Small sample issues for microarray-based classification

In order to study the molecular biological differences between normal and diseased tissues, it is desirable to perform classification among diseases and stages of disease using microarray-based gene-expression values. Owing to the limited number of microarrays typically used in these studies, serious issues arise with respect to the design, performance and analysis of classifiers based on microarray data. This paper reviews some fundamental issues facing small-sample classification: classification rules, constrained classifiers, error estimation and feature selection. It discusses both unconstrained and constrained classifier design from sample data, and the contributions to classifier error from constrained optimization and lack of optimality owing to design from sample data. The difficulty with estimating classifier error when confined to small samples is addressed, particularly estimating the error from training data. The impact of small samples on the ability to include more than a few variables as classifier features is explained.