of significant genes/pathwaysFunctional analysis of significant genes/pathwaysDAVID databaseDAVID database
Primary literaturePrimary literature
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Computing Comparison Metrics
DIFFERENTIAL EXPRESSION
t-test statistic computed for each gene, t(i)
DIFFERENTIAL CONNECTIVITY
K1(i) = k1(i) K2(i) = k2(i) max(k1)
max(k2)
DiffK(i): difference in normalized connectivities for each gene:
DiffK(i) = K1(i) – K2(i)
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Sector Plot
We visualize the comparison metrics via a sector plot:
• x-axis: DiffK
• y-axis: t statistics
We establish sector boundaries to identify regions of differentially expressed and/or connected regions
• |t| = 1.96 corresponding to p = 0.05
• |DiffK| = 0.4
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no.perms: number of permutations
For each sector j, we compare the number of genes in unpermuted and permuted sectors (nobs and nperm)
Permutation test:Identifying significant sectors
p j # times (nobs
j npermj ) 1
no.perms1
NETWORK 1 NETWORK 2
PERMUTE
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Sector Plot Results
0.010.001
0.001 0.001X
X X
X
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Functional AnalysisSECTOR 3
High t statistic High DiffK
Yellow module in leanGrey in obese
(63 genes)
Genes in these sectors have higher connectivity in lean than obese mice: ~ pathways potentially
disregulated in obesity ~
SECTOR 5Low t statistic
High Diff K(28 genes)
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Sector 3:Functional Analysis Results
DAVID Database• “Extracellular”:
– extracellular region (38% of genes p = 1.8 x 10-4)– extracellular space (34% of genes p = 5.7 x 10-4)
• signaling (36% of genes p = 5.4 x 10-4)• cell adhesion (16% of genes p = 7.7 x 10-4)• glycoproteins (34% of genes p = 1.6 x 10-3) • 12 terms for epidermal growth factor or its related proteins
– EGF-like 1 (8.2% of genes p = 8.7 x 10-4), – EGF-like 3 (6.6% of genes p = 1.6 x 10-3), – EGF-like 2 (6.6% of genes p = 6.0 x 10-3), – EGF (8.2% of genes p = 0.013)– EGF_CA (6.6% of genes p = 0.015)
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Sector 3:Functional Analysis Results
Primary Literature
• Results supported by a study on EGF levels in mice (Kurachi et al. 1993)– EGF found to be increased in obese mice– Obesity was reversed in these mice by:
• Administration of anti-EGF • Sialoadenectomy
Kurachi H, Adachi H, Ohtsuka S, Morishige K, Amemiya K, Keno Y, Shimomura I, Tokunaga K, Miyake A, Matsuzawa Y, et al. (1993) Involvement of epidermal growth factor in inducing obesity in ovariectomized mice. The American journal of physiology 265, E323-331
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Sector 5: Functional Analysis Results
DAVID Database
• Enzyme inhibitor activity (p = 2.9 x 10-3)*• Protease inhibitor activity (p = 6.0 x 10-3)• Endopeptidase inhibitor activity (p = 6.0 x 10-3)• Dephosphorylation (p = 0.012)• Protein amino acid dephosphorylation (p =
0.012)• Serine-type endopeptidase inhibitor activity (p
= 0.042)
* p values shown are corrected using Bonferroni correction
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Itih1 and Itih3• Enriched for all categories shown previously• Located near a QTL for hyperinsulinemia (Almind and
Kahn 2004)• Itih3 identified as a gene candidate for obesity-related
traits based on differential expression in murine hypothalamus (Bischof and Wevrick 2005)
Serpina3n and Serpina10• Enriched for enzyme inhibitor, protease inhibitor, and
endopeptidase inhibitor• Serpina10, or Protein Z-dependent protease inhibitor (ZPI) has
been found to be associated with venous thrombosis (Van de Water et al. 2004)
Sector 5: Functional Analysis Results
Primary Literature
Almind K, Kahn CR (2004) Genetic determinants of energy expenditure and insulin resistance in diet-induced obesity in mice. Diabetes 53, 3274-3285 Bischof JM, Wevrick R (2005) Genome-wide analysis of gene transcription in the hypothalamus. Physiological genomics 22, 191-196 Van de Water N, Tan T, Ashton F, O'Grady A, Day T, Browett P, Ockelford P, Harper P (2004) Mutations within the protein Z-dependent protease inhibitor gene are associated with venous thromboembolic disease: a new form of thrombophilia. Bjh 127, 190-194
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Discussion• If applicable, always report findings from a
standard differential expression analysis as well.• A host of network concepts exists for describing
the network topology.• Relatively few people use differential network
analysis which may reflect the fact that large sample sizes are needed.– A large sample size is needed to compare two
correlation coefficients• To check whether a module is preserved in
another network use the modulePreservation function.
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AcknowledgementsAcknowledgementsHORVATH LABDissertation work of Tova FullerJun DongPeter Langfelder
An R tutorial may be found at:http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/DifferentialNetworkAnalysis
Mouse data collaboration
LUSIS LABJake LusisAnatole GhazalpourThomas Drake