Extensions of ROC curves and AUCs for classification and survival analysis, with applications to mathematical models for diagnosis and prognosis.

Core tasks in the development of sound mathematical models for diagnosis and prognosis include input selection and model evaluation. Very often, the performance of a mathematical model is evaluated using ROC (receiver operating characteristic) curves and the area under the ROC curve (AUC). A disadvantage of the AUC is that it does not take the exact probabilities given by the model into account. A model that makes, on average, a larger distinction between cases from both classes, can be seen as a more robust model because perturbations in the predicted probabilities will have little effect on the AUC. With respect to binary classification, two weighted AUC metrics have been suggested in the literature. This project deals with the development of weighted AUC metrics for multi-class classification, and with the development of a weighted alternative for the AUC-based C-index for prognostic models. Such metrics can be used for both input selection and model evaluation. In addition, we intend to develop an ROC curve (called the resampled ROC curve) consisting of a combination of individual ROC curves that are obtained using repeated splits of the data into training and test parts. A resampled ROC curve is smoother than a single nonparametric ROC curve. These methodologies will be applied to diagnostic and prognostic models for ovarian tumors, pregnancies of unknown location, and breast cancer.

Keywords:Bio statistics

Disciplines:Artificial intelligence, Cognitive science and intelligent systems, Applied mathematics in specific fields, Statistics and numerical methods, Morphological sciences, Oncology