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研究生:謝進見
論文名稱:半競爭風險下雙樣本之比較
論文名稱(外文):Two-Sample Comparison under Semi-comprting Risks
指導教授:王維菁王維菁引用關係
指導教授(外文):Weijing Wang
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:48
中文關鍵詞:加速時間模型相關設限位置平移模型多重階段模型不可辨識性半競爭風險
外文關鍵詞:accelerated failure time modeldependent censoringlocation-shift modelmulti-state modelnon-identifiabilitysemi-competing risks
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半競爭風險下雙樣本之比較
謝進見、王維菁
交通大學統計學研究所
摘要
本論文考慮多重階段模型“中介階段變數”之雙樣本比較。這種資料型態受制於相關設限, Fine et al. (2001) 將其稱之為半競爭風險資料 (semi- competing risks data)。過去 Lin et al. (1996) 和 Chang (2000) 分別假設 location-shift model 和 accelerated failure time model,並提出估計 “群體差異” 參數之估計函數。雖然此兩種方法均不需要給定相關設限變數與感興趣變數間的關聯性結構,卻假設了兩個樣本之關聯性結構為相同。我們認為這樣的假設有時候不盡合理。基於這樣的動機,我們提出在三種常見的群體差異模式下,參數估計的推論方法。此方法可以允許兩個樣本擁有不同的關聯結構。在論文中我們以 copula models 作為推導的例子。我們的目的並非取代過去的兩種方法,而是當研究者懷疑兩個樣本的關聯性可能不同時,我們的方法可提供更具彈性的選擇。

Abstract
In the thesis we consider two-sample comparison based on “time to progression under dependent censoring. The data structure considered here is called “semi-competing risks data” by Fine et al. (2001). The problems of dependent competing risks and non-identifiability complicate statistical inference. Lin et al. (1996) and Chang (2000) propose estimating equations for estimating the group effect parameters based on the location-shift model and accelerated failure time model, respectively. Although these two methods do not specify the joint distribution between the variable of interest and the dependent censoring variable, they both make an implicit assumption that the dependence structure is the same for the two groups. However, we feel that such an assumption may not be reasonable in some practical situations.
In our proposal, we allow the dependent relationship to be different in the two groups. The price of such flexibility is that we need to specify the form of dependence. Here in the thesis, we use copula models to illustrate our ideas. Three group-effect models are considered, namely the Cox model, the location-shift model and the accelerated lifetime model respectively. In simulations, we find that the proposed inference procedures are robust even when the dependence structure is mis-specified.

Table of Content
Chapter 1: Introduction ………………………………………….…. 1
1-1 Background ………………………….… ……………. 1
1-2 Literature review … …………………………….……. 2
1-2-1: The paper by Lin , Robins and Wei ….….. 2
1-2-2: The paper by Chang … ……………………………..… 4
1-3 Discussion ………………………………………… 5
Chapter 2: The Main Ideas …………………………………….…… 6
Chapter 3: The Proposed Inference Procedures ….…………….. 8
3-1: Estimating nuisance parameters … ……..…... 10
3-2: Estimating for the Group-Difference Parameter 16
3-3: Large sample properties …………………………..18
Chapter 4: Simulation Study … …………………………..…….. 22
Chapter 5: Data Analysis …………………………….…………... 28
Chapter 6: Conclusion …………………………………………….. 32
References ……………………………………………………….……. 33
Appendix ………………………………………………………….…... 34

References
Genest, C. and Mackay, J. (1986). The Joy of Copulas: Bivariate Distributions With Uniform Marginals. The American Statistician, vol. 40, No. 4.
Genest, C. (1987). Frank’s Family of Bivariate Distributions. Biometrika, 74, 3, 549-555.
Genest, C. and Rivest L. P. (1993). Statistical Inference Procedures for Bivariate Archimedean Copulas. Journal of the American Statistical Association, vol. 88, No. 423.
Oakes, D. (1989). Bivariate Survival Models Induced by Frailties. Journal of the American Statistical Association. Vol. 84, No. 406.
Lin, D. Y., Robins, J. M. and Wei, L. J. (1996). Comparing Two Failure Time Distribution in The Presence of Dependent Censoring. Biometrika, 83, 2, 381-393.
Fine, J. P., Jiang, H. and Chappell, R. (2001). On Semi-Competing Risks Data. Biometrika, 88, 4, 907-919.
Prentice, R. L. and Cai, J. (1992). Covariance and Survivor Function Estimation Using Censored Multivariate Failure Time Data. Biometrika, 79, 3, 495-512.
Day, R., Bryant, J. and Lefkopoulou, M. (1997). Adaptation of Bivariate Frailty Models for Prediction, with Application to Biological Markers as Prognostic Indicators. Biometrika, 84, 45-56.
Chang, S. H. (2000). A Two-Sample Comparison for Multiple Ordered Event Data. Biometrics, 56, 183-189.
Wang, W. and Wells, M. T. (2000). Model Selection and Semiparametric Inference for Bivariate Failure-Time Data. Journal of the American Statistical Association. Vol. 95, No. 449.
Wang (2002). Estimating the Association Parameter for Copula Models under Dependent Censoring. Under revise by JRSSB.

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