貝氏存活分析對右設限資料和現狀數據一致性之研究

The Consistency in Bayesian Survival Analysis for Right Censor Data and Current Status Data

陳寶珠(Pao-Chu Chen)

指導教授 ： 吳裕振

中原大學/理學院/應用數學系/碩士(2008年)

https://doi.org/10.6840/CYCU.2008.00034

摘要

本篇論文主要是對 “貝氏存活分析對右設限資料和現狀數據一致性之證明” 作研究，其中針對貝氏估計存活分析的大樣本性質做了詳細的整理與證明，包括了右設限資料和現狀數據兩種型態的資料理論與證明。而存活分析在統計上或實際上是非常重要的，且可被應用在保險或計算病人存活時間上。雖然統計方法眾多，但卻缺乏理論來證明這些統計方法是正確的，因此我們將利用本篇論文來驗證那些統計方法滿足某些條件具有一致性的理論。
本篇論文主要共分為五大部份︰第一節介紹右設限資料和現狀數據之參考文獻及其重要性；第二、三、四節主要利用 Fang & Wu (2007) 和 Wang & Wu (2007) 等等的參考文獻來說明模型架構和統計推論。第二節主要是根據Bernstein多項式的幾何圖形和它的係數之關係，作為分配函數的模型，此模型架構有利於貝氏方法計算其事後分佈；第三節主要在說明事後分配的理論架構；第四節對右設限資料分析之研究，主要是取〔0 ,τ〕為區間來作分析與研究（可參看Chang 2005）；第五節則是本篇論文主要的研究結果，是對現狀數據之貝氏估計（Fang & Wu 2007）的方法做一致性的相關證明。相信本篇的研究結果可對進一步的Cox-model 的貝氏理論證明方法應有相當的幫助。

關鍵字

貝氏 ； 右設限資料 ； 現狀數據

並列摘要

“The Consistency in Bayesian Survival Analysis for Right Censor Data and Current Status Data” is the main subject of this essay, and related studies are also broadly described in this essay. In particular, detail proof for big sample property of Bayesian survival analysis estimation is collected as research objective. Right censoring data and current status data are both used to assist this research. In reality and statistically, survival analysis is very important and broadly applied on calculations for insurance and the survival time of patience. Although these are lots of statistical methods, these methods are still lack of systematic theory to prove their accuracy. Thus, this essay also provides demonstration for survival statistic.
This dissertation is divided into five chapters. Chapter 1 introduces right censoring data and current data references and importance. In Chapter 2, 3 and 4, Fang & Wu (2007) and Wang & Wu (2007) research results are used to state framework of the model and statistical deduction. The distribution function model in chapter 2 is based on the relationship of geometric graphs and its coefficient in Bernstein polynomial. This distribution is beneficial for using Bayesian theory to calculate post distribution. And the post distribution theory structure is described in Chapter 3. For right censoring data,〔0 ,τ〕is defined as the analysis interval and reviewed in Chapter 4 (Chang 2005). Finally, the key research result, the consistency in Bayesian survival analysis for current status data (Fang & Wu 2007), is proved in Chapter 5. It is believed that the research finding of this essay will be helpful to the demonstration of Bayesian Cox-model in further discussion .

並列關鍵字

Bayesian ； Right Censor Data ； Current Status Data

參考文獻

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Arjas, E. & Gasbarra, D. (1994). Nonparametric Bayesian inference