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系統識別號 U0002-1807201317130500
中文論文名稱 使用優劣比-風險模型對現狀數據之迴歸診斷
英文論文名稱 Regression Diagnostics for Current Status Data using the Odds-Rate Model
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 洪筱涵
研究生英文姓名 Hsiao-Han Hung
學號 600190234
學位類別 碩士
語文別 英文
口試日期 2013-06-26
論文頁數 24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 現狀數據  優劣比-風險模型  配適度指標 
英文關鍵字 Goodness of fit index  Current status data  Odds-rate model 
學科別分類 學科別自然科學數學
中文摘要 在進行迴歸分析之前,應先執行迴歸診斷,即對觀測數據評估迴歸模型的合適性。對於完整或右設限毀壞時間資料的迴歸診斷,許多的圖形法或量化法已被建立(如,Collett (1994), Klein and Moeschberger (2003), and Lawless (2003))。在本文中,對於現狀數據在優劣比-風險模型下,我們發展了評估比例風險假設和比例優劣比假設之診斷方法(Scharfstein, Tsiatis, and Gilbelt (1998)),同時對所提估計提供一穩定且快速計算法則。我們藉由模擬研究和三個實例分析來說明所提方法的表現。
英文摘要 The regression diagnostics that assess the adequacy of a regression model for observed data should be conducted before the regression analysis. For complete or right censored failure time data, several graphical or quantitative methods have been established for regression diagnostics (e.g. Collett (1994), Klein and Moeschberger (2003), and Lawless (2003)). In the thesis, we develop a diagnostic method for assessing the proportional hazards and proportional odds assumptions with current status data under the odds-rate model (Scharfstein, Tsiatis, and Gilbelt (1998)) and provide a stable and efficient computation method for proposed estimators. We illustrate the performance of our method via simulation studies and three real data analysis.
論文目次 Contents
1 Introduction 1
2 Odds-rate model 2
3 Some modeling checking methods 5
3.1 Log-log survival plots/ log odds plots 5
3.2 Observed versus expected survival plots 6
3.3 Cox-Snell residuals method 7
3.4 Brier-Score method 8
4 The proposed approach 9
4.1 Diagnostics based on OR model 9
4.2 Computation algorithm 11
5 Numerical studies and applications 13
5.1 Simulation studies 13
5.2 Applications 14
6 Concluding remarks 16
References 18
參考文獻 References
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Chang, Y. S. (張晏昇) (2013). Evaluating the Proportional Odds Assumption with Current Status Survival Data. Master Thesis, Tamkang University.
Collett, W. E. (1994). Modelling survival data in medical research. Chapman and Hall, London.
Cox, D. R. & Snell, E. J. (1968). A general definition of residuals (with discussion). Journal of the Royal Statistical Society, Series B, 30, 248-275.
Groeneboom, P. & Wellner, J. A. (1992). Information bounds and nonparametric maximum likelihood estimation. DMV Seminar, Band 19, Birkhauser,
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Groeneboom, P. (1995). Nonparametric estimators for interval censoring problems. Analysis of Censored Data (Pune, 1994/1995), (Eds. Koul, H. L. & Deshpande, J. V.), IMS Lecture Notes-Monograph Series 27, 105-128.
Hoel, D. G. & Walburg, H. E. (1972). Statistical analysis of survival experiments. Journal of National Cancer Institute, 49, 361-372.
Huang, J. (1996). Efficient estimation for the Cox model with interval censoring. Annals of Statistics, 24, 540-568.
Klein, J. P. & Moeschberger, M. L. (2003). Survival Analysis: Techniques for Censored and Truncated Data, 2nd edition. Springer Verlag, New York.
Korosok, M. R. (2008). Introduction to Empirical Processes and Semiparametric Inference. Springer, New York.
Lawless, J. F. (2003). Statistical models and methods for lifetime data. John Wiley, New York.
Lin, D. Y., Oakes, D. & Ying, Z. (1998). Additive hazards regression with current status data. Biometrika, 85, 289-298.
Rossini, A. J. & Tsiatis, A. A. (1996). A semiparametric proportional odds regression model for the analysis of current status data. Journal of the American Statistical Association 91, 713-721.
Scharfstein, D. O., Tsiatis, A. A. & Gilbert, P. B. (1998). Semiparametric Efficient Estimation in the Generalized Odds-Rate Class of Regression Models for Right-Censored Time-to-Event Data. Lifetime Data Analysis, 4, 355-391.
Self, S. G. & Liang, K. Y. (1987). Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions. Journal of the American Statistical Association, 82, 605-610.
Sun, J. & Sun, L. (2005). Semiparametric linear transformation models for current status data. The Canadian Journal of Statistics, 33, 85-96.
Tian, L. & Cai, T. (2006). On the accelerated failure time model for current status and interval censored data. Biometrika, 93, 329-342.
Wang, W. (王維) (2013). Evaluating the Proportional Hazards Assumption with Current Status Survival Data. Master Thesis, Tamkang University.
Xue, H., Lam, K. F. & Li, G. (2004). Sieve maximum likelihood estimation for semiparametric regression models with current status data. Journal of the American Statistical Association, 99, 346-356.
Yu, Q.,Wong, G. Y. C. & Li, L. (2001). Asymptotic properties of sel-fconsistent estimators with mixed interval-censored data. Annals of the Institute of Statistical Mathematics, 53, 469-486.
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