Identification of Differential Genes

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Identification of Differential Genes
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Identification of differential genes

• The most basic experimental design comparison
  between 2 conditions treatment vs control
• The goal to identify genes that are
  differentially expressed in the examined
  conditions
• Number of replicates is usually low (n2-4)

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Approaches for identification of differential
genes

• Fold Change
• T-test
• Cyber-T
• SAM

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1. Fold Change

• Consider genes whose mean expression level was
  change by at least 1.75-2 fold as differential
  genes
• Limits
• Usually no estimation of false positive rate is
  provided
• Biased to genes with low expression level
• Ignores the variability of gene levels over
  replicates.

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Fold Change limit Biased to low expression
levels
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70
110
Determine floor cut-off according to estimate
of background level and set all expression levels
below it to this floor level
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Fold Change limit ignores variability over
replicates

• Seek for score that punishes genes with high
  variability over replicates

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Approaches for identification of differential
genes

• Fold Change
• T-test
• Cyber-T
• SAM

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2. T-test

• Compute a t-score for each gene

mc, mt mean levels in Control and
Treatment Sc2, St2 variance estimates in
Control and Treatment nc, nt number of
replicates in in Control and Treatment
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T - test

• The t-score can be associated with statistical
  significance (p-value) under the assumption that
  expression levels follow normal distribution
• Log-transformation
• Set cut-off for p-value (a0.01)
• Consider all genes with p-value lt a as
  differential genes

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Multiple Testing

• P-valg associated with the t-score Tg is the
  probability for obtaining by random a t-score
  that is at least as extreme as Tg.
• Multiplicity problem thousands of genes are
  tested simultaneously.
• e.g. suppose
• 10,000 genes on a chip
• not a single one is differentially expressed.
• a0.01
• 10000x0.01 100 genes are expected to have a
  p-value lt 0.01 just by chance.

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Multiple testing

• Individual pvalues of e.g. 0.01 no longer
  correspond to significant findings.
• Need to adjust for multiple testing when
  assessing the statistical significance of findings

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Multiple Testing Bonferroni correction

• Consider as differential genes only those with
  p-value lt (a/N)
• N number of tests
• a0.01, N10,000 cut-off0.000001
• Ensure very low probability for having any false
  positive genes (less than a)
• Advantage very clean list of differential genes
• Limit the list usually contains very few genes
  unacceptable high rate of false negatives

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Multiple Testing FDR correction (Benjamini
Hochberg)

• False Discovery Rate
• In high-throughput studies certain proportion of
  false positives is tolerable
• Control the expected proportion of false
  positives among the genes identified as
  differential (q10).
• Scheme
• Rank genes according to their p-vals
  p(1)ltp(2)ltp(N)
• Consider as differential genes the top k that
  satisfy
• p(i) lt i(q/N), 1ik

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Approaches for identification of differential
genes

• Fold Change
• T-test
• Cyber-T
• SAM

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3. Cyber-T (Baldi Long)

• Regularized t-test
• Problem Low number of replicates ? unstable
  estimations of gene variances
• Found that in microarray datasets, after
  log-transformation, the variance is dependant on
  the expression level
• Lower expression level ? larger variance

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• Utilize this rule to improve the estimation of
  gene variances

• Lower expression level ? larger variance

In t-test, use s2 in place of s2 s2 genes
variance over the replicates n number of
replicates s02 expected variance given the
expression level of the gene ?0 weight of
s0 s02 estimated over a window of size 101
genes ?0 n 10
Log (expression)
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Stabilization of the variance estimation
s2
s2
Log (expression)
Log (expression)
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Cyber-T

• Regularized t-test performs better than the
  conventional t-test when the number of replicates
  is low (2-3)
• By 5 replicates (5 control, 5 treatment) the
  performances were similar

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Approaches for identification of differential
genes

• Fold Change
• T-test
• Cyber-T
• SAM

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4. SAM (Tusher, Tibshirani Chu)

• Significance Analysis of Microarray
• Limit of analytical FDR approach assumes that
  the tests are independent
• However in the microarray context, the expression
  levels of some genes are highly correlated ?
  unreliable FDR estimate
• SAM uses permutations to get an estimate for the
  FDR of the reported differential genes

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SAM

• Scheme
• Compute for each gene a statistic that measures
  its relative expression difference in control vs
  treatment (t-score or a variant)
• Rank the genes according to their difference
  score
• Set a cut off (d0) and consider all genes above
  it as differential (Nd)
• Permute the condition labels, and count how many
  genes got score above d0 (Np)
• Repeat on all possible permutations and count
  (Npj)
• estimate FDR as the proportion ltNpjgt/Nd

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Permutation on condition labels
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