Micro Array Literature

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High Throughput Target Identification

Stan Young, NISS

Doug Hawkins, U Minnesota

Christophe Lambert, Golden Helix

Machine Learning, Statistics, and Discovery

25 June 03

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PublicationYear

All Journals PNAS

1992 0 01993 0 01994 0 01995 4 01996 3 11997 8 21998 37 11999 134 82000 409 342001 773 46

Micro Array Literature

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Guilt by Association :

You are known

by the company you keep.

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Data Matrix

Goal: Associations over the genes.

Guilty Gene

Genes

Tissues

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Goals

1. Associations.

2. Deep associations – beyond 1st level correlations.

3. Uncover multiple mechanisms.

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Problems

1. n < < p

2. Strong correlations.

3. Missing values.

4. Non-normal distributions.

5. Outliers.

6. Multiple testing.

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Technical Approach

1. Recursive partitioning.

2. Resampling-based, adjusted p-values.

3. Multiple trees.

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Recursive Partitioning

Tasks

1. Create classes.

2. How to split.

3. How to stop.

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Differences:

Recursive Partitioning• Top-down analysis• Can use any type of descriptor.• Uses biological activities to

determine which features matter.

• Produces a classification tree for interpretation and prediction.

• Big N is not a problem!• Missing values are ok.• Multiple trees, big p is ok.

Clustering• Often bottom-up

• Uses “gestalt” matching.

• Requires an external method for determining the right feature set.

• Difficult to interpret or use for prediction.

• Big N is a severe problem!!

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Forming Classes, Categories, Groups

Profession Av. Income

Baseball Players 1.5MFootball Players 1.2M

Doctors .8MDentists .5M

Lawyers .23MProfessors .09M

. . . . .

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Forming Classes from “Continuous” Descriptor

0 31 2 4 5 6-1-2-3

How many “cuts” and where to make them?

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Splitting : t-test

n = 1650ave = 0.34sd = 0.81

n = 1614ave = 0.29sd = 0.73

n = 36ave = 2.60sd = 0.9

Signal 2.60 - 0.29t = = = 18.68Noise 0.734 1 1

36 1614+

TT: NN-CCNN-CC

rP = 2.03E-70

aP = 1.30E-66

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Splitting : F-test

n = 1650ave = 0.34sd = 0.81

n = 1553ave = 0.21sd = 0.73

n = 36ave = 2.60sd = 0.9

n = 61ave = 1.29sd = 0.83

n = 61ave = 1.29sd = 0.83

Signal Among Var (Xi. - X..)2/df1F = = =

Noise Within Var (Xij - Xi.)2/df2

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How to Stop

Examine each current terminal node.

Stop if no variable/class has a

significant split, multiplicity adjusted.

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Levels of Multiple Testing

1. Raw p-value.

2. Adjust for class formation, segmentation.

3. Adjust for multiple predictors.

4. Adjust for multiple splits in the tree.

5. Adjust for multiple trees.

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Understanding observations

NB: Splitting variables govern the process,NB: Splitting variables govern the process, linked to response variable.linked to response variable.

MultipleMechanisms

Conditionally important descriptors.

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Multiple Mechanisms

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Reality: Example Data

60 Tissues

1453 Genes

Gene 510 is the “guilty” gene, the Y.

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1st Split of Gene 510 (Guilty Gene)

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Split Selection

14 spliters

with adjusted

p-value

< 0.05

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Histogram

Non-normal, hence

resampling p-values

make sense.

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Resampling-based Adjusted p-value

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Single Tree RP Drawbacks

• Data greedy.

• Only one view of the data. May miss other mechanisms.

• Highly correlated variables may be obscured.

• Higher order interactions may be masked.

• No formal mechanisms for follow-up experimental design.

• Disposition of outliers is difficult.

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Etc.

Multiple Trees, how and why?Multiple Trees, how and why?

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How do you get multiple trees?

1. Bootstrap the sample, one tree per sample.

2. Randomize over valid splitters.

Etc.

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RandomTreeBrowsing,

1000 Trees.

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Example Tree

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1st Split

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Example Tree, 2nd Split

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Conclusion for Gene G510

If G518 < -0.56

and

G790 < -1.46

then

G510 = 1.10 +/- 0.30

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Using Multiple Trees to Understand variables

• Which variables matter?

• How to rank variables in importance.

• Correlations.

• Synergistic variables.

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CorrelationInteractionMatrix

Red=Syn.

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Summary

• Review recursive partitioning.

• Demonstrated multiple tree RP’s capabilities– Find associated genes

– Group correlated predictors (genes)

– Synergistic predictors (genes that predict together)

• Used to understand a complex data set.

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Needed research

• Real data sets with known answers.

• Benchmarking.

• Linking to gene annotations.

• Scale (1,000*10,000).

• Multiple testing in complex data sets.

• Good visualization methods.

• Outlier detection for large data sets.

• Missing values. (see NISS paper 123)

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Teams

NC State University :Jacqueline Hughes-OliverKatja Rimlinger

U Waterloo :Will WelchHugh ChipmanMarcia WangYan Yuan

U. Minnesota :Douglas Hawkins NISS :

Alan Karr(Consider post docs)GSK :

Lei ZhuRay Lam

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References/Contact

1. www.goldenhelix.com.

2. www.recursive-partitioning.com.

3. www.niss.org, papers 122 and 123.

4. [email protected]

5. GSK patent.

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Questions