Fr

1
Statistics and bioinformaticsapplied to omics
technologiesPart II Integrating biological
knowledge

• Frédéric Schütz
• Frederic.Schutz_at_isb-sib.ch

Center for Integrative Genomics University of
Lausanne, Switzerland
Bioinformatics Core Facility Swiss Institute of
Bioinformatics
2
Contents
Slides

• Class prediction 1-19
• Gene Ontology analysis 20-29
• Geneset analysis (GSEA, etc) 30-39

3
Class discovery and class prediction

• Example patients from which we obtained
  measurements (e.g. gene expression)

Class discovery
Class prediction
?
Gene 2
Gene 2
Gene 1
Gene 1
Given previous measurements for whichthe
grouping is known (red and blue), can we predict
the group to which a newobservation belongs ?
Find natural groups in the data (e.g. setsof
patients with similar gene expression)
4
Why do we want to do class prediction ?

• Many questions in biology and medicine are class
  prediction questions
• Does a patient have a predisposition for a given
  disease ?
• What is the prognosis for this patient ?
• What will be the response of this patient to a
  given drug ?
• Is this tumour benign or malign ?
• What type is this tumour ?
• Which treatment should be used ?

5
Class prediction easy case
Gene 2
Gene 1
Classify everythingon this side as blue
Classify everythingon this side as red
Threshold
6
Example
Blue points represent oestrogen receptor (ER)
status positive determinedby immunohistochemistr
y.
Pierre Farmer et al. Identification of molecular
apocrine breasttumours by microarray analysis.
Oncogene (2005) 24, 46604671
7
Class prediction in practice
Gene 2
Gene 1

• The two groups are not perfectly separated (and
  this is still a pretty good case)
• One variable (gene) is not sufficient to assign
  patients to groups
• Remember that with microarrays, we are not
  talking about just 2 measurements, but several
  10,000s.

8
Discrimination in general

• Goal assign objects (e.g. patients) to classes
  based on some measurements (e.g. gene expression)
• Typically, in a microarray setting
• 10s or (at best) 100s of patients
• 10,000s genes
• Unsupervised learning nothing is known about the
  grouping of the data, and we try to find natural
  groups in the data
• Supervised learning the classes are predefined
  we use previously labelled objects to create a
  procedure for classification of future
  observations.

9
Some supervised analysis methods

• K-nearest neighbours
• Linear Discriminant Analysis
• Classification trees
• Support Vector Machines (SVM)
• etc.

10
Example 3-nearest neighbours
Gene 2
Gene 1
Red or blue ?
11
Example 3-nearest neighbours
Gene 2
Gene 1
2 red vs 1 blue the point is assigned to red
12
K-nearest neighbours

• Choose a value for k (typical values 3 or 5) in
  practice it can be chosen using the learning data
  (value that produces the best result)
• Find the k observations in the learning set that
  are closest to the new, unknown, observation
• Predict the class by a majority vote, that is,
  choose the class that is most common among the
  neighbours.
• Very simple method, with surprisingly good
  performance

13
Linear Discriminant Analysis

• Suggested by R.A. Fisher in 1935
• Procedure to find a linear combination of the
  observed variables that best separates
  (discriminates) two classes of objects.
• Using the new variable, objects from the same
  class are close together, and objects from
  different class are further away.
• Straightforward to calculate
• Can easily be extended to more than two classes
• Similar idea to Principal Component Analysis
  (PCA)
• Often forgotten in favour of PCA

14
Back to the easy case
Gene 2
Gene 1
Classify everythingon this side as blue Low
value ofthe discriminant
Classify everythingon this side as red High
value ofthe discriminant
Threshold
Discriminant Gene 1
15
Linear Discriminant Analysis Example
Gene 2
Gene 1

• The two groups are well separated
• Neither Gene1 nor Gene2 is able to discriminate
  between the two categories

16
Linear Discriminant Analysis Example
High values
Gene 2
Low values
Gene 1

• However, the linear combination
• L Gene1 Gene2
• discriminates well between the two groups
• Blue points tend to have smaller L values
• Red points tend to have bigger L values

17
Linear Discriminant Analysis Example
High values
Gene 2
Low values
Gene 1
Threshold

• A threshold is set in between the mean of the two
  groups
• Points with a value L above the threshold are
  classified as red
• Points with a value L below the threshold are
  classified as blue

18
Caveats Overfitting

• It is easy to create classifiers which fit the
  training data perfectly
• It is harder to find classifiers which still work
  as well when validated on new data
• A classifier must ALWAYS be tested on data
  independent from the one used to actually train
  the classifier.
• This is particularly important in microarray
  analysis
• Few samples
• Many different measurements
• If not careful, it is always possible to find a
  classifier that works well for your training data
  !

19
Caveats Overfitting
Gene 2
Classify everything in this region as red
Gene 1

• Perfect classifier for this data
• Probably not so good with any new data

20
Gene Ontology analysis

• Many microarray experiments produce lists of
  genes that are significantly differently
  expressed between two conditions (gene
  comparison).
• In some (rare) cases, only a few genes are of
  interest, and they can easily be examined and
  validated.
• In most cases, however, a long list of
  differentially expressed genes is returned, and
  these genes can not be considered individually.
• It is harder to obtain biological understanding
  from this data.
• One strategy consider the functional annotation
  of the differentially expressed genes.
• Question what do these genes have in common that
  could be of interest ?

21
Reminder Gene Ontology (GO) project

• Collaborative effort to address the need for
  consistent descriptions of gene products in
  different databases.
• Three structured, controlled vocabularies
  (ontologies) that describe gene products in terms
  of their associated
• biological processes
• cellular components
• molecular functions
• in a species-independent manner.

(From http//www.geneontology.org/)
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Example
PPARA, NR1C1, PPAR Peroxisome proliferator-activa
ted receptor alpha
(TAS Traceable Author Statement, IPI Inferred
from Physical Interaction)
(From http//www.geneontology.org/)
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Example of GO analysis

• Simple microarray experience WT vs KO
• The microarray has 10,000 genes, 100 of which
  have GO annotation fatty acid transport
• I obtain 1000 differentially expressed genes (10
  of all genes)

• If my experiment has nothing to do with fatty
  acid transport, I expect in average about 10 of
  genes (or 10) to be differentially expressed.
• If this proportion is higher, it means the list
  of differentially-expressed genes is enriched in
  fatty acid transport genes
• If the difference is significant, it suggests a
  link between differential expression and this GO
  annotation genes with this annotation are more
  likely to be differentially expressed than others
• This indicates that this biological process may
  be related to my KO experiment.

1000 genesdifferentiallyexpressed
10
10,000genes in total
90
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Number of genes fatty acid transport
1000 genesdifferentiallyexpressed
10
10 (10)
100 (100)
10,000genes in total
. . .
0 (0)
90 (90)
90
Looks like a random distribution No apparent
association
?
Strong association
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Statistical analysis

• Assume that I found 20 differential expression
  with the GO annotation of interest.
• Count the numbers of genes with the GO annotation
  or not, and compare with differential expression
• A statistical test such as Fishers exact test
  can tell us what is the probability of observing
  this result (or more extreme) if there is no
  association between the rows and columns
• In this case, this probability (p-value) is 0.002
• This indicates that this biological process may
  be important in the difference between WT and KO.

Differentially expressed Not D.E. Total
Fatty acid transport 20 80 100
Others 980 8980 9900
Total 1000 9000 10000
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In practice

• One can either suggest a GO annotation and see if
  it is enriched in the list of differentially
  expressed genes
• Or we may want to go fishing and try all
  potentially interesting GO annotations to see if
  any of them is enriched.
• Easy to do
• Multiple services available on the web
• User indicates the list of genes differentially
  expressed
• Returns the most significant GO annotations

27
Gene Ontology analysis example. I

• Microarray with about 22,000 genes
• We look at the 1 of the genes that are most
  different between different subtypes of cancer.
• Which processes are likely to be different
  between these subtypes ?
• Those for which more than 1 of the genes are
  differentially expressed are good candidates

Pierre Farmer et al. Identification of molecular
apocrine breasttumours by microarray analysis.
Oncogene (2005) 24, 46604671
28
Gene Ontology analysis example. II

• To apply this GO analysis, we need first to
  define a list of differentially expressed genes.
• This usually means calculating a score (e.g.
  p-value), and selecting a cut-off point.
• While there are some traditional cut-off points
  (0.001, 0.01 or the magical 0.05), they remain
  fairly arbitrary
• Is there really a difference between a gene
  associated with a p-value of 0.049 and another
  one with a p-value of 0.051 ?

29
Gene Ontology analysis example. III

• Some genes may be differentially expressed, but
  the change may be so small (lost in the noise)
  that it will not appear in the list.
• However, the difference in expression may appear
  at the level of a set of genes rather than
  individual genes
• Set of genes may correspond e.g. to co-regulated
  genes, or genes belonging to the same pathway
• If the change of expression is consistent across
  genes in the set, it may indicate that the set is
  of interest, even if no individual gene shows a
  significant difference.

30
Gene set enrichment analysis (GSEA)
31
Gene set enrichment analysis (GSEA)

• Series of papers describing a method for
  analyzing the expression of sets of genes
• Software available, along with a database of
  biologically relevant gene sets
• Relatively hot topic in bioinformatics/statistics
  many differerent papers and methods published on
  the topic, with small or large differences
• GSEA usually refers to this particular program,
  but sometimes indicates any such method which
  examines sets of genes.

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Principle of GSEA

• We have a list of genes sorted according to a
  given measure (score for differential expression,
  correlation to a phenotype, etc)
• Among this list, we have a smaller set of genes
  of interest (e.g. all belonging to a given
  pathway)
• Is the smaller set distributed randomly in the
  sorted list of genes ?
• If yes, the set is less likely to be of interest
• If no, it may indicate that the function
  represented by the set is linked with the measure.

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Principle of GSEA (most methods)
All genes, sorted
Low values (e.g. down-regulated)
High values (e.g. upregulated)
Position in the list of genes of our set of
interest
The location of the genes of our set of interest
within the list seem random (uniform) the set
does not appearto be linked with differential
expression.
34
Principle of GSEA (most methods)
All genes, sorted
Low values (e.g. down-regulated)
High values (e.g. upregulated)
Link withup-regulation
Position in the list of genes of our set of
interest
Link withdown-regulation
Position in the list of genes of our set of
interest
35
Statistical analysis

• Random walk
• The list of genes is walked down from left to
  right
• Everytime a gene belong to our list S, the score
  goes up
• Everytime a gene does not belong to the list, it
  goes down

• If the genes of the set are uniformly
  distributed, the score will never go very high
  (up soon followed by a down)
• If the genes are distributed together, the score
  will go higher before getting back to 0.
• Using a permutation test, a p-value can be
  associated to the geneset.

From fig. 1 of Subramanian et al. PNAS 2005 102
15545-15550
36
Statistical analysis

• How can we summarise and assess an apparent link
  between a set and differential expression ?
• Each method uses different statistics
• Original GSEA method based on the
  Kolmogorov-Smirnov test (compare the distribution
  of genes with a uniform distribution)
• Later replaced by an Enrichment Score (similar
  but weighted)

37
Example

• mRNA expression profiles from lymphoblastoid cell
  lines derived from 15 males and 17 females
• Identify gene sets correlated with the difference
  between males and females

(False Discovery Rate)
From table 2 of Subramanian et al. PNAS 2005
102 15545-15550
38
Example

• Gene expression patterns from a collection of 50
  cancer cell lines
• p53 regulates gene expression in response to
  various signals of cellular stress
• 33 cell lines carry a mutation on the p53 gene,
  and 17 are normal.

From table 2 of Subramanian et al. PNAS 2005
102 15545-15550
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Conclusions

• GeneSet Enrichment Analysis methods have quickly
  become widespread in the microarray community.
• Intuitive method
• Can be used to confirm an association known or
  suspected (use a given geneset)
• or to go fishing for unknown association (use
  a database of genesets)
• More generally, microarray analysis uses more and
  more this external biological knowledge.