A new procedure for discriminating between two patient populations using multivariate decision limits: application in...

A simple, nonparametric discrimination procedure was developed and tested for use in discriminating between two populations, especially in those cases where the properties of the distributions lead to unsatisfactory results by classical discrimination procedures. The procedure is based on transferring the conventional concept of a decision limit from one to several variables, with combinations (in set theory terms: unions and intersections) of multidimensional intervals serving as the discriminant regions (referred to here as simple discriminant regions). The procedure was applied to two groups of patients, alcoholics and non-alcoholics. A level of efficiency 20% higher than that attainable with conventional procedures was obtained using only six clinical chemical parameters. In addition, the procedure is more flexible than conventional procedures. It enables the solution of optimization problems for each of the three common discrimination criteria (sensitivity, specificity and efficiency) with no fundamental difficulties, and it is still possible to select at will the range(s) for the decision point and for the order of the discriminant regions. For all of the clinical chemical parameters studied the distributions of the results for the two patient samples overlapped very markedly. If, for example, a sensitivity of 100% was specified, the best specificity attainable using the six parameters that discriminated best was only about 53%, and if a specificity of 100% was required, the best sensitivity was about 56%. The analogy between the discrimination principle and the principle of a statistical test (the relationship between detection and exclusion of alcoholism) is also discussed.