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    题名: 相依競爭風險邊際分配估計之探討
    作者: 張簡嘉詠
    贡献者: 陳麗霞
    張簡嘉詠
    关键词: 競爭風險
    無法識別
    關聯結構
    相關性參數
    機率積分轉換
    關聯結構-圖形估計量
    competing risks
    non-identifiable
    copula
    dependence parameter
    probability integral transformations
    copula-graphic estimator
    日期: 2007
    上传时间: 2009-09-14
    摘要: 競爭風險之下對邊際分配的估計，是許多領域中常遇到的問題。由於主要事件及次要事件互相競爭，只要一種事件先發生即終止對另一事件的觀察，在兩事件同時發生的機率為0之下，連一筆完整的資料我們都無法蒐集到。除非兩事件互為獨立或加上其它條件，否則會有邊際分配無法識別的問題。但是獨立的條件在有些情況下並不合理，為解決相依競爭風險之邊際分配無法識別的問題，可先假定兩事件發生時間之間的關係。
    由於關聯結構定義出兩變數間的結合關係，我們可利用關聯結構解釋兩事件發生時間之間的關係。假定兩變數之相關性參數為已知，且採用機率積分轉換的觀念，本論文討論了Zheng 與 Klein提出的關聯結構-圖形估計量，是否會依設限程度、相關性強度和關聯結構形式的不同，以致估計能力有別。
    The problem of estimating marginal distributions in a competing risks study is often met in scientific fields. Because main event and secondary event compete with each other, and a first occurring event prevents us from observing another event promptly, the intact lifetimes or survival times are unable to be collected in the circumstances that the probability of both lifetimes coinciding is 0. Unless lifetimes being independent or adding other conditions, there is a problem that the marginal distributions are non-identifiable. But the condition of independence is not always reasonable, we may assume the relation between lifetimes has some special form
    Because the copula defines the association between two variables, it can be employed to explain relation between lifetimes. Assuming that the dependence parameter in the copula framework is known, and adopting the concept of the probability integral transformations, this thesis has demonstrated whether the estimating abilities of the copula-graphic estimator, that Zheng and Klein put forward, are different in rates of censoring, intensities of dependence, and forms of the copula.
    參考文獻: Andersen, P. K., Ekstrøm, C. T., Klein, J. P., Shu, Y. & Zhang, M. J. (2005), A class of goodness of fit tests for a copula based on bivariate right-censored data, Biometrical Journal, 47, 815-824.
    Bacigál, T. & Komorníková, M. (2006), Fitting Archimedean copulas to bivariate geodetic data, Proceedings in Computational Statistics.
    Bedford, T. (2005), Competing risk modeling in reliability, Modern Statistical & Mathematical Methods in Reliability, 1-16.
    Brown, B. W., Hollander, M. & Korwar, R. M. (1974), Nonparametric tests of independence for censored data, with applications to heart transplant studies, Reliability and Biometry, 327-354.
    Chen, M. C. & Bandeen-Roche, K. (2005), A diagnostic for association in bivariate survival models, Lifetime Data Analysis, 11, 245–264.
    Davis, C. E. & Quade, D. (1968), On comparing the correlations within two pairs of variables, Biometrics, 24, 987-995.
    Genest, C. & Rivest, L. P. (1993), Statistical inference procedures for bivariate Archimedean copulas, Journal of the American Statistical Association, 88, 1034-1043.
    Genest, C. (1987), Frank s family of bivariate distributions, Biometrika, 74, 549-555.
    Genest, C. & MacKay, J. (1986), The joy of copulas: Bivariate distributions with uniform marginals, The American Statistician, 40, 280-283.
    Hougaard, P. (1984), Life table methods for heterogeneous populations: Distributions describing the heterogeneity, Biometrika, 71, 75-83.
    Joe, H. (1993), Parametric families of multivariate distributions with given margins, Journal of Multivariate Analysis, 46, 262-282.
    Kaplan, E. L. & Meier, P. (1958), Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 53, 457-481.
    Klein, J. P. & Moeschberger, M. L. (1988), Bounds on net survival probabilities for dependent competing risks, Biometrics, 44, 529-538.
    Moeschberger, M. L. & Klein, J. P. (1995), Statistical methods for dependent competing risks, Lifetime Data Analysis, 1, 195–204.
    Nelsen, R. B. (1999), An Introduction to Copulas, Springer, New York.
    Oakes, D. (1989), Bivariate survival models induced by frailties, Journal of the American Statistical Association, 84, 487-493.
    Peterson, A. V. (1977), Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions, Journal of the American Statistical Association, 72, 854-858.
    Schweizer, B. & Sklar, A. (1983), Probabilistic Metric Spaces.
    Schwettzer, B. & Wolff, E. (1981), On nonparametric measures of dependence for random variables, The Annals of Statistics, 9, 879-885.
    Sklar, A. (1959), Fonctions de répartition à n dimensions et leurs marges, Publications de l’Institut de Statistique de l’Université de Paris, 8, 229-231.
    Slud, E. V. & Rubinstein, L. V. (1983), Dependent competing risks and summary survival curves, Biometrika, 70, 643-649.
    Tsiatis, A. A. (1975), A nonidentifiability aspect of the problem of competing risks, Proceedings of the National Academy of Sciences, 72, 20-22.
    Vaupel, J. W., Manton, K. G., & Stallard, E. (1979), The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography, 16, 439-454.
    Wang, W. (2004), Estimating the association parameter for copula models under dependent censoring, Journal of the Royal Statistical Society, Series B. 65, 257-273.
    Wang, W. & Wells, M. T. (2000), Estimation of Kendall s tau under censoring, Statistica Sinica, 10, 1199–1215.
    Zheng, M. & Klein, J. P. (1995), Estimates of marginal survival for dependent competing risks based on an assumed copula, Biometrika, 82, 127-138.
    描述: 碩士
    國立政治大學
    統計研究所
    94354011
    96
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0094354011
    数据类型: thesis
    显示于类别:[統計學系] 學位論文

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