Title: Normalization in the Presence of Differential Expression in a Large Subset of Genes
1Normalization in the Presence of Differential
Expression in a Large Subset of Genes
- Elizabeth Garrett
- Giovanni Parmigiani
2Motivation (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.
3Raw data log gene expression median versus log
gene expression in sample i
4Problem with raw data
- V pattern in many of the slides
- Curvature
- Non-constant variance
5V 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?
6Crude 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.
7High abundance 3 or greater
8A 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.
9Latent Variable Model
- Allow different slopes and intercepts for the two
classes of genes - Details
10Results
- 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
11Posterior Probabilities of Class Membership
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13Normalization
- Use loess normalization where class 0 genes are
the reference
rsg residuals ysg - loess
Sample 43
14Before and after loess normalization (R function
loess with weights 1 - c_g)
Before
After
15Variance 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.
16Final Step
- Calculate normalized data
Slide median
Residual from first loess
gene median
Variance stabilizer from second loess
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