【摘要】：區(qū)間刪失數(shù)據(jù)是生存分析中的一種常見且非常重要的數(shù)據(jù)類型,針對(duì)這種數(shù)據(jù)的現(xiàn)有研究大多假設(shè)了獨(dú)立刪失機(jī)制,也就是說刪失時(shí)間與事件失效時(shí)間是獨(dú)立的,但這種假設(shè)在現(xiàn)實(shí)問題中并不一定成立,此時(shí)忽略刪失時(shí)間與事件失效時(shí)間之間的相依性很可能會(huì)造成分析結(jié)果的有偏甚至錯(cuò)誤。已有文獻(xiàn)采用Cox模型(也稱比例風(fēng)險(xiǎn)模型)對(duì)相依區(qū)間刪失數(shù)據(jù)進(jìn)行研究。而加法風(fēng)險(xiǎn)模型是生存分析中除Cox模型以外的另一種重要模型,和Cox模型不同,在加法模型中,協(xié)變量對(duì)壽命變量的危險(xiǎn)率的影響是以加法形式呈現(xiàn),協(xié)變量效應(yīng)直接刻畫了危險(xiǎn)率的絕對(duì)變化量。當(dāng)前對(duì)加法模型的研究還不是很多,且大多數(shù)研究針對(duì)右刪失數(shù)據(jù)或者獨(dú)立刪失機(jī)制下的區(qū)間刪失數(shù)據(jù)。本文討論了加法風(fēng)險(xiǎn)模型下相依區(qū)間刪失數(shù)據(jù)的半?yún)?shù)回歸問題,通過引入隱變量來刻畫失效時(shí)間與刪失時(shí)間兩者之間的相關(guān)關(guān)系,并采用極大似然方法對(duì)參數(shù)進(jìn)行估計(jì)。此外,本文還給出了估計(jì)量的漸近正態(tài)性的證明,并采用模擬試驗(yàn)來對(duì)文中算法的效果進(jìn)行評(píng)估,數(shù)值模擬結(jié)果顯示文中的估計(jì)算法是合理有效的。
[Abstract]:Interval censored data is a common and very important data type in survival analysis. Most of the existing researches on this kind of data assume independent deletion mechanism, that is to say, deletion time and event failure time are independent. However, this assumption is not always true in practical problems, and neglecting the dependence between censored time and event failure time may lead to bias or even error of the analysis results. Cox model (also called proportional risk model) has been used to study the censored data of dependent interval. In addition to the Cox model, the additive risk model is different from the Cox model. In the additive model, the influence of the covariable on the risk rate of the life variable is presented in the form of addition. The covariable effect directly characterizes the absolute variation of the risk rate. At present, there are not many researches on addition model, and most of the researches focus on right censored data or interval censored data under independent delete mechanism. In this paper, the semi-parametric regression problem of dependent interval censored data under additive risk model is discussed. Implicit variables are introduced to describe the correlation between failure time and censored time, and the maximum likelihood method is used to estimate the parameters. In addition, the asymptotic normality of the estimator is proved, and the effectiveness of the proposed algorithm is evaluated by simulation experiments. The numerical simulation results show that the proposed estimation algorithm is reasonable and effective.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

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本文編號(hào)：2423608