Diagnosis of multiple cancer types by shrunken centroids of gene expression

Abstract

We have devised an approach to cancer class prediction from gene expression profiling, based on an enhancement of the simple nearest prototype (centroid) classifier. We shrink the prototypes and hence obtain a classifier that is often more accurate than competing methods. Our method of "nearest shrunken centroids" identifies subsets of genes that best characterize each class. The technique is general and can be used in many other classification problems. To demonstrate its effectiveness, we show that the method was highly efficient in finding genes for classifying small round blue cell tumors and leukemias.

Figure 1

Centroids (grey) and shrunken centroids (red) for the SRBCT dataset. The overall centroid has been subtracted from the centroid from each class. The horizontal units are log ratios of expression. From left to right, the numbers of training samples for each class are 8, 23, 12, and 20. The order of the genes is arbitrary.

Figure 2

SBRCT classification: training (tr, green), cross-validation (cv, red), and test (te, blue) errors are shown as a function of the threshold parameter Δ. The value Δ = 4.34 is chosen and yields a subset of 43 selected genes.

Figure 3

Shrunken differences d′_ik for the 43 genes having at least one nonzero difference. The genes with nonzero components in each class are almost mutually exclusive.

Figure 4

(Top) Heat map of the chosen 43 genes. Within each of the horizontal partitions, we have ordered the genes by hierarchical clustering, and similarly for the samples within each vertical partition. (Bottom) Heat map of three genes reported in the literature to characterize SRBCT tumors. They are c-myc (Top), CD45 (Middle) and myogenin (Bottom).

Figure 5

Estimated probabilities for the training data (Upper) and test data (Lower). Samples are partitioned by the true class (Upper) and the predicted class (Lower). All 63 of the training samples and all 20 of the test samples known to be SRBCT are correctly classified. Five of the test samples were non-SRBCT and hence should not be classified as such. The maximum estimated probability for each of these five samples is marked with a circle; they are below the maximum probabilities for the other test samples in each class.

Figure 6

Leukemia classification: training (tr, green), cross-validation (cv, red), and test (te, blue) errors. The value Δ = 4.06 yields a subset of 21 genes.