Pathway Analysis

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Pathway Analysis
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Goals

• Characterize biological meaning of joint changes
  in gene expression
• Organize expression (or other) changes into
  meaningful chunks (themes)
• Identify crucial points in process where
  intervention could make a difference
• Why? Biology is Redundant! Often sets of genes
  doing related functions are changed

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Gene Sets

• Gene Ontology
• Biological Process
• Molecular Function
• Cellular Location
• Pathway Databases
• KEGG
• BioCarta
• Broad Institute

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Other Gene Sets

• Transcription factor targets
• All the genes regulated by particular TFs
• Protein complex components
• Sets of genes whose protein products function
  together
• Ion channel receptors
• RNA / DNA Polymerase
• Paralogs
• Families of genes descended (in eukaryotic times)
  from a common ancestor

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Approaches

• Univariate
• Derive summary statistics for each gene
  independently
• Group statistics of genes by gene group
• Multivariate
• Analyze covariation of genes in groups across
  individuals
• More adaptable to continuous statistics

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Univariate Approaches

• Discrete tests enrichment for groups in gene
  lists
• Select genes differentially expressed at some
  cutoff
• For each gene group cross-tabulate
• Test for significance (Hypergeometric or Fisher
  test)
• Continuous tests from gene scores to group
  scores
• Compare distribution of scores within each group
  to random selections
• GSEA (Gene Set Enrichment Analysis)
• PAGE (Parametric Analysis of Gene Expression)

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Multivariate Approaches

• Classical multivariate methods
• Multi-dimensional Scaling
• Hotellings T2
• Informativeness
• Topological score relative to network
• Prediction by machine learning tool
• e.g. random forest

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Contingency Table 2 X 2
Signif. Genes NS Genes
Group of Interest k n-k n
Others K-k (N-n)-(K-k) N-n
K N-K N
P
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Categorical Analysis

• Fishers Exact Test
• Condition on margins fixed
• Of all tables with same margins, how many have
  dependence as or more extreme?
• Hard to compute when n or k are large
• Approximations
• Binomial (when k/n is small)
• Chi-square (when expected values gt 5 )
• G2 (log-likelihood ratio compare to c2)

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Issues in Assessing Significance

• P-value or FDR?
• Heuristic only use FDR
• If a child category is significant, how to assess
  significance of parent category?
• Include child category
• Consider only genes outside child category
• What is appropriate Null Distribution?
• Random sets of genes? Or
• Random assignments of samples?

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Critiques of Discrete Approach

• No use of information about size of change
• Continuous procedures usually have twice the
  power of analogous discrete procedures on
  discretized continuous data
• No use of covariation knowing covariation
  usually improves power of test

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(2003)
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GSEA

• Uses Kolmogorov-Smirnov (K-S) test of
  distribution equality to compare t-scores for
  selected gene group with all genes

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Update Fixes a Problem

• Sometimes ranks concentrated in middle
• Hack Ad-hoc weighting by scores emphasizes peaks
  at extremes

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Group Z- or T- Scores

• Under Null Hypothesis, each genes z-score (zi)
  is distributed N(0,1)
• Hence the sum over genes in a group G
• Identify which groups have highest scores
• Same issues as discrete
• Null Distribution permute which indices?
• Hierarchy

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Issues for Pathway Methods

• How to assess significance?
• Null distribution by permutations
• Permute genes or samples?
• How to handle activators and inhibitors in the
  same pathway?
• Variance Test
• Other approaches

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Pathway Analysis of Genotype Data
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The Pathways Proposal

• Complex disease ensues from the malfunction of
  one or a few specific signaling pathways
• Alternatives
• Common variants of several genes in the pathway
  each contribute moderate risk
• Rare de novo variants confer great risk and
  persist for generations in LD with typed markers
  within unidentified subpopulations of the study
  group

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Approach 1 - Adaptation of GSEA

• Order log-odds ratios or linkage p-values for all
  SNPs
• Map SNPs to genes, and genes to groups
• Use linkage p-values in place of t-scores in GSEA
• Compare distribution of log-odds ratios for SNPs
  in group to randomly selected SNPs from the chip

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Possible Association Models

1. Each of several genes may have a variant that
   confers increased RR independent of other genes
2. Several genes in contribute additively to the
   malfunction of the pathway
3. There are several distinct combinations of gene
   variants that increase RR but only modest
   increases in risk for any single variant

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Approach 2 Combining p-values

• 1. Compute gene-wise p-value
• Select most likely variant - best p-value
• Selected minimum p-value is biased downward
• Assign gene-wise p-value by permutations
  (Westfall-Young)
• Permute samples and compute best p-value for
  each permutation
• Compare candidate SNP pvalues to this null
  distribution of best p-values
• 2. Combine p-values by Fishers method

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Methods 2

• Additive model
• Where ni indexes the number of allele Bs of a
  SNP in gene i in the gene set G
• Select subset of most likely SNPs
• Fit by logistic regression (glm() in R)
• Significance by permutations
• Permute sample outcomes
• Select genes and fit logistic regression again
• Assess goodness of fit each time
• Compare observed goodness of fit

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Multivariate Approaches to Gene Set Analysis
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Key Multivariate Ideas

• PCA (Principal Components Analysis)
• SVD (Singular Value Decomposition)
• MDS (Multi-dimensional Scaling)
• Hotelling T2

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PCA
PCA1 lies along the direction of maximal
correlation PCA 2 at right angles with the next
highest variation.
Three correlated variables
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Multi-Dimensional Scaling

• Aim to represent graphically the most
  information about relationships among samples
  with multi-dimensional attributes in 2 (or 3)
  dimensions
• Algorithm
• Transform distances into cross-product matrix
• Initial PCA onto 2 (or 3) axes
• Deform until better representation
• Minimize strain measure

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Separating Using MDS
Left distributions of individual
variables Right MDS plot (in this case PCA)
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Multivariate Approaches to Selection

• Visualizing differences by MDS
• Hotellings T-squared

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MDS for Pathways

• BAD pathway
• Normal
• IBC
• Other BC
• Clear separation between groups
• Variation differences

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Hotellings T2

• Compute distance between sample means using
  (common) metric of covariation
• Where
• Multidimensional analog of t (actually F)
  statistic

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Principles of Kong et al Method

• Normal covariation generally acts to preserve
  homeostasis
• The transcription of genes that participate in
  many processes will be changed
• The joint changes in genes will be most
  distinctive for those genes active in pathways
  that are working differently

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Critiques of Hotellings T

• Not robust to outliers
• Assumes same covariance in each sample
• S1 S2 ? Usually not in disease
• Small samples unreliable S estimates
• N lt p