基于复合分位数回归和最大秩相关想法的ROC回归曲线估计

The covariate-specific receiver operating characteristic curve or ROC regression is frequently used to evaluate the classification accuracy of a diagnostic test when it is associated with certain covariates. Indirect modeling of ROC regression is widely discussed in the literature. This method first builds a disease-specific regression model between test results and covariates as well as disease status, and estimates model parameters based on quasilikelihood method or local polynomial regression; then it estimates the targeted ROC curve based on nonparametric or kernel smoothing estimates of the disease-specific survival function using fitted residuals obtained previously. Considering the limitations of this method (e.g.: depending heavily on properties of the random errors, and is sensitive to outliers), we propose in this project a new series of methods for ROC regression based on the ideas of composite quantile regression and maximum rank correlation. We discuss these methods both in the absense or presence of missing data at random. These include missing test result, missing covariates, missing gold standard, or a mixture of them. To facilitate the use and comparison of different regression methods, we also propose a new formulation for a class of traditional location-scale model. Under the new framework,the ROC regression curve is much simpler than it was under the old framework. Furthermore, it is more convenient to compare the asymptotic variances among the different methods. Due to the complexity of the estimated ROC curve expression, we shall establish the asymptotic results of the proposed estimators, based on M-estimation theories and empirical process method. We shall conduct extensive numerical simulations to compare the finite sample performances of different methods. We shall also apply the different procedures in a real example from the National Alzheimer's Coordinating Center.

受试者操作特征（ROC）回归曲线广泛用于评估连续型诊断检验的分类精度。文献上常使用间接建模方法估计ROC回归曲线：首先对诊断检验结果关于协变量和疾病状态建立位置刻度模型，并通过拟似然或局部多项式回归估计模型参数；然后基于获得的拟合残差使用非参或核光滑方法估计目标ROC曲线。这类方法对模型随机误差分布有很强的依赖性，且对观测数据中的异常值特别敏感。本课题中，我们拟使用复合分位数及最大秩相关等技巧估计ROC回归曲线。我们分别考虑数据完全观测和含随机缺失两种情况。为便于使用上述方法,我们针对一类参数位置刻度模型提出一种新的模型描述方法。在新的模型描述框架下，目标ROC回归曲线形式更加简洁，且更便于理论上比较各种估计的渐近方差。考虑到ROC曲线估计表达式的复杂性，我们拟借助M-估计理论及经验过程知识证明估计量的渐近正态性。我们拟通过大量数值模拟及老年痴呆症方面的实际数据考察各类方法的有限样本表现。

受试者操作特征（ROC）回归曲线是评估诊断检验分类精度的一种基本工具。本项目中，我们分别使用复合分位数回归、加权秩回归等技巧估计ROC回归曲线。我们分别考虑数据完全观测和含随机缺失两种情况。为便于使用上述估计方法， 我们对一类参数位置刻度模型提出了一种新的模型描述方法。在新的模型描述框架下，目标ROC回归曲线形式更加简洁，且更便于理论上比较各种估计的渐近性质。我们借助M-估计理论及经验过程知识证明了估计量的渐近性质，并通过大量数值模拟及老年痴呆症方面的实际数据考察了所提方法的有限样本表现。本项目提出的“位置刻度模型的重参数化”，将对基于不同方法位置刻度模型参数估计效率的渐近比较提供统一框架。

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