STAT 435: Topics in Advanced Statistics Data analysis for ...

STAT 435: Topics in Advanced Statistics
Data analysis for bioinformatics
Dr Mik Black
Department of Biochemistry
University of Otago
Lecture 7

Annotation
• From wikipedia.org: “Annotation is extra information
associated with a particular point in a document or other
piece of information.”
• Here our “document” is the genome.
• The goal of annotating the genome is to link all information
relating to sequences, genes, protein, function...

Gene annotation
• Once a fragment of a gene has been sequenced, it is
assigned a unique identifier called an accession number.
• The accession number is used to track that sequence, with
additional information (e.g., function, other sequences)
becoming associated with it as more is learned.
• Sequences used on microarrays can be tracked back to an
accession number.
• Databases of these identifiers are maintained by the
National Center for Biotechnology Information (NCBI), and
others.

Entrez Gene
• With the sequencing of the human genome, individual
sequence fragments can be mapped to their position in the
genome, and annotated (in conjunction with other
fragments) as “genes”.
• Each putative gene in the genome is also assigned an
identifier in the “Entrez gene” database (also at NCBI).
• The accession numbers of the constituent fragments are
then associated with this identifier (and vice versa).
• The gene identifier is also linked to a more descriptive gene
name. This usually conveys some information about what
that gene does (or at least what it was understood to be
involved in at the time it was named).

Microarrays
• Each spot on a microarray represents a gene fragment, and
has a unique accession number.
• Through this number we can find out about the gene which
the fragment represents (if known), where in the genome
this fragment is located, and (maybe) what it does.
• In microarray experiments this means that we can find out
the identity of genes which undergo differential expression.
• Depending on what is known about these genes, this
information may provide important clues about the
underlying biological process being studied.

Gene function
• For biologists, it’s not particularly interesting to find out
that a gene is significantly differentially expressed if no
other information is known about that gene.
• One (very good) reason for this is that in microarray
experiments there are often a lot of false positives, so
biologists tend to be a little bit skeptical...
– Remember: we can only have as much faith in the
analysis as we do in the underlying assumptions. Were
those gene REALLY independent How about the
residuals - normally distributed

Gene function
• If enough is known about a differentially expressed gene for
it to “make sense” or be “interesting” in the context of the
experiment, then biologists tend to get a bit more excited.
• Although a gene name is often somewhat informative, vast
amounts of information about that gene may reside in
journal publications and internet databases - how do we get
this information

PubMed identifiers
• PubMed is a service provided by the National Library of
Medicine.
• Contains over 15 million citations from MEDLINE and
other life sciences publications.
• Every journal publication is given a unique PubMed
identifier.
• Those that relate to a particular gene or sequence are linked
back to the appropriate identifiers.
• Based on this the NCBI search engine (the Bioinformatics
Institute (www.bioinformatics.org.nz) hosts a local
copy of the NCBI databases) can be used to retrieve
information about differentially expressed genes.

Problem - too much information
• For situations where large numbers of genes are differentially
expressed, there is simply too much information available.
• Anyway, are we really interested in individual genes
• Wouldn’t it be better to find groups of differentially
expressed genes which share a common function

Biological pathways
• In reality genes are members of pathways, which perform
major biological functions.
• As more biological experimentation is done, researchers are
able to build a better picture of how genes interact, and
how pathways function.
• Information about pathway membership and gene function
are stored in publicly available databases.
• This information can be used to define gene sets (groups of
genes which are functionally related), to which statistical
analysis can be applied.

Biological pathways: KEGG
• Kyoto Encyclopedia of Gene and Genomes.
www.genome.jp/kegg/kegg4.html
• Provides nice (user-created) pathway diagrams.
• XML output includes information about genes involved in
pathways, and inter-gene (and gene product) relationships.
– Can produce graphic representation of pathway based
on XML alone.

KEGG pathway diagram (apoptosis)

XML output file for apoptosis pathway

XML-based KEGG pathway diagram (apoptosis)

Biological pathways: Biocarta
• Maintain “open source” pathway database, and provide lab
supplies for related experiments:
www.biocarta.com
• Pathway database is edited by “gurus”.
• Very nice pathway diagrams (user created).
• No non-html output.

Biocarta pathway diagram (apoptosis)

Gene ontology
• Gene Ontology (GO) defines a collection of words (an
ontology) which are used to classify the function of a gene.
• Three broad classifications:
– Molecular function.
– Biological process.
– Cellular component.
• Each of these broad terms contains a hierarchy of
categories, going from general to specific.
• Each category is indexed by an identifier.

Example of GO hierarchy (apoptosis)
* all : all ( 218850 )
o GO:0008150 : biological_process ( 145098 )
+ GO:0009987 : cellular process ( 91236 )
# GO:0050875 : cellular physiological process (81383 )
* GO:0008219 : cell death ( 2714 )
o GO:0012501 : programmed cell death ( 2395 )
+ GO:0006915 : apoptosis ( 2061 )
+ GO:0007582 : physiological process ( 96419 )
# GO:0050875 : cellular physiological process ( 81383 )
* GO:0008219 : cell death ( 2714 )
o GO:0012501 : programmed cell death ( 2395 )
+ GO:0006915 : apoptosis ( 2061 )
# GO:0016265 : death ( 3054 )
* GO:0008219 : cell death ( 2714 )
o GO:0012501 : programmed cell death ( 2395 )
+ GO:0006915 : apoptosis ( 2061 )

Annotation for microarrays
• Linking information back to the array spots.
• Types of information:
– Sequence.
– Gene.
– Chromosome location.
– Publications.
– Function.
– Other (e.g., transcription factors, orthologs, proteins).
• Amount of information available is organism-specific.

Common identifiers
• Microarray experiments often utilize the following identifiers:
– Manufacturer’s ID (e.g., Affymetrix probe ID, MWG ID
number).
– Accession number (sequence identifier).
– Entrez Gene ID or LocusLink ID (gene identifier).
– KEGG ID (KEGG pathway membership).
– GO term ID (functional information).
• This information can be used to enhance (or be
incorporated into) a statistical analysis.

Annotation in Bioconductor
• Bioconductor includes metadata packages which contain
annotation information.
– Oligo-set specific (e.g., MWG 30K set).
– Array specific (e.g., Affymetrix HGU133A).
– Organism specific (e.g., human, rat, mouse).
• These packages provide linkage between the sequences used
in array experiments, and the genes from which they are
derived.
• Go and KEGG libraries are also available, with links to
LocusLink IDs (old name for Entrez Gene).

Bioconductor example: hu6800
• Annotation package for Affymetrix array used in Golub et
al. paper:
> library(hu6800.db)
> hu6800()
Quality control information for hu6800:
This package has the following mappings:
hu6800ACCNUM has 7129 mapped keys (of 7129 keys)
hu6800ALIAS2PROBE has 23712 mapped keys (of 110391 keys)
hu6800CHR has 6178 mapped keys (of 7129 keys)
hu6800CHRLENGTHS has 93 mapped keys (of 93 keys)
hu6800CHRLOC has 6136 mapped keys (of 7129 keys)
hu6800CHRLOCEND has 6136 mapped keys (of 7129 keys)
...

• Gene symbols:
Bioconductor example: hu6800
> library(hu6800.db)
> sym sym[1:3]
$U30894_at
[1] "SGSH"
$X85178_at
[1] "SURF5"
• KEGG pathways:
> KEGG.list KEGG.list[1:2]
$U30894_at
[1] "00531" "01032"
$X85178_at
[1] NA

Bioconductor example: KEGG Pathway names
> library(KEGG.db)
> kg kg[1:3]
$‘00010‘
[1] "Glycolysis / Gluconeogenesis"
$‘00020‘
[1] "Citrate cycle (TCA cycle)"
> kg[match("00860",names(kg))]
$‘00860‘
[1] "Porphyrin and chlorophyll metabolism"

Detecting pathway-level changes
• Microarrays are able to measure changes in gene expression
across treatment conditions.
• Can obtain information about gene sets (e.g., GO, KEGG,
Biocarta).
• Allows microarray data to be used to assess whether
changes in expression occur at the group level.
• Such changes often provide greater information than single
gene changes.

Hypergeometric distribution
• Simple approach to investigating coordinated gene
expression - involves hypergeometric distribution.
• Look for functional groupings within a set of significantly
differentially expressed genes:
– e.g., what is the probability of getting 10 apoptosis
genes in my 100 differentially expressed genes
• Similar to classic hypergeometric problem:
– e.g., what is the probability of selecting k white balls in
a sample of size n from a bag containing m white and
N − m black balls

P (X = x) =
Hypergeometric distribution
`M
´`N−M
x n−x
`N
n
´
´ for x = max(0, n + M − N) to x = min(n, M)
• Here x is the number of genes from a particular pathway
(of size M) which showed up in our list of n differentially
expressed genes (then are N genes in total).
• To calculate a p-value for this “test” we need to sum up all
of the probabilities from x (which we observed) up to
min(M, n).
• This is done for each gene set, and then the p-values are
adjusted to take multiple comparisons into account.

P (X = x) =
Example: hypergeometric distribution
`M
´`N−M
x n−x
`N
n
´
´ for x = max(0, n + M − N) to x = min(n, M)
• Suppose that we observe 10 apoptosis genes in our 100
differentially expressed genes.
• There are 10,000 genes on our array, of which 500 are
apoptosis genes.
P (X = 10) =
( 500
)( 9500
10 90
( 10,000
100
)
) = 0.012
• Summing the values from x = 10 to x = 100 gives a
p-value of 0.0205.
• Would then have to adjust this for the number of pathways
being tested.

Limitations
• The hypergeometric test only takes the size of gene sets
into account.
• All genes for the same group that are not significant are
treated the same.
– What if they are “almost” significant
• We are now thinking about the ranks of the genes.
• Want to incorporate this rank information into our
calculations.

Gene Set Analysis
• How to incorporate functional information into statistical
analysis
• Want to make inferences about groups of genes (“gene
sets”) rather than individual genes.
• First publication to do this was by Mootha et al. (2003),
which introduced an approach called gene set enrichment
analysis (GSEA).
– Somewhat limited - calculated the significance of the
“most up-regulated” gene set in an experiment.
– Later a second publication from the same group
appeared in PNAS - nothing new (or exciting).
– R code available, but not part of Bioconductor.

GSEA methodology (Mootha et al., 2003)

Significance analysis of function and expression
• Barry et al. (2005) published a method called Significance
Analysis of Function and Expression (SAFE) for detecting
gene sets undergoing significant changes in expression
between two experimental conditions.
• Provided a simple approach to this type of analysis.
• Also provided an Bioconductor package (safe) which
allows this method to be used in R.

SAFE methodology
• Gene sets are pre-defined using existing grouping (e.g.,
KEGG, GO, Biocarta) or expert knowledge.
• Like the earlier GSEA method, SAFE breaks the analysis
into two parts:
1. Rank genes based on their level of differential expression
between experimental conditions (local).
2. Rank gene sets based on the ranking of the genes they
contain (global).
• Various methods can be used for each of the ranking steps.

SAFE gene (local) ranking
• The default method used to rank genes based on their level
of differential expression is the two sample t-test.
– This provides an ordered list based on the absolute value
of the test statistic for each gene.
– Other statistics are obviously possible (e.g., SAM,
limma etc).
• No need to assess significance of differential expression -
just want to rank the genes.

SAFE pathway (global) ranking
• The default pathway-ranking method is to take the ranks
for the genes in each pathway, and use a Wilcoxon Rank
Sum statistic to rank the pathways.
– Produces ranked list of pathways, based on the ranks of
their constituent genes.
– Again, other rank-based statistics are possible (e.g.,
Kolmogorov-Smirnov).
• Permutation-based resampling used to assess significance,
while accounting for correlation between pathways, and
multiple testing.

SAFE output
• SAFE produces a list of significantly changed gene sets,
based on a permutation p-value (and MCP adjustment
incorporating dependency, if selected), using an α-level
specified by the user.
SAFE results:
Local: t.Student
Global: Wilcoxon
Method: permutation
Size Mean.Rank Emp.pvalue
00860 15 2412.2 0.001
04110 57 1955.9 0.003
00561 12 2086.6 0.008
04966 10 2312.9 0.011
05144 32 1953.0 0.012
00970 16 2133.1 0.018
• Graphical summary (the “safeplot”) is also available.

Safeplot

Interpreting the safeplot
• Significant changes in gene set activity are indicated by
deviation from the diagonal.
• The safeplot also shows the direction of differential
expression observed for each gene in the group (of course to
figure this out you need to know how the rankings relate to
the comparison of interest).

R code for running SAFE
library(safe)
library(multtest)
library(hu6800.db)
data(golub)
dimnames(golub)[[1]]

SAFE: summary
• The SAFE methodology provides a relatively simple
approach to investigating changes in the activity of
pre-defined gene sets.
• Various deficiencies exists (e.g., correlation between genes
within a pathway not taken into account, magnitude of
changes not accouted for by ranking method), but it is still
a useful tool for this type of problem.

Extensions and improvements
• Goeman and Buhlmann (2007) defined two different types
of hypotheses that could be tested in a gene set analysis:
– a self-contained test, where each gene set is tested for
differential expression between the sample classes
independently of the other gene sets (the null
distribution is generated by permuting the samples).
– a competitive test, where each gene set is tested for
differential expression between the sample classes
relative to the other gene sets (the null distribution is
generated by permuting the genes).
• Tests of each type are implemented within the limma
package, allowing use of a linear models approach.

Gene set analysis with Limma
• The roast command performs “rotation gene set testing”
for linear models (mroast does the same for multiple gene
sets): this is a self-contained test.
• geneSetTest and wilcoxGST perform a simple competitive
gene set tests (similar to SAFE, but permuting genes rather
than samples).
• romer provides “gene set enrichment analysis for linear
models using rotation tests” as a competitive test.

geneSetTest (Limma)
fit

geneSetTest (Limma)
gst[which.min(gst)]
04120
0.0180696
library(KEGG.db)
path

Barcode plot (Limma)
barcodeplot(selected=seq(1:length(tstat))[C.matrix[,which.min(gst)]==1],
statistics=tstat,labels=c("Up","Down"),main=paste(path[
match(names(gst[whi\ch.min(gst)]),names(path))][[1]],": p=",
round(min(gst),5),sep=’’))

Rotation-based gene set testing
• Uses rotation of orthogonalized residuals from a linear
model to generate p-values (other methods simply permute
either genes or samples).
• Applicable to correlated tests (e.g., correlations between
genes), small sample sizes, and arbitrary experimental
designs.
• Wu et al. ROAST: rotation gene set tests for complex
microarray experiments. Bioinformatics (2010) vol. 26 (17)
pp. 2176-82.