Tree Based Methods for Analyzing Tissue Microarray Data

1
Tree Based Methodsfor Analyzing Tissue
Microarray Data

• Steve Horvath
• Human Genetics and Biostatistics
• University of California, Los Angeles

2
Acknowledgements

• Horvath Lab
• Yunda Huang
• Xueli Liu Ph.D.
• Zeke Fang Ph.D.
• Tuyen Hoang
• UCLA Tissue Microarray Core
• David Seligson
• Aarno Palotie
• Clinicians
• Hyung Kim
• Arie Belldegrun

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Contents

• Statistical issues with tissue microarray (TMA)
  data
• Random forest (RF) predictors
• RF clustering
• Application of RF clustering to TMA data
• Supervised Learning Methods

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Background TMA data
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Description of TMA data

• TMA data are a high-throughput tool in validating
  newly-identified biomarker in genome wide
  discovery
• Basic technique was summarized in Kononen et al.
  1998

6

Tissue Microarray (TMA) Technology Kononen et al.
Nature Medicine 1998

• Hundreds of tiny (typically 0.6 mm diameter)
  cylindrical tissue cores
• densely and precisely arrayed into a single
  histologic paraffin block.
• From this new array block, up to 300 serial
  4-8 ?m thick sections may be produced.
• Targets for fluorescence in situ hybridization
  (FISH) and protein expression by
  immunohistochemical studies.

donor block array block slide
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Non-normal and highly correlated
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Several Spots per Pathology Case Several
Scores per Spot

• Each case is usually represented by 4 or more
  spots
• gt3 malignant lesions, 1 matched normal

• Maximum intensity Max (1 4)
• Percent of cells staining Pos (0 100)
• Percent of cells staining with the
• maximum intensity PosMax (0 100)
• Spots have a spot grade NL,1,2,..
• Indicator of informativeness

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Histogram of tumor marker expression scores POS
and MAX
Percent of Cells Staining(POS)
EpCam
P53
CA9
Maximum Intensity (MAX)
10
P53 and Ki67 Max versus Pos
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Characteristics of TMA data

• Non-normal, discrete, strongly correlated
• Mixed variable types
• Pooling (combining) spot measurements across
  every patient
• between 1 to 10 spots of different grade
• current strategy pools tumor spots and forms
  median, mean, minimum or max
• Message tumor marker intensity is measured by up
  to 12 highly correlated staining scores?
  multicollinearity

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Our main tool are random forest predictors

• Unsupervised analysis of TMA data
• RF clustering
• Supervised Analysis
• RF based pre-validation method

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Background random forest predictorsL. Breiman
1999
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Random Forests (RFs)

• RFs are a collection of tree predictors such that
  each tree depends on the values of an
  independently sampled random vector

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Classification and Regression Trees (CART)

• by
• Leo Breiman,
• UC Berkeley
• Jerry Friedman, Stanford University
• Charles J. Stone,
• UC Berkeley
• Richard Olshen, Stanford University

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An example of CART

• Goal For the patients admitted into ER, to
  predict who is at higher risk of heart attack
• Training data set
• of subjects 215
• Outcome variable High/Low Risk determined
• 19 noninvasive clinical and lab variables were
  used as the predictors

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CART construction
High 17 Low 83
Is BP lt 91?
No
Yes
High 12 Low 88
High 70 Low 30
Is age lt 62.5?
Classified as high risk!
No
Yes
High 2 Low 98
High 23 Low 77
Classified as low risk!
Is ST present?
Yes
No
High 11 Low 89
High 50 Low 50
Classified as low risk!
Classified as high risk!
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CART Construction

• BINARY RECURSIVE PARTITIONING
• Binary split parent node into two child nodes
• Recursive each child node can be treated as
  parent node
• Partitioning data set is partitioned into
  mutually exclusive subsets in each split

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RF Construction

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Prediction by plurality voting

• The forest consists of N trees.
• Class prediction
• Each tree votes for a class the predicted class
  C for an observation is the plurality, maxC ?k
  fk(x,T) C
• Regression random forest
• predicted value is the average prediction

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Clustering with random forest predictors
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Intrinsic Proximity Measure

• Terminal tree nodes contain few observations
• If case i and case j both land in the same
  terminal node, increase the proximity between i
  and j by 1.
• At the end of the run divide by 2 no. of trees.
• Dissimilaritysqrt(1-Proximity)

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Casting an unsupervised problem into a supervised
RF problem

• Key Idea (Breiman 1999)
• Label observed data as class 1
• Generate synthetic observations and label them as
  class 2
• Construct a RF predictor to distinguish class 1
  from class 2
• Use the resulting dissimilarity measure in
  unsupervised analysis

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How to generate synthetic observations

• Synthetic observations are simulated to contain
  no clusters
• e.g. randomly sampling from the product of
  empirical marginal distributions of the input.

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RF clustering

• Compute distance matrix from RF
• distance matrix sqrt(1-proximity matrix)
• Compute the first 23 classical multi-dimensional
  scaling coordinates based on the distance matrix
• Conduct partitioning around medoid (PAM)
  clustering analysis
• input parameterno. of clusters k
• use the Euclidean distance between the resulting
  scaling points

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Theoretical Study of RF Clustering
Ref Using random forest proximity for
unsupervised learning, BIOKDD-CBGI'03, 7th Joint
Conference on Information Sciences, Cary, North
Carolina.
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Applying Random Forest Clustering to Tissue
Microarray Data--Application to Kidney Cancer

• Tao Shi and Steve Horvath

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Scientific QuestionCan one discover cancer
subtypes based on the protein expression patterns
of tumor markers?
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Why use RF clustering for TMA data?

• no need to transform the often highly skewed
  features
• based on ranks of features
• natural way of weighing tumor marker
  contributions to the dissimilarity
• elegant way to deal with missing covariates
• intrinsic proximity matrix handles mixed variable
  types well

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Kidney Multi-marker Data

• 366 patients with Renal Cell Carcinoma (RCC)
  admitted to UCLA between 1989 and 2000.
• Immuno-histological measures of total 8 tumor
  markers were obtained from tissue microarrays
  constructed from the tumor samples of these
  patients.

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MDS plot of clear cell patients

• Labeled and colored
• by their RF cluster

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Interpreting the clusters in terms of survival
Clustering label Non clear Cell patients Clear cell patients
1 0 92
2 20 215
3 30 9
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Hierarchical clustering with Euclidean distance
leads to less satisfactory results

Cluster- ing label Non clear Cell patients Clear cell patients
1 9 (20) 286 (307)
2 41 (30) 30 (9)
RF clustering grouping in red
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Euclidean vs. RF Distance
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Molecular grouping vs. Pathological grouping

Molecular Grouping
Pathological Grouping
1.0
1.0
0.8
0.8
p 9.03e-05
0.6
0.6
p 0.0229
Survival
Survival
0.4
0.4
327 patients in cluster 1 and 2
0.2
0.2
316 non-clear cell patients
39 patients in cluster 3
50 clear cell patients
0.0
0.0
0
2
4
6
8
10
12
0
2
4
6
8
10
12
Time to death (years)
Time to death (years)
Message molecular grouping is superior to
pathological grouping
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Identify irregular patients
Clustering label Non clear Cell patients Clear cell patients
1 0 92
2 20 215
3 30 9
1.0
0.8
0.6
Survival
0.4
p 0.00522
0.2
50 non-clear cell patients
Message molecular grouping can be used to
refine clear cell definition.
9 irregular clear cell patients
307 regular clear cell patients
0.0
0
2
4
6
8
10
12
Time to death (years)
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Detect novel cancer subtypes

• Group clear cell grade 2 patients into two
  clusters with significantly different survival.

K-M curves
1.0
0.8
0.6
Survival
p value 0.0125
0.4
0.2
0.0
0
2
4
6
8
10
12
Time to death (years)
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Results TMA clustering

• Clusters reproduce well known clinical subgroups
• Ex global expression differences between clear
  cell and non-clear cell patients
• RF clustering works better than clustering based
  on the Euclidean distance for TMA data
• RF clustering allows one to identify outlying
  tumor samples.
• Can detect previously unknown sub-groups

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Boxplots of tumor marker expression vs. cluster
Message clusters can be explained in terms of
tumor expression values, i..e in terms of
biological pathways.
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Conclusions

• There is a need to develop tailor made data
  mining methods for TMA data
• Major differences
• highly non-normal data
• Euclidean distance metrics seems to be
  sub-optimal for TMA data
• tree or forest based methods work well for kidney
  and prostate TMA data