區間設限資料之非比例風險模型之貝氏研究

Bayesian Studying on Nonproportional Hazard Model with Interval Censored Data

蔡譯賢(Yi-Hsien Tsai)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2018年)

https://doi.org/10.6840/cycu201800234

摘要

本論文只要研究存活分析、共變量為二元情形下的 CaseⅡ區間設限資料，對存活累積分佈函數之研究分析。其中使用伯氏多項式來描述其累積分佈函數。利用伯氏多項式來描述分布函數，其演算法是用馬可夫鏈蒙地卡羅法來估計，進而去估算他們的風險比。

關鍵字

CaseⅡ區間設限資料 ； 伯氏多項式 ； 風險比

並列摘要

In this thesis, as long as the survival analysis and the case II of covariates are studied, the cumulative distribution function of survival is analyzed. Wherein the use of the Bernstein Polynomial to describe its cumulative distribution function. The distribution function is described by using the Bernstein Polynomial. The algorithm is estimated by the Markov chain Monte Carlo method, and then the risk ratio is estimated.

並列關鍵字

Case Ⅱ Interval Censored Data ； Bernstein Polynomial ； Risk Ratio

參考文獻

7.參考文獻 [1 ]I.S. Chang , C.A. Hsiung , Y.J. Wu , C.C. Yang (2005),“Bayesian Survival Anal- ysis Using Bernstein Polynomials ” , Scandinavian Journal of Statistics Vol. 32 P.447-466 [2 ]P. Groeneboom (1991),“Nonparametric maximum likelihood estimators for interval censoring and deconvolution ”, Technical Report 378, Department of Statistics, Standford University [3 ]P.J. Green (1995),“ Reversible jump Markov chain Monte Carlo computation and Bayesian model determination ”, Biometrika 82, 711732 [4 ]Christian P. Robert, George Casella (1999),“Monte Carlo Statistical Methods ” , Springer-Verlag, New York

[5 ]Yuh-Jenn Wu, Wei-Quan Fang, Li-Hsueh Cheng, Kai-Chi Chu, Yin-Tzer

Shih and Li-Chu Chien(2018), A flexible Bayesian non-parametric

approach for fitting the odds to case II interval censored data, submit