16.4: Tumor Classification with SVMs

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A generic approach for classifying two types of acute leukemias acute myeloid leukemia (AML) and acute lymphoid leukemia (ALL) was presented by Golub et al. [4]. This approach centered on effectively addressing three main issues:

Whether there were genes whose expression pattern to be predicted was strongly correlated with the class distinction (i.e. can ALL and AML be distinguished)
How to use a collection of known samples to create a “class predictor” capable of assigning a new sample to one of two classes
How to test the validity of their class predictors

They addressed (1) by using a “neighbourhood analysis” technique to establish whether the observed correlations were stronger than would be expected by chance. This analysis showed that roughly 1100 genes were more highly correlated with the AML-ALL class distinction than would be expected by chance. To address (2) they developed a procedure that uses a fixed subset of “informative genes” (chosen based on their correlation with the class distinction of AML and ALL) and makes a prediction based on the expression level of these genes in a new sample. Each informative gene casts a “weighted vote” for one of the classes, with the weight of each vote dependent on the expression level in the new sample and the degree of that genes correlation with the class distinction. The votes are summed to determine the winning class. To address (3) and effectively test their predictor by first testing by cross-validation on the initial data set and then assessing its accuracy on an independent set of samples. Based on their tests, they were able to identify 36 of the 38 samples (which were part of their training set!) and all 36 predictions were clinically correct. On the independent test set 29 of 34 samples were strongly predicted with 100% accuracy and 5 were not predicted.

A SVM approach to this same classification problem was implemented by Mukherjee et al.[5]. The output of classical SVM is a binary class designation. In this particular application it is particularly important to be able to reject points for which the classifier is not confident enough. Therefore, the authors introduced a confidence interval on the output of the SVM that allows for rejection of points with low confidence values. As in the case of Golub et al.[4] it was important for the authors to infer which genes are important for the classification. The SVM was trained on the 38 samples in the training set and tested on the 34 samples in the independent test set (exactly in the case of Golub et al.). The authors results are summarized in the following table (where |d| corresponds to the cutoff for rejection).

These results a significant improvement over previously reported techniques, suggesting that SVMs play an important role in classification of large data sets (as those generated by DNA microarray experiments).