影响诊断结果可靠性的变量选择问题的研究

Many diagnostic procedures have been developed in modern medical studies. ROC curves are commonly used for evaluating the accuracy of diagnostic tests. If we standardize the test result of the diseased population according to the distribution function of the test result in the non-diseased population ,and denote the standardized values U^D, the ROC curve can be interpreted as a cumulative distribution function of U^D, where U^D quantifies the separation between the populations. While U^D depends the unknown distribution function. To make use of some auxiliary information from the real data, we will propose a more efficient estimate of U^D. In the real data analysis, there will be a lot of covariates which may affect the separation between the populations, such as gender, age and so on. Accounting for covariates can improve the diagnostic accuracy. However, including all of them may lead to over-fitting. So we will construct the linear regression model. If the distribution of the error term is unknown and the real data is with auxiliary information, we will use the empirical likelihood method to estimate the parameters. In classical statistics, a variety of variable selection criteria have been suggested. But most of them aim at selecting a subset of variables with good overall properties, say, formulated via the average prediction quality. The AIC, BIC, to name just a few, are example of such methods. The FIC proposed by Claeskens and Hjort take the view that the variable selector should instead focus on the parameter of interest. In ROC analysis, we are not interested in predicting the response of the diagnostic test conducted on one individual, but in distinguishing diseased subjects from non-diseased subjects. Moreover, the AUC is the most popular summary index of the discriminatory accuracy. In this project, we will develop some versions of FIC with focus on the AUC and select some important covariates to get the optimal model.

诊断试验是临床研究的重要组成部分，ROC曲线是目前诊断试验评价方法中最常用的一种.若根据健康人群测试结果的分布函数将得病人群测试结果标准化，ROC曲线是标准化后的测试结果 U^D 的累计分布函数，其中U^D刻画了得病和健康人群的分离程度。而U^D依赖未知分布函数，要准确估计它并有效利用辅助信息，我们对它进行核平滑经验似然估计。现实中有很多因素会影响得病和健康人群的分离程度U^D，如性别，年龄等，进而影响诊断可靠性，因此需对U^D建立回归模型并进行变量选择。本项目我们将建立线性回归模型，特别的，当误差项的分布函数未知而数据带有辅助信息时，我们将用经验似然方法确定回归系数。协变量的选择是为了提高诊断可靠性，因此传统的旨在提高模型预测能力而不管其应用的变量选择方法如AIC，BIC等不再适用。对此，我们将用FIC准则进行变量选择，使得诊断可靠性最大。

诊断试验是临床研究的重要组成部分，诊断试验的可靠度至关重要，ROC 曲线是目前诊断试验评价方法中最常用的一种，而 AUC作为衡量诊断结果可靠性的综合单值指标引起了人们的重视。现实中有很多因素会影响测试结果，进而影响诊断可靠性。尽管影响因素有很多，但是有相当一部分因素其影响并不显著，从中找出重要的因素，变量选择至关重要。本项目分别从两个不同的角度来建立相应的模型。一是在健康人群和得病人群的测试结果的分布已知的情况下，分别对测试结果及相关因素之间建立参数模型，基于FIC准则进行变量选择；二是在得病人群定位值UD及其影响因素之间建立参数模型利用FIC准则进行变量选择。通过数值模拟将新方法与传统的变量选择方法相比较，进一步应用到实际问题中去。

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