In the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cut-off point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of bi-Exponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to derive the precise formula of AUC and study the maximus likelihood estimation (MLE) of the AUC. Finally, we obtain the asymptotoc distribution of the estimated AUC. Simulation studies are used to check the performance of MLE of AUC under the moderate sample sizes. The second part fo the dissertation is to study the estimation of AUC under the crossing model, which extends the AUC formula in Gonen and Heller (2007). / by Fazhe Chang. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Bibliography: leaves 223-229. / xiii, 229 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis considers several aspects of multivariate analysis motivated by the South Australian prenatal Down's syndrome screen, which seeks to identify those pregnancies at high risk to Down's syndrome from several risk factors, amongst them maternal age and measurements from four analyte concentrations found in maternal blood. The primary aim is to discriminate between the unaffected and affected pregnancies in terms of these observed risk factors. Through the development of multivariate regression models it is examined how the Mahalanobis distance might be decomposed into distances that give more insight into where the discrimination is derived and how this might change with the gestational age at which the analyte concentrations are measured. A second multivariate aspect motivated by the screen surrounds the detection of directional outliers and the incorporation of knowledge of likely departures into the outlier identification technique. A method is also developed to account for misreporting in inferences of gestational age. Similarities with measurement error and misclassification models are explored. / Thesis (Ph.D.)--University of Adelaide, Dept. of Statistics, 1998?

Systems pathology attempts to introduce more holistic approaches towards pathology and attempts to integrate clinicopathological information with “-omics” technology. This doctorate researches two examples of a systems approach for pathology: (1) a personalized patient output prediction for ovarian cancer and (2) an analytical approach differentiates between individual and collective tumour invasion. During the personalized patient output prediction for ovarian cancer study, clinicopathological measurements and proteomic biomarkers are analysed with a set of newly engineered bioinformatic tools. These tools are based upon feature selection, survival analysis with Cox proportional hazards regression, and a novel Monte Carlo approach. Clinical and pathological data proves to have highly significant information content, as expected; however, molecular data has little information content alone, and is only significant when selected most-informative variables are placed in the context of the patient's clinical and pathological measures. Furthermore, classifiers based on support vector machines (SVMs) that predict one-year PFS and three-year OS with high accuracy, show how the addition of carefully selected molecular measures to clinical and pathological knowledge can enable personalized prognosis predictions. Finally, the high-performance of these classifiers are validated on an additional data set. A second study, an analytical approach differentiates between individual and collective tumour invasion, analyses a set of morphological measures. These morphological measurements are collected with a newly developed process using automated imaging analysis for data collection in combination with a Bayesian network analysis to probabilistically connect morphological variables with tumour invasion modes. Between an individual and collective invasion mode, cell-cell contact is the most discriminating morphological feature. Smaller invading groups were typified by smoother cellular surfaces than those invading collectively in larger groups. Interestingly, elongation was evident in all invading cell groups and was not a specific feature of single cell invasion as a surrogate of epithelialmesenchymal transition. In conclusion, the combination of automated imaging analysis and Bayesian network analysis provides an insight into morphological variables associated with transition of cancer cells between invasion modes. We show that only two morphologically distinct modes of invasion exist. The two studies performed in this thesis illustrate the potential of a systems approach for pathology and illustrate the need of quantitative approaches in order to reveal the system behind pathology.