In cancer studies, analyses have typically focused on one of three problems. First, investigators have looked for genes that discriminate neoplastic from benign tissue. Statistically, this is the problem assessing differential expression of genes and has been studied by several authors; see, for example, Efron et al [4]. A second problem is clustering the samples to find subtypes of disease using algorithms such as those in [5]. The final class of problems is classification or supervised learning, which involves using the profile to predict some clinical outcome, such as the stage of disease. Suppose that in this instance, we treat the gene expression profile as the independent variables and tissue type as the response. A particular feature of microarray experiments is that the dimension of the predictor space (number of genes) is typically larger than the number of samples. This is known as the “large p, small n” paradigm (West [6]), so classification methods must take this into account.
