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系統識別號 U0002-1407201401114800
中文論文名稱 配對病例對照研究中條件羅吉斯模型的資訊矩陣適合度檢定
英文論文名稱 An information matrix goodness-of-fit test of the conditional logistic model for matched case-control studies
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 102
學期 2
出版年 103
研究生中文姓名 蔡靜雯
研究生英文姓名 Ching-Wen Tsai
學號 601650046
學位類別 碩士
語文別 中文
口試日期 2014-06-05
論文頁數 34頁
口試委員 指導教授-陳麗菁
委員-王俊毅
委員-陳蔓樺
中文關鍵字 適合度檢定  資訊矩陣檢定  羅吉斯模型  配對病例對照資料 
英文關鍵字 goodness-of-fit  information matrix  logistic model  matched case-control data 
學科別分類
中文摘要 在流行病學研究中,經常使用病例對照設計來調查疾病和風險因子之間的關係。然而干擾因子的存在會對風險因子和疾病之間的相關性造成影響。一般調整干擾作用的方法可以先在設計階段做分層的動作,或是使用多元迴歸的方法。可是當干擾因子無法量化時,就必須在資料收集前的研究設計階段作控制,此時透過配對設計,將干擾因子當作配對的層變數,即可解決這個問題。本文根據 Breslow & Day (1980) 所採用的條件概似法消除層效應的截距項,以增加估計的效率。進一步地,針對配對病例對照資料,推廣White (1982) 和Zhang (2001) 的資訊矩陣檢定,提出條件羅吉斯模型的資訊矩陣適合度檢定,以評估羅吉斯模型的合適性。最後,將所提出的檢定方法應用在低出生體重新生兒的資料上。
英文摘要 In epidemiological studies, the case-control design has been widely applied to investigate the association between risk factors and a given disease. While a confounder may have an important influence on the apparent relationship between risk factors and a disease. In general, to adjust effects for confounding factors, methods such as stratification at the design stage and/or multiple regression methods at the analysis stage may be adopted. When some major confounding factors are difficult to be quantified, a matching design is used to control the confounding effects. The conditional approach is adopted to eliminate the stratum-specific intercepts to increase the efficiency of the estimate (Breslow and Day 1980). Further, this paper generalizes the idea of White (1982) and Zhang (2001), and proposes an information matrix test for the goodness-of-fit of the logistic model for matched case-control data. Finally, this study illustrates the information matrix test by a low birth weight study.
論文目次 目錄
第一章 緒論.................................................1
第二章 條件羅吉斯模型的適合度檢定方法............................9
第一節 條件羅吉斯模型.......................................9
第二節 建構條件羅吉斯模型的資訊矩陣檢定統計量...................12
第三節 拔靴法........................................... .16
第三章 模擬研究.............................................20
第四章 實例分析.............................................25
第五章 討論與結論...........................................28
參考文獻...................................................30
附錄:原始資料..............................................32

表目錄
1. 所有病人的糖尿病類型之死亡和設限個數(比例).....................3
2. 以年齡分類後的糖尿病類型之死亡和設限個數(比例)..................3
3. 改良拔靴法-檢定統計量模擬的經驗型一誤差率.....................23
4. 改良拔靴法-檢定統計量模擬的經驗檢定力........................23
5. 傳統拔靴法-檢定統計量模擬的經驗型一誤差率.....................23
6. 傳統拔靴法-檢定統計量模擬的經驗檢定力........................24
7. 低出生體重新生兒資料的檢定統計量值和p值.......................27
8. 低出生體重新生兒研究資料的變數介紹...........................27

參考文獻 參考文獻
Aitchison, J. and Silvey, S. D. (1958). Maximum-likelihood estimation of parameters subject to restraints. The Annals of Mathematical Statistics, 39, 813-828
Arbogast, P. G. and Lin, D. Y. (2004). Goodness-of-fit methods for matched case-control studies. The Canadian Journal of Statistics, 32, 373-386.
Bedrick, E. J. and Hill, J. R. (1996). Assessing the fit of the logistic regression model to individual matched sets of case-control data. Biometrics, 52, 1-9.
Breslow, N. E., Day, N. E., Halvorsen, K. T., Prentioe, R. L. and Sabai, C. (1978). Estimation of multiple relative risk functions in matched case-control studies. American Journal of Epidemiology, 108, 299-307.
Breslow, N. E. and Day, N. E. (1980). Statistical Methods in Cancer Research, 1, The Analysis of Case-Control Studies. International Agency for Research on Cancer, Lyon, France.
Chen, L. C. and Wang, J. Y. (2013). Testing the fit of the logistic model for matched case-control studies. Computational Statistics and Data Analysis, 57, 309-319.
Cheng, K. F. and Chen, L. C. (2004). Testing goodness-of-fit of a logistic regression model with case-control data. Journal of Statistical Planning and Inference, 124, 409-422.
Fokianos, K., Peng, A. and Qin, J. (1999). A generalized-moments specification test for the logistic link. The Canadian Journal of Statistics, 27, 735–750.
Holford, T., White, C. and Kelsey, J. L. (1978). Multivariate analysis for matched case-control strdies. American Journal of Epidemiology 107, 245-256.
Hosmer, D. W. and Lemeshow, S. (1980). Goodness-of-fit tests for the multiple logistic regression model. Communications in Statistics-Theory and Methods, 9, 1043-1069.
Hosmer, D. W. and Lemeshow, S. (2013). Applied Logistic Regression, 3rd Edition. Wiley, New York.
Moolgavkar, S. H., Lustbader, E. D. and Venzon, D. J. (1984). A geometric approach to nonlinear regression diagnostics with application to matched case-control studies. The Annals of Statistics, 12, 816-826.
Moolgavkar, S. H., Lustbader, E. D. and Venzon, D. J. (1985). Assessing the adequacy of the logistic regression model for matched case-control studies. Statistics in Medicine, 4, 425-435.
Newey, W. K. (1985). Maximum likelihood specification testing and conditional moment tests. Econometrica, 5, 1047-1070.
Pregibon, D. (1984). Data analytic methods for matched case-control studies, Biometrics, 40, 639-651.
Qin, J. and Zhang, B. (1997). A goodness-of-fit test for logistic regression models based on case-control data. Biometrika, 84, 609-618.
Smith, P. G., Pike, M.C., Hill, A.P., Breslow, N.E. and Day, N.E.(1981). Multivariate condictional logistic analysis of stratum matched case-control studies. Applied Statistics 30, Algorithm AS162, 190-197.
Julious, S. A. and Mullee, M. A (1994). Confounding and Simpson's paradox. BMJ 309, 1480–1481.
White, H. (1982). Maximum likelihood estimation of misspecified models. Econoomnetrica, 50, 1-25.
Woodward, M (2004). Epidemiology-Study Design and Data Analysis, 2nd Edition. Chapman & Hall/CRC, London.
Zhang, B. (1999). A chi-squared goodness-of-fit test for logistic regression models based on case-control data. Biometrika, 86, 531-539.
Zhang, B. (2001). An information matrix test for logistic regression models based on case-control data. Biometrika, 88, 921-932.
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