Parametric and non-parametric confidence intervals of the probability of identifying early disease stage given sensitivity to full disease and specificity with three ordinal diagnostic groups

In practice, there exist many disease processes with three ordinal disease classes, that is, the non-diseased stage, the early disease stage, and the fully diseased stage. Because early disease stage is likely the best time window for treatment interventions, it is important to have diagnostic tests that have good diagnostic ability to discriminate the early disease stage from the other two stages. In this paper, we present both parametric and non-parametric approaches for confidence interval estimation of probability of detecting early disease stage given the true classification rates for non-diseased group and diseased group, namely, the specificity and the sensitivity to full disease. We analyze a data set on the clinical diagnosis of early-stage Alzheimer's disease from the neuropsychological database at the Washington University Alzheimer's Disease Research Center using the proposed approaches.