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

受试者工作特征(ROC)曲线通常用来衡量诊断试验在区分疾病和非疾病方面的准确性。本文研究了密度比模型在半参数ROC曲线曲面分析中的四个重要统计应用。类似于基于非参数核的ROC曲线分析，在两样本密度比模型下，基于基础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，研究人员提出了三种方法来比较两个诊断测试与配对或非配对数据的准确性。此外，通过直接对密度比模型下的似然比函数建模，研究了两个或多个诊断检验的最佳组合的最大半参数似然估计。此外，作为半参数ROC曲线分析到半参数ROC曲面分析的推广，通过将两样本密度比模型推广到多样本密度比模型，研究了多类诊断问题下ROC曲面及其体积的最大半参数似然估计。作为Cox比例风险模型和Lehmann替代模型的替代模型，半参数密度比模型和Logistic回归模型之间的天然联系使其在最近得到了广泛的应用。预计基于密度比模型的统计推断将比完全参数方法更稳健，并且将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测试的准确性，使人们能够确定新的诊断测试是否与标准参考测试一样好，或者是否廉价的测试在灵敏度或特异度方面具有可接受的劣势。在临床实践中，经常有几种医学诊断测试，但它们可能不是完美的，因为没有一种测试本身对人口疾病筛查的目的具有足够的敏感性和特异性。改进筛查性能的一种方法是组合多个诊断试验，以获得具有更高灵敏度的最佳综合诊断试验，该综合诊断试验更准确地检测疾病的存在。拟议的活动在医学诊断测试的评估中具有重要的应用，所有这些都有利于生物和医学界的从业者。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可靠和更有效的统计方法，从而加强了对医疗诊断测试的统计评估，以便进行分类和预测。因此，拟议的活动将广泛适用于诊断医学领域和其他相关的跨学科问题。此外，拟议的研究活动对统计学的教学和学习有更大的教育影响，因为许多拟议的材料可用于课堂教学，并纳入统计学和生物统计学硕士和博士生半参数模型的教科书。

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.