Abstract: We consider the performance of a diagnostic test based on continuous measurements in its ability to distinguish between healthy and diseased individuals. For a performance criterion we use Youden's (1950) index which is essentially the sum of the sensitivity and specificity. Based on available training set data, two types of nonparametric estimators for the optimal cutoff level and for the index are proposed. The first type is constructed from empirical distribution functions, the other from kernel smoothed density estimates. We compare their asymptotic properties, including rates of convergence. Finite sample properties are investigated by means of a small simulation study. Finally, the methods are applied to results of a glucose tolerance test for diabetes in a sample of 578 individuals from the NHANES-II study.
Key words and phrases: Classification, consistency, convergence rates, diagnostic markers, discrimination, empirical distribution function, empirical processes, kernel density estimate, sensitivity, specificity, Youden index.