Monotone Discriminant Functions and Their Applications in Rheumatology

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Abstract
Some applications of discriminant analysis (e.g., in rheumatology) naturally require that the discriminator satisfies certain monotonicity constraints in terms of the measurements on which the classification is based. This article presents a dynamic programming approach to the problem of finding the monotone function that minimizes the total misclassification cost incurred when classifying two types of cases on the basis of two variables measured on each case. Questions of uniqueness and convexity are explored, and the way in which the solution varies with choice of misclassification costs is investigated. The use of the bootstrap 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 classification tree methods are made.

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