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研究生:杞育霖
研究生(外文):Yu-Lin Chi
論文名稱:半競爭風險資料之分量迴歸分析
論文名稱(外文):Quantile regression based on semi-competing risks data
指導教授:謝進見
指導教授(外文):Jin-Jian Hsieh
口試委員:黃郁芬黃士峰
口試委員(外文):Yu-Fen HuangShih-Feng Huang
口試日期:2011/06/09
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數理統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:57
中文關鍵詞:Copula 模型相關設限分量迴歸半競爭風險資料
外文關鍵詞:Copula modelDependent censoringQuantile regressionSemi-competing risks data
相關次數:
  • 被引用被引用:1
  • 點閱點閱:292
  • 評分評分:
  • 下載下載:4
  • 收藏至我的研究室書目清單書目收藏:0
本篇論文主要探討半競爭風險資料下分量迴歸的估計。由於非終端事件會受到終端事件的相關設限,使得分量迴歸的參數估計變的困難。沒有額外的假設下,我們無法對非終端事件做出推論。因此,我們利用 copula 模型說明非終端事件與終端事件之間的相關性結構。我們採用 IPW 方法估計半競爭風險下分量迴歸的參數。在 Hz(t) 已知的假設下,我們提供了此估計量的大樣本性質,並介紹模型診斷方法。根據模擬實驗的結果顯示我們所提出的方法表現的還不錯。最後,我們將應用我們所提出的方法分析骨髓移植資料作為描述。

This thesis focuses on the quantile regression analysis for semi-competing risks data. Since the non-terminal event may be censored by the terminal event dependently, the estimation of quantile regression parameters becomes difficult. Without extra assumptions, we can not make inference on the non-terminal event. Thus, we utilize the copula function to specify the dependence between the non-terminal event time and the terminal event time. We adopt the inverse probability weight (IPW) technique to estimate the coefficients of quantile regression for semi-competing risks data. Under the assumption that Hz(t) is known, we also prove the large sample properties of the proposed estimator. We introduce a model diagnostic approach to check model adequacy. According to the simulation studies, the performance of our proposed approach are well. We also apply our approach into a real data which is Bone Marrow Transplant data for illustration.

1 INTRODUCTION..........1
2 DATA and MODELS..........4
2.1 Semi-Competing Risks Data..........4
2.2 Quantile Regression Model..........5
2.3 Copula Model..........6
3 LITERATURE REVIEW..........8
3.1 Estimating Survival and Association in a Semicompeting Risks Model (Lakhal, Rivest and Abdous, 2008)..........8
3.2 Power-Transformed Linear Quantile Regression With Censored Data (Yin, Zeng and Li, 2008)..........11
3.3 Competing Risks Quantile Regression (Peng and Fine, 2009)..........14
4 THE PROPOSED INFERENCE PROCEDURE..........18
4.1 The Estimation of β(γ) ..........18
4.2 Asymptotic Properties of the Proposed Estimator..........22
4.3 Model Checking and Model Diagnosis..........23
5 SIMULATION STUDIES..........26
6 DATA ANALYSIS..........33
7 CONCLUDING REMARKS..........38
References..........39
Appendix..........45
A Connection between Sn(b,γ) and Un(b,γ)..........45
B Proofs of Theorems..........47
Alexander, K. (1984). Probability-Inequalities for Empirical Processes and a Law of the Iterated Logarithm. Annals of Probability 12, 1041-1067.
Buchinsky, M. and J. Hahn (1998). A Alternative Estimator for Censored Quantile Regression. Econometrica 66, 653-671.
Day, R. and J. Bryant (1997). Adaptation of bivariate frailty models for prediction, with application to biological markers as prognostic indicators.
Biometrika 84 (1), 45-56.
Efron, B. and R. J. Tibishirani (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
Fine, J., H. Jiang, and R. Chappell (2001). On semi-competing risks data. Biometrika 88, 907-919.
Fitzenberger, B. (1997). A Guide to Censored Quantile Regressions. In Maddala, G. S. and Rao, C. R. (Ed.), AIDS Epidemiology-Methodological Issues, Volume 15, pp. 405-437. Amsterdam: North-Holland.
He, X. and L. Zhu (2003). A Lack-of-Fit Test for Quantile Regression. Journal of the American Statistical Association 98, 1013-1022.
Horowitz, J. L. and V. G. Spokoiny (2002). An adaptive, Rate-Optimal Test of Linearity for Median Regression Models. Journal of the American Statistical Association 97, 822-835.
Jiang, H., J. Fine, and R. Chappell (2005). Semiparametric analysis of survival data with left truncation and dependent right censoring. Biometrics 61 (2), 567-575.
Kaplan, E. and P. Meier (1958). Nonparametric Estimation From Incomplete Observations. Journal of the American Statistical Association 53, 457-481.
Klein, J. and M. Moeschberger (2003). Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer.
Lai, T. L. and Z. Ying (1988). Stochastic Integrals of Empirical-Type Processes With Applications to Censored Regression. Journal of Multivariate Analysis 27, 334-358.
Lakhal, L., L.-P. Rivest, and B. Abdous (2008). Estimating survival and association in a semicompeting risks model. Biometrics 64, 180-188.
Lin, D., L. Wei, and Z. Ying (1993). Checking the Cox Model With Cumulative Sums of Martingle-Based Residuals. Biometrika 80, 557-572.
Lin, D. Y. and Z. Ying (1993). A simple nonparametric estimator of the bivariate survival function under univariate censoring. Biometrika 80, 573-582.
Oakes, D. (1989). Bivariate survival models induced by frailties. Journal of the American Statistical Association 84, 487-493.
Peng, L. and J. P. Fine (2009). Competing Risks Quantile Regression. Journal of the American Statistical Association 104, 1440-1453.
Peng, L. and Y. Huang (2008). Survival Analysis Based on Quantile Regression Models. Journal of the American Statistical Association 103, 637-649.
Portnoy (2003). Censored Regression Quantiles. Journal of the American Statistical Association 98, 1001-1012.
Powell, J. (1984). Least Absolute Deviations Estimation for the Censored Regression Model. Journal of Econometrics 25, 303-325.
Powell, J. (1986). Censored Regression Qunatiles. Journal of Econometrics 32, 143-155.
Robins, J. M. (1996). Locally Ecient Median Regression With Random Censoring and Surrogate Makers. In Jewell, N. P., Kimber, A. C., Lee, M. L. T., and Whitmore, G. A. (Ed.), Lifetime Data: Models in Reliability and Survival Analysis, pp. 263-274. Kluwer Academic.
Robins, J. M. and A. Rotnitzky (1992). Recovery of Information and Adjustment for Dependent Censoring Using Surrogate Markers. In Jewell, N., Dietz, K., and Farewell, V. (Ed.), AIDS Epidemiology-Methodological Issues, pp. 24-33. Boston: Birkhauser.
Wang, W. (2003). Estimating the association parameter for copula models under dependent censoring. Journal of the Royal Statistical Society 65, 257-273.
Yang, S. (1999). Censored Median Regression Using Weighted Empirical Survival and Hazard Functions. Journal of the American Statistical Association 94, 137-145.
Yin, G., D. Zeng, and H. Li (2008). Power-Transformed Linear Quantile Regression With Censored Data. Journal of the American Statistical Association 103, 1214-1224.
Ying, Z., S. Jung, and L. Wei (1995). Survival Analysis With Median Regression Models. Journal of the American Statistical Association 90, 178-184.
Zheng, J. X. (1998). A Consistent Nonparametric Regression Models Under Quantile Restrictions. Econometric Theory 14, 123-138.
Zheng, M. and J. Klein (1995). Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika 82, 127-138.

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