CGH Data

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CGH Data

• BIOS 691-804

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Chromosome Re-arrangements
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Normal Human Variation
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Array CGH Technology
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Chromosome 8 (241 genes) in 10 cell lines and
many tumor samples
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Pre-processing CGHa Data

• QA Same as for expression
• Normalization
• Are values comparable across arrays?
• Can noise be reduced?
• Segmentation
• Where do copy number aberrations start and stop?
• Better estimates for how many copies

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Normalization

• Most copy numbers are 2
• Centering necessary
• Dynamic range varies
• Mixtures of tumor with normal
• Saturation not usually a problem
• Few instances of 10X copy
• Dye bias sometimes strong
• loess procedure unreliable

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Centering

• Where is the center (log ratio 0)?
• Sometimes modal copy number is 3
• Variability in labeling and tissue extraction
• CGH cant give direct measures of counts
• Most researchers set modal copy to log-ratio of 0
• Does it matter?
• Take 3 as equivalent to 2 for comparison?

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Dynamic Range

• Ratios of signal are often less (sometimes much
  less) than actual ratios of copy numbers between
  samples

From Bilke et al, Bioinformatics, 2005
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Fractional Copy Numbers

• Often samples are mixtures of tumor and normal
• Many tumors have two (or more) distinct clones
  with distinct karyotypes
• Observed copy numbers may lie in between values
  corresponding to whole numbers

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Probe Bias

• If errors are random then plot of self vs self
  ratios should be random
• Actual Corr gt 60
• Clear bias!
• Try to estimate it

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Segmentation

• Individual probe values are noisy
• Most aberrations are segments
• Most segments have many probes
• Average neighboring probe values to better
  estimate segment value how far?

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Segmentation

• Issues
• How to identify where a segment starts or stops
• How to find these points efficiently

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Noise and Signal
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How to Find Segments?

• Could be large copy number change over short
  interval or small change over large
• Look for jumps in running averages
• Distribution of jumps between probes
• DNACopy is Maximum Likelihood estimate of change
  points, using all intervals
• StepGram is efficient computation of (subset of)
  t-scores

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Theory

• Classical change-point test statistic
• Let be values let
  be partial sums
• Set , where
  
• are the differences in levels before and after i
• Now for segments in middle
• Let
  , where
• This is Circular Binary Segmentation
• Implemented in DNACopy

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DNACopy

• In Bioconductor
• Does ML identification of segments recursively
• Apply procedure within identified segments
• Double-checks points near the boundary
• Does permutation testing to estimate null
  distribution
• Often data are not Normal

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StepGram

• DNACopy is slow!
• Could try to compute only a fraction of possible
  scores
• StepGram tries to find a subset of most likely
  scores to compute
• Much faster!
• Some inaccuracies
• Doesnt handle chromosome ends well

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StepGram Method 1

• Key Idea
• Dont compute
• all possible t-scores
• Compute only those
• likely to show
• significant change
• Bound the
• estimated t-scores
• in future based on
• current t-scores

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StepGram Algorithm 2