貝氏存活右設限資料風險函數之研究

Bayesian Survival Analysis of Hazard Function for Right Censor Data

黃志誠(Chih-Cheng Huang)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2011年)

https://doi.org/10.6840/CYCU.2011.00119

摘要

本篇主要對右設限下的資料, 用貝氏方法去估計他們的風險險函數, 其風險函數
的值是正的, 我們可用最原始伯氏多項式來做為風險函數之模型, Wang (2007) &
Chang (2005) 分別用分配函數及累積風險函數, 其理由其模型之伯氏多項事之係
數的限制為非負, 在其撰寫演算法較容易. 並且利用貝氏方法, 以及馬可夫鏈蒙地
卡羅去計算其事後分佈. 而在模擬研究中, 把已估的風險函數換算累積風險函數並
和Kaplan-Meier estimator (KM) 之方法做比較, 我們的方法比古典Kaplan-
Meier estiator 之方法好, 而且所得也是連續函數, 而模擬研究也有不錯之表現.

關鍵字

貝氏 ； 風險函數 ； 伯氏多項式 ； 馬可夫鏈蒙地卡羅

並列摘要

This paper aims to estimate risk function of data in right censor by
applying Bayesian Method, and its value is positive. We may adopt the
initial Bernstein Polynomial as model of risk function, and Wang (2007)
& Chang (2005) may adopt distribution function and accumulative risk
function respectively, since the limitation of Bernstein Polynomial coefficient
of its model is not negative and it is easier to compose an algorithm.
This paper also employed Bayesian Method and Markov Chain Monte
Carlo to calculate posterior distribution. In simulation research, the estimated
risk function is converted into accumulative risk function and
compared with the method of Kaplan-Meier estimator (KM). The result
shows that our method performed better than the classic Kaplan-Meier
estimator, the function obtained is continuous, and the performance of
simulation research is good.

並列關鍵字

Bayesian ； Hazard Function ； Bernstein Polynomial ； Markov Chain Monte Carlo

參考文獻

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參考文獻