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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/83251
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/83251


    Title: 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
    Authors: 黃偉傑
    Huang, Wei-Jie
    Contributors: 陳麗霞
    Chen, Li-Shya
    黃偉傑
    Huang, Wei-Jie
    Keywords: 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
    Date: 2000
    Issue Date: 2016-03-31 14:44:56 (UTC+8)
    Abstract: 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.
    Reference: [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.
    Description: 碩士
    國立政治大學
    統計學系
    87354002
    Source URI: http://thesis.lib.nccu.edu.tw/record/#A2002001945
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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