Normalization in the Presence of Differential Expression in a Large Subset of Genes

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Normalization in the Presence of Differential
Expression in a Large Subset of Genes

• Elizabeth Garrett
• Giovanni Parmigiani

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Motivation (again)

• Class discovery Find breast cancer subtypes
  within 81 samples of previously unclassified
  breast cancer tumor samples
• Gene selection Find small subset of genes which
  allows us to cluster tumor samples
• Gene clustering Look for genes which are
  differentially expressed and genes that behave
  similarly.

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Raw data log gene expression median versus log
gene expression in sample i
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Problem with raw data

• V pattern in many of the slides
• Curvature
• Non-constant variance

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V Patterns

• Debate
• We thought..Oops, something went wrong in the
  lab. We should either
• correct the Vs so that we see only one line
• remove the genes that are causing the V
• They (i.e. experts) thought..Its REAL
  differential expression!
• Assuming it is real, how do we normalize to
  straighten and stabilize variance?

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Crude Initial Approach

• Approach
• Fit a regression to each plot and identify points
  with large negative (positive) residuals.
• Remove the genes with negative (positive)
  residuals (and high abundance?) and normalize
  using the remaining points.
• Problem Points near origin get truncated in odd
  way and there is no obvious way to decide how to
  include exclude near origin.

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High abundance 3 or greater
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A better (and not hard to implement) approach

class 0
1. Assume 2 classes of genes
class 1
2. Take subset of samples where V is obvious
(we picked four samples) 3. Fit a latent
variable model using MCMC to predict which
genes are in class 1 and which in class 0.
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Latent Variable Model

• Allow different slopes and intercepts for the two
  classes of genes
• Details

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Results

• Goal is to estimate gene classes, cg
• ?s are nuisance parameters
• Based on chain, we estimate ?g P(cg 1)
• at each iteration, each gene is assigned to class
  0 or class 1
• by averaging class assignments over iterations,
  we get posterior probability of class membership
• To do normalization, we restrict attention to
  genes with ?g lt 0.95

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Posterior Probabilities of Class Membership
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Normalization

• Use loess normalization where class 0 genes are
  the reference

rsg residuals ysg - loess
Sample 43
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Before and after loess normalization (R function
loess with weights 1 - c_g)
Before
After
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Variance Stabilization

• Take residuals from previous loess fit.
• Fit loess to squared residuals versus median
• Square-root of fitted value approximates standard
  deviation.
• Rescale so that overall slide variability is not
  lost by dividing by average slide variance.

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Final Step

• Calculate normalized data

Slide median
Residual from first loess
gene median
Variance stabilizer from second loess
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