Discriminant analysis.

Discriminant analysis (DA) is a pattern recognition technique that has been widely applied in medical studies. It allows multivariate observations ("patterns" or points in multidimensional space) to be allocated to previously defined groups (diagnostic categories). The relationships between DA and other multivariate statistical techniques of interest in medical studies will be briefly discussed. The main emphasis is on linear discriminant functions (LDF). The theoretic assumptions underlying DA using LDFs will be presented, and the effect of violations to these assumptions will be reviewed in detail. Alternative methods will be presented when violations cause serious problems. It has been shown that the familiar LDF is fairly robust to departures from the assumptions. The application of the LDF in less than ideal situations therefore often does not cause much harm (if the violations are not too grotesque). Another set of problems reviewed is how to estimate the misallocation probabilities when using discriminant functions. The selection of the "best" subset of variables out of the complete set will be discussed. Practical guide lines are given based on the theoretic studies reviewed. When possible, available computer programs for various problems of DA will be indicated. The review does not aim at covering all medical studies where DA has been applied, since emphasis is on the practical conclusions of the theory of DA.