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系統識別號 U0026-0802201013432600
論文名稱(中文) 集群現時狀態資料之迴歸分析方法
論文名稱(英文) Regression analysis for clustered current status data based on additive hazards models
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 98
學期 1
出版年 99
研究生(中文) 蘇佩芳
研究生(英文) Pei-Fang Su
學號 r2890101
學位類別 博士
語文別 英文
論文頁數 60頁
口試委員 指導教授-嵇允嬋
口試委員-蔡偉彥
口試委員-陳玉英
口試委員-任眉眉
口試委員-溫敏杰
口試委員-陳珍信
中文關鍵字 現時狀態資料  估計函數  線性風險模式  評分函數 
英文關鍵字 current status data  estimating function  additive hazards model  scoring function 
學科別分類
中文摘要 在動物毒物實驗、生物醫學、計量經濟學及社會學的研究中,往往受限於資料蒐集方式,而會獲得現時狀態的資料 (current status data)。在現時狀態資料中,真正的存活時間是觀測不到的,所獲得的資訊僅有存活時間的發生是在調查的時間之前或之後。針對現時狀態資料,當觀測值間彼此獨立,用無母數最大概似估計法所得的存活函數其收斂速度只有 ,而且收斂到複雜的極限分配。相對而言,半參數迴歸模式或線性迴歸模式的係數估計則較為簡單且其收斂速度較快能達到 。
然而,針對有集群存在的現時狀態資料 (clustered current status data),直接應用分析獨立現時狀態資料的統計方法是不適當的。在線性風險模式 (additive hazards model) 之下,本論文針對集群現時狀態資料,提出邊際方法建構估計函數 (estimating function) 來估計迴歸係數。當邊際存活時間來自於線性風險模式,可以用Lin et al. (1998) 所提出的偏評分函數 (partial score function) 以及Martinussen and Scheike (2002) 所提出的有效評分函數 (efficient score function) 來做為估計函數,但這些估計量的理論特性必須探討。本論文推導出這些估計量的漸近分配,以利進行正確的統計推論。
英文摘要 Current status data arise naturally from tumorigenicity experiment, biomedicine, econometrics, demographic and sociology studies. Moreover, clustered current status data often occur when animals are from same litter in tumorigenicity experiments. The only information extracted from current status data is that the true survival times are before or after the monitoring times. Consequently, the nonparametric maximum likelihood estimator of survival function converges at rate to a complicated limiting distribution (Groeneboon and Wellner, 1992). Hence, semiparametric regression and linear regression have been extended for independent current status data to estimate the survival functions whose rate converge at .
However, a straightforward application of these statistical methods to clustered current status data is not appropriate. Therefore, marginal approaches are applied in this dissertation to construct estimating functions for deriving the estimators of regression parameters in additive hazards models with clustered current status data. When the marginal survival times follow an additive hazards model, it is natural to use the partial score function derived by Lin et al. (1998) and the efficient score function derived by Martinussen and Scheike (2002) as estimating functions. Then, the asymptotic properties of the estimators of regression parameters in additive hazards models obtained by marginal approaches will be investigated. The implementation of the methods is illustrated through one dataset.
論文目次 CHAPTER 1 INTRODUCTION 1
1.1 Overview 1
1.2 Studies with current status data 2
CHAPTER 2 REGRESSION PARAMETER ESTIMATION IN ADDITIVE HAZARDS MODELS WITH INDEPENDENT CURRENT STATUS DATA 5
2.1 The partial score functions 5
2.1.1 Independent monitoring situation 5
2.1.2 Dependent monitoring situation 9
2.2 The efficient score functions 11
2.2.1 Independent monitoring situation 11
2.2.2 Dependent monitoring situation 13
CHAPTER 3 REGRESSION PARAMETER ESTIMATION IN ADDITIVE HAZARDS MODELS WITH CLUSTERED CURRENT STATUS DATA 16
3.1 LOY type estimating function for independent monitoring situation 17
3.1.1 Preliminary 17
3.1.2 The asymptotic distribution of U_CL 18
3.1.3 The asymptotic distribution of beta_CL 21
3.2 MS type estimating function for independent monitoring situation 22
3.2.1 Preliminary 22
3.2.2 The asymptotic distribution of U_CE 23
3.2.3 The asymptotic distribution of beta_CE 27
3.3 MS type estimating function for dependent monitoring situation 27
3.3.1 Preliminary 27
3.3.2 The asymptotic distribution of U_DCE 28
3.3.3 The asymptotic distribution of beta_DCE 31
CHAPTER 4 NUMERICAL RESULTS 33
4.1 Estimation under independent monitoring situation 33
4.1.1 Simulation setting 33
4.1.2 Simulation results 35
4.2 Power comparison under independent monitoring situation 37
4.2.1 Simulation setting 37
4.2.2 Power comparison 37
4.3 Estimation under dependent monitoring situation 40
CHAPTER 5 AN EXAMPLE 42
CHAPTER 6 CONCLUSION AND FUTURE RESEARCH 44
6.1. Conclusion 44
6.1. Future research 44
APPENDIX 47
A. The regularity conditions 47
B. The result in Ying and Wei and its application 48
C. Proof of the asymptotic properties of LOY type estimating function 51
D. The asymptotic distribution of beta_CL 53
E. The expectation of 54
F. Proof of the asymptotic properties of MS type estimating function 56
G. The kernel density estimator 57
References 58

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