發(fā)布時(shí)間：2018-04-28 08:07

  本文選題：ROC + 曲線(xiàn)��； 參考：《四川大學(xué)》2005年碩士論文

【摘要】：醫(yī)學(xué)診斷檢測(cè)的準(zhǔn)確性一般由敏感度和特異度來(lái)描述。對(duì)于連續(xù)的檢測(cè)結(jié)果,通常用ROC 曲線(xiàn)來(lái)刻畫(huà)其準(zhǔn)確性。因此,在醫(yī)學(xué)統(tǒng)計(jì)中如何估計(jì)ROC 曲線(xiàn)一直是人們關(guān)注的研究課題。 在ROC 曲線(xiàn)的各種非參數(shù)估計(jì)中,經(jīng)驗(yàn)ROC 曲線(xiàn)是最常用的方法,但經(jīng)驗(yàn)ROC 曲線(xiàn)的函數(shù)值是跳躍的,往往與真實(shí)ROC 曲線(xiàn)的光滑性不符。Lloyd 給出ROC 曲線(xiàn)一種核光滑估計(jì),并證明了他的這種核光滑估計(jì)比經(jīng)驗(yàn)ROC 曲線(xiàn)估計(jì)好。但是Lloyd 的估計(jì)也有缺陷:第一,他對(duì)有病和沒(méi)病的分布函數(shù)分別用兩個(gè)不同的核估計(jì),然后再對(duì)沒(méi)病的分布函數(shù)的核估計(jì)求逆代入ROC 曲線(xiàn),這種估計(jì)過(guò)程會(huì)導(dǎo)致最終的ROC 曲線(xiàn)經(jīng)過(guò)一個(gè)單調(diào)的變化后會(huì)改變;第二,他只關(guān)心單個(gè)分布函數(shù)的最優(yōu)擬合,而不是直接對(duì)ROC 曲線(xiàn)做最優(yōu)估計(jì)。 針對(duì)這些情況,本文給出一種新的核光滑估計(jì)即用局部多項(xiàng)式方法來(lái)擬合ROC 曲線(xiàn)。新方法不僅可以減少均方誤差(MSE),而且只用一個(gè)窗寬來(lái)估計(jì),克服了Lloyd 的缺點(diǎn)。另外,本文還討論了當(dāng)檢測(cè)結(jié)果服從位置尺度族,且其均值經(jīng)過(guò)一個(gè)未知的函數(shù)變化與協(xié)變量有函數(shù)關(guān)系的模型。我們用偽似然估計(jì)和局部多項(xiàng)式擬合的方法估計(jì)這個(gè)未知的函數(shù)和各參數(shù),從而估計(jì)出ROC 曲線(xiàn)。
[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.
【學(xué)位授予單位】：四川大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2005
【分類(lèi)號(hào)】：R311

【引證文獻(xiàn)】

相關(guān)期刊論文 前1條

1 林昌浩;;關(guān)于多個(gè)總體判別分析ROC曲面及其一些性質(zhì)[J];統(tǒng)計(jì)與信息論壇;2008年05期

相關(guān)碩士學(xué)位論文 前2條

1 高嘉偉;非平衡數(shù)據(jù)集分類(lèi)算法及其應(yīng)用[D];山西大學(xué);2008年

2 孔蓮芳;胃癌環(huán)境因素風(fēng)險(xiǎn)預(yù)測(cè)模型初探[D];鄭州大學(xué);2012年

，

本文編號(hào)：1814461