Differentially Expressed Genes, Class Discovery

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Differentially Expressed Genes, Class Discovery
Classification
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Finding Differentially Expressed Genes

• Two types of motivation
• Direct
• Relate the genes to known biology functions,
  pathways etc. Infer about their rule, the
  mechanisms governing the process etc.
• Indirect Use as a pruning stage for tools
  that perform learning tasks
• Infer regulatory mechanisms and relations
• Classification ( disease Vs. normal, disease
  subtypes)

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Example Tumor vs. Normal tissues
Normalsamples
Tumorsamples

• Identify differentially expressed genes
• Diagnostic Markers
• Therapeutic targets
• Understanding the disease process

Under expressed
Non-small cell lung carcinomas Sheba medical
center U. of Colorado Medical Center
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What We Need

• Score the genes, hopefully in a meaningful way..
• Attach a measure of statistical significance to
  the score so we can
• Choose a subset of genes wisely
• Have a measure of how strong our signal is

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Simplest Score Fold Change
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Fold Change problems

• Not reliable at the low end of the scale
• (0/0 effects large variance)
• Sensitive to outliers
• Variant pairwise fold change
• compute fold change over all possible sample
  pairs
• If in e.g. 75 of the pairs, change gt D gt
  significant

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Relevance Scores - TNoM

• Beyond fold change
• Both genes have gt15 fold change
• TNoM (Total Number of Misclassifications) score
• Find the threshold that best separates tumors
  from normals,
• count the number of errors committed there.

tumor
normal
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Scoring Informative Genes
Expression pattern of a gene a Pathological
diagnosis information (annotation) L v(a,L), a
vector of s and s, ordered by the a values
- - - - - -
- a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11
a12 a13 a14 a15
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TNoM Score
Find the threshold that best separates tumors
from normals, count the number of errors
committed there.
Ex 1
- - - - - - -
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TNoM vs. Fold Change
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TNoM

• Cons
• Ones-sided vs. two sided errors
• Absolute values ignored
• For any given level s, we can efficiently
  compute p-Val(s) Prob( TNoM(V) ? s ),where V
  is uniformly drawn over the appropriate space.
• (H0 the gene expression values are independent
  of the labels)
• Computed using DP

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Wilcoxon Rank Test

• Another gene score, which similarly to TNoM
• Ignores absolute values
• Takes into account only order of measurements

• Sort the expression values of both groups
• - - - - - -
  -
• a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12
  a13 a14 a15
• W(g) sum of ranks of the positive examples
• W(g) 1 2 5 6 7 10 13 14 58

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Wilcoxon Rank Test

• A common test in statistics
• Again, we can compute p-Values given the null
  hypothesis H0
• P(W(g) gt sn,k) the probability of getting a
  score gt s given a total of n samples, out of
  which k are labeled as ().

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SAM (Tusher et al., PNAS 01)

• Where a (1/n1 1/n2)/(n1 n2-2)
• d(i) is exactly the paired t-statistic
• Tests the assumption are the means of the two
  processes the same?
• Underlying assumption two normal distributions
• A known p-value the t-distribution

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SAM Alternative to P-Value

• P-value relies on t-test assumptions -
  problematic
• Can we assess the significance of d(i) without
  parametric assumptions?
• Define a balanced permutation division of
  samples to 2 groups, where in each group the
  number of and - is balanced
• Perform all possible balanced permutations p to
  the data and compute

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False Discovery Rate for SAM

• Genes with D above a given threshold
  significant
• FDR False discovery rate the of genes
  passing as significant which are expected to be
  false positives
• Each threshold on D(i) can be given an FDR value
• compute the avg. number of FP crossing this
  threshold in the permuted sets

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Different Scores

• TNoM
• Info
• Wilcoxon
• t Test
• Fold Change

Different scores and null hypothesis (parametric,
non parametric etc.) All can be found in the
ScoreGene package http//www.cs.huji.ac.il/labs/
compbio/scoregenes/
Can we assess which scoring method is the best
for our case?
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Overabundance Analysis

• Data on 30 samples from normal and tumor lung
  tissues.
• 7000 genes.
• Naftali Kaminskis lab, Sheba Medical Center

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Why Test Overabundance?

• Tests how informative is a set of genes w.r.t. a
  given classification of the data and a scoring
  method.
• Can be used to compare different
• gene scoring methods
• normalization methods

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Comparing Normalization Methods
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Why Test Overabundance?

• But also a method to discover new classes in the
  data
• Intuition biologically meaningful partitions
  will have a high overabundance of informative
  genes

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Overabundance Analysis in Class Discovery
AML/ALL

• Score Genes
• Count
• Compare torandom

BRCA1/2
Melanoma
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Class Discovery Approach
Seek partitions with statistically significant
overabundance of informative genes

• Use local search techniques, e.g
• Steepest ascent
• Simulated annealing

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Scoring a Partition

• At a given score level s, set p p-Val(s) .
• Suppose that in the data we observe n(s) genes
  with score ? s .
• The number of genes with score ? s we observe for
  uniformly and independently drawn labeling
  vectors is a random variable N(s) with N(s)
  Binom(n,p)where n is the total number of genes.
• The surprise rate at s is defined as ?(s)
  Prob( N(s) ? n(s) ) ?kn(s)n n
  choose n(s)pk(1-p)n-p.
• Finally, the max surprise score for the suggested
  partition is Maxs ?(s)

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Overabundance Max-Surprise
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Example Survival Prediction
Good Prognosis Patients
All Patients
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Class 2
Good Prognosis Patients
All Patients
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Class 3
Good Prognosis Patients
All Patients
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Tissue Classification

• Given a set of labeled samples, we can try to
  classify a new sample
• Supervised methods SVM, Adaboost, Naïve Bayes
• Semi-supervised methods Clustering
• Issues
• Evaluating the methods
• Feature Selection
• Sample contamination/composition

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Evaluating Classification

• LOOCV Leave one out cross validation
• For all samples i 1M
• Take sample i out
• Learn from M-1 remaining samples
• Test on sample i

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Feature Selection

• How many of the informative genes do we choose
  for our classifier?
• A question of choosing a cutoff

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Tissue Composition
Small celllung carcinoma
Lung adenocarcinoma
Serous carcinoma
Lung metastasa
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Tissue Composition

• The tissue is composed of many cell types (tumor,
  blood, muscle, )
• The arrayed samples are not always pure!
• Major difference differentialy expressed genes
  which are
• Causes of the disease state
• Outcome of the disease state

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Summary

• Many methods for choosing differentially
  expressed genes
• These can be compared, e.g. using overabundance
  tests
• Overabundance can also be used for new class
  discovery
• Expression patterns can be used to classify a
  tissue