Lehmann ROC regression and spatial classification.
Receiver Operating Curves (ROC) are a widely used measure of accuracy in diagnostic tests. Recently, there has been an increased interest in the effect that covariates have on the accuracy of the tests. As a result, several regression models for the ROC have been proposed. Two existing methods, a binormal model and a more recently proposed method based upon the beta distribution are discussed in the first chapter. A third model based upon the Lehmann assumption and the commonly used proportional hazard ratio model is considered. An objective of this dissertation is to introduce this method and to compare it with the existing methods in order to determine if and when it performs well. We do this by constructing simulated data from three distributions, the normal, extreme-value, and Weibull. The methods are further illustrated using real leukocyte elastase data. In the second chapter, we expand our investigation of the ROC models beyond diagnostic testing to the problem of identifying cases and controls using repeated measurement data. Little is found concerning this problem in the literature. So we begin with a very simple case of having a simple dose response model. The results are based upon simulations when using the beta model with the Lehmann model with normal, extreme-value, and Weibull data. The dependency structure of the repeated measures makes use of a Copula model. In the third chapter the emphasis changes as we address the question, “Will there be precipitation at a given location?". There are multiple statistical and machine learning methods available to address this question. We consider two statistical and three machine learning methods for estimating precipitation area. Since this problem involves spatial areas, we expanded the above models by incorporating spatial information into the estimation problem. The data were obtained from a network consisting of VIS rain gauges, automated weather system (AWS) tipping-bucket rain gauges, and a S-band dual-polarimetric weather radar for ten different rain events in South Korea. The mean squared prediction error (MSPE) and leave-one-out cross validation (LOOCV) are used to measure the performance of the methods.