Diagnosis of multiple cancer types by shrunken centroids of gene expression

Course: 550.635 Topics in Bioinformatics Presenter: Ting YangTeacher: Professor Geman

By Robert Tibshirani, Trevor Hastie, Balasubramanian Narasimhan, and Gilbert Chu

Nearest Centroid Classification

Example: small round blue cell tumors of childhood

• 63 training samples, 25 testing samples

• 4 classes: BL, EWS, NB, RMS

• Figure 1

• Nearest centroid classification

• Disadvantage

Nearest shrunken Centroids

• A modification of the nearest centroid method

• Idea: First normalize class centroids by the within-class standard deviation for each gene, shrink each class centroid towards the overall centroid.

Details:

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Mean expression value in class k for gene i

ith component of the overall centroid

Pooled within class standard deviation for gene i

:t statistics

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:t statistics0( )

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• It measures the difference between the gene i in class k and gene i in all classes combined.

• Idea: a gene that discriminates one class from the rest will have a statistic of large absolute value.

• Shrink it toward zero to eliminate the genes that do not provide sufficient information.

• ‘De-noising’ step

( )( )ik ik ikd sign d d

Choosing the amount of shrinkage• Shrinkage amount is allowed to vary over a wide range.

• 10-fold cross validation ( choose the one that has the smallest error rate)

• Divide the set of samples (at random)into 10 equal size parts.

(classes were distributed proportionally among each of the 10 parts)

• Fit the model on 90% of the samples and then predict the class label of the remaining 10% (test samples).

• Repeat 10 times, add together the error (overall error).

• Figure 2

• Figure 1

More Figures

• Figure 3

• Figure 4

Classification

• A new sample is classified by comparing its expression profile with each shrunken centroid, over those 43 active genes.

• Distance function: prior information included.

Statistical details:

• t-statistic

• Estimates of the class probabilities (Figure 5)

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