半競爭風險資料下估計非終端事件時間之存活函數

Estimating the survival function of the non-terminal event time under semi-competing risks data

許家豪(Chia-Hao Hsu)

指導教授 ： 謝進見

國立中正大學/理學院/數學系統計科學研究所/碩士(2014年)

摘要

本篇論文探討半競爭風險資料下非終端事件時間之存活函數的估計。在沒有額外假設下我們無法對非終端事件進行推論，因為非終端事件受到終端事件的相關設限影響，因此我們利用Archimedean copula 模型說明非終端事件和終端事件的相依關係。
在Archimedean copula 假設下，我們利用重新分配的方法去估計存活函數並與Lakhal et al. (2008) 提到的方法去做比較。根據模擬實驗重新分配方法的表現略佳於Lakhal et al. (2008) 使用的方法，我們也應用我們的方法去分析一筆骨髓移植的資料。

關鍵字: Archimedean copula 模型; 相關設限; 半競爭風險資料; 重新分配。

關鍵字

半競爭風險資料 ； 存活函數

並列摘要

This thesis focuses on estimating the survival function of the nonterminal event time for semi-compting risks data. Without extra assumptions, we can not make inference on the non-terminal event time because the terminal event time dependently censores the nonterminal event time. Thus, we utilize the Archimedean copula model to specify the dependency between the non-terminal event time and the terminal event time.
Under the Archimedean copula assumption, we apply the redistribution method to estimate the survival function of the non-terminal event time and compare it with the method introduced by Lakhal et al. (2008). According to the simulation studies, the performance of the redistribution method is slightly better than the method of Lakhal et al. (2008). We also apply our suggested approach to analyze the Bone Marrow Transplant data.

Keywords: Archimedean Copula model; Dependent censoring; Semicompeting risks data; Redistribution method.

並列關鍵字

Semi-competing risks data ； Survival function

參考文獻

markers as prognostic indicators. Biometrics 84, 45-56.

[2] Efron, B. (1967). The two sample problem with censored data. Proceedings

of the Fifth Berkeley Symposium on Mathematical Statistics

[3] Fine, J. P., Jiang, H., and Chappel, R. (2001). On semicompeting

risks. Biometrika. 99, 907-919