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System No. U0002-1807201317130500
Title (in Chinese) 使用優劣比-風險模型對現狀數據之迴歸診斷
Title (in English) Regression Diagnostics for Current Status Data using the Odds-Rate Model
Other Title
Institution 淡江大學
Department (in Chinese) 數學學系碩士班
Department (in English) Department of Mathematics
Other Division
Other Division Name
Other Department/Institution
Academic Year 101
Semester 2
PublicationYear 102
Author's name (in Chinese) 洪筱涵
Author's name(in English) Hsiao-Han Hung
Student ID 600190234
Degree 碩士
Language English
Other Language
Date of Oral Defense 2013-06-26
Pagination 24page
Committee Member advisor - Chi-Chung Wen
co-chair - 黃逸輝
co-chair - 吳裕振
Keyword (inChinese) 現狀數據
優劣比-風險模型
配適度指標
Keyword (in English) Goodness of fit index
Current status data
Odds-rate model
Other Keywords
Subject
Abstract (in Chinese)
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。
Abstract (in English)
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.
Other Abstract
Table of Content (with Page Number)
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
References
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,
New York.
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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