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系統識別號	U0002-2607201213561900
中文論文名稱	現狀數據在比例風險模型下之概似比檢定
英文論文名稱	Likelihood Ratio Test for Proportional Hazards Model with Current Status Data
校院名稱	淡江大學
系所名稱(中)	數學學系碩士班
系所名稱(英)	Department of Mathematics
學年度	100
學期	2
出版年	101
研究生中文姓名	陳俊緯
研究生英文姓名	Jyun-Wei Chen
學號	698190369
學位類別	碩士
語文別	中文
口試日期	2012-06-20
論文頁數	34頁
口試委員	指導教授-溫啟仲委員-黃逸輝委員-吳裕振
中文關鍵字	概似比檢定比例風險模型現狀數據資料自身一致方程式
英文關鍵字	Likelihood Ratio Test Proportional hazards Model Current Status Data Self-Consistency Equations
學科別分類	學科別＞自然科學＞數學
中文摘要	現狀設限毀壞時間的觀察數據包含檢查時間和毀壞事件發生時間是否在檢查時間之前發生。在現狀數據中，有關於毀壞事件發生時間和共變量之間的關係的數個半母數迴歸方法，已被廣泛地研究。在本論文中，我們考慮在比例風險模型下之現狀數據，對於共變量效應之概似比檢定。並提出一個可以簡單執行的演算法來計算此檢定量。此演算法是根據一系列的自身一致方程式且我們利用收縮原理來證明其局部收斂性。此外我們探討了此演算法的收斂速度。接著進行了模擬計算並分析三筆真實數據，來說明此概似比統計量之卡方漸進性的適當性和此演算法的可行性。
英文摘要	Current status censored failure time observation consists only of an examination time and knowledge of whether the failure time has occurred before the exam. Several semiparametric regression methods which examine the relationship between the failure time and covariates have been proposed extensively for current status data. In this thesis, we consider the likelihood ratio test for testing covariate effect under the proportional hazards model with current status data and propose an easily implemented algorithm for computing the statistics. The algorithm proposed is based on a set of self-consistency equations and its convergence is proved by contraction principle. Besides we discuss the rate of convergence of the algorithm. The adequacy of the Chi-squared approximation for likelihood ratio statistics and the availability of the algorithm are demonstrated in simulation studies and in the analyses of three real data.
論文目次	致謝......................................................I 論文中文摘要.............................................II 論文英文摘要............................................III 第一節　前言..............................................1 第二節　資料與模型敘述....................................3 2.1資料與模型...................................3 2.2概似比檢定...................................4 第三節　演算法............................................5 第四節　模擬試驗..........................................9 第五節　實例分析.........................................24 5.1肺腫瘤數據分析............................. 24 5.2水晶體鈣化數據分析......................... 26 5.3 白內障數據分析.............................27 第六節　結論.............................................30 參考文獻.................................................31 附錄一...................................................33 附錄二...................................................34
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