右設限與區間限制混合資料下的貝氏存活率之研究

Bayesian Survival Analysis for Mixed Right Censored and Interval Censored Data

廖秀淇(Hsiu-Chi Liao)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700156

摘要

近代醫學裡，各種疾病的資料型態的存活分析，是大家想知道。因此本篇論文主要針對右設限區間限制下的資料做存活分佈函數估計。在模型部分則是使用伯氏多項式來描述存活分佈函數，再利用貝氏估計做為統計方法。但因計算貝氏估計非常複雜，所以我們將使用馬可夫鏈蒙地卡羅法來計算估計。
而在本篇論文我們假設事前分佈的參數為均勻分佈，而所得事後分佈之參數計算出其期望值，再利用M.H演算法之後，可看出在樣本數相同的情況下，當混合資料下，右設限資料比例越大較有準確的估計，且混合資料越大，估計越會準確，我們符合估計的一致性。而我們對此研究方法的結果也相當滿意。

關鍵字

貝氏估計 ； 伯氏多項式 ； 型二和右設限混合資料

並列摘要

Survival analysis of various types of disease data always interest people in modern medicine. Therefore, this thesis aims at survival analysis function estimation for right-censored and interval restrictions data.
We used Bernstein polynomial as model to describe the survival analysis distribution function, and Bayesian estimation method was used to estimate. But due to Bayesian estimation method is complex, we use Markov chain Monte Carlo method to calculate the estimate. In this thesis, we supposed prior distribution function subject to Uniform distribution, and used the parameters of its posterior distribution to calculate expectation. By the Metropolis-Hastings method, we had an exact estimate when right-censored data of mixed data was larger under the same sample size. The larger the mixed data is, the more accurate the estimate is, and also it is in accordance with the nature of the large sample theory ─consistency. Consequently, we are satisfied with this methodology.

並列關鍵字

Bayesian estimation ； Bernstein polynomial ； mixed right censored and interval censored data

參考文獻

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