Semiparametric Statistical Inferences for ROC Curves and Surfaces under Density Ratio Models

University Of Toledo, Toledo OH

Investigators

Abstract

Receiver operating characteristic (ROC) curves are commonly used to measure the accuracy of diagnostic tests in discriminating disease and nondiasease. The investigator studies four important statistical applications of the density ratio model in semiparametric ROC curve and surface analyses. Analogous to the nonparametric kernel-based ROC curve analysis, the investigator studies the semiparametric kernel estimators of the ROC curve and its area on the basis of the maximum semiparametric likelihood estimators of the underlying distribution functions under a two-sample density ratio model. Furthermore, the investigator proposes three approaches for comparing the accuracy of two diagnostic tests with paired or unpaired data. Moreover, the investigator studies the maximum semiparametric likelihood estimator of the best combination of two or more diagnostic tests by directly modeling the likelihood ratio function under a density ratio model. In addition, as a generalization of semiparametric ROC curve analysis to semiparametric ROC surface analysis, the investigator studies maximum semiparametric likelihood estimation of the ROC surface and its volume in the context of multiple-class diagnostic problems by extending the two-sample density ratio model to a multiple-sample density ratio model. As an alternative to the Cox proportional hazards model and the Lehmann alternative model, the natural connection between the semiparametric density ratio model and the logistic regression model has enhanced its recent popularity. It is anticipated that statistical inferences based on the density ratio model would be more robust than a fully parametric approach and would be more efficient than a fully nonparametric approach. An important role of research in diagnostic medicine is to estimate and compare the accuracies of diagnostic tests, enabling one to determine if a new diagnostic test is as good as the standard reference test or if an inexpensive test has an acceptable inferiority in sensitivity or specificity. In clinical practice, several medical diagnostic tests are often available, yet they may not be perfect in the sense that no single test is sufficiently sensitive and specific on its own for the purpose of population disease screening. One approach to improving the performance of screening is to combine multiple diagnostic tests so as to obtain an optimal composite diagnostic test with higher sensitivity that detects presence of the disease more accurately. The proposed activity has important applications in the evaluation of medical diagnostic tests, all of which are beneficial to practitioners in biological and medical communities. In particular, the proposed activity provides a more robust and efficient statistical methodology for assessing the accuracy of diagnostic tests used in the practice of medicine, thereby enhancing the statistical evaluation of medical diagnostic tests for classification and prediction. Thus, the proposed activity would be widely applicable in the field of diagnostic medicine and other related interdisciplinary problems. In addition, the proposed research activity has greater educational impacts on statistics teaching and learning, in that much of the proposed material can be utilized in classroom teaching and incorporated into textbooks on semiparametric models for master and doctoral students in statistics and biostatistics.