Raged: robust analysis of gene expression data

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September 22-25, 2002
Virtual Seminars on Genomics and Bioinformatics
www.ndsu.edu/virtual-genomics
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Microarray Gene Expression Data Analysis and
Visualization

• Imad Rahal

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Analysis of Microarray Gene Expression Data

• DNA microarrays are increasing the level of
  understanding of complex biological systems
• an exponential growth in the size and complexity
  of the data available
• data increase can mean less information to the
  user
• new challenges for analysis

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Unsupervised Analysis Clustering

• no existing knowledge about the functionality of
  genes is available prior to the analysis
• most common form for interpreting microarray data
• Simple
• Graphical representations (dendograms)
• Execution speed
• divides the elements into distinct groups that
  are mutually exclusive and collectively
  exhaustive

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• elements in the same cluster exhibit similar
  biological functions
• the choice of similarity is very critical
• different types of clustering algorithms

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• Partitional clustering makes implicit assumptions
  on the form and number of clusters.
• K-means

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Supervised Analysis Classification

• requires previously assembled training sets with
  each element having a label
• classifies samples with unknown labels
  (functional category in our case)
• can be of two forms
• trained/eager
• Decision tree
• Neural nets
• lazy/example-based
• KNN

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Supervised VS Unsupervised

• Incorporates human direction (class labels)
• Tends to be more robust specially with datasets
  having complex features (large, noisy and
  incomplete)

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Visualization

• achieved thru GUIs
• provides different views of the results
• facilitate the biological interpretation of gene
  dynamics
• stimulates human visual pattern recognition (one
  of the best!) save processing time
• examples

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Department of Mathematics and Statistics,
University of Massachusetts, Amherst.
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Decoding Gene Expression Control Using
Generalized Gamma Networks
Paola SebastianiDepartment of Mathematics and
Statistics, University of Massachusetts
Amherst Marco Ramoni Childrens Hospital
Informatics Program Harvard Medical School
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Objective

• Objective To develop models for decoding gene
  control interactions, and elucidate gene
  functions. This is one of the goals of the modern
  approach to functional genomics.
• Modern approach
• Genome wide Complete sequence of the genome of
  many organisms.
• Microarray based Technology for measurement of
  thousands of gene expression level in parallel.
• Statistically needy Incredible wealth of
  information that is not fully exploited or
  structured.

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Central Dogma

• A gene is expressed when it makes proteins.
• Proteins are produced in two steps
• Transcription The gene code is transcribed into
  mRNA dual coding
• TranslationThe mRNA is transformed and
  transported out of the nucleus and translated
  into proteins.
• Expression level mRNA abundance

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From Image to Data
sample
genes
P. Sebastiani, E. Gussoni, I. S. Kohane and M.
Ramoni, (2003), Statistical Challenges in
Functional Genomics. (With discussion)
Statistical Science. To appear.
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Common Analysis

• Differential analysis to identify genes that
  have different level of expression in two or more
  conditions.
• Classification rules model the dependency
  between the genes that have differential
  expression and the classes to build predictive
  models.
• Cluster analysis to identify groups of genes
  that have same expression profiles. Intuition
  genes that belong to the same group may have
  similar functions.

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Information and Knowledge

• Differential analysis, naïve predictive models,
  clustering techniques increase information but
  not knowledge about the gene interaction
  mechanisms.
• Genes do not act independently, for example

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Example

• Prostate cancer data set, available from the
  website of the Cancer genomics group at the
  Whitehead institute.
• 50 samples from normal tissues 52 samples from
  cancer tissues. Expression levels of 12,625 genes
  was measured with Affymetrix U95a chip and Mas 5
  software.
• For about 10 genes, evidence of differential
  expression was found to be very strong (posterior
  probability close to 1). Selection done with
  BADGE (www.genomethods.org/badge).

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Models
Normal specimens
Tumor specimens
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Formalism

• Bayesian network.
• A directed acyclic graph in which nodes are
  random variables describing gene expression
  levels, and arcs define directed stochastic
  dependencies from parents to children.
• Advantage describe the dependency structure in
  probabilistic terms and simplify it by using
  Markov properties. Look at a multivariate model
  by looking at its components.

Y1
parent
Y2
child
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Big Advantage

• The DAG encodes local and global Markov
  properties that make learning and reasoning with
  the model very efficient.

Local Markov property Y ? ND(Y) P.
Global Markov property Y ? Y\MB(Y) MB(Y).
Y3 ?Y1 Y2 Y5 ? (Y1,Y2) Y3,Y4
Y3 ?Y1 Y2,Y5 Y4,
NDNon descendants of Y are all nodes from which
Y can be reached along a directed path.
MBMarkov blanket parentschildrenparents of
the children.
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Factorization
Factorize the joint density as
Yi is a child variable with parents pa(Yi).
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Advantages

• Can exploit the factorization of the likelihood
  for
• Quantifying the network locally
• Learning the network structure by using a
  sequence of local searches.
• Because the exhaustive search over all networks
  structures is unfeasible, many search algorithms
  have been developed to explore a subset of all
  possible networks.
• Exact solutions for discrete, Gaussian and
  mixed networks if parents are discrete.

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Distributional Assumptions

• Microarrays produce data with skewed
  distributions.
• Log-normal take the logarithm, data are normal.
• Gamma they remain asymmetrical (exponential).

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Gamma Networks

• Gamma distributions are flexible enough to
  describe a variety of different shapes.

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Generalized Gamma Networks

• Encode general non linear dependencies

Yi2
Yi3
Can choose different link functions
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Learning Dependencies

• Given a link function, and a specification of the
  linear predictor
• Use MCMC to estimate the parameters.
• Compute standard MLE of the parameters qi. These
  can be computed independently of ai.
• Given qi, compute MLE of ai (efficient procedure
  to compute this using a Taylor expansion to order
  5 about the moment estimator).

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Likelihood Function
A product of family contributions
Multiply over k to get the full likelihood
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Learning the Structure

• Search the model space and assign a score to each
  network structure.
• Select the network with optimal score.
• The score is the posterior probability, or
  marginal likelihood when all networks are a
  priori equally likely.
• We use BIC-MDL
• that factorizes according to the family
  structures and allows local learning.

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Greedy Search
Four parents
For each Y, have the set of k possible parents.
Three parents

• In each level, choose the dependency with minimum
  MDL.
• If smaller than the smallest in the previous
  level, accept and move up.
• Otherwise stop and accept the last smallest in
  previous level.

Two parents
One parent
(k)
Y alone
(1)
Procedure implemented in Bayesware Discoverer
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Models
Normal specimens
Tumor specimens
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Validation of the Structure

• Use blanket residuals for validation.
• For each case in the data set
• Compute the expected value given its Markov
  blanket
• Repeat for all cases in the dataset

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Structural Differences
Normal specimens
Tumor specimens
37605 collagene is independent of all other
nodes, and becomes a child of 914 oncogene with
transcription regulation functions.
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Dependency Differences
Normal specimens
m1/(.011.8/y.40282)
Tumor specimens
m1/(0.022/y.40282)
32598 gene with putative growth and
transcription regulation functions
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Reasoning
Networks learned from 50 normal prostatectomy
samples
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To fully decode gene interactions, propagate
evidence in the network.
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Evidence Propagation

• Well known algorithms work for networks with all
  discrete, or all Gaussian variables.
• Problems with all Gamma distributed variables
• The joint/marginal distributions are not easy to
  compute.
• We can use stochastic algorithms for
  probabilistic reasoning.
• Several algorithms developed in the 90s. Focus on
  discrete networks. (Cheng and Druzdzel, AIJ
  2000).
• Gibbs sampling appears to be the most promising.

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Gibbs Sampling
Assumptions standard links.
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Normal Specimens
Marginal densities when no evidence is propagated.
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Normal Specimens
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Tumor Specimens
Network learned from prostate cancer data set 52
tumor samples. All inverse links. Compared to the
other network, 40282_S_AT has less espression,
whereas the tumor related genes have higher
expression.
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Normal Specimens
Mean16
a marker of tumor differentiation
Mean12
Growth and differentiation factors
Observe 40282_S_AT300 (average value in normal
specimens). Gene supposed to have a role in
immune system biology.
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Tumor Specimens
Evidence70
Look at how changes in 40282_S_AT determine
changes of expression in tumor markers.
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Open Issues

• Decoding gene control How to report the results?
• Mixing nodes with different distributions.
• How feasible is Gibbs sampling in large networks?
• Can we improve learning?
• In silico biology.

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www.genomethods.org/caged
www.genomethods.org/badge
www.genomethods.org/best
www.bayesware.com