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230 Kohlmann et al.
predictions for each sample (so that each sample is classified once in the n
iterations).
3.4.2.2. 10-FOLD CV
Ten-fold CV is another method used to estimating the apparent accuracy,
i.e., the overall rate of correct predictions of the complete data set. This classification
task means that the data set is divided into 10 equally sized subsets,
balanced for the respective subclasses of the data. Then, differentially expressed
genes are identified in the training set (9 subsets), and a model is trained
based on the top genes that demonstrate differential expression between each
of the respective subclasses in the training set. This model is used to generate
predictions for the remaining subset. This training and prediction process has
to be repeated 10 times to include predictions for each subset (so that each
sample is classified once in the 10 iterations).
3.4.2.3. RESAMPLING ANALYSIS
A resampling approach can be used to assess the robustness of class predictions.
Here again, the data set is randomly (but balanced for the respective
subtypes) split into a training set, consisting of two-thirds of samples, and an
independent test set with the remaining third. Differentially expressed genes
are identified in the training set, a support vector machine (SVM) model is
built from the training set, and predictions are made in the test set. This complete
process is repeated 100 times. By this means, 95% confidence intervals
for accuracy, sensitivity, and specificity can also be estimated. Sensitivity and
specificity are calculated as follows:
Sensitivity = (number of positive samples predicted)/(number of true-positives)
Specificity = (number of negative samples predicted)/(number of true-negatives)
3.4.3. Hierarchical Clustering
Two-dimensional hierarchical cluster analysis is a popular method of organizing
expression data, i.e., arranging genes and patients according to similarity
in their patterns of gene expression (Fig. 3). This method helps to organize
but not to alter tables containing the primary expression data. The output format
is a graphic display that allows the clustering and the underlying expression
data to be conveyed in an intuitive form to biologists (14). By adopting a
mathematical description of similarity, the object of this algorithm is to compute
a dendrogram that assembles all elements into a single tree. For any set of
n genes, an upper-diagonal similarity matrix is computed by the Euclidean distance
metric, which contains similarity scores for all pairs of genes. The matrix