存活現狀數據下風險函數之最大概似估計

Maximum Likelihood Estimator of Hazard Function for Current Status Data

賴京鈺(Ching-Yu Lai)

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.2011.00117

摘要

存活, 當人得到某些絕症時, 給予治療時都會問還可活多久, 因存活分析是非常重要研究, 不同的病, 不同的治療方式, 可存活多久? 變成一個重要和嚴肅的問題, 而本篇論文, 研究資料型態為現狀數據, 我們想估計它的風險函數, 而在楊雅雯(2009)論文, 是研究累積風險函數, 差別在限制條件不同, 演算法我們比較容易撰寫. 在模擬研究中, 我們的估計會比用Step-函數所估計的Maximum Likelihood Estimator(M.L.E.) 較好, 而且樣本越大, 估計越靠近真實.

關鍵字

風險函數 ； 伯氏多項式 ； 最大概似估計 ； 馬可夫鏈蒙地卡羅

並列摘要

People getting some fatal disease always ask ”How long can I survive?”during the treatment. Therefore, the analysis of surviving is definitely an important research related to a serious issue of how long to survive with different treatment. And for this research paper , its researching information is collected from the status data, and we intend to calculate
its risk function. However, in the paper writen by Yang Ya-Wen in 2009,its topic mainly researches the accumulation of risk function. And the difference between Yang’s paper and mine is the dissimilarity of the restricted conditions. So based on this situation, this study could do better algorithm. Besides, our calculation is more precise than Step function’s
Maximun Likelihood Estimator in the simulation research. And more samples this study has, more closer to truth the caculaiton is.

並列關鍵字

Hazard Function ； Bernstein Polynomial ； Maximum Likelihood Estimator ； Markov Chain Monte Carlo

參考文獻

[1] 楊雅雯(2009). Maximum Likelihood Estimator of Survival Analysis for Current

Status Data Using Bernstein Polynomials. Department of Applied Mathematics,

[2] Chang, I. S., Hsiung, C. A., Wu, Y. J. and Yang, C. C. (2005). Bayesian survival analysis using Bernstein polynomials. Scandinavian Journal of Statistics 32, 447-466.

[4] Green, P. G. (1995). Reversible Jump Markov Chain Monte Carlo Computation

[5] Groeneboom, P. and Wellner, J. A. (1992). Intorduction Bounds and Nonparametric Maximum Likelihood Estimation Birk¨auser, Boston.