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研究生:楊幼君
研究生(外文):You-Jun Yang
論文名稱:不同抽樣限制下條件存活函數之無母數平滑估計
論文名稱(外文):Nonparametric smooth estimation of conditional survival functions under various sampling schemes
指導教授:鄭明燕鄭明燕引用關係
指導教授(外文):Ming-Yen Cheng
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:27
中文關鍵詞:無母數估計非獨立截切條件存活分佈平滑估計設限截切
外文關鍵詞:Conditional survival distributionNonparametric estimationDependent truncationTruncationSmooth estimationCensoring
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  • 被引用被引用:1
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  • 收藏至我的研究室書目清單書目收藏:0
在釵h追蹤研究中,存活資料常以橫斷面抽樣方法收集,而此種抽樣方法常受制於蒐集條件或抽樣限制,而造成資料上的設限或截切。例如:研究個體因種種原因失去追蹤而造成資料上的設限,或因只能收集已發生起始事件而尚未進展至終止事件的個體,無法觀察到母體中不合如此抽樣條件的個體,因而造成資料上的截切。在此我們考慮存活時間之分佈和起始事件之發生時間相關的右設限和左截切資料。當存活時間和起始事件到設限或截切之時段為獨立時,Kaplan-Meier 估計量為非參數假設下之最大概似估計量。但上述性質在存活時間之分佈和起始事件之發生時間有關時可能不成立。在此我們應用廣義 Kaplan-Meier 估計量的想法來估計給定起始事件時間下之條件存活函數,並且使用 kernel 平滑方法以得到平滑估計量。最後給予其理論及模擬上的探討。
In many follow-up studies, survival data are often collected by a cross-sectional sampling scheme. Such sampling schemes causes censoring or truncation in the data. We consider the case that the survival time distribution depends on the occurrence time of the initiating event in right-censored data and left-truncated data. When the survival time distribution does not depend on the censoring period of time or the truncation period of time, the Kaplan-Meier estimator is the nonparametric MLE for the censored data or truncated data, respectively. But this may not true if the survival time distribution depends on the initiating time. Here we construct a generalized Kaplan-Meier estimator to estimate the conditional survival function of the survival time given the initiating time, and then kernel smooth it with respect to the survival time to obtain a smooth estimator. Theoretical and numerical justifications are given.
Table of Contents iv
Abstract v
Abstract (in Chinese) vi
Acknowledgements vii
1 Introduction 1
2 Nonparametric Estimation of Survival Function 3
2.1 Kaplan-Meier Estimator for Right-Censored Data .... 3
2.2 Kaplan-Meier Estimator for Left-Truncated Data .... 4
3 Nonparametric Estimation of Conditional Survival Function 7
3.1 Generalized Kaplan-Meier Estimator for Right-Censored Data with Covariates ........................... 7
3.2 Generalized Kaplan-Meier Estimator for Right-Censored Data Conditional on Initiating Time ..................... 9
3.3 Generalized Kaplan-Meier Estimator for Left-Truncated Data Conditional on Initiating Time .................... 15
4 Simulation 22
5 Discussion 25
Bibliography 26
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