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系統識別號 U0002-2707201015255900
中文論文名稱 半母數迴歸模型對多變量區間設限資料分析
英文論文名稱 A Semiparametric Regression Model of Multivariate Interval-censored Data
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 98
學期 2
出版年 99
研究生中文姓名 林建宏
研究生英文姓名 Chien-Hung Lin
學號 697650389
學位類別 碩士
語文別 中文
口試日期 2010-06-29
論文頁數 51頁
口試委員 指導教授-陳蔓樺
委員-陳麗菁
委員-陳瓊梅
中文關鍵字 多變量區間設限  比例風險脆弱模型  EM演算法 
英文關鍵字 Multivariate interval-censored  Propotional hazard frailty model  EM algorithm 
學科別分類 學科別自然科學統計
中文摘要 右設限失效時間資料的分析方法在過去三十年間已發展的非常完善,隨著發展生物醫學研究,在醫療後續研究中一般所遇到的資料為區間設限資料,例如我們對病患定期調查或觀察,因此真實的失效時間也許未能準確觀察,我們只知道會在某些時間區間當中。
另一個在分析上所遇到的問題為多變量區間設限失效時間資料,我們所感興趣的失效時間不只一個,且每個失效時間中有相關性的存在。本篇論文考慮使用脆弱模型(frailty model)分析多變量區間設限失效時間資料,使用EM演算法(EM algorithm)估計其迴歸參數,並透過模擬驗證之。
英文摘要 A voluminous literature on right-censored failure time data has been developed very well in the pust 30 years. Due to advances in biomedical research, interval censoring has become common in medical follow-up studies. For example, each study subject is observed periodically, thus the observed failure time falls into a time period.
Another problems is multivariate interval-censored failure time data. Multivariate failure time data occur when one is interested in several related failure times. This thesis considers regression analysis of multivariate interval-censored failure time data using by the random effect
approach. For estimation, an Expectation Maximization (EM) algorithm is developed and simulation studies suggest that the frailty model approach.
論文目次 目錄
第一章序論.................................................1
第一節失效時間..........................................3
1.1.1 急性白血病臨床試驗............................3
第二節區間設限失效時間..................................5
1.2.1 肺癌動物實驗(型一區間設限)....................5
1.2.2 乳癌研究(型二區間設限)........................6
第三節使用迴歸模型分析失效時間..........................8
1.3.1 比例風險模型.................................11
1.3.2 比例勝算模型.................................12
1.3.3 可加性風險模型...............................13
1.3.4 脆弱模型.....................................13
第四節迴歸分析多變量區間設限失效時間資料...............14
1.4.1 多變量失效時間資料...........................14
1.4.2 邊際模型.....................................14
1.4.3 脆弱模型.....................................15
第五節論文大綱.........................................16
第二章模式建立與假設......................................17
第一節模式建立: 脆弱模型...............................17
第二節基底風險函數的估計...............................19
第三節EM演算法(Expectation-maximization Algorithm).....20
2.3.1 EM演算法推導.................................20
2.3.2 EM演算法的收斂性.............................25
第三章參數估計............................................26
第一節E-step...........................................26
第二節M-step...........................................29
第三節Fisher InformationMatrix.........................32
第四章模擬分析............................................34
第一節生成資料.........................................34
第二節模擬結果.........................................35
第五章結論................................................39
附錄...................................................41
參考文獻...............................................49
表目錄
1.1 急性白血病臨床試驗資料..............................4
1.2 老鼠死亡時間........................................6
1.3 乳癌病患乳房外貌惡化攣縮時間........................7
4.1 Estimates of parameter with ρ =0.5, n = 100.......36
4.2 Estimates of parameter with ρ = 0.5, n = 200......37
附錄1 Shapiro-Wilk test with ρ = 0.25, n = 100 .......41
附錄2 Estimates of parameter with ρ = 0.25, n = 100...42
附錄3 Shapiro-Wilk test with ρ = 0.25, n = 200........43
附錄4 Estimates of parameter with ρ = 0.25, n = 200...44
附錄5 ACTG181資料(1)..................................45
附錄6 ACTG181資料(2)..................................46
附錄7 ACTG181資料(3)..................................47
附錄8 ACTG181資料(4)..................................48
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林建甫(2008) 。存活分析。雙葉書廊, 台北。
許靖涵博士。生醫影像專題系列: EM 演算法
http://mx.nthu.edu.tw/~cghsu/EMAlgorithm.pdf
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