**4. Discussion**

196 Biomarker

The only exception was for one dataset with 60 Cases and 60 Controls. This increased accuracy was due to an unusual pattern in one of the randomly generated features. The intensities for this feature are shown in Figure 5, where the "+" marks in the left column are the intensities of the 60 samples in Group-1 and the marks in the right column are for the 60 samples in Group-2. While there is no overall difference between these columns, a closer examination shown a clumping of intensities in one group at values that have gaps in the

Fig. 5. Intensities for the 60 cases (left column) and 60 controls (right column) for the peak

In many cases the accuracy of a 3-feature classifier is not significantly better than a 2-feature classifier. This is due to the fact that as the dimensionality of the classification space

that yielded a quality score of 151.7 (sensitivity=78.3%, specificity=73.3%,

undetermined=0.0%) in the dataset of random peak intensities.

other group.

The results presented in the tables above show that very good results can be obtained from DT, MCA, SVM and LDA classifiers for datasets that contain no information. It can be argued that the procedures used here are selected to obtain the maximum possible accuracy, and that is exactly the point. If a 7-node decision tree used 40 Cases and 40 Controls in the training set and 20 Cases and 20 Controls in the testing set and obtained an accuracy of 87.5% for the testing samples, one could propose that the set of seven features denotes a fingerprint that accurately classifies the samples. The results in Table 1 show that this accuracy can be obtained from a dataset with only 300 randomly generated feature values for each sample. A 7-feature MCA classifier is able to achieve an average accuracy of over 90% when the dataset contains 300 Cases, 300 Controls, and only 300 non-informative features. This should draw into question the results of any study that uses this classification method.

SVM and LDA classifiers have testing set accuracies above 97.4 and 99.7%, respectively, for all but the largest datasets. It is only when the number of samples is at least as large as the number of features that these methods break down. Current methods for obtaining information from biological samples generate many more features that the 300 used here.

The BMDK classifier did not achieve an average accuracy above 80% for even the smallest dataset. This result is not unexpected. Since the datasets do not contain any information, there are no biomarkers and a biomarker-based classifier should not perform well. Fortuitous results can be obtained and a closer examination of the putative biomarkers should be performed (Figure 5).

For the DT and MCA methods there is some selection of which samples should be placed in the training and testing sets, but this is basically what is required because of the coverage problem. If a given terminal node in a DT classifier contains 7 Cases and 4 Controls, and 4 of the Cases were moved to the testing set, this terminal node would change from a Case-node to a Control-node and the classification accuracy of the testing data would be decreased. The MCA classifier is based on the premise of a fingerprint that associates a sample in the testing set with a sample in the training set. If that sample were removed from the training set, the association could not be made and the accuracy of the classifier would be decreased.
