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研究生:張光輘
研究生(外文):Guang-Ling Chang
論文名稱:在克萊頓模型之下以邏輯斯迴歸和比例勝算模型分析家族中具治癒性之存活資料
論文名稱(外文):Model Familiar Survival By Clayton’s Model Data With Logistic Regression Model For Cure And Proportional Odds Model For Survival Time
指導教授:陳瓊梅陳瓊梅引用關係
指導教授(外文):Chyong-Mei Chen
學位類別:碩士
校院名稱:靜宜大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008/07/
畢業學年度:96
語文別:中文
論文頁數:53
中文關鍵詞:邏輯斯迴歸比例勝算模型治癒性存活分析克萊頓模型柯克斯
外文關鍵詞:proportional odds modelcureSurvival analysisClanton&apos&aposs modelCoxlogistic regression
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存活分析(Survival analysis)是目前於生物醫學上最常見的分
析,主要使用在於有關注事件與不完整資料的使用上,一般將不完整資料視為無效資料,若因此將資料皆捨棄,不僅浪費許多可提供分析的資訊,甚至在做統計推論時產生嚴重偏差,但是如何加以應用,在統計上卻是個難題。柯克斯的比例風險迴歸模型有一些缺點(Cox’s proportional hazards model),吾人使用了克萊頓模型(Clanton’s model)與比例勝算模型(Proportional odds model)來配適存活時間,並且於事件機率使用邏輯斯迴歸模型(Logistic regression model)。

在此篇論文中,吾人將針對具有相關性的存活資料進行分析與使用Lu and Ying ( 2004 ) 估計有興趣的變數,針對相關性問題使用「克萊頓模型」( Clanton’s model ) 描述,並使用統計軟體R進行模擬與估計,由估計結果探討吾人所提方法的成效。
Survival analysis is the most familiar analysis in Biomedical study, and it is used for analyzing incomplete data and the interesting events primarily. Therefore, if we delete some of them, it will not only waste a lot of information, but also affect the statistical conclusion. Moreover, how to apply it is a difficult problem. Since Cox’s proportional hazards model have some drawbacks, we propose Clayton’s model with proportional odds model to fit the event time. And we build the cure proportion by the logistic regression model.

In this paper, we use the Clayton’s model to analyze the correlation of the survival data, and estimate the interesting parameter by Lu and Ying ( 2004 ). Then we analyze it by using the R and simulation. According the to result, we can explore the efficiency of the method.
1. 緒論………………………………………………………………… 1
1.1 研究背景………...…………………………………………… 1
1.2 研究目的與內容……………………………………………... 3
2. 文獻回顧…………………………………………………………… 7
3. 模型與估計方法………………………………………………….. 11
3.1 資料與模型…………………………………………………. 11
3.2 估計方法……………………………………………………. 18
4. 模擬……………………………………………………………….. 21
4.1 資料的生成…………………………………………………. 21
4.2 模擬結果……………………………………………………. 26
5. 結論……………………………………………………………….. 35
A. 附錄一…………………………………………………………….. 37
B. 附錄二…………………………………………………………….. 38
C. 附錄三…………………………………………………………….. 40
D. 附錄四…………………………………………………………….. 42
E. 參考文獻………………………………………………………….. 44
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