Order Restricted Clustering for Dose- Response Microarray Data - - PowerPoint PPT Presentation

Order Restricted Clustering for Dose- Response Microarray Data

Adetayo Kasim

Interuniversity Institute for Biostatistics and Statistical Bioinformatics Universiteit Hasselt & Katholieke Universiteit Leuven

Dan Lin , Ziv Shkedy , An De Bondt, Willem Talloen, Hinrinch Gohlman and Luc Bijnens

Joint work with:

Outline of Presentation Introduction biclustering Clustering of Dose-response data Application to Data Conclusion

δ -

Introduction

Dose-response microarray experiments

Monitoring of gene expression with respect to increasing dose of compound To establish a dose-response relationship. To determine the shape of the relationship To identify the minimum effective dose.

Dose-Response Data

A cell line was treated with 3 compounds 4 doses per compound 3 rats per dose 16,998 genes

Introduction

1,1 1,2 1, 2,1 2,2 2, ,1 ,2 , p p n n n p

y y y y y y y y y ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ L L M M O M L

Structure

Testing for trend in dose-response microarray experiments – Lin et al., (2007a) Classification of trends in dose-response microarray experiments using information theory selection

• methods. - Lin et al., (2007b)

Related Works

Introduction

Introduction

Clustering Hierarchical clustering K-means Self organizing maps (SOM)

Introduction

Biclustering

clustering of genes under subset of conditions Madeira and Oliveira, 2004 reviewed biclustering methods biclustering (Cheng and Church, 2000)

δ −

Biclustering

δ -

ij i j ij

x r μ α β = + + +

δ <=

IJ

H

>= δ

Criterion

δ -

Model Similarity Score

∑

=

j i ij IJ

r H

, 2

| J || I |

Clustering of Dose-response Data

For Each gene; Model Clustering of Dose-Response Data Example

jk j jk

d y ε μ + = ) (

p

μ μ μ L ≤ ≤

2 1

p

μ μ μ L ≥ ≥

2 1

• r

Ordered Constraints

Clustering of Dose-Response Data

ijk j i ijk

r y + + + =

*

β α μ

ij j i j i

r d + + + =

*

) ( β α μ μ

Clustering using observed data and isotonic means Clustering using only isotonic Means

clustering

δ-

clustering of genes under all conditions relative choice for delta specification

• f

minimum members of a cluster (phi)

Clustering of Dose-Response Data Choice of δ

1 ≤ ≤ λ

H * λ δ =

Clustering of Dose-Response Data Input:

, a matrix of real number; , minimum number of genes in a cluster; and

Output:

, a subset of Y with rows set and Column set ; with score not larger than

• r

Initialization: , where

is the mean squared residue score of the observed data.

Algorithm 1: clustering δ -

H * λ δ =

H

Clustering of Dose-Response Data Iteration :

• 1. Apply node deletion algorithm of Cheng and Church (2000) only in

gene direction with fixed conditons/dose levels.

• 2. if mean squared residue score of the reduced matrix satisfies

criterion or number of genes in the reduced matrix is at most , then output the reduced matrix as a cluster.

• 3. Delete members of cluster found in step 2.
• 4. Repeat Steps 1 to 3 on the non-clustered gene until every gene

belongs to a cluster.

Algorithm 1: clustering δ -

Clustering of Dose-Response Data Input:

, a matrix of real number; a matrix of isotonic means, minimum number of genes in a cluster; and

Output:

, a subset of with rows set and Column set ; with score no larger than

• r

Algorithm 2: Order restricted clustering based on

• bserved data and isotonic means

Clustering of Dose-Response Data Algorithm 2: Order restricted clustering based on

• bserved data and isotonic means

Iteration :

• 1. Using global likelihood ratio statistics, assign each gene to a

direction

• 2. Apply Algorithm 1 using model;

Initialization: , where

is the mean squared residue score of the observed data.

H

H * λ δ =

ijk j i ijk

r y + + + =

*

β α μ

Application to Data

Initial Filtering

Global likelihood ratio test – Lin et al, (2007) Clustering only significant genes

Application to Data

Observed Data and Isotonic Means

Application to Data

Isotonic Means

Application to Data

Choice of Lambda and phi up Down

Conclusion

fast exploratory tool for dose-response microarray data resulting clusters have intrinsic ordering quality and number of clusters depends on choice

• f lambda and phi

the method can be used with or without initial filtering

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