论文标题
在可能排序下的两样本问题的统计推断，并应用于ROC曲线估计
Statistical inference for the two-sample problem under likelihood ratio ordering, with application to the ROC curve estimation
论文作者
论文摘要
接收器操作特性（ROC）曲线是一种强大的统计工具，已广泛应用于医学研究。在ROC曲线估计中，一个常用的假设是，生物标志物值较大，严重程度更高。在本文中，我们在数学上将``疾病的严重程度''解释为``患病的概率''。反过来，这相当于假设患者和健康个体之间生物标志物的似然比顺序。有了这个假设，我们首先提出了伯恩斯坦多项式方法来对两个样品的分布进行建模。然后，我们通过最大的经验可能性原理估算分布。随后获得了ROC曲线估计和相关的摘要统计数据。从理论上讲，我们建立了估计量的渐近一致性。通过广泛的数值研究，我们将方法的性能与竞争方法进行了比较。我们的方法的应用由Real-Data示例说明。
The receiver operating characteristic (ROC) curve is a powerful statistical tool and has been widely applied in medical research. In the ROC curve estimation, a commonly used assumption is that larger the biomarker value, greater severity the disease. In this paper, we mathematically interpret ``greater severity of the disease" as ``larger probability of being diseased". This in turn is equivalent to assume the likelihood ratio ordering of the biomarker between the diseased and healthy individuals. With this assumption, we first propose a Bernstein polynomial method to model the distributions of both samples; we then estimate the distributions by the maximum empirical likelihood principle. The ROC curve estimate and the associated summary statistics are obtained subsequently. Theoretically, we establish the asymptotic consistency of our estimators. Via extensive numerical studies, we compare the performance of our method with competitive methods. The application of our method is illustrated by a real-data example.
