本文選題：半?yún)?shù)加速失效時(shí)間模型 + Gehan統(tǒng)計(jì)量��； 參考：《山西醫(yī)科大學(xué)》2007年碩士論文

【摘要】： 在生存數(shù)據(jù)分析領(lǐng)域當(dāng)中,半?yún)?shù)加速失效時(shí)間模型做為一種線性回歸模型,它把生存時(shí)間的對(duì)數(shù)作為反應(yīng)變量,而且誤差項(xiàng)的分布也是未知的。在分析含有刪失數(shù)據(jù)的生存資料時(shí),半?yún)?shù)加速失效時(shí)間模型是Cox比例風(fēng)險(xiǎn)模型的一種很好的替代模型。 在用加速失效時(shí)間模型處理刪失數(shù)據(jù)時(shí),許多人都研究基于秩的估計(jì)方法,秩估計(jì)量可以由最小化凸目標(biāo)函數(shù)通過(guò)標(biāo)準(zhǔn)的線性規(guī)劃的方法得到。但在用傳統(tǒng)方法估計(jì)秩估計(jì)量的方差時(shí)有很大困難。這里介紹Zhou的一種經(jīng)驗(yàn)似然的分析方法來(lái)對(duì)秩估計(jì)量做推斷。這里的似然定義為誤差變量的刪失經(jīng)驗(yàn)似然,用經(jīng)驗(yàn)似然的方法進(jìn)行假設(shè)檢驗(yàn),而且用它來(lái)為模型的回歸系數(shù)建立可信區(qū)間。同時(shí)表明了在原假設(shè)下,對(duì)數(shù)經(jīng)驗(yàn)似然比的限制分布是一個(gè)中心卡方分布,標(biāo)準(zhǔn)的卡方分布用來(lái)計(jì)算P值和建立可信區(qū)間。 經(jīng)驗(yàn)似然方法避免了估計(jì)方差,只需要計(jì)算刪失經(jīng)驗(yàn)似然的約束最大化即可,而這種方法的計(jì)算是很可靠的。因此,為了檢驗(yàn)假設(shè)和計(jì)算P值,經(jīng)驗(yàn)似然的方法需要解決最優(yōu)化的問(wèn)題。模擬分析和實(shí)例分析都顯示了對(duì)數(shù)經(jīng)驗(yàn)似然比的分布很好地接近卡方分布,而且展現(xiàn)出了比其它方法更多的優(yōu)點(diǎn)。 我們同時(shí)介紹了Arnost Komarek的一種加速失效時(shí)間模型的半?yún)?shù)估計(jì)方法。這種方法主要是利用懲罰B樣條來(lái)光滑誤差項(xiàng)。用了Eilers和Marx(1996)的光滑技術(shù)來(lái)表達(dá)誤差項(xiàng)的密度函數(shù),因?yàn)檎`差項(xiàng)密度是無(wú)限支撐的,所以用正態(tài)密度來(lái)替換B樣條,其實(shí)正態(tài)密度是B樣條的極限情形。樣條系數(shù)和回歸參數(shù)都可由懲罰最大似然的方法快速準(zhǔn)確的計(jì)算得到。用“偽方差估計(jì)”的方法在基于懲罰最大似然的基礎(chǔ)上做出準(zhǔn)確的推斷。這種方法可以在固定協(xié)變量時(shí)直接預(yù)測(cè)生存曲線,而且這種方法可以處理左刪失、右刪失和區(qū)間刪失的生存數(shù)據(jù)。 本課題模擬分析及實(shí)例分析使用R軟件作為運(yùn)算分析平臺(tái)。
[Abstract]:In the field of survival data analysis, the semi-parametric accelerated failure time model is a linear regression model, which takes the logarithm of survival time as a response variable, and the distribution of the error term is unknown. In the analysis of survival data with censored data, the semi-parametric accelerated failure time model is a good substitute for Cox proportional risk model. When processing censored data with the accelerated failure time model, many people have studied the rank estimation method, which can be obtained by minimizing convex objective function through the standard linear programming method. However, it is difficult to estimate the variance of rank estimator by traditional method. This paper introduces an empirical likelihood analysis method of Zhou to infer rank estimators. Here the likelihood is defined as the erasure empirical likelihood of error variables. The empirical likelihood method is used to test the hypothesis, and it is used to establish the confidence interval for the regression coefficient of the model. It is also shown that the restricted distribution of logarithmic empirical likelihood ratio is a central chi-square distribution under the original assumption, and the standard chi-square distribution is used to calculate P value and establish confidence intervals. The empirical likelihood method avoids the estimation of variance and only needs to compute the constraint maximization of erasure empirical likelihood. The calculation of this method is very reliable. Therefore, in order to test the hypothesis and calculate P value, the empirical likelihood method needs to solve the optimization problem. Both simulation analysis and case analysis show that the distribution of logarithmic empirical likelihood ratio is close to the chi-square distribution and shows more advantages than other methods. We also introduce a half parameter estimation method for accelerated failure time model of Arnost Komarek. This method mainly uses the penalty B spline to smooth the error term. The density function of the error term is expressed by the smooth technique of Eilers and Marks 1996. Because the density of the error term is infinitely supported, the normal density is replaced by the B-spline. In fact, the normal density is the limit of the B-spline. The spline coefficients and regression parameters can be calculated quickly and accurately by the maximum likelihood penalty method. The method of pseudo-variance estimation is used to infer accurately based on the maximum likelihood of punishment. This method can directly predict the survival curve when the covariable is fixed, and this method can deal with the survival data of left, right and interval deletions. In this paper, R software is used as the platform of calculation and analysis.
【學(xué)位授予單位】：山西醫(yī)科大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2007
【分類(lèi)號(hào)】：R311

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相關(guān)碩士學(xué)位論文 前1條

1 任曉衛(wèi);半?yún)?shù)加速失效時(shí)間模型及其在醫(yī)學(xué)中的應(yīng)用[D];山西醫(yī)科大學(xué);2007年

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本文編號(hào)：1895609