Multiclass classification of microarray data with repeated measurements: application to cancer

Abstract

Prediction of the diagnostic category of a tissue sample from its gene-expression profile and selection of relevant genes for class prediction have important applications in cancer research. We have developed the uncorrelated shrunken centroid (USC) and error-weighted, uncorrelated shrunken centroid (EWUSC) algorithms that are applicable to microarray data with any number of classes. We show that removing highly correlated genes typically improves classification results using a small set of genes.

Figure 1

Comparison of prediction accuracy of USC and SC on the NCI 60 data. The percentage of prediction accuracy is plotted against the number of relevant genes using the USC algorithm at ρ₀ = 0.6 and the SC algorithm (USC at ρ₀ = 1.0). The horizontal axis is shown on a log scale. Because no independent test set is available for this data, we randomly divided the samples in each class into roughly three parts multiple times, such that a third of the samples are reserved as a test set. Thus the training set consists of 43 samples and the test set of 18 samples. The graph represents typical results over these multiple random runs.

Figure 2

Prediction accuracy on the multiple tumor data using the EWUSC algorithm over the range of Δ from 0 to 20. The percentage of classification errors is plotted against Δ on (a) the full training set (96 samples) and (c) the test set (27 samples). In (b) the average percentage of errors is plotted against Δ on the cross-validation data over five random runs of fourfold cross-validation. In (d), the number of relevant genes is plotted against Δ. Different colors are used to specify different correlation thresholds (ρ₀ = 0.6, 0.7, 0.8, 0.9 or 1). Results of ρ₀ < 0.6 are shown in Figure S1 on [30]. Optimal parameters are inferred from the cross-validation data in (b).

Figure 3

Comparison of feature stability of EWUSC, USC and SC on the multiple tumor data. The average Jaccard index is plotted against the number of relevant genes over five random runs of fourfold cross-validation using EWUSC and USC at ρ₀ = 0.8 and SC. A high average Jaccard index indicates high feature stability. The EWUSC algorithm selects the most stable features. Note that the horizontal axis is shown on a log scale.

Figure 4

Comparison of prediction accuracy of EWUSC, USC, SVM and SC algorithms on the multiple tumor data. The horizontal axis shows the total number of distinct genes selected over all binary SVM classifiers on a log scale. Some results are not available on the full range of the total number of genes. For example, the maximum numbers of selected genes for EWUSC and USC are roughly 1,000. The reported prediction accuracy is 78% [10] using all 16,000 available genes on the full data. The EWUSC algorithm achieves 89% prediction accuracy with only 89 genes. With 680 genes, EWUSC produces 93% prediction accuracy.

Figure 5

Comparison of prediction accuracy of EWUSC, USC and SC on the breast cancer data. The percentage of prediction accuracy is plotted against the number of relevant genes using the EWUSC algorithm at ρ₀ = 0.7, the USC algorithm at ρ₀ = 0.6 and the SC algorithm (USC at ρ₀ = 1.0). Note that the horizontal axis is shown on a log scale.

Figure 6

Comparison of feature stability of EWUSC, USC and SC on the breast cancer data. The average Jaccard index is plotted against the number of relevant genes over five random runs of 10-fold cross-validation using the EWUSC algorithm at ρ₀ = 0.7, the USC algorithm at ρ₀ = 0.6 and the SC algorithm (USC at ρ₀ = 1). The EWUSC algorithm produces relatively more stable features when the number of relevant genes is small.