系統識別號 | U0002-2807201013420700 |
---|---|
DOI | 10.6846/TKU.2010.01057 |
論文名稱(中文) | 以隨機效應模型分析區間設限下的多變量存活資料 |
論文名稱(英文) | A flexible model approach for regression analysis 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) | 林坤宏 |
研究生(英文) | Kuen-Hung Lin |
學號 | 697650447 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
口試日期 | 2010-06-29 |
論文頁數 | 81頁 |
口試委員 |
指導教授
-
陳蔓樺
委員 - 李百靈 委員 - 陳瓊梅 |
關鍵字(中) |
EM演算法 脆弱模型 區間設限 最大概似法 多變量失效時間資料 |
關鍵字(英) |
EM algorithm frailty model interval censoring maximum-likelihood estimate multivariate failure time data |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
過去已經有許多學者,在考慮每一個併發症之間彼此獨立下,對於回歸分析應用在多變量區間設限型的資料上,提出相關的邊際模型進行討論。 然而這些模型有著無法探討併發症之間相關性的問題,因此近來學者 |
英文摘要 |
For regression analysis of multivariate interval-censored data, several authors proposed some marginal model approaches, which modeled each time of interest individually. For the problem, those models does not allow for inference about the relationship or association between correlated failure times. The frailty model approach has been commonly used in the analysis of multivariate failure time data and it provides a flexible approach for directly modeling the relationship between correlated failure times. In the thesis, we present a full likelihood approach based on the proportional hazard frailty model and estimate of regression parameters by Expectation Maximization (EM) algorithm. The method is applied to a set of bivariate interval-censored data arising from an AIDS clinical trial. |
第三語言摘要 | |
論文目次 |
Contents Chapter 1 Introduction .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1 1.1 Survival Analysis .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2 1.2 Censored Data.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4 1.3 Terminology and Notation .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 6 1.4 Concepts and Some Regression Models .. .. .. .. .. .. .. .. 9 Chapter 2 Model and Assumptions .. .. .. .. .. .. .. .. .. .. .. .. 11 2.1 Types of Interval-censored Analysis .. .. .. .. .. .. .. .. .. .. 12 2.2 The Proportinal Hazards Model .. .. .. .. .. .. .. .. .. .. .. .. 16 2.3 The Proportional Hazards Frailty Model.. .. .. .. .. .. .. 20 Chapter 3 Parameter Estimation .... .. .. .. .. .. .. .. .. .. .. .. .. 23 3.1 Expectation-maximization Algorithm.. .. .. .. .. .. .. .. .. 24 3.2 E-step .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 28 3.3 M-step .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 32 3.4 Estimative Procedure .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 35 Chapter 4 Application .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .... .. .. .. .. 40 4.1 Source of Data .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 41 4.2 Fundamental Analysis .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 45 4.3 Turnbull’s Algorithm.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 47 4.4 Result of Analysis .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 58 Chpater 5 Conclusion.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 62 5.1 Baseline Hazard Function .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 63 5.2 Future Work .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 68 Appendix I Fisher Information Matrix .. .. .. .. .. .. .. .. .. .. 71 Appendix II ACTG181.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .... .. .. .. 74 Reference .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .... .. .. .. .. .. .. .. 75 List of Tables 2.1 Summary of Case I and Case II Interval-censoring . 15 4.1 Number of Censored Patients and Censored Status 43 4.2 Numerical Check Difference Between Turnbull and KM for Blood . . . . . . . . . . . . . . . . . . . . . . . 52 4.3 Numerical Check Difference Between Turnbull and KM for Blood . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 Numerical Check Difference Between Turnbull and KM for Urine . . . . . . . . . . . . . . . . . . . . . . . . 53 4.5 Numerical Check Difference Between Turnbull and KM for Urine . . . . . . . . . . . . . . . . . . . . . . . . 53 4.6 Observe Time and Estimate Survival Function under Turnbull Method . . . . . . . . . . . . . . . . . . . 57 4.7 Proportional Hazards Model . . . . . . . . . . . . . . 59 4.8 Hazard Ratio . . . . . . . . . . . . . . . . . . . . . . . . 59 4.9 Wald test: H0 : = 0 v.s H1 : 6= 0 . . . . . . . . . . . . 60 4.10Marginal Proportional Hazards Model . . . . . . . . 61 List of Figures 3.1 The idea of algorithm . . . . . . . . . . . . . . . . . . . 35 4.1 Number of Patients in Each Type of Censoring . . . 45 4.2 (a)Pie Chart of Blood Sample. (b)Pie Chart of Urine Sample . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Estimates of Baseline Survival Functions for Blood under Turnbull Method . . . . . . . . . . . . . . . . . 49 4.4 Estimates of Baseline Survival Functions for Urine under Turnbull Method . . . . . . . . . . . . . . . . . 50 4.5 Estimates of Baseline Survival Functions for Blood Comparing with Turnbull and KM . . . . . . . . . . 51 4.6 Estimates of Baseline Survival Functions for Urine Comparing with Turnbull and KM . . . . . . . . . . 51 4.7 Estimates of Baseline Survival Functions for Blood and Urine under Turnbull Method . . . . . . . . . . . 55 5.1 The Relationship of Failure Time . . . . . . . . . . . 64 |
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