Statistical inference of the Youden index
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In many diagnostic studies, the Receive Operating Characteristic (ROC) curve and its area under the ROC curve are important tools in assessing the discriminating ability of biomarkers or diagnostic ability of tests between non-diseased and diseased populations. In order to classify a patient into non-diseased or diseased groups, an optimal cut-point of a continuous biomarker is desirable. Youden's index ( J ), defined as the maximum vertical distance between the ROC curve and the diagonal chance line, serves as another global measure of overall diagnostic accuracy and can be used to choose an optimum cut-point. The objectives of this thesis are to construct confidence intervals for the single Youden index and its corresponding optimal cut-off point, as well as the difference in paired Youden indices, the side products of Youden index or the paired Youden indices: the sensitivity and the specificity at an optimal cut-point, the difference in paired Youden indices with the absence of a gold standard test, and observations with a low limit of detection (LOD). We apply the generalized pivotal quantity approach to construct the confidence intervals of single Youden index, paired Youden indices, and paired Youden indices in the absence of a gold standard test. For the purpose of comparisons, delta method, quantile-based parametric bootstrap method or quantile-based non-parametric bootstrap method are used to construct the confidence intervals. However, delta method is not easy to derive the confidence interval of the difference in paired Youden indices and paired Youden indices with the absence of a gold standard test. Instead, in these two cases, quantile-based parametric bootstrap and non-parametric bootstrap methods will be used for comparisons with the generalized pivotal quantity approach. For data with a LOD, the traditional non-parametric Kaplan-Meier method for Type I censored data as well as the Persson-Rootzén method and the parametric maximal likelihood (ML) method are used to construct the confidence intervals.