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研究生:偕埕堉
研究生(外文):Jie, Chengyu
論文名稱:左截右設限下,Aalen加成模型之適合度檢定
論文名稱(外文):On Goodness-of-fit Test For Aalen's Additive Model Base On Left-truncated Right-censored Data
指導教授:沈葆聖沈葆聖引用關係
指導教授(外文):Shen, Paosheng
口試委員:林正祥戴政
口試日期:2012-07-03
學位類別:碩士
校院名稱:東海大學
系所名稱:統計學系
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:2012
畢業學年度:100
語文別:英文
論文頁數:11
外文關鍵詞:Aalen modelGoodness-of-fitCox regression
相關次數:
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Gandy and Jensen (2005)提出了在右設限下之適合度檢定。在這篇論文當中證明出Gandy and Jensen (2005)的方法
可以推廣到左截右設限資料,並且進行模擬研究。建議使用在心臟移植的數據分析。
Gandy and Jensen (2005) proposed goodness-of- t tests for Aalen's additive risk
model based on right-censored data. In this article, we demonstrate that the ap-
proach of Gandy and Jensen (2005) can be extended to left-truncated right-censored
(LTRC) data. A simulation study is conducted to investigate the performance of
the proposed tests. The proposed tests are applied to analyze heart transplant data.
1.Introduction

Example 1: prevalent cohort data 2

2.The Proposed Tests

3.Simulation Studies

3.1 Estimated Type I Error

Table 1

3.2 Estimated Statistical Power

Table 2

4. Conclusion

References
Aalen, O. O. (1980). A model for non-parametric regression analysis of counting
process. In:Klonecki, W., Kozek, A., Rosiski, J. (Eds). Lecture Notes on Mathe-
matical Statistics and Probability, Vol. 2. Springer, New York, pp. 1-25.

Aalen, O. O. (1989). A linear regression model for analysis of life times. Statistics
in Medicine, 8, 907-925.

Aalen, O. O. (1993). Further results on the non-parametric linear regression model
in survival analysis. Statistics in Medicine, 17, 1569-1588.

Chang, M. N. and Yang, G. L. (1987), Strong consistency of a nonparametric esti-
mator of the survival function with doubly censored data. Annals of Statistics 15,
1536-1547.

Chang, M. N. (1990), Weak convergence of a self-consistent estimator for the sur-
vival function with doubly censored data. Annals of Statistics 18, 391-404.
Cox, D. (1972). Regression models and life tables (with Discussion). J. R. Statist.
Soc. B, 34, 187-220.

The CSHA working group (1994). Canadian study of health and aging: study
methods and prevalence of dementia. Journal of the Canadian Medical Association,
150, 899-913.

Gandy, A. and Jensen U. (2005). On goodness-of- t tests for Aalen's additive risk
model. Scan. J. Stat., 32, 425-445.

Gu, M. G. and Zhang, C. H. (1993), Asymptotic properties of self-consistent esti-
mators based on doubly censored data. Annals of Statistics 21, 611-624.
Hu er, F. W. and Mckeague, F. W. (1991). Weighted least squares estimation for
Aalen's additive risk model. Journal of the American Statistical Association, 86,
114-129.

McKeagues, I. W. (1988). Asymptotic theory for weighted least squares estimators
in Aalen's additive risk model. in Statistical Inference from Stochastic Processes,
page 139-152.

McKeagues, I. W. and Utikal, K. J. (1991). Goodness-of- t tests for additive haz-
ards and proportional hazards models. Scandinavian Journal of Statistics, 18, 177-
195.

Mandel, M. (2007) Censoring and Truncation - Highlighting the Di erences. Amer.
Statist., 61, 321-324.

Pan, W. and Chappell, R. (2002). Estimation in the Cox proportional hazards
model with left-truncated and interval-censored data. Biometrics, 58, 64-70.
Shen, P.-S. (2011). Semiparametric Analysis of Transformation Models with Doubly
Censored Data. Journal of Applied Statistics, 38, 367-377.

Teodorescu, B and Keilegom, I. V. (2010). A goodness of t test for generalized
conditional linear models under left truncation and right censoring. Journal of
Nonparametric Statistics, 22, 547-566.

Tsai, W. Y. and Crowley, J. (1985), A large sample study of generalized maximum
likelihood estimators from incomplete data via self-consistency. Annals of Statistics,
13, 1317-1334.

Turnbull, B. W. (1974), Nonparametric estimation of a survivorship function with
doubly censored data. Journal of the American Statistical Association, 69, 169-173.
Wang, M.-C. (1991). Nonparametric estimation from cross-sectional survival data.
Journal of the American Statistical Association, 86, 130-143.
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