貝氏對現狀數據勝算比模型之研究

Bayesian Survial Analysis for Proportional Odds Model with Current Status Data

倪裕程(Yu-Cheng Ni)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200170

摘要

此篇論文的目的在於, 用貝氏方法利用比例勝算比模型在現狀數據下去估計其參數, 並觀察其是否符合一致性。

現狀數據為一種區間設限資料, 其觀察值只包含檢查時間以及事件是否在檢查時間之前發生, 其為一種在存活分析上的重要應用, 而在現狀數據中, 半母迴歸模型有很多的應用,半母回歸模型為探討事件發生時間和共變量Z之間關係, 例如, 今天一項醫學研究想知道抽菸是否影響人得到肺癌, 令共變量 Z=0 為不抽菸, 而 Z=1 為抽菸,
每個檢查時間點去檢查是否得到癌症, 而本篇論文選用的是勝算比模型。

我們認為勝算比函數為一種連續函數, NPMLE方法去估計現狀數據存活函數只能得到一個步階式函數, 只有在樣本數極大時才能估計出平滑曲線, 所以我們提出Bernstein多項式來進行估計,因為Bernstein多項式易於考慮其幾何資訊並以較小的樣本數去估計一平滑曲線。

關鍵字

馬可夫鏈蒙地卡羅 ； 伯氏多項式 ； 共變量現狀數據 ； 比例勝算比模型

並列摘要

The mainly discuss to estimate parameters from proportional odds model with current status data by bayesian survival analysis in this paper.

Current Status data is an interval censored data. The observation only include the examination time and the failure time is larger than examination time or not. For example, suppose a study is conducted to measure the impact of smoking cigarette on lung cancer. Let the covariate Z=0 mean no smoking and Z=1 mean smoking. And then check the subject got cancer or not at the examination time. We choose proportional odds model in this paper.

We consider the proportional odds function that is a continuous function, but the NPMLE can only show us a step function in small sample.
Thus we use the bernstein polynomial to estimate a smooth function.

並列關鍵字

Bernstein polynomial ； Markov Chain Monte Carlo ； Current Status Data with Covariate ； Proportional Odds Model

參考文獻

model for the analysis of current status data" , Journal of th American Statistical Association 1996.

[1] 柯興杰. " Likelihood Ratio Test for Proportional Odds Model with Current Status Data ". Department of Mathematic, Tamkang University, master thesis 2011.

[2] J. Sun "The Statistical Analysis of interval-censored Failure Time Data". Springer-Verlag 2006.

[4] A. J. Rossini , A. A. Tsiatis "A semiparametric proportional odds regression

[5] Bennett, S. "Analysis of Survival Data by Proportional Odds Model" Statistics