Bioinformatics: The Analysis of Microarray Data

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BioinformaticsThe Analysis of Microarray Data

• Robert Gentleman
• Department of Biostatistics
• Harvard University
• DFCI

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Bioconductor

• a new project aimed at providing software
  resources for analysing and manipulating
  biological data
• the project has multiple goals (they include)
• provide high quality software to researchers
• provide structure and examples that will enable
  rapid development of new methodology
• explore new methods in both statistics and
  computing and to make these available as rapidly
  as possible

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Bioconductor

• web site will be located at www.bioconductor.org
• not active yet but it should be in the next
  couple of weeks
• initial offerings will be several libraries of
  functions providing
• infrastructure support in the form of data
  structures
• annotation support in the form of a synthesis of
  different databases into a form that is useful
  for the analyses we want to carry out

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Bioconductor

• is a collaborative project, we have participants
  from
• DFCI and Harvard School of Public Health and FAS
• UC Berkeley, Department of Biostatistics
• University of Heidelberg
• ETH, Zurich
• Technical University, Vienna

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Bioconductor

• our current membership is mainly statisticians
  with a strong computing background
• we would like to have a team of statisticians,
  computer scientists and biologists identifying
  both problems and potential solutions

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Bioinformatics
Computer Science
Biology
Statistics
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Bioinformatics

• there are many challenges
• large and complex data
• complex models
• computational requirements can be enormous
• data are often a mix of numeric and non-numeric
  (we can deal with the former better than the
  latter)
• perhaps the largest challenge is to develop tools
  that easily and accurately reveal the biology

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Bioinformatics

• the tools used to analyse the data are themselves
  complex and they need to be!
• we are asking and answering very complex
  questions
• the user interface should be simple and intuitive
• we need a flexible system for the development of
  new tools

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Bioinformatics Tools

• some methods that have been successfully employed
  in similar situations
• object-oriented programming
• visualization
• statistical modeling
• parallel algorithms

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Bioinformatics Tools

• I contend that the basis for constructing
  bioinformatics tools should be a proper
  programming language

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Bioinformatics Tools

• the ideal development environment should have
  some properties
• high quality graphics (preferably interactive)
• seamless access to databases
• good numerics (preferably with many math/stat
  algorithms as primitives)
• a system for producing packages
• an intuitive user interface
• it doesnt exist!

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Bioinformatics Tools

• our approach is to start with a language that has
  most, but not all of these properties.
• we will then work on extending that language to
  provide the missing pieces
• the language
• R a language for statistical computing and
  graphics
• www.r-project.org

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Bioinformatics

• in the remainder of this talk I will consider
  some basic tasks that we are interested in
  carrying out and show how our use of R has
  simplified the implementation
• note that a number of other teams working on the
  development of tools for Bioinformatics have also
  adopted R however they typically have a less
  aggressive strategy

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Specifics

• we now turn our attention to the analysis of DNA
  microarray data (only as a specific example)
• most of the important points here are
  transferable to the analysis of other types of
  data

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Experimental Design

• random errors exact replication using the same
  reagents, same samples, same technicians etc will
  still yield variation
• systematic variation
• between technicians
• between batches/reagents
• dont want systematic components to align with
  experimental conditions (confounding)

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Types of assays

• The main types of gene expression assays
• Serial analysis of gene expression (SAGE)
• Short oligonucleotide arrays (Affymetrix)
• Long oligonucleotide arrays (Agilent)
• Fibre optic arrays (Illumina)
• cDNA arrays (Brown/Botstein).

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Microarray Data

• data are typically obtained from three distinct
  sources
• the experimental data that provides expression
  level data for a selected set of genes (or ESTs)
• the sample level covariates, including
  experimental conditions
• the biological metadata (GenBank, LocusLink,
  KEGG, and so on)

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Applications of microarrays

• Measuring transcript abundance (cDNA arrays)
• Genotyping
• Estimating DNA copy number (CGH)
• Determining identity by descent (GMS)
• Measuring mRNA decay rates
• Identifying protein binding sites
• Determining sub-cellular localization of gene
  products

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Some Questions

• Which genes have expression levels that are
  correlated with some external variable?
• For a given pathway, which of the genes in our
  collection are most likely to be involved?
• For a diffuse disease, which genes are associated
  with different outcomes?

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Answering the questions

• we need to obtain and then analyse the expression
  data
• preprocessing of the image
• normalization of the images
• modeling to extract expression level data
• gene-filtering
• clustering
• relating to biologic data

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Steps in image analysis
1. Addressing. Estimate location of spot centers.
2. Segmentation. Classify pixels as foreground
(signal) or background.

• 3. Information extraction. For
• each spot on the array and each
• dye
• signal intensities
• background intensities
• quality measures.

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Addressing
Automatic addressing within the same batch of
images.

• Estimate translation of grids.
• Estimate row and column positions.

4 by 4 grids
Other problems -- Mis-registration --
Rotation -- Skew in the array
Foreground and background grids.
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Segmentation
Adaptive segmentation, SRG
Fixed circle segmentation
Spots usually vary in size and shape.
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Image Analysis

• we need a mechanism for storing and accessing the
  raw data (note databases are not really the
  answer)
• we need tools to allow us to go back from the
  expression data to the set of spots that were
  used to compute that expression data

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Image processing

• Almost all steps in this process seem to lend
  themselves to a Bayesian analysis.
• Many processing techniques use only the single
  slide of interest but there are usually other
  slides with similar structure that could be used.
• In most cases there is structure that exists
  across slides, technicians, machines.

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An Image Storage Solution

• we have developed an HDF5 library
• http//hdf.ncsa.uiuc.edu/
• HDF5 is a storage format for image data that is
  widely used
• our package allows users to access image data in
  R as if it were an ordinary array but the image
  data remains in a disk file
• we have used Rs ability to link with other
  software to quickly and effectively implement this

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Post-Processing

• once the spot intensities have been obtained
  further processing is required to obtain
  expression level data (expression is often in
  terms of mRNA levels)
• for Affymetrix arrays the spot intensities are
  for short oligos and must be processed to obtain
  gene level data
• in all cases some form of normalization is
  required (basically an intensity alignment)

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Expression Level Data

• now, for each array we have obtained expression
  level data
• the next step is to select those genes that have
  interesting expression levels.
• interesting is interpreted in many different ways
• high levels of expression in a subgroup of
  interest
• lack of expression in a subgroup of interest
• pattern of expression that correlates well with
  experimental conditions.

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Data Structures

• one of our goals is to introduce some standard
  data structures
• in an object oriented setting these are called
  classes
• a particular data set is referred to as an
  instance of the class
• they allow us to model complex data in a natural
  way

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Data Structures

• if the class is well defined and describes the
  physical data well then using it is natural
• methods or functions can be written to perform
  calculations on instances of the class
• this makes it easier to both write the functions
  and to share methods across developers

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Data Structures

• one of the difficult tasks that confronts a data
  analyst in this field is to ensure that the data
  are correctly aligned
• the expression data for each sample must be
  related to the correct phenotypic data and the
  gene annotation must be aligned correctly with
  the genes on the microarray
• the class structure can help ensure proper
  alignment

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Data Structures

• these problems will become more severe as we
  obtain more data
• for example relating data from several different
  experiments with different sources (ie both cDNA
  array and short oligo arrays)
• starting to look at pathways or binding/promoter
  sites

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The Evolution of Gene Selection

• first fold-change ratio of expression levels
  between two groups
• then t-tests now statistical variation comes in
  to play
• other statistical models Anova, Cox Model, etc
• for large enough samples we can tailor the test
  to the distribution (which might be different in
  the two groups)

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Filters and Orders

• what sorts of questions can we answer
• does a gene have a pattern of expression that
  correlates well with experimental conditions?
• does a gene express at a reasonably high level in
  a reasonably large portion of my samples?
• can we find genes that have a pattern of
  expression that is similar to that of some known
  gene(s)?

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Filters

• A filter is a mechanism for removing a gene from
  further consideration
• we want to reduce the number of genes under
  consideration so that we can concentrate on those
  that are more interesting (it is a waste of
  resources to study genes that are not likely to
  be of interest)

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Orders or Rankings

• while there is a strong desire to have methods
  that determine which genes are important, such
  methods do not exist and cannot exist
• we can rank genes according to some measure of
  interesting
• a test statistic, a p-value, etc
• such rankings can be used to select genes (those
  with high ranks) for further study

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Non-specific filters

• at least k (or a proportion p) of the samples
  must have expression values larger than some
  specified amount, A.
• the gene should show sufficient variation to be
  interesting
• either a gap of size A in the central portion of
  the data
• or a interquartile range of at least B
• genes that fail to pass can be eliminated early

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Specific Filters

• any filter based on a statistical comparison
• t-test, ANOVA, Cox Model and so on
• these are all readily available in R and hence in
  our gene filtering package

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Multiple Testing

• to assess the significance of the p-values one
  must make some adjustments for multiple testing
  (Dudoit et al)
• this is especially important if the expression
  data are coming from multiple sources

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An Example

• two cell lines
• observed at four time points
• we want to select genes that have interesting
  patterns
• non-linear mixed effects models seem appropriate
• R provides the filter without any extra coding

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Annotation

• obtained from multiple sources
• align it using a combination of R, XML and
  Postgres into a coherent collection
• we can produce uniform annotation for any set of
  genes
• Unigene, Locus Link
• chromosome, cytoband,
• GO Ontology

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Annotation

• in some cases knowing the chromosome or cytoband
  is useful
• hyperdiploid samples, hypodiploid samples
• examine gene amplification/deletion patterns
• if multiple genes are involved we may be able to
  detect this
• given information of this kind we want access to
  visualization tools
• where are the top expressing genes located?

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Annotation

• Pathways
• given pathway information can we determine which
  genes express in a manner similar to known genes
  in the pathway
• Need to link, via browser technology, with other
  sources. It is particularly useful if the
  information can be parsed and analysed by machine
  (eg XML)
• again R has support for exactly this type of
  processing

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Clustering

• Supervised
• some clusters are determined a priori, the
  training set, and we assign new samples to those
  clusters (classification)
• Unsupervised
• data are grouped, using some method, to provide
  (potentially) new groupings or classifications

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Some References

• Classification, A.D. Gordon Chapman and Hall
• Finding Groups in Data, L.Kaufman and P. J.
  Rousseeuw Wiley.
• Pattern Recognition and Neural Networks, B. D.
  Ripley Cambridge University Press.
• The Elements of Statistical Learning, T. Hastie,
  R. Tibshirani, and J. Friedman Springer

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Clustering

• Clustering is often used to answer the following
  questions.
• Can I find a set of genes that help me to
  correctly classify the samples into specific
  groups (often disease categories)
• If I can do this, which genes were used and how
  important are they?

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Inference

• Permutation tests
• Cross-validation
• How many clusters are there?
• Gordon Ch 3 addresses some of these issues
• Are my clusters significant?
• it is more important to ask whether they provide
  a meaningful representation or reduction of the
  data

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Variable Selection

• how do we select genes to help in clustering?
• this process has been studied in other areas of
  statistics, however, few of the solutions seem
  appropriate

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Model Selection

• gene selection can be characterized as a model
  selection procedure
• most statistical research in this area has been
  concentrated on the situation where the number of
  variables is much less than the number of
  observations
• we need to develop model selection procedures for
  the situation where there are many more variables
  than observations

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Selection Problems

• may need to adjust for other variables
• this makes the bootstrap and cross validation
  algorithms more complex
• computing is already hard -- now it is getting
  much more difficult data structures play an
  essential role in simplifying the computations

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Selection Problems

• use bootstrap or crossvalidation type
  experiments to do variable selection
• for example select genes that show up as
  important predictors in many different subsets
• to assess variable importance (when there are
  several variables) Breiman has proposed
  reclassifying using a new data set that has the
  covariate values permuted.

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Cross-validation

• leave one out CV is easy to implement but
  probably not the best method to use for assessing
  or selecting a model
• the problem is that leaving out one observation
  yields too small a change to the data
• in general we need to consider perturbations on
  the order of about the square root of the number
  of observations

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Cross-validation

• make sure that you are cross-validating the
  experiment that you have carried out
• in particular, if you are selecting genes, rather
  than working with known genes, you must
  cross-validate the gene selection process as well
• most examples I have seen with low classification
  error rates do not cross-validate properly
  (model/gene selection was not validated)

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Classification

• Breimans Random Forest ideas
• notions of boosting using several weak
  classifiers to obtain a good classifier
• weighted averages of predictions the weights
  might be different in different parts of the
  covariate (gene) space

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Acknowledgements

• Vincent Carey, Channing Laboratory
• Jianhua Zhang
• Sabina Chiaretti
• The DFCI for funding

• Dirk Iglehart
• Cheng Li
• Byron Ellis
• Sandrine Dudoit