Classifying Gene Expression Profiles from Pairwise mRNA Comparisons

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Classifying Gene Expression Profiles from
Pairwise mRNA Comparisons

• Yan Qi
• Biomedical Engineering Department
• 10/3/2006

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Outline

• The problem of Molecular classification
• The TSP classifier
• Results on three Cancer datasets
• Extensions of the TSP classifier

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Molecular Classification

• Objective predict class labels, e.g. cancer
  subtypes, disease states using gene expression
  profiles
• Data G x n matrix, G is number of genes, n is
  number of samples, each column is a gene
  expression profile

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Mathematical formulation

• Gene expression profile X ( X1, X2, , XG)
• Binary Class label Y 1 or Y 2
• Classifier A mapping f from X to Y
• Training dataset
• A G x n matrix, n n1n2
• Y G x 1 vector where n1 entries are 1, n2
  entries are 2
• Learning find a mapping from A to f that
  minimizes generalization error

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Challenges to standard learning methods

• Statistical dilemma n ltlt G
• Examples
• Consequence Over-fitting hence poor
  generalizability
• Practical issue complex f and DB
• Example ANN, SVM, random forests
• Consequence results are hard to interpret
  biologically, inefficient in diagnostic settings

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The TSP classifierMotivation and strategy

• Rank-based scoring exploits the expression levels
  of genes relative to each other and obtains
  invariance to normalization.
• Reduce model complexity by making the classifier
  parameter free
• Select informative gene pairs by proper LOOCV and
  construct intuitive and biologically
  interpretable classification rule by voting.

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TSP classifierrank-based score

• Idea replace expression value by genes ranks
  within profiles.
• Feature
• Score
• where

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Gene pair selection

• TSP
• The number of TSP and sample size
• A few when sample size is not too small ( gt102 ).
• Many when sample size is small ( lt 102 ).
• Example myocardial tissue gene expression
  profiles
• G 22283 n112, n210
• 2460 statistically significant TSPs

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Classification with one gene pair

• Let be a unique TSP
• Suppose
• TSP classifier
• Error on training set

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An Example
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Classification with multiple gene pairs
majority vote

• Seek a mapping from outputs of multiple single
  TSP classifiers to a final prediction.
• Let
• Output from represent a vote from
  TSP i.
• Final prediction class that receives the
  majority vote from
• Assume the features are
  conditionally independent given the class and
  equal, a Naïve Bayes classifier is equivalent to
  using majority vote

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Classification with multiple TSPsmajority vote
Naïve Bayes classifier

• Assume
• Where
• Let
• Naïve Bayes Classifier
• Each TSP contribute equally if

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Loop of cross-validation

• Leave-one-out CV
• Estimated accuracy 1 - e/n where e is total
  number of errors in cross-validation
• Only the TSPs are determined by CV, unbiased
  error estimate.
• More complicated models, e.g. ANN and Decision
  tree need to include both model topology and
  parameters in CV loop, more likely to be biased.

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Three bench-mark cancer datasets

• Determine lymphnode status in breast tumor
  samples ( West et al. 2001, G7129, n 49 )
• Classify leukemia subtypes ( Golub et al 1999, G
  7129, n72)
• Distinguish prostate tumors from normal samples (
  Singh et al. 2002, G 12600, n102)

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Statistical significance of the score is
evaluated by permutation test

• Repeat e.g. 1000 times
• Keep feature matrix A
• Randomize class labels by keeping
• n1 and n2 unchanged
• Get top score Zmax
• Get histogram of Zmax

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The top scoring gene pairs for the three cancer
studies
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What does TSP represent?

• Change weak predictors into strong predictors?
• Change reference e.g. gene 3 as reference for
  gene 1 and gene 2
• Combine two markers e.g. x4 and X5 might be
  individual markers, one for each class, x4-X5 ?

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Performance of TSP classifier compared with
previous studies

• Breast cancer k-nearest neighbors (8-26) DLDA
  (8-19) DQDA (11-26)
• logitboost (9-21)
  random forests (6-20) SVM (7-29)
• Leukemia correlation analysis weighted vote
  (85 on test set and 95
• on CV set.
• Prostate cancer k-nearest neighbour to genes
  chosen by t-statistic

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Discussion and extensions

• Multiple class classification
• Unique TSP when there are gtgt1 TSPs, which is the
  most informative?
• kTSP there might be many pairs of genes with
  informative ordering, combine this information
  for more accurate classification?
• Normalization invariance a suitable method to
  integrate heterogeneous microarray datasets where
  experimental conditions and normalization schemes
  differ.