右設限資料下勝算比之研究

Estimation of odds rate for right-censored data

王乙如(Yi-Ju Wang)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2015年)

https://doi.org/10.6840/cycu201500149

摘要

本篇論文將對存活資料最簡單資料型態─右設限資料分析。在丘真绮(2010)與Chang(2005)也對它們做過研究，而Chang(2005)是對累積風險函數做貝氏推論，和丘真绮(2010)是對其分佈函數做最大概似估計，而本篇論文將對勝算比函數(odds)做最大概似估計，其模型假設為伯氏多項式，使用馬可夫鏈蒙地卡羅法之Simulated Annealing做計算並且估計，但也提供遞增演算法及凹口向下且遞增演算法作比較，其模擬方面也符合我們理論及大樣本性質。

關鍵字

伯氏多項式 ； 最大概似估計 ； 勝算比函數 ； 右設限資料

並列摘要

The aim of the research is to analyze the simplest type of survival analysis—the right censored data. The similar research had been conducted ( Chang,2005 Chiu,2010 ). Chang(2005) proved the cumulative hazard function by using Bayesian inference, and Chiu(2010) estimated the distribution function by MLE. In this research, the maximum likelihood estimation is adopted to estimate the odds function. This model is assumed as Bernstein polynomials and Markov chain’s Monte Carlo simulated annealing is used to calculate and estimate the data. And I also offered incremental algorithm and concave downward algorithm to compare. Their simulations are also consistent with our theory and large sample properties.

並列關鍵字

Bernstein polynomials ； Maximum likelihood estimation ； Odds function ； Right-censored data

參考文獻

[6 ] 吳基溢 (2011) 存活右設限資料下風險函數之最大概似估計，中原

[1 ] Chang ,I.S., Hsiung ,C.A., Wu , Y.J., Yang, C.C. ” Bayesian Survival Anal- ysis Using Bernstein Polynomials ” , Scandinavian Journal of Statistics

[2 ]G. Casella , R.L. Berger ” Statistical inference ” , Duxbury Press 1990.

[3 ]Christian P. Robert, George Casella ” Monte Carlo Statistical Methods

[4 ]P. Green ” Reversible jump Markov chain Monte Carlo computation and