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。

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.

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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