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系統識別號 U0002-1601201316292000
中文論文名稱 評量現狀存活數據的比例風險假設
英文論文名稱 Evaluating the Proportional Hazards Assumption with Current Status Survival 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 101
學期 1
出版年 102
研究生中文姓名 王維
研究生英文姓名 Wei Wang
學號 699190053
學位類別 碩士
語文別 中文
口試日期 2012-12-25
論文頁數 45頁
口試委員 指導教授-溫啟仲
委員-黃逸輝
委員-吳裕振
委員-温啟仲
中文關鍵字 現狀存活數據  比例風險假設  配適度指標 
英文關鍵字 current status survival data  Cox proportional hazards assumption  goodness-of-fit index 
學科別分類 學科別自然科學數學
中文摘要 右設限存活資料的迴歸診斷問題,已被廣泛的研究,但對於現狀存活數據之迴歸診斷問題較少。現狀存活數據包含共變量,檢查時間和在檢查時間事件是否發生的指標。在本論文中我們發展四種圖形法或量化法即:「log-log存活曲線圖」;「觀察與預期存活曲線圖」;「柯斯-斯奈爾殘差法」和「布萊爾-分數方法」來評量現狀存活數據的比例風險假設。並且提出四個對應的配適度指標。模擬結果顯示,此四個方法的表現是不錯的。另外,分析三組實際的現狀存活數據來說明所提方法的應用程序。
英文摘要 Regression diagnostic problems have been extensively studied in the context of right-censored survival data but not many for current status survival data. Here the current status survival data, including covariates, an examination time, and an indicator for whether the failure has occurred by the examination time. In this thesis, we develop four graphical or quantitative methods for evaluating the Cox proportional hazards assumption of current status survival data, namely the “log-log survival curve plots”, “observed and expected survival curve plots”, “Cox-Snell residual method”, and “Brier-score method”. The corresponding goodness-of-fit indices for four methods are also proposed. Simulation results reveal good performance of four methods. Three real data sets are analyzed to illustrate the applications of the proposed methods.
論文目次 目錄
第一節 前 言 ----------------------------------------- 1
第二節 log-log存活曲線圖 ----------------------------- 4
第三節 觀察與預期存活曲線圖 ------------------------- 13
第四節 考克斯-斯奈爾殘差法 -------------------------- 20
第五節 布萊爾-分數方法 ------- ---------------------- 32
第六節 結 論 ------------------------------------------ 39
參考文獻 ----------------------------------------------- 41
附 錄 A ------------------------------------------------ 43
附 錄 B ------------------------------------------------ 44
附 錄 C ------------------------------------------------ 45
參考文獻 參考文獻

1.Barlow, R. E., Bartholomew, D., Bremner, J. M. and Brunk, H. D. (1972), Statistical infer¬ence under order restrictions; the theory and application of isotonic regression, Wiley, New York.

2.Cox, D. R. and Snell, E. J. (1986). A general definition of residuals. Journal of the Royal Statistical Society, Series B 30, 248-275

3.Chang, Y. S. (張晏昇)(2013). Evaluating the Proportional Odds Assumption with Current Status Survival Data. Master Thesis, Tamkang University.

4.Farrington, C. P. (2000). Residuals for Proportional Hazards Models with Interval- Cen¬sored Survival Data. Biometric 56 , 473-482.

5.Hoel, D. G. and Walburg, H. E. (1972). Statistical analysis of survival experiments. Jour¬nal of National Cancer Institute. 49, 361-372.

6.Jianguo. and Sun. (2006). The Statistical Analysis of Interval-Censored Failure Time Data. Springer-Verlag.

7.Kleinbaum, D. G. and Klein, M. (2005). Survival Analysis: A Self-Leaming Text,2nd edition. Springer-Verlag.

8.Robertson, T., Wright, F. T. and Dykstra, R. L. (1988), Order restricted statistical inference, Wiley, New York.

9.Schoenfeld, D. (1982). Partial residuals for the proportional hazards model. Biometrika, 69, 51–55.

10.Xue, H., Lam, K. F. and Li, G. (2004). Sieve maximum likelihood estimation for semiparamet¬ric regression models with current status data. Journal of the American Statisti¬cal Association. 99, 346-356.

11.Yu, A. K. F., Kwan, K. Y. W., Chan, D. H. Y. and Fong, D. Y. T. (2001). Clinical fea-tures of 46 eyes with calcified hydrogel intraocular lenses. Journal of Cataract and Refrac¬tive Surgery. 27, 1596-1606.

12.Zeng, D. and Lin, D.Y. (2007). Semiparametric Transformation Models With Random Effects for Recurrent Events, Journal of the American Statistical Association.
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