Physical Sciences and Mathematics Commons^™

Some Topics In Roc Curves Analysis, Xin Huang

Mathematics Dissertations

The receiver operating characteristic (ROC) curves is a popular tool for evaluating continuous diagnostic tests. The traditional definition of ROC curves incorporates implicitly the idea of "hard" thresholding, which also results in the empirical curves being step functions. The first topic is to introduce a novel definition of soft ROC curves, which incorporates the idea of "soft" thresholding. The softness of a soft ROC curve is controlled by a regularization parameter that can be selected suitably by a cross-validation procedure. A byproduct of the soft ROC curves is that the corresponding empirical curves are smooth.

The second topic is on …

A Generalization Of Auc To An Ordered Multi-Class Diagnosis And Application To Longitudinal Data Analysis On Intellectual Outcome In Pediatric Brain-Tumor Patients, Yi Li

Mathematics Dissertations

Receiver operating characteristic (ROC) curves have been widely used in evaluation of the goodness of the diagnostic method in many study fields, such as disease diagnosis in medicine. The area under the ROC curve (AUC) naturally became one of the most used variables in gauging the goodness of the diagnosis (Mossman, Somoza 1991). Since medical diagnosis often is not dichotomous, the ROC curve and AUC need to be generalized to a multi-dimensional case. The generalization of AUC to multi-class case has been studied by many researchers in the past decade. Most recently, Nakas & Yiannoutsos (2004) considered the ordered d …

New Non-Parametric Confidence Interval For The Youden, Haochuan Zhou

Mathematics Theses

Youden index, a main summary index for the Receiver Operating Characteristic (ROC) curve, is a comprehensive measurement for the effectiveness of a diagnostic test. For a continuous-scale diagnostic test, the optimal cut-point for the positive of disease is the cut-point leading to the maximization of the sum of sensitivity and specificity. Finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. In this thesis, we propose a new non-parametric confidence interval for the Youden index. Extensive simulation studies are conducted to compare the relative performance …

Empirical Likelihood-Based Nonparametric Inference For The Difference Between Two Partial Aucs, Yan Yuan

Mathematics Theses

Compare the accuracy of two continuous-scale tests is increasing important when a new test is developed. The traditional approach that compares the entire areas under two Receiver Operating Characteristic (ROC) curves is not sensitive when two ROC curves cross each other. A better approach to compare the accuracy of two diagnostic tests is to compare the areas under two ROC curves (AUCs) in the interested specificity interval. In this thesis, we have proposed bootstrap and empirical likelihood (EL) approach for inference of the difference between two partial AUCs. The empirical likelihood ratio for the difference between two partial AUCs is …