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系統識別號 U0002-1507201316263800
中文論文名稱 評量現狀存活數據的比例勝算比假設
英文論文名稱 Evaluating the Proportional Odds Assumption with CurrentStatus 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 2
出版年 102
研究生中文姓名 張晏昇
研究生英文姓名 Yan-Sheng Zhang
學號 699190343
學位類別 碩士
語文別 中文
口試日期 2013-06-26
論文頁數 46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 現狀存活數據  比例勝算比假設  配適度指標 
英文關鍵字 current status survival data  proportional odds assumption  goodness-of-fit indices 
學科別分類 學科別自然科學數學
中文摘要 評量完整或右設限存活資料的迴歸診斷問題較已被廣泛的研究,但對於現狀存活數據卻很少。這裡的現狀存活數據包含檢查時間,一個在檢查時間知道毀壞事件是否已發生的狀態指標,以及共變量。在本論文中,我們建立四種方法來評量現狀存活數據的比例勝算比假設。 他們分別是「對數勝算比曲線圖」、「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資料的比例勝算比假設。同時提出四個方法相對應的配適度指標。模擬結果顯示所提方法的表現是不錯的,且以三個實例敘述所提方法的應用性。
英文摘要 Regression diagnostic problems have been extensively studied for complete or right-censored survival data but so less for current status survival data. Here the current status survival data include an examination time, an status indicator for whether or not the failure has occurred by the examination time, and covariates. In this thesis, we have established four methods for evaluating the proportional odds assumption of current status survival data. They are the log odds curve plots, the observed and expected survival curve plots, the Cox-Snell residual method, and the Brier-score method. Also, the corresponding goodness-of-fit indices for four methods are proposed. Simulation results reveal good performance of the proposed methods and three real examples illustrate the applications of the proposed methods.
論文目次 第一節 前言…………………………………………………………1
第二節 方法介紹…………………………………………………4
2.1 對數勝算比曲線圖…………………………………4
2.2 觀察與預期存活曲線圖…………………………5
2.3 柯斯-斯奈爾殘差法………………………………6
2.4 布萊爾-分數法………………………………………9
第三節 模擬試驗………………………………………………11
第四節 實例分析………………………………………………20
4.1 肺腫瘤數據……………………………………………20
4.2 水晶體鈣化數據……………………………………22
4.3 白內障數據……………………………………………25
第五節 結論………………………………………………………40
參考文獻…………………………………………………………………42
附 錄 A……………………………………………………………44
附 錄 B……………………………………………………………45
附 錄 C……………………………………………………………46

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

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

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

6.Kleinbaum, D. G. and Klein, M. (2005). Survival Analysis: A Self-Leaming Text,
2nd edition. Springer-Verlag.
7.Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order restricted statistical inference, Wiley, New York.

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

9.Wang, W. (王維) (2013). Evaluating the Proportional hazards Assumption with Current Status Survival Data. Master Thesis, Tamkang University.

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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