Colon cancer subtypes from gene expression data

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1 Colon cancer subtypes from gene expression data Nathan Cunningham Giuseppe Di Benedetto Sherman Ip Leon Law Module 6: Applied Statistics 26th February 2016

2 Aim Replicate findings of Felipe De Sousa et al. (2013) Cluster analysis to identify subtypes of colon cancer Construct a classifier to identify clusters Identify a suitable subset of the data to perform these analyses Consider robustness of findings to changes in methods and perturbations in the data

3 Data GSE33113 data set (Academic Medical Centre, Amsterdam) Patients with stage II colon cancer 90 patients, 54, 675 gene expressions recorded

4 Data processing Normalisation to remove batch effects Gene expression presence detected using barcode algorithm and those not present in at least one sample removed Genes with a median absolute deviation > 0.5 retained and median centred Felipe De Sousa et al. (2013) find 7, 846 genes remain we find anywhere from none to all of the genes remain Use 146 genes identified by Felipe De Sousa et al. (2013) in analyses

5 Cluster Analysis Hierarchical agglomerative, average linkage K-Means Consensus Model-based (Fraley & Raftery, 2002)

6 How many clusters?

7 Clustering methods comparison Homogeneity: reflects compactness of the clusters Separation: reflects the distance between clusters Silouette: s(i) = b(i) a(i) max{a(i),(b(i)}

8 Clustering methods comparison Homogeneity: reflects compactness of the clusters Separation: reflects the distance between clusters Silouette: s(i) = b(i) a(i) max{a(i),(b(i)} WADP (weighted avarage discrepancy pairs)

9 Robustness under perturbation 0.20 value variable cons_kmeans mclust cons_hierclust sd

10 Cluster methods comparison Cluster comparison WADP value C-k-means VS C-hierarchical MClust VS C-hierarchical C-k-means VS Mclust 0.081

11 Classification: PAM R package for implementing nearest shrunken centroid classification.

12 Classification: PAM R package for implementing nearest shrunken centroid classification. Gives higher weights to genes in a class that are far away from the overall centroid of the genes.

13 Classification: PAM R package for implementing nearest shrunken centroid classification. Gives higher weights to genes in a class that are far away from the overall centroid of the genes. A threshold parameter specifies a shrinkage for the weights giving higher weights to genes which are stable within the class.

14 Classification: PAM R package for implementing nearest shrunken centroid classification. Gives higher weights to genes in a class that are far away from the overall centroid of the genes. A threshold parameter specifies a shrinkage for the weights giving higher weights to genes which are stable within the class. Can eliminate the weaker effect of genes, allowing automatic feature selection.

15 Classification: PAM R package for implementing nearest shrunken centroid classification. Gives higher weights to genes in a class that are far away from the overall centroid of the genes. A threshold parameter specifies a shrinkage for the weights giving higher weights to genes which are stable within the class. Can eliminate the weaker effect of genes, allowing automatic feature selection. Classification by considering the smallest distance to the shrunken centroid.

16 Classification: Multi-Class SVM The R package e1071 was used to perform the multi-class SVM with a RBF kernel.

17 Classification: Multi-Class SVM The R package e1071 was used to perform the multi-class SVM with a RBF kernel. Uses a one vs one approach (i.e. 3 binary classifiers) with class prediction done by a voting scheme.

18 Classification: Multi-Class SVM The R package e1071 was used to perform the multi-class SVM with a RBF kernel. Uses a one vs one approach (i.e. 3 binary classifiers) with class prediction done by a voting scheme. If a linear kernel was used instead, could perform feature selection based on ranking of the features using their weights,

19 Classification: Random Forest The R package randomforest was used to train a random forest.

20 Classification: Random Forest The R package randomforest was used to train a random forest. A total of 300 trees were built, with 12 variables randomly chosen as candidates at each split.

21 Classification: Random Forest The R package randomforest was used to train a random forest. A total of 300 trees were built, with 12 variables randomly chosen as candidates at each split. Feature selection can be done using mean decrease accuracy, which uses permutation of the features and out of bag error.

22 Results: PAM Number of genes Misclassification Error x x x x x x x x x x x x x x x x x x x Value of threshold Misclassification Error Label 1 Label 2 Label Value of threshold Figure: 10-fold cross validation error. Optimal threshold was estimated to be 6.2 ± 0.2.

23 Results: SVM and Random Forest and PAM Method 10-Fold Cross Validation Error SVM (C = 1, γ = ) 1.1% PAM (threshold = 6.2) 2.2% Random Forest 3.3% Table: 10-fold cross validation average error on the trained classifiers

24 Results: SVM and Random Forest and PAM Method 10-Fold Cross Validation Error SVM (C = 1, γ = ) 1.1% PAM (threshold = 6.2) 2.2% Random Forest 3.3% Table: 10-fold cross validation average error on the trained classifiers Error bars can be estimated using bootstrapping.

25 Results: PAM Bootstrapping Validation Error (%) Threshold (unknown units) Figure: Median (point) and 95% percentile (error bar) of the 10-fold cross validation error, bootstrapping 500 times.

26 Results: PAM Bootstrapping Number of genes which survived thresholding (genes) Threshold (unknown units) Figure: Mean (point) and standard deviation (error bar) of the number of genes which survived thresholding, bootstrapping 500 times.

27 Results: PAM Bootstrapping Method PAM (threshold = 0.0) PAM (threshold = 6.2) SVM Random Forest 10-Fold Cross ( Validation Error ( 1.1) % ( 2.2) % ( 0.0) % ) % Table: Median and 95% percentile of the 10-fold cross validation error, bootstrapping 500 times. For PAM with threshold 6.2, (36.5 ± 6.3) genes survived thresholding.

28 Conclusion Clustering methods were robust PAM performed similar to other methods More thresholds to be investigated Scale to larger datasets

29 References Felipe De Sousa, E. M., Wang, X., Jansen, M., Fessler, E., Trinh, A., de Rooij, L. P.,... others (2013). Poor-prognosis colon cancer is defined by a molecularly distinct subtype and develops from serrated precursor lesions. Nature medicine, 19(5), Fraley, C., & Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American statistical Association, 97(458),

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