Selected Topics on Statistical Methods for Three and Multiple Class Diagnostic Studies
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Many disease processes such as Alzheimer'sDisease have three ordinal disease classes, i.e. the non-diseased stage, the early diseased stage and the fully diseased stage. Since the early diseased stage is likely the best time window for treatment interventions, it is important to have diagnostic tests which have good diagnostic ability to discriminate the early diseased stage from the other two. We present both parametric and non-parametric approaches for confidence interval estimation of probability of detecting the early diseased stage (sensitivity to early stage) given the true classification rates for non-diseased group (specificity) and diseased group (sensitivity to full disease). Similar parametric and non-parametric approaches are also proposed for estimating the confidence interval for the difference between sensitivities to the early diseased stage for two markers. The semi-parametric confidence intervals for the sensitivity to the early diseased stage, which utilize the empirical likelihood approach, are also proposed, and one of them is shown to outperform the existing methods in some distribution settings. The AUC and Youden index are the most well-known diagnostic measures for diseases with binary outcome. Both of them have been generalized to disease processes with three or more disease stages. We propose a new measure which can be applied naturally to any k -class diseases ( k ≥ 2). The geometric and probabilistic interpretation for the new measure is illustrated, and comparisons between the new measure and the extensions of AUC and Youden index, are examined through a power study. Moreover, the new measure can also be utilized as a criterion to select the optimal cut-off points, and its performance is compared with the generalized Youden index criterion through a simulation study for the three-class and four-class diseases.