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系統識別號 U0002-2401201020314900
中文論文名稱 配對病例對照研究中羅吉斯迴歸模型的適合度檢定
英文論文名稱 Goodness-of-fit test of logistic regression model in 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 98
學期 1
出版年 99
研究生中文姓名 曾靖茹
研究生英文姓名 Ching-ju Tseng
學號 696650042
學位類別 碩士
語文別 中文
口試日期 2010-01-08
論文頁數 40頁
口試委員 指導教授-陳麗菁
委員-鄧文舜
委員-林哲揚
中文關鍵字 配對病例對照資料  雙樣本半參數化模型  羅吉斯迴歸模型  條件最大概似估計量  適合度檢定  隨機效應模型 
英文關鍵字 matched case-control data  two-sample semiparametric model  logistic regression model  condictional maximum likelihood estimator  goodness-of-fit  random effects model 
學科別分類 學科別自然科學統計
中文摘要 在流行病學研究中,羅吉斯迴歸模型常用來推論風險因子和二元反應變數之間的關係。在稀有疾病常以病例對照研究改善抽樣效率。當主要的干擾變數太多時,配對病例對照設計比病例對照設計更能消除偏差。Breslow & Day(1980)使用條件概似方法消除過多的截距項。羅吉斯迴歸模型能依靠方便的統計軟體簡易且快速執行,然而常有羅吉斯迴歸模型錯置的案例,因此以模型的適合度檢定確認最後模型。我們推廣Cheng & Chen(2004)的想法,在配對病例對照資料下提出分數型態的檢定以檢定羅吉斯迴歸模型。由Arbogast & Lin (2004)的結果可知,我們提出的分數檢定會弱收斂至高斯過程。最後,進行模擬研究以評估檢定統計量的有限樣本性質,並以低出生重量研究做實例分析。
英文摘要 In epidemiology studies, the logistic regression model is used popularly for inferring the relation of risk factors and a binary response variable. For rare diseases, we usually take case-control studies to improve sampling efficiency. When some major confounding variables are difficult to quantity, a matched case-control design can be adopted to eliminate biased comparisons between cases and controls. Breslow & Day (1980) use the conditional likelihood to eliminate the too many intercept terms. Relying on convenient statistical software, the logistic regression models are easily and rapidly implemented. It is, however, often misplace to examine whether a logistic model fit the data well. It should be recognized that before constructing the final model, a goodness-of-fit test of the model is still an important issue. We generalized the idea of Cheng & Chen (2004), and propose a Score type test for the logistic regression model under matched case-control data. The Score test converges weakly to a centered Gaussian process by the result of Arbogast & Lin (2004).We assess the performance of the proposed test through simulation studies in finite sample and illustrate the score test by a low birth weight study.
論文目次 第一章 緒論 ---------------------------------------------------------------------------01
第二章 羅吉斯迴歸模型的適合度檢定 ------------------------------------------07
第一節 羅吉斯迴歸模型的介紹 -------------------------------------------------07
第二節 迴歸參數的估計 ----------------------------------------------------------09
第三節 迴歸模型的適合度檢定 -------------------------------------------------14
第四節 1:1配對病例對照資料 ---------------------------------------------------23
第三章 模擬研究 ---------------------------------------------------------------------24
第一節 適合度檢定的數值模擬 ---------------------------------------------24
第二節 適合度檢定的實例分析 ---------------------------------------------27
第四章 結論 --------------------------------------------------------------------------31
參考文獻 -------------------------------------------------------------------------------33
附錄:原始資料 ----------------------------------------------------------------------37

表目錄
1. 分數檢定和上界檢定的模擬結果 ----------------------------------------26
2. 低出生重量研究資料的變數名稱與變數值描述 ----------------------30

參考文獻 [1] Agresti, A. (2002). Categorical Data Analyasis. 2nd ed. New York: John
Wiley.
[2] Allison, P.D. (1999). Logistic regression using the SAS system: theory
and application. Cary, N.C.:SAS Institute.
[3] Arbogast, P.G. & Lin, D.Y. (2004). Goodness-of-fit methods for matched
case-control studies. The Canadian Journal of Statistics 32, 373-386.
[4] Arbogast, P.G. & Lin, D.Y. (2005). Model-checking techniques for
stratified case-control studies. Statistics in Medicine 24, 299-247.
[5] Bedrick, E. J. & Hill, J.R. (1996). Assessing the fit of the logistic
regression model to individual matched sets of case-control data.
Biometrics 52,1-9.
[6] Breslow, N.E. & Day, N.E. (1980). Statistical Methods in Cancer
Research,1,The Analysis of Case-Control Studies. International
Agency for Research on Cancer, Lyon, France.
[7] Breslow, N.E., Day, N.E., Halvorsen, K. T., Prentioe, R. L. & Sabai, C.
(1978). Estimation of multiple relative risk functions in matched
case-control studies. American Journal of Epidemiology 108, 299-307.

[8] Cheng, K.F. & 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.
[9] Cox, D.R. (1970). The Analysis of Binary Data. London: Methuen.
[10] Faraway, J.J. (2006). Extending the linear model with R : generalized
linear, mixed effects and nonparametric regression models. Boca
Raton, Fla.:Chapman & Hall/CRC
[11] Gail, M.H., Lubin, J.H., & Rubinstein, L.V.(1981). Likelihood
calculations for matched case-control studies and survival studies
with tied death times. Biometrika 68,703-707.
[12] Hirji, K.F., Mehta, C.R. & Patel, N.R. (1988). Exact inference for
matched case-control studies. Biometrics 44,803-814.
[13] Holford, T. (1978). The analysis of pair-matched case-control studies, a
multivariate approach. Biometrics 34,665-672.
[14] Holford, T.,White, C. & Kelsey, J.L. (1978). Multivariate analysis for
matched case-control studies. American Journal of Epidemiology
107, 245-256.
[15] Hosmer, D.W. & Lemeshow, S. (2000). Applied logistic regression.
2nd ed. New York: Wiley.
[16] Lecessie, S. & Vanhouwelingen, H.C.(1995). Testing the fit of a
regression model via score tests in random effects models. Biometrics
51, 600-614.
[17] Liu, I., Mukherjee, B., Suesse, T., Sparrow, D. & Park, S.K.(2009).
Graphical diagnostics to check model misspecification for the
proportional odds regression model. Statistics in medicine 28, 412–429.
[18] Moolgavkar, S.H., Lustbader, E.D. & Venzon, D.J. (1985). Assessing
the adequacy of the logistic regression model for matched case-
control studies. Statistics in Medicine 4, 425-435.
[19] Pike, M.C., Hill, A.P. & Smith, P.G.(1980). Bias and efficiency in
logistic analyses of stratified case-control studies. International Journal
of Epidemiology 9, 89-95.
[20] Pregibon, D. (1984). Data analytic methods for matched case-control
studies, Biometrics 40,639-651.
[21] Prentice, R. L. & Pyke, R. (1979). Logistic disease incidence models
and case-control studies. Biometrika 66, 403-411.
[22] Qin, J. & Zhang, B. (1997). A goodness-of-fit test for logistic
regression models based on case-control data. Biometrika 84,
609-618.
[23] Qin, J. (1998). Inferences for case-control and semiparametric
two-sample density ratio models. Biometrika 85, 619-630.
[24] SAS Institute. (1995). Logistic regression examples using the SAS
system. 1st ed. Cary, N.C. : SAS Institute.
[25] Smith, P.G., Pike, M.C., Hill, A.P., Breslow, N.E. & Day, N.E.(1981).
Multivariate condictional logistic analysis of stratum matched
case-control studies. Applied Statistics 30, Algorithm AS162,190-197.
[26] Woodward, M. (2005) Epidemiology: study design and data analysis.
2nd ed. Chapman & Hall /CRC.
[27] Zhang, B. (1999). A chi-squared goodness-of-fit test for logistic
regression models based on case-control data. Biometrika 86,
531-539.
[28] Zhang, B.(2006). A score test under logistic regression models based
on case-control data. Statistica Neerlandica 60, 477-496.
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