New statistical procedures with parametric and nonparametric likelihood structures with applications to evaluations of discriminant ability of biomarkers measured with/without measurement errors

The receiver operating characteristic (ROC) curve is a popular graphical representation to evaluate the classification accuracy of a diagnostic system. The area under the ROC curve (AUC) summarizes the information and is frequently used to assess the general performance of the diagnostic system. Improvement of the diagnostic accuracy has always been an important topic in public health since it enables researchers to identify a more appropriate and beneficial procedure for diagnosing or screening for a specific disease. In this thesis, we first consider the best linear combination (BLC) that maximizes the AUC among all possible linear combinations in both paired and independent design settings. Proceeding from derived BLC of biomarkers' measurements, an efficient technique via parametric likelihood ratio tests is proposed to compare treatment effects. When data distributions are completely known, the parametric likelihood ratio tests are most powerful decision rules by virtue of the Neyman-Pearson lemma. However, when the data distribution deviates from the assumptions assumed, inaccurate statistical conclusions can be expected. Toward this end, we propose a novel smoothed empirical likelihood (EL) approach to make a nonparametric inference on the AUC that incorporates kernel estimation of the AUC based on the BLC of biomarkers. Finally, complete/incomplete data subject to different sorts of measurement error (ME) are also considered. Statistical inferences are made to avoid bias and inconsistency in the context of additive MEs and limit of detection. Furthermore, a broad spectrum of dependence structures without MEs as well as with additive and multiplicative MEs are examined thoroughly. Classical and novel tests of independence under a variety of dependence structures with/without MEs are compared.