MONOTONE DISCRIMINANT FUNCTIONS AND THEIR APPLICATIONS IN RHEUMATOLOGY

Some applications of discriminant analysis (e.g., in rheumatology) nat urally require that the discriminator satisfies certain monotonicity c onstraints in terms of the measurements on which the classification is based. This article presents a dynamic programming approach to the pr oblem of finding the monotone function that minimizes the total miscla ssification cost incurred when classifying two types of cases on the b asis of two variables measured on each case. Questions of uniqueness a nd convexity are explored, and the way in which the solution varies wi th choice of misclassification costs is investigated. The use of the b ootstrap to estimate the accuracy of summary statistics of interest is discussed. The methodology is illustrated using data on rheumatology patients. Some comparisons with linear discriminant functions and clas sification tree methods are made.