Tree Based Methodsfor Analyzing

Tissue Microarray Data

Steve HorvathHuman Genetics and Biostatistics

University of California, Los Angeles

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

Contents

• Statistical issues with tissue microarray (TMA) data

• Random forest (RF) predictors

• RF clustering

• Application of RF clustering to TMA data

• Supervised Learning Methods

Background TMA data

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

donor block array block slide

Tissue Microarray (TMA) TechnologyKononen 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.

Pathologists score each spot by looking through a microscope. slide by David Seligson

Non-normal and highly correlated

Several Spots per Pathology Case Several “Scores” per Spot

• 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

• Each case is usually represented by 4 or more spots

– >3 malignant lesions, 1 matched normal

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P53 CA9 EpCamPercent of Cells Staining(POS)

Maximum Intensity (MAX)

Histogram of tumor marker expression scores: POS and MAX

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

Our main tool are random forest predictors

• Unsupervised analysis of TMA data– RF clustering

• Supervised Analysis– RF based pre-validation method

Background random forest predictors

L. Breiman 1999

Random Forests (RFs)

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

Classification and Regression Trees (CART)

by– Leo Breiman,

UC Berkeley– Jerry Friedman,

Stanford University– Charles J. Stone,

UC Berkeley– Richard Olshen,

Stanford University

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

High 12%Low 88%

High 17%Low 83%

Is BP <= 91?

High 70%Low 30%

High 11%Low 89%

High 50%Low 50%

High 2%Low 98%

High 23%Low 77%

Is age <= 62.5?Classified as high risk!

Classified as low risk!

Classified as high risk! Classified as low risk!

Is ST present?

CART construction

Yes No

No

No

Yes

Yes

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

RF Construction

…

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

Clustering with random forest predictors

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.

• Dissimilarity=sqrt(1-Proximity)

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

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.

RF clustering

• Compute distance matrix from RF– distance matrix = sqrt(1-proximity matrix)

• Compute the first 2~3 classical multi-dimensional scaling coordinates based on the distance matrix

• Conduct partitioning around medoid (PAM) clustering analysis

– input parameter=no. of clusters k – use the Euclidean distance between the resulting

scaling points

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.

Applying Random Forest Clustering to Tissue Microarray Data--Application to Kidney Cancer

Tao Shi and Steve Horvath

Scientific Question:Can one discover cancer subtypes

based on the protein expression patterns of tumor markers?

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

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.

MDS plot of clear cell patients

• Labeled and colored by their RF cluster

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Interpreting the clusters in terms of survival

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K-M curves

Time to death(Months)

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1 Log Rank p value= 0.00037423

Clustering label

Non clearCell

patients

Clear cellpatients

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Hierarchical clustering with Euclidean distance leads to less satisfactory results

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Cluster Dendrogram

hclust (*, "average")dist(KidneyRF)

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Cluster-ing label

NonclearCell

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Clearcell

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1 9 (20)

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30 (9)

* RF clustering grouping in red

Euclidean vs. RF Distance

RF

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Euclidean distance

Molecular grouping vs. Pathological grouping

Message: molecular grouping is superior to pathological grouping

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Time to death (years)

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p = 0.0229p = 9.03e-05

Molecular Grouping Pathological Grouping

Identify “irregular” patients

Clustering label

Non clearCell

patients

Clear cellpatients

1 0 92

2 20 215

3 30 9

Message: molecular grouping can be used to refine clear celldefinition.

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Time to death (years)

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9 irregular clear cell patients307 regular clear cell patients

50 non-clear cell patients

Detect novel cancer subtypes

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

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K-M curves

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

Boxplots of tumor marker expression vs. cluster

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Message: clusters can be explained in terms of tumor expression values, i..e in terms of biological pathways.

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