【摘要】：在諸如社會(huì)學(xué)、醫(yī)療、工業(yè)技術(shù)、經(jīng)濟(jì)學(xué)和流行病學(xué)等領(lǐng)域的時(shí)間數(shù)據(jù)的研究中,考慮到,部分研究對(duì)象其實(shí)際的失效時(shí)間可能超出觀測(cè)時(shí)間的上限,為成本計(jì),人們通常會(huì)采用刪失的方法進(jìn)行處理。這會(huì)造成刪失數(shù)據(jù)的存在。如何處理和分析刪失數(shù)據(jù)是失效時(shí)間數(shù)據(jù)分析中的主要內(nèi)容。關(guān)于右刪失數(shù)據(jù)(T,?)的研究,大多數(shù)都是基于獨(dú)立刪失(Independent censoring or Non-informative censoring)假定進(jìn)行的,即失效時(shí)間和刪失時(shí)間相互獨(dú)立。但是在很多實(shí)際問(wèn)題中,這種獨(dú)立假設(shè)常常不成立。因此相依刪失的研究十分必要。在相依刪失數(shù)據(jù)下,必須對(duì)刪失時(shí)間和失效時(shí)間的相依關(guān)系進(jìn)行描述。假定刪失時(shí)間和失效時(shí)間的相依關(guān)系可以由一個(gè)copula函數(shù)表示。失效時(shí)間和刪失時(shí)間的聯(lián)合分布可以表示為它們邊際分布的copula函數(shù),通過(guò)對(duì)這個(gè)聯(lián)合分布函數(shù)進(jìn)行討論,可以對(duì)于不同模型進(jìn)行統(tǒng)計(jì)推斷。本文主要對(duì)相依右刪失數(shù)據(jù)進(jìn)行了討論。本文主要基于兩種模型進(jìn)行研究:指數(shù)分布模型、cox比例風(fēng)險(xiǎn)模型。基于失效時(shí)間變量和刪失時(shí)間變量的copula模型采用截面似然(profile likelihood)的辦法構(gòu)造似然函數(shù),利用迭代計(jì)算的方法對(duì)似然函數(shù)進(jìn)行求解。同時(shí)為了說(shuō)明方法的有效性,本文還對(duì)copula函數(shù)和copula函數(shù)中的參數(shù)進(jìn)行敏感性分析。模擬計(jì)算結(jié)果顯示,統(tǒng)計(jì)推斷的結(jié)果關(guān)于copula函數(shù)比較穩(wěn)健,但是對(duì)于copula函數(shù)中的參數(shù)十分敏感。
[Abstract]:In the study of time data in areas such as sociology, medicine, industrial technology, economics and epidemiology, it was considered that some of the subjects' actual failure times might exceed the upper limit of the observed time and be costing. People usually use censored methods to deal with it. This results in the existence of censored data. How to deal with and analyze censored data is the main content of failure time data analysis. On right censored data Most of the researches in this paper are based on the assumption of independent censored (Independent censoring or Non-informative censoring, that is, the time of failure and the time of deletion are independent of each other. But in many practical problems, this independent assumption is often not true. Therefore, the study of dependent deletion is very necessary. Under the dependent censored data, we must describe the dependent relationship between the deletion time and the failure time. It is assumed that the dependence of the deletion time and the failure time can be represented by a copula function. The joint distribution of failure time and censored time can be expressed as the copula function of their marginal distribution. In this paper, we mainly discuss the right censored data. This paper is mainly based on two models: exponential distribution model and cox proportional risk model. The copula model based on the failure time variable and the censored time variable uses the cross-section likelihood (profile likelihood) method to construct the likelihood function, and the iterative calculation method is used to solve the likelihood function. In order to illustrate the validity of the method, the sensitivity of the parameters in copula function and copula function is also analyzed. The simulation results show that the result of statistical inference is robust for copula function, but sensitive to the parameters in copula function.
【學(xué)位授予單位】：江西師范大學(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)：2407721