隨機右設限數據之風險率的貝氏估計方法

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姓名

陳光堯(Guang-Yao Chen) 查詢紙本館藏

畢業系所

數學系

論文名稱

隨機右設限數據之風險率的貝氏估計方法
(A Bayesian method for hazard rate estimation based on right-censored data)

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摘要(中)

Hess and Brown(1999) 回顧多種對於右設限數據之風險率的核估計方法，且經由模擬比較發現，Muller and Wang(1994) 所提出的邊界核估計法的估計效果較好。本文之目的是在貝氏模型下，提出對於右設限數據之風險率的估計。在這貝氏方法中，我們利用 Bernstein 多項式來表達累積風險率，而將先驗分佈建立在這些 Bernstein 多項式的次數及係數上；統計推論所需之後驗分佈是利用 MCMC 的方法來做。最後，我們把我們的方法與 Muller and Wang(1994) 的邊界核估計法做模擬比較，結果顯示我們的貝氏方法有較小的均方誤差。

摘要(英)

Hess and Brown(1999) reviewed various kernel methods for hazard rate estimation based on right-censored data. Through simulations, they found that the boundary kernel estimator by Muller and Wang(1994) had improved performance. In this paper, we will propose a Bayesian estimator for hazard rate, using prior on Bernstein polynomials, and make inference using MCMC methods. Comparison using simulation shows that our Bayesian estimator performs better than the boundary kernel estimator of Muller and Wang(1994) in terms of mean-squared error.

關鍵字(中)

★ 伯氏多項式
★ 邊界核估計
★ 貝氏存活分析

關鍵字(英)

★ boundary kernels
★ Bernstein polynomial
★ Bayesian survival analysis

論文目次

1 簡介.......................................1
2 一個估計風險率的貝氏方法...................3
2.1 Bernstein 多項式的幾何性質..............3
2.2 先驗分佈的建立..........................5
2.3 模型建構................................6
2.4 演算法..................................7
3 邊界核估計方法.............................9
3.1 方法介紹................................9
3.2 演算法..................................11
4 模擬研究...................................13
4.1 有效模擬次數............................13
4.2 模擬結果與討論..........................14
參考文獻.....................................18

參考文獻

[1] Chang, I. S., Hsiung, C. A., Wu, Y. J., and Yang, C. C. (2005). Bayesian survival analysis using Bernstein polynomials. Scand J. Statist. 32, 447-466.
[2] Green, P. G. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
[3] Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian data analysis(2nd ed.). Chapman and Hall/CRC, New York, 295-297.
[4] Robert, C. P. and Casella, G. (1999). Monte Carlo Statistical Methods. Springer-Verlag, New York.
[5] Resnick, S. I. (1999). A Probability Path. Basel: Birkhauser.
[6] Muller, H. G. and Wang, J. L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics 50, 61-76.
[7] Wang, J. L. (1997). Smoothing hazard rates, in Encyclopedia of Biostatistics. Wiley, London, 4140-4150.
[8] Hess, K. R., Serachitopol, D. M. and Brown, B. W.(1999). Hazard function estimators:a simulation study. Statistics in Medicine 18, 3075-3088.
[9] Watson, G. S. and Leadbetter, M. R. (1964). Hazard analysis I. Biometrika 51, 175-184.
[10] Ramlau-Hansen, H. (1983). Smoothing counting process intensities by means of kernel functions. Annals of Statistics 11, 453-466.
[11] Tanner, M. A. and Wong, W. H. (1983). The estimation of the hazard function from randomly censored data by the kernel method. Annals of Statistics 11, 989-993.
[12] Yandell, B. S. (1983). Nonparametric inference for rates with censored survival data. Annals of Statistics 11, 1119-1135.
[13] Breslow, N. E. and Day, N. E. (1987). Nonparametric estimation of background rates, in Statistical Methods in Cancer Research, vol. II, The Design and Analysis of Cohort Studies, IARC Scientific Publications, Lyon,192-195.
[14] Keiding, N. and Andersen, P. K. (1989). Nonparametric estimation of transition intensities and transition probabilities: A case study of a two-state Markov process. Applied Statistics 38, 319-329.
[15] Gray, R. J. (1990). Some diagnostic methods for Cox regression models through hazard smoothing. Biometrics 46, 93-102.

指導教授

張憶壽、趙一峰
(I-Shou Chang、I-Feng Chao)

審核日期

2007-7-6

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