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

受试者工作特征（ROC）曲线通常用于衡量诊断试验在区分疾病和非疾病方面的准确性。研究者研究了密度比模型在半参数ROC曲线和曲面分析中的四个重要统计应用。与基于非参数核的ROC曲线分析类似，研究者在双样本密度比模型下，基于底层分布函数的最大半参数似然估计研究了ROC曲线及其面积的半参数核估计。此外，研究者提出了三种方法来比较两种诊断测试与配对或非配对数据的准确性。此外，研究者通过在密度比模型下直接建模似然比函数，研究了两个或多个诊断试验最佳组合的最大半参数似然估计量。此外，作为半参数ROC曲线分析到半参数ROC曲面分析的推广，研究者通过将双样本密度比模型扩展到多样本密度比模型，研究了多类诊断问题背景下ROC曲面及其体积的最大半参数似然估计。半参数密度比模型作为Cox比例风险模型和Lehmann替代模型的替代品，其与logistic回归模型之间的天然联系使其近年来得到了广泛的应用。可以预期，基于密度比模型的统计推断将比完全参数方法更稳健，比完全非参数方法更有效。诊断医学研究的一个重要作用是估计和比较诊断试验的准确性，使人们能够确定一种新的诊断试验是否与标准参考试验一样好，或者一种廉价的试验是否在敏感性或特异性方面具有可接受的劣势。在临床实践中，通常有几种医学诊断测试，但它们可能并不完美，因为没有一种测试本身具有足够的敏感性和特异性，无法用于人群疾病筛查。提高筛查性能的一种方法是将多种诊断试验相结合，以获得灵敏度更高的最佳复合诊断试验，更准确地检测疾病的存在。拟议的活动在评估医学诊断测试方面具有重要的应用，所有这些都有利于生物和医学界的从业人员。特别是，拟议的活动为评估医学实践中使用的诊断测试的准确性提供了一种更有力和更有效的统计方法，从而加强了对医学诊断测试进行分类和预测的统计评估。因此，拟议的活动将广泛适用于诊断医学领域和其他有关的跨学科问题。此外，所提出的研究活动对统计学的教学和学习具有更大的教育影响，因为所提出的许多材料可以用于课堂教学，并纳入统计和生物统计硕士和博士生的半参数模型教科书。

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.