Recursive partitioning for tumor classification with gene

microarray data

Heping Zhang, Chang-Yung Yu, Burton Singer, Momian Xiong

What is Recursive Partitioning?

Basic Idea:

Technical description of recursive partitioning

Example:

Technical description of recursive partitioning

Algorithm:

• Examine all of the available gene expression levels and all possible thresholds for each of the expression levels

• Select the combination of gene expression level and threshold that results in the best separation of cancer and normal tissues on the basis of the node purity function

Quality of the tree classification:

Error rate based on cross-validation

Technical description of recursive partitioning

Node Purity: A little bit of math

One example of entropy function:

P log(P) + (1-P) log(1-P), where

P is the probability of a tissue being normal within the node

Note:

• Maximum purity ( =0 )When all tissues are of the same type within the node ( P = 0 or 1)

• Minimum purity ( = -log2)When all tissues are of the same type within the node ( P = 0.5)

Expression profiles of 2,000 genes using an Affimetrix oligonucleotide array in 22 normal and 40 colon cancer tissues(www.sph.uth.tmc.edu/hgc)

Results: Using 5-fold cross validation, The error rate is between 6-8%, which is much better than that obtained by exsiting analysis.

Example from the article

Fig1. Classification trees for tissue types by using expression data from three genes ( M26383, R15447, M28214)

Correlation among gene expression profiles

Another Tree Based on A Different Set of Three Genes (Fig.6)

Correlation Matrix among Genes in Fig.1 and Fig. 6

1. Hierachical2. K-means3. Self-orgnizing maps4. Coupled two-way clustering

Other clustering classification

1. Efficient with large number of genes2. More than two types of tissues simultaneously3. Automatically selects valuable genes as predictors4. More precise than other classification methods

Advantage of recursive partitioning classification methods

1.It is likely that the information contained in a large number of genes can be captured by a small number of genes without significant loss of information.

2.The precision of classification of recursive partitioning is important for clinical application.

Conclusion: