Yanxin%20Shi1,%20Fan%20Guo1,%20Wei%20Wu2,%20Eric%20P.%20Xing1

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GIMscan A New Statistical Method for Analyzing
Whole-Genome Array CGH Data
RECOMB 2007 Presentation

• Yanxin Shi1, Fan Guo1, Wei Wu2,Eric P. Xing1

1 School of Computer Science, Carnegie Mellon
University2 Division of Pulmonary, Allergy, and
Critical Care Medicine, University of Pittsburgh
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Outline

• Motivation and Background
• Computational framework
• Experiments and Results
• Summary

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Copy number aberration and Array CGH

• DNA copy number (a.k.a. dosage state)
• Normal 2 DNA copies
• Aberrations deletion(0 copy), loss (1 copy),
  gain(3 copies), amplification(gt3 copies)
• Array CGH a high throughput method to measure
  DNA copy number

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Array CGH data
Ideally,
Deletion (0 copy) LR log(0/2) Loss (1
copy) LR log(1/2) -1 Normal (2 copies) LR
log(2/2) 0 Gain (3 copies) LR log(3/2)
0.58 Amplification (gt4 copies) LR gt log(4/2)
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However

• Factors influencing the LR values
• Impurity of the test sample (e.g. mixture of
  normal and cancer cells)
• Variations of hybridization efficiency
• Base compositions of different probes
• Saturation of array
• Divergent sequence lengths of the clones
• Many others
• Measurement noises, etc

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Segmental pattern and spatial drift
Spatial drift
Segmental pattern
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Existing Computational Methods

• Threshold Method
• Mixture Models (e.g. Hodgson et al., 2001)
• Assume observations are iid samples from a
  mixture distribution.
• Regression Models (e.g., Hsu et al., 2005 Myers
  et al., 2004)
• Smoothing for visual inspection to detect copy
  number states.
• Segmentation Models (e.g. Hupé et al., 2004)
• Directly search for breakpoints in sequential
  data
• Spatial Dynamics Models (e.g. Fridlyand et al.,
  2004)

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Spatial Dynamic Methods

• Hidden Markov Models
• Dosage states form a Markov chain of hidden
  variables
• Observed LR ratios are generated from
  state-specific Gaussian distributions

dosage states
LR ratios
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Dosage-Specific Kalman Filters

• Introduce hidden trajectory to model
  state-specific LR distributions (no longer fixed
  mean)

Linear Dynamics for dosage state m
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Switching Kalman Filters
Trajectory 1
Trajectory M
Dosage state chain

• A SKF generates observations from one of the
  trajectories.

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Posterior Inference

• Dosage annotation is equivalent to the estimate
  of the posterior .
• Recovering the hidden trajectory
  .

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Variational Inference

• Posterior Inference is intractable.
• Variational inference decouple the hidden
  chains.
• Decoupled chains have tractable distributions.

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Variational Inference

• Use this tractable distribution to approximate
  the true distribution by minimizing KL
  divergence.
• Fixed point equations to update the variational
  parameters.

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Parameter Sharing

• The CGH dataset contains whole-genome
  measurements for multiple individuals.
• Chromosome-specific parameters shared across
  individuals
• Individual-specific parameters shared across
  chromosomes

trajectory parameters
All other parameters e.g. output noise variance
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Experiment Design

• Simulation Analysis
• Data generated from SKFs.
• Compare with threshold, HMM.
• aCGH profiles of 125 colorectal tumors (Nakao et
  al. 2004)
• Case studies of 3 representative chromosomes.
• Populational analysis over 125 genomes

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Simulation Analysis (1)
Performance of dosage state prediction (b
noise in hidden dynamics, r noise in
observation, M5)
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Simulation Analysis (2)
Prediction by HMM
Synthetic Data
Prediction by SKF
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Experiment Design

• Simulation Analysis
• Data generated from SKFs.
• Compare with threshold, HMM.
• aCGH profiles of 125 colorectal tumors (Nakao et
  al. 2004)
• Case studies of 3 representative chromosomes.
• Populational analysis over 125 genomes

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Real aCGH Profile
Spatial Patterns Difficult for Conventional
Methods(1) Flat-Arch Pattern
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Real aCGH Profile
Spatial Patterns Difficult for Conventional
Methods(2) Step Pattern
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Real aCGH Profile
Spatial Patterns Difficult for Conventional
Methods(3) Spikes Pattern
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Populational Analysis
Frequency of dosage state alteration of 125
individuals
red bar copy number gain or
amplification blue bar copy number loss or
deletionsolid vertical lines boundary between
chromosomes
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Populational Analysis
Frequency of dosage state alteration on 2
chromosomes
top, red square copy number
gain top, blue circle copy
number loss bottom, red square copy
number amplification bottom, blue
circle copy number deletion
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Summary

• SKF for whole-genome analysis of aCGH data.
• SKF can capture variations in the hybridization
  efficiency.
• Parameter sharing scheme for data integration.
• Possible Extensions
• Gene expression concordance analysis
• Incorporate information about sequence length and
  distance between clones

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Thank you!
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Populational Analysis
Detailed spectrum of GIM rates over 125
Colorectal cancer patients in 4 hotspots region
with annotation of cancer related gene
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• M is selected by AIC.
• We also have done experiments to compare SKF with
  segmentation methods (result now shown here).

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Switching Kalman Filters

• A SKF generates observations from one of the
  trajectories.
• is the switching process as in an
  HMM.
• are observed LR ratios.