系統識別號 | U0002-2707201015255900 |
---|---|
DOI | 10.6846/TKU.2010.01005 |
論文名稱(中文) | 半母數迴歸模型對多變量區間設限資料分析 |
論文名稱(英文) | A Semiparametric Regression Model of Multivariate Interval-censored Data |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 統計學系碩士班 |
系所名稱(英文) | Department of Statistics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 98 |
學期 | 2 |
出版年 | 99 |
研究生(中文) | 林建宏 |
研究生(英文) | Chien-Hung Lin |
學號 | 697650389 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
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 |
關鍵字(中) |
多變量區間設限 比例風險脆弱模型 EM演算法 |
關鍵字(英) |
Multivariate interval-censored Propotional hazard frailty model EM algorithm |
第三語言關鍵字 | |
學科別分類 | |
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. |
第三語言摘要 | |
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 |
參考文獻 |
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