Discrimination and clustering with microarray gene expression data

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Discrimination and clustering with microarray
gene expression data

• Terry Speed, Jane Fridlyand, Yee Hwa
  Yang and Sandrine Dudoit

Department of Statistics, UC Berkeley,
Department of Biochemistry, Stanford University

ENAR, Charlotte NC, March 27 2001
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Outline

• Introductory comments
• Classification
• Clustering
• A synthesis
• Concluding remarks

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Tumor classification

• A reliable and precise classification of
  tumors is essential for successful treatment
  of cancer.
• Current methods for classifying human
  malignancies rely on a variety of morphological,
  clinical and molecular variables.
• In spite of recent progress, there are still
  uncertainties in diagnosis. Also, it is likely
  that the existing classes are heterogeneous.
• DNA microarrays may be used to characterize
  the molecular variations among tumors by
  monitoring gene expression on a genomic scale.

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Tumor classification, ctd

• There are three main types of statistical
  problems associated with tumor classification
• 1. The identification of new/unknown tumor
  classes using gene expression profiles
• 2. The classification of malignancies into known
  classes
• 3. The identification of marker genes that
  characterize the different tumor classes.
• These issues are relevant to other questions
  we meet , e.g. characterising/classifying neurons
  or the toxicity of chemicals administered to
  cells or model animals.

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Gene Expression Data

• Gene expression data on p genes for n samples

mRNA samples
sample1 sample2 sample3 sample4 sample5 1
0.46 0.30 0.80 1.51 0.90 ... 2 -0.10 0.49
0.24 0.06 0.46 ... 3 0.15 0.74 0.04 0.10
0.20 ... 4 -0.45 -1.03 -0.79 -0.56 -0.32 ... 5 -0.
06 1.06 1.35 1.09 -1.09 ...
Genes
Gene expression level of gene i in mRNA sample j
Log( Red intensity / Green intensity)

Log(Avg. PM - Avg. MM)
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Comparison of discrimination methods

• In this field many people are inventing new
  methods of classification or using quite complex
  ones (e.g. SVMs). Is this necessary?
• We did a study comparing several methods on
  three publicly available tumor data sets the
  Leukemia data set, the Lymphoma data set, and the
  NIH 60 tumor cell line data, as well as some
  unpublished data sets.
• We compared NN, FLDA, DLDA, DQDA and CART, the
  last with or without aggregation (bagging or
  boosting).
• The results were unequivocal simplest is best!

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Images of correlation matrix between 81 samples
4,682 genes
50 genes
Lymphoma data set 29 B-CLL, 9 FL, 43 DLBCL,
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Cluster Analysis

• Can cluster genes, cell samples, or both.
• Strengthens signal when averages are taken within
  clusters of genes (Eisen).
• Useful (essential ?) when seeking new subclasses
  of cells, tumors, etc.
• Leads to readily interpreted figures.

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Clusters
Taken from Nature February, 2000 Paper by A
Alizadeh et al Distinct types of diffuse large
B-cell lymphoma identified by Gene expression
profiling,
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Discovering sub-groups
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Clustering problems

• Suppose we have gene expression
• data on p genes for n tumor mRNA
• samples in the form of gene expression
• profiles xi (xi1, , xip), i1,,p.
• Three related tasks are
• 1. Estimating the number of tumor clusters
  
• 2. Assigning each tumor sample to a
  cluster
• 3. Assessing the strength/confidence of
  cluster assignments for individual tumors.
• These are generic clustering problems.

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Assessing the strength/confidence ofcluster
assignments

• The silhouette width of an observation is
• s (b-a )/max(a,b)
• where a is the average dissimilarity between
  the observation and all others in the cluster to
  which it belongs, and b is the smallest of the
  average dissimilarities between the observation
  and ones in other clusters. Large s means well
  clustered.

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Bagging

• In discriminant analysis, it is well known that
  gains in accuracy can be obtained by aggregating
  predictors built from perturbed versions of the
  learning set (cf. bagging and boosting).
• In the bootstrap aggregating or bagging
  procedure, perturbed learning sets of the same
  size as the original learning set are formed by
  drawing at random with replacement from the
  learning set, i.e., by forming non-parametric
  bootstrap replicates of the learning set.
• Predictors are build for each perturbed dataset
  and aggregated by plurality voting.

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Bagging a clustering algorithm

• For a fixed number k of clusters
• Generate multiple bootstrap learning sets (B50)
• Apply the clustering algorithm to each bootstrap
  learning set
• Re-label the clusters for the bootstrap learning
  sets so that there is maximum overlap with the
  original clustering of these observations
• The cluster assignment of each observation is
  then obtained by plurality voting.
• Record for each observation its cluster vote
  (CV), which is the proportion of votes in favour
  of the winning cluster.

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Lymphoma data set
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Leukemia data set
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Comparison of clustering and other approaches to
microarray data analysis

• Cluster analyses
• 1) Usually outside the normal framework of
  statistical inference
• 2) less appropriate when only a few genes are
  likely to change.
• 3) Needs lots of experiments
• Single gene approaches
• 1) may be too noisy in general to show much
• 2) may not reveal coordinated effects of
  positively correlated genes.
• 3) harder to relate to pathways.

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Clustering as a means to an end

• We and others (Stanford) are working on methods
  which try to combine combine clustering with more
  traditional approaches to microarray data
  analysis.
• Idea find clusters of genes and average their
  responses to reduce noise and enhance
  interpretability.
• Use testing to assign significance with averages
  of clusters of genes as we would with single
  genes.

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Clustering genes
E.g. p5

• Let p number of genes.
• 1. Calculate within class correlation.
• 2. Perform hierarchical clustering which will
  produce (2p-1) clusters of genes.
• 3. Average within clusters of genes.
• 4 Perform testing on averages of clusters of
  genes as if they were single genes.

Cluster 6(1,2)
Cluster 7(1,2,3)
Cluster 8(4,5)
Cluster 9 (1,2,3,4,5)
1
2
3
4
5
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Data - Ro1

• Transgenic mice with a modified Gi coupled
  receptor (Ro1).
• Experiment induced expression of Ro1 in mice.
• 8 control (ctl) mice
• 9 treatment mice eight weeks after Ro1 being
  induced.
• Long-term question Which groups of genes work
  together.
• Based on paper Conditional expression of a
  Gi-coupled receptor causes ventricular conduction
  delay and a lethal cardiomyopathy, see Redfern C.
  et al. PNAS, April 25, 2000.
• http//www.pnas.org also
• http//www.GenMAPP.org/ (Conklin lab, UCSF)

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Histogram
Cluster of genes (1703, 3754)
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Top 15 averages of gene clusters
T Group ID

• -13.4 7869 (1703, 3754)
• -12.1 3754
• 11.8 6175
• 11.7 4689
• 11.3 6089
• 11.2 1683
• -10.7 2272
• 10.7 9955 (6194, 1703, 3754)
• 10.7 5179
• 10.6 3916
• -10.4 8255 (4572, 4772, 5809)
• -10.4 4772
• -10.4 10548 (2534, 1343, 1954)
• 10.3 9476 (6089, 5455, 3236, 4014)

Might be influenced by 3754
Correlation
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Closing remarks

• More sophisticated classification methods may
  become justified when data sets are larger.
• There seems to be considerable room for
  approaches which bring cluster analysis into a
  more traditional statistical framework.
• The idea of using clustering to obtain
  derived variables seems promising, but has yet to
  realise this promise.

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Acknowledgments

• UCB
• Yee Hwa Yang
• Jane Fridlyand
• WEHI
• Natalie Thorne
• PMCI
• David Bowtell
• Chuang Fong Kong

• Stanford
• Sandrine Dudoit
• UCSF
• Bruce Conklin
• Karen Vranizan