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標題: 貝氏對區間限制資料下勝算比之研究
Bayesian odds rate estimation for Case II interval-censored data
作者: 朱凱琪
Kai-Chi Chu
關鍵字: 伯氏多項式;勝算比;Case II資料;貝氏方法;Bernstein polynomial;odds rate;Case II interval-censored data;Bayesian method
引用: [1]Chang, I.S., Hsiung, C.A., Wu, Y.J., Yang, C.C. (2005), “Bayesian survival analysis using Bernstein polynomials”, Scandinavian journal of statistics, vol. 32, p447-466 [2]Devroye, L. and Györfi, L. (1984), “Nonparametric density estimation: the L1 view”, John Wiley and Sons, New York [3]Green, P.J. (1995), “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination”, Biometrika, vol. 82, p711-732 [4]Groeneboom, P. (1991), “Nonparametric maximum likelihood estimators for interval censoring and deconvolution”, Technical Report 378, Department of Statistics, Standford University [5]Petrone, S. (1999), “Random Bernstein polynomials”, Scand. J. Statist, vol. 26, p373-393 [6]Petrone, S. and Wassweman, L. (2002), “Consistency of Bernstein polynomial posteriors”, J. Roy. Statist. Soc., Ser. B, vol. 64, p79-100 [7]Piet Groeneboom, Jon A Wellner (1992), “Information bounds and nonparametric maximum likelihood estimation”, Springer Science and Business Media [8]Robert, C.P. and Casella, G. (1999), “Monte Carlo Statistical Methods”, Springer-Verlag, New York [9]Sheldon M. Ross (2006), “Simulation”, Epstein Department of Industrial and Systems Engineering University of Southern California, Fourth Edition [10]van der Vaart, A.W. (1998), “Asymptotic statistics”, Cambridge University Press, Cambridge [11]van der Vaart, A.W. and Wellner, J.A. (1996), “Weak convergence and empirical processes”, Springer-Verlag, New York [12]尤冠喬 (2015), “現狀數據資料下貝氏對勝算比之研究”, 中原大學碩士論文 [13]陳寶珠 (2008), “貝氏存活分析對右設限資料和現狀數據一致性之研究”, 中原大學碩士論文
本論文主要對存活Case II資料下,做貝氏統計分析,而在Chang等[1]提出對右設限資料下,使用伯氏多項式來描述累積風險函數之貝氏理論及其演算法,而我們將用他們的想法把伯氏多項式架構在勝算比函數,並且參考了他們的演算法,來對Case II資料做勝算比研究,而本篇論文也證明了大樣本性質(一致性),在模擬計算方面也表現不錯,也符合我們的理論。

In this paper, we mainly study the survival analysis of Case II data by using the method of Bayesian estimation. In Chang et al. [1] use Bernstein Polynomial to discribe the cumulative risk function of Bayesian theory and algorithm for right censored data. Here we will use their method to describe the odds rate on Bernstein polynomial and will implement their algorithm to the odds rate of Case II data. We attain a good performance in computation simulation which satisfies the large sample theory.
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