ROC曲线的估计方法研究

发布时间：2018-04-28 08:07

本文选题：ROC + 曲线　；参考：《四川大学》2005年硕士论文

【摘要】：医学诊断检测的准确性一般由敏感度和特异度来描述。对于连续的检测结果,通常用ROC 曲线来刻画其准确性。因此,在医学统计中如何估计ROC 曲线一直是人们关注的研究课题。在ROC 曲线的各种非参数估计中,经验ROC 曲线是最常用的方法,但经验ROC 曲线的函数值是跳跃的,往往与真实ROC 曲线的光滑性不符。Lloyd 给出ROC 曲线一种核光滑估计,并证明了他的这种核光滑估计比经验ROC 曲线估计好。但是Lloyd 的估计也有缺陷:第一,他对有病和没病的分布函数分别用两个不同的核估计,然后再对没病的分布函数的核估计求逆代入ROC 曲线,这种估计过程会导致最终的ROC 曲线经过一个单调的变化后会改变;第二,他只关心单个分布函数的最优拟合,而不是直接对ROC 曲线做最优估计。针对这些情况,本文给出一种新的核光滑估计即用局部多项式方法来拟合ROC 曲线。新方法不仅可以减少均方误差(MSE),而且只用一个窗宽来估计,克服了Lloyd 的缺点。另外,本文还讨论了当检测结果服从位置尺度族,且其均值经过一个未知的函数变化与协变量有函数关系的模型。我们用伪似然估计和局部多项式拟合的方法估计这个未知的函数和各参数,从而估计出ROC 曲线。
[Abstract]:The accuracy of medical diagnostic tests is generally described by sensitivity and specificity. ROC curves are usually used to describe the accuracy of continuous detection results. Therefore, how to estimate ROC curves in medical statistics has always been a subject of concern. Among the nonparametric estimation of ROC curves, empirical ROC curves are the most commonly used methods, but the function values of empirical ROC curves are jumping, which is often inconsistent with the smoothness of real ROC curves. Lloyd gives a kernel smooth estimate of ROC curves. It is proved that his kernel smooth estimation is better than the empirical ROC curve estimation. However, Lloyd's estimation also has some defects: first, he estimates the distribution function with two different kernels, and then inverts the kernel estimation of the undiseased distribution function into the ROC curve. This estimation process will result in a monotonic change of the final ROC curve. Secondly, he only cares about the optimal fitting of a single distribution function, not the direct optimal estimation of the ROC curve. In this paper, a new kernel smooth estimator is presented to fit the ROC curve by means of local polynomial method. The new method not only reduces the mean square error (MSE), but also uses only one window width to estimate, which overcomes the shortcoming of Lloyd. In addition, this paper also discusses a model in which the mean value of the detection results is dependent on the position scale family and has a functional relationship with the covariables. We estimate the unknown function and parameters by using pseudo-likelihood estimation and local polynomial fitting to estimate the ROC curve.
【学位授予单位】：四川大学
【学位级别】：硕士
【学位授予年份】：2005
【分类号】：R311

【引证文献】