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Student Number 942205009 Author Xin-ru Kao(高欣如) Author's Email Address No Public. Statistics This thesis had been viewed 2011 times. Download 3503 times. Department Graduate Institute of Statistics Year 2008 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title Discussion on Cox Proportional Hazards Assumption and Application of Extended Hazard Model Date of Defense 2009-05-25 Page Count 50 Keyword Cox proportional hazards model Extended hazard model Longitudinal data Proportional hazards assumption Schoenfeld residual Abstract The Cox proportional hazards model has been widely used to describe the relationship between survival information and covariates. The validity to apply the Cox model for data is usually based on checking the proportional hazards assumption. It’s an interesting problem to investigate whether checking this assumption is sufficient as an evidence to fit data with the Cox model. On the other hand, when proportional hazards assumption fails, the Accelerated Failure Time (AFT) model is a popular alternative to the Cox model. However, when data include time-dependent covariates there are no convenient tools to check if AFT is appropriate for the data. An general class model termed “extended hazard model”, which contains the Cox and AFT models as its special case may be helpful to study the above problems. Because under the nested structure, we may test the fit of Cox and AFT models for data. Finally, we demonstrate the new model through a case study of Taiwanese HIV/AIDS cohort data. Table of Content 摘要 i

Abstract ii

誌謝辭 iii

目錄 v

圖目錄 vii

表目錄 viii

第一章緒論 1

1.1 研究背景及動機. . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 本文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

第二章統計方法 10

2.1 線性混合隨機效應模型. . . . . . . . . . . . . . . . . . . . . 11

2.2 Cox 比例風險模型. . . . . . . . . . . . . . . . . . . . . . . 12

2.3 加速失敗時間模型. . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 擴充風險模型. . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Schoenfeld 殘差. . . . . . . . . . . . . . . . . . . . . . . . 16

第三章統計模擬 19

3.1 模擬方法. . . . . . . . . . . . . . . . . . . . . . . . . . . .20

3.2 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . .23

第四章實例研究 25

4.1 台灣愛滋病病患資料與背景. . . . . . . . . . . . . . . . . . . 26

4.2 實例分析. . . . . . . . . . . . . . . . . . . . . . . . . . . .29

第五章結論與討論 34

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942205009.pdf Date of Submission 2009-06-25

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