Download Pathway Methods - people.vcu.edu

Pathway Analysis
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
Gene Sets
• Gene Ontology
– Biological Process
– Molecular Function
– Cellular Location
• Pathway Databases
– KEGG
– BioCarta
– Broad Institute
Other Gene Sets
• Transcription factor targets
– All the genes regulated by particular TF’s
• 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
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
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)
Multivariate Approaches
• Classical multivariate methods
– Multi-dimensional Scaling
– Hotelling’s T2
• Informativeness
– Topological score relative to network
– Prediction by machine learning tool
• e.g. ‘random forest’
Contingency Table – 2 X 2
Signif. NS
Genes Genes
Group of
Interest
k
n-k
Others
K-k
(N-n)- N-n
(K-k)
N-K
N
K
n
P=
Categorical Analysis
• Fisher’s 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 > 5 )
– G2 (log-likelihood ratio; compare to c2)
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?
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
(2003)
GSEA
• Uses Kolmogorov-Smirnov (K-S) test of
distribution equality to compare t-scores
for selected gene group with all genes
Update Fixes a Problem
• Sometimes ranks concentrated in middle
• Hack: Ad-hoc weighting by scores
emphasizes peaks at extremes
Group Z- or T- Scores
• Under Null Hypothesis, each gene’s z-score (zi)
is distributed N(0,1)
• Hence the sum over genes in a group G:
z /
iG
i
G ~ N (0,1)
• Identify which groups have highest scores
• Same issues as discrete:
– Null Distribution: permute which indices?
– Hierarchy
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
Pathway Analysis of Genotype
Data
The Pathways Proposal
•
•
Complex disease ensues from the
malfunction of one or a few specific
signaling pathways
Alternatives:
1. Common variants of several genes in the
pathway each contribute moderate risk
2. Rare de novo variants confer great risk and
persist for generations in LD with typed
markers within unidentified subpopulations
of the study group
Approach 1 - Adaptation of GSEA
• Order log-odds ratios or linkage p-values
for all SNP’s
• Map SNP’s to genes, and genes to groups
• Use linkage p-values in place of t-scores
in GSEA
– Compare distribution of log-odds ratios for
SNP’s in group to randomly selected SNP’s
from the chip
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
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 (WestfallYoung)
• 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 Fisher’s method
V    log( pi )
g i G
p  P( c (22 k )  2V )
Methods – 2
p
)   i ni
• Additive model: log(
1  p gi G
– Where ni indexes the number of allele B’s of a
SNP in gene i in the gene set G
– Select subset of most likely SNP’s
– 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
Multivariate Approaches to
Gene Set Analysis
Key Multivariate Ideas
•
•
•
•
PCA (Principal Components Analysis)
SVD (Singular Value Decomposition)
MDS (Multi-dimensional Scaling)
Hotelling T2
PCA
Three correlated variables
PCA1 lies along the direction of
maximal correlation; PCA 2 at
right angles with the next highest
variation.
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 (dˆ  d ) 2
• Minimize ‘strain’ measure:

1i , j  N
ij
ij
d ij
2
3
Density
Separating Using MDS
0
2
-2
-1
0
1
2
N = 20 Bandw idth = 0.3849
-2
0
2
4
-1
0
1
2
1
3
4
N = 20 Bandw idth = 0.4832
4
4
N = 20 Bandw idth = 0.6724
-2
Density
3
2
cc[,2]
4
N = 20 Bandw idth = 0.4766
0
-2
-2
-2
N = 20 Bandw idth = 0.7575
Density
N = 20 Bandw idth = 0.5232
-4
0
4
-1
2
-2
0
2
4
-4
N = 20 Bandw idth = 0.4896
Density
0
-2
0
2
cc[,1]
6
Density
-2
-4
-2
0
2
4
N = 20 Bandw idth = 0.6962
6
Left: distributions of individual variables
Right: MDS plot (in this case PCA)
Multivariate Approaches to Selection
• Visualizing differences by MDS
• Hotelling’s T-squared
MDS for Pathways
• BAD pathway
Normal
IBC
Other BC
• Clear separation
between groups
• Variation
differences
Hotelling’s T2
• Compute distance between sample means
using (common) metric of covariation
• Where
• Multidimensional analog of t (actually F)
statistic
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
Critiques of Hotelling’s T
• Not robust to outliers
• Assumes same covariance in each sample
– S1 = S2 ? Usually not in disease
• Small samples: unreliable S estimates
–N<p