【摘要】：目前,生存分析中最常用的方法即COX比例風(fēng)險(xiǎn)模型,該模型在慢性流行病學(xué)研究中已有廣泛的應(yīng)用,而基于各種分布的參數(shù)型比例風(fēng)險(xiǎn)回歸模型在生物學(xué)、醫(yī)學(xué)、工程科學(xué)還有社會(huì)學(xué)、心理學(xué)、經(jīng)濟(jì)學(xué)、保險(xiǎn)精算學(xué)和可靠性等領(lǐng)域有重要的工具性作用。本文主要針對(duì)區(qū)間刪失兩種類型(區(qū)間刪失case I和區(qū)間刪失case II)的數(shù)據(jù),分別建立了廣義指數(shù)COX比例風(fēng)險(xiǎn)模型,給出了不同的模型估計(jì)方法。這里選取廣義指數(shù)分布,是因?yàn)樵摲植荚诤芏喾矫婺芎芎玫膹浹a(bǔ)韋布爾分布和伽馬分布的不足,針對(duì)危險(xiǎn)率函數(shù)具有很強(qiáng)的靈活性,可以適用很多類型的危險(xiǎn)率的數(shù)據(jù)進(jìn)行建模分析。當(dāng)然對(duì)于區(qū)間刪失時(shí)間數(shù)據(jù)也有相對(duì)較好的更靈活的分析效果,并且在壽命試驗(yàn)和可靠性研究等很多領(lǐng)域中都有著重要的應(yīng)用。重點(diǎn)從兩方面進(jìn)行創(chuàng)新性的研究,首先針對(duì)區(qū)間刪失II型數(shù)據(jù),基于廣義指數(shù)分布,建立了廣義指數(shù)比例風(fēng)險(xiǎn)回歸模型,由于數(shù)據(jù)的復(fù)雜性,模型的極大似然估計(jì)方法不能給出明顯的估計(jì)結(jié)果,應(yīng)用Newton-Rapson算法進(jìn)行比例風(fēng)險(xiǎn)回歸模型的參數(shù)估計(jì),通過(guò)設(shè)置各種情形的大量的模型研究,驗(yàn)證了所提出的模型及估計(jì)方法的有效性。并將此模型方法應(yīng)用到31名艾滋病患者參加的艾滋病治療臨床試驗(yàn)數(shù)據(jù)的分析中。其次針對(duì)區(qū)間刪失I型數(shù)據(jù)建立廣義指數(shù)分布的比例風(fēng)險(xiǎn)回歸模型,由于數(shù)據(jù)和似然函數(shù)的復(fù)雜性,故嘗試使用帶有先驗(yàn)信息的貝葉斯估計(jì)方法估計(jì),分層給出的各參數(shù)后驗(yàn)分布沒有顯示表達(dá)式,應(yīng)用了MCMC的各種算法進(jìn)行抽樣,得到參數(shù)的貝葉斯估計(jì)。并設(shè)計(jì)了大量的模擬實(shí)驗(yàn),驗(yàn)證了提出的模型和算法的有效性。并將此模型和貝葉斯估計(jì)算法應(yīng)用到實(shí)際數(shù)據(jù)是144只雄性RFM小鼠肺腫瘤的致瘤性實(shí)驗(yàn)數(shù)據(jù)的分析中。
[Abstract]:At present, COX proportional risk model, which is the most commonly used method in survival analysis, has been widely used in chronic epidemiology, while parametric proportional risk regression model based on various distributions has been applied in biology and medicine. Engineering science also plays an important instrumental role in sociology, psychology, economics, actuarial insurance and reliability. In this paper, the generalized exponential COX proportional risk model is established for two types of interval censored data (interval censored case I and interval-censored case II), and different estimation methods are given. The generalized exponential distribution is chosen here because it can make up for the deficiency of Weibull distribution and gamma distribution in many aspects. Many types of hazard rate data can be applied for modeling and analysis. Of course, the interval censored time data also has a relatively better and more flexible analysis results, and has important applications in many fields such as life test and reliability research. The innovative research is focused on two aspects. Firstly, based on generalized exponential distribution, a generalized exponential proportional risk regression model is established for interval-censored II data. Because of the complexity of the data, a generalized exponential proportional risk regression model is established. The maximum likelihood estimation method of the model can not give obvious estimation results. The Newton-Rapson algorithm is used to estimate the parameters of the proportional risk regression model. The validity of the proposed model and estimation method is verified. The model was applied to the analysis of clinical trial data of 31 AIDS patients. Secondly, the proportional risk regression model of generalized exponential distribution is established for interval censored I-type data. Because of the complexity of data and likelihood function, Bayesian estimation method with prior information is used to estimate the model. The posteriori distribution of each parameter given by stratification has not shown the expression. The Bayesian estimation of parameters is obtained by sampling by using various algorithms of MCMC. A large number of simulation experiments have been designed to verify the effectiveness of the proposed model and algorithm. The model and Bayesian estimation algorithm were used to analyze the tumorigenicity of lung tumors in 144 male RFM mice.
【學(xué)位授予單位】：長(zhǎng)春工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：C81

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 李麗賢;湯茗;曾彥彥;沈羅英;李釗洪;陳慧林;郭勝楠;陳金寶;侯雅文;陳征;;區(qū)間刪失生存數(shù)據(jù)的統(tǒng)計(jì)分析方法及其應(yīng)用[J];中國(guó)衛(wèi)生統(tǒng)計(jì);2016年03期

2 沈新娣;丁幫俊;;Pareto分布在逐步Ⅱ型區(qū)間刪失下的參數(shù)估計(jì)[J];應(yīng)用概率統(tǒng)計(jì);2016年02期

3 何朝兵;;左截?cái)嘤覄h失數(shù)據(jù)下伽瑪分布參數(shù)多變點(diǎn)的貝葉斯估計(jì)[J];四川師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2015年03期

4 鄧勇;;基于等長(zhǎng)區(qū)間刪失數(shù)據(jù)的指數(shù)分布參數(shù)估計(jì)研究[J];內(nèi)蒙古師范大學(xué)學(xué)報(bào)(自然科學(xué)漢文版);2015年02期

5 丁邦俊;;區(qū)間刪失情況下的Pareto分布估計(jì)(英文)[J];應(yīng)用概率統(tǒng)計(jì);2014年04期

6 苑延華;;廣義I型逐階區(qū)間刪失混合Weibull數(shù)據(jù)的參數(shù)估計(jì)[J];黑龍江科技大學(xué)學(xué)報(bào);2014年03期

7 徐永紅;高曉歡;王正熙;;含有右刪失和區(qū)間刪失數(shù)據(jù)的生存函數(shù)的非參數(shù)估計(jì)[J];生物醫(yī)學(xué)工程學(xué)雜志;2014年02期

8 萬(wàn)威;張子明;;Ⅰ型區(qū)間數(shù)據(jù)下參數(shù)的矩型估計(jì)[J];江西科學(xué);2012年03期

9 程從華;陳進(jìn)源;;區(qū)間刪失數(shù)據(jù)情形下GE分布參數(shù)的最大似然估計(jì)(英文)[J];蘭州大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年03期

10 ;Maximum Likelihood Estimator for the Proportional Hazards Model with Incomplete Information[J];Wuhan University Journal of Natural Sciences;2012年02期

，

本文編號(hào)：2259373