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題名 設限與截斷資料Weibull模式之研究
A Weibull-based proportional hazards model for arbitrarily censored and truncated data
作者 黃偉傑
Huang, Wei-Jie
貢獻者 陳麗霞
Chen, Li-Shya
黃偉傑
Huang, Wei-Jie
關鍵詞 成比例危險迴歸模式
設限
截斷
中點估計
Proportional hazards regression model
Censoring
Truncation
Midpoint estimation
日期 2000
上傳時間 31-Mar-2016 14:44:56 (UTC+8)
摘要 成比例危險迴歸模式常被用於分析存活資料，Weibull模式更是其中惟一兼具加速失敗特性者。本論文將利用兩種分析方法，以研究任意設限及截斷資料的Weibull迴歸模式。第一種方法是利用最大概似估計法求算設限及截斷資料下的參數估計值（MLE），第二種方法則是對左設限及區間設限分別以所在區間之中點代入，稱其為中點估計法，再求算模式中的參數估計值（MDE）。並對此兩種估計方法進行比較。模擬結果顯示，相當地大樣本之下，最大概似估計法在許多情況均優於中點估計法；而在樣本少、危險率為平穩或接近平穩且區間設限比率約為0.5時，中點估計法是可被推薦的。而且，本論文亦提出對設限及截斷資料的Weibull模式之適合度檢驗程序。
The proportional hazards regression model is most commonly used model for lifetime data. The Weibull model is the only parametric model which has both a proportional hazards representation and an accelerated failure-time representation. This paper studies the use of a Weibull-based proportional hazards regression model when any censored and truncated data are observed. Two alternative methods of analysis are considered. First, the maximum likelihood estimates（MLEs） of parameters are computed for the observed censoring and truncation pattern. Second, the estimates where midpoints are substituted for left- and interval-censored data（midpoint estimation, MDE）are computed. Then, MLEs are compared with MDEs. Simulation studies indicate that for relative large samples there are many instances when the MLE is superior to the MDE. For small samples where the hazard rate is flat or nearly so, and the percentage of interval-censored data is nearly half of samples, the MDE is adequate. Also, an evaluation of the adequacy of the Weibull model for any censored and truncated data is proposed.
參考文獻 [1]Alioum, A., and Commenges, D. (1996). “A proportional hazards model for arbitrarily censored and truncated data”, Biometrics, vol. 52, p.512-524.
[2]Barlow, W, E and Prentice, R. (1988). “Residuals for relative risk regression”, Biometrika, vol. 75, p.65-74.
[3]Brookmeyer, R., and Goedert, J. J. (1989). “Censoring in an epidemic with an application to hemophilia-associated AIDS”, Biometrics, vol. 45, p.325-335.
[4]Cox, D. R. (1972). “Regression model and life tables (with discussion)”, Journal of the Royal Statistical Society, Series B, vol. 39, p. 1-38.
[5]Crowley, J. and Hu, M. (1977). “Covariance analysis of heart transplant survival data”, Journal of the American Statistical Association, vol. 73, p.27-36.
[6]Finkelstein, D. M. (1986). “A proportional hazards model for interval-censored failure time data”, Biometrics, vol. 42, p.845-854.
[7]Finkelstein, D. M., Moore, D. F., and Schoenfeld, D. A. (1993). “A proportional hazards model for truncated AIDS data”, Biometrics, vol. 49, p.731-740.
[8]Flygare, M. E., Austin, J. A., and Buckwalter, R. M. (1985). “Maximum likelihood estimation for the 2-parameter Weibull distribution based on interval-data”, IEEE transactions on reliability, vol. 34, p.57-59.
[9]Frydman, H.(1994). “A note on nonparametric estimation of the distribution function from interval-censored and truncated observations”, Journal of the Royal Statistical Society, Series B, vol. 56, p.71-74.
[10]Gentleman, R., and Geyer, C. J. (1994). “Maximun likelihood for interval censored data: consistency and computation”, Biometrika, vol. 81, p.618-623.
[11]Klein, J. P., and Moeschberger, M. L. (1997). Survival Analysis. New York: Springer-Verlag.
[12]Odell, P. M., Anderson, K. M., and D’Agostino, R. B. (1992). “Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model”, Biometrics, vol. 48, p.951-959.
[13]Pan, W., and Chappell, R. (1998). “Computation of the NPMLE of distribution functions for interval censored and truncated data with applications to the Cox model”, Computational Statistics & Data Analysis, vol. 28, p.33-50.
[14]Peto, R. (1973). “Experimental survival curves for interval-censored data”, Applied Statistics, vol. 22, p.86-91.
[15]Turnbull, B. W. (1976). “The empirical distribution function with arbitrary grouped, censored and truncated data”, Journal of the Royal Statistical Society, Series B, vol. 38, p.290-295.
描述 碩士
國立政治大學
統計學系
87354002
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001945
資料類型 thesis
dc.contributor.advisor 陳麗霞zh_TW
dc.contributor.advisor Chen, Li-Shyaen_US
dc.contributor.author (Authors) 黃偉傑zh_TW
dc.contributor.author (Authors) Huang, Wei-Jieen_US
dc.creator (作者) 黃偉傑zh_TW
dc.creator (作者) Huang, Wei-Jieen_US
dc.date (日期) 2000en_US
dc.date.accessioned 31-Mar-2016 14:44:56 (UTC+8)-
dc.date.available 31-Mar-2016 14:44:56 (UTC+8)-
dc.date.issued (上傳時間) 31-Mar-2016 14:44:56 (UTC+8)-
dc.identifier (Other Identifiers) A2002001945en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83251-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 87354002zh_TW
dc.description.abstract (摘要) 成比例危險迴歸模式常被用於分析存活資料，Weibull模式更是其中惟一兼具加速失敗特性者。本論文將利用兩種分析方法，以研究任意設限及截斷資料的Weibull迴歸模式。第一種方法是利用最大概似估計法求算設限及截斷資料下的參數估計值（MLE），第二種方法則是對左設限及區間設限分別以所在區間之中點代入，稱其為中點估計法，再求算模式中的參數估計值（MDE）。並對此兩種估計方法進行比較。模擬結果顯示，相當地大樣本之下，最大概似估計法在許多情況均優於中點估計法；而在樣本少、危險率為平穩或接近平穩且區間設限比率約為0.5時，中點估計法是可被推薦的。而且，本論文亦提出對設限及截斷資料的Weibull模式之適合度檢驗程序。zh_TW
dc.description.abstract (摘要) The proportional hazards regression model is most commonly used model for lifetime data. The Weibull model is the only parametric model which has both a proportional hazards representation and an accelerated failure-time representation. This paper studies the use of a Weibull-based proportional hazards regression model when any censored and truncated data are observed. Two alternative methods of analysis are considered. First, the maximum likelihood estimates（MLEs） of parameters are computed for the observed censoring and truncation pattern. Second, the estimates where midpoints are substituted for left- and interval-censored data（midpoint estimation, MDE）are computed. Then, MLEs are compared with MDEs. Simulation studies indicate that for relative large samples there are many instances when the MLE is superior to the MDE. For small samples where the hazard rate is flat or nearly so, and the percentage of interval-censored data is nearly half of samples, the MDE is adequate. Also, an evaluation of the adequacy of the Weibull model for any censored and truncated data is proposed.en_US
dc.description.tableofcontents 封面頁
證明書
致謝詞
論文摘要
目錄
表目錄
圖目錄
第一章 緒論
1.1 研究動機與目的
1.2 文獻回顧
1.3 研究限制及論文架構
第二章 Weibull模式的參數估計
2.1 簡介
2.2 模式
2.2.1 概似函數
2.2.2 Weibull模式
2.3 參數估計
2.3.1 最大概似估計（MLE）
2.3.2 中點估計法（MDE）
第三章 模式適合度之圖形檢驗
3.1 存活函數之無母數最大概似估計量
3.1.1 介紹
3.1.2 自行一致估計量
3.2 殘差適合度之圖形檢驗
第四章 模擬方法與結果
4.1 模擬方法
4.1.1 左截斷及設限資料之模擬
4.1.2 數值分析方法
4.2 模擬結果
第五章 結論與建議
5.1 結論
5.2 建議
參考文獻
附錄
附錄一 MLE法之S-PLUS程式
附錄二 MDE法之S-PLUS程式		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001945en_US
dc.subject (關鍵詞) 成比例危險迴歸模式zh_TW
dc.subject (關鍵詞) 設限zh_TW
dc.subject (關鍵詞) 截斷zh_TW
dc.subject (關鍵詞) 中點估計zh_TW
dc.subject (關鍵詞) Proportional hazards regression modelen_US
dc.subject (關鍵詞) Censoringen_US
dc.subject (關鍵詞) Truncationen_US
dc.subject (關鍵詞) Midpoint estimationen_US
dc.title (題名) 設限與截斷資料Weibull模式之研究zh_TW
dc.title (題名) A Weibull-based proportional hazards model for arbitrarily censored and truncated dataen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1]Alioum, A., and Commenges, D. (1996). “A proportional hazards model for arbitrarily censored and truncated data”, Biometrics, vol. 52, p.512-524.
[2]Barlow, W, E and Prentice, R. (1988). “Residuals for relative risk regression”, Biometrika, vol. 75, p.65-74.
[3]Brookmeyer, R., and Goedert, J. J. (1989). “Censoring in an epidemic with an application to hemophilia-associated AIDS”, Biometrics, vol. 45, p.325-335.
[4]Cox, D. R. (1972). “Regression model and life tables (with discussion)”, Journal of the Royal Statistical Society, Series B, vol. 39, p. 1-38.
[5]Crowley, J. and Hu, M. (1977). “Covariance analysis of heart transplant survival data”, Journal of the American Statistical Association, vol. 73, p.27-36.
[6]Finkelstein, D. M. (1986). “A proportional hazards model for interval-censored failure time data”, Biometrics, vol. 42, p.845-854.
[7]Finkelstein, D. M., Moore, D. F., and Schoenfeld, D. A. (1993). “A proportional hazards model for truncated AIDS data”, Biometrics, vol. 49, p.731-740.
[8]Flygare, M. E., Austin, J. A., and Buckwalter, R. M. (1985). “Maximum likelihood estimation for the 2-parameter Weibull distribution based on interval-data”, IEEE transactions on reliability, vol. 34, p.57-59.
[9]Frydman, H.(1994). “A note on nonparametric estimation of the distribution function from interval-censored and truncated observations”, Journal of the Royal Statistical Society, Series B, vol. 56, p.71-74.
[10]Gentleman, R., and Geyer, C. J. (1994). “Maximun likelihood for interval censored data: consistency and computation”, Biometrika, vol. 81, p.618-623.
[11]Klein, J. P., and Moeschberger, M. L. (1997). Survival Analysis. New York: Springer-Verlag.
[12]Odell, P. M., Anderson, K. M., and D’Agostino, R. B. (1992). “Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model”, Biometrics, vol. 48, p.951-959.
[13]Pan, W., and Chappell, R. (1998). “Computation of the NPMLE of distribution functions for interval censored and truncated data with applications to the Cox model”, Computational Statistics & Data Analysis, vol. 28, p.33-50.
[14]Peto, R. (1973). “Experimental survival curves for interval-censored data”, Applied Statistics, vol. 22, p.86-91.
[15]Turnbull, B. W. (1976). “The empirical distribution function with arbitrary grouped, censored and truncated data”, Journal of the Royal Statistical Society, Series B, vol. 38, p.290-295.		zh_TW