在分層病例對照研究下，針對羅吉斯迴歸模型的適合度檢定，我們考慮在一個廣義的隨機效應模型下建構分數形式檢定統計量。此檢定與梁正憲(2008)所提之動差形式檢定統計量相同。本文進一步地整理Arbogast-Lin檢定，以及實務上常遭誤用的Hosmer-Lemeshow檢定，並針對這幾個檢定進行模擬比較。最後呈述一個關於食道癌研究的範例。

We present the score type test for assessing the adequacy
of the logistic regression model in stratified case-control study. This score test is construct based on a random effect model. The proposed test statistic is identical to the moment specification test of Liang(2008). We also review the Arbogast-Lin test and Hosmer-Lemeshow test. The Hosmer-Lemeshow test is valid for prospective data, but if is constantly misapplied for retrospective data. Some comparisons between these methods are performed by simulation studies. An illustration of a research about cancer of the esophagus is provided.

目錄
第一章 緒論...............................................1
第二章 羅吉斯迴歸模型的適合度檢定.........................6
   第一節 羅吉斯迴歸模型..................................6
   第二節 迴歸模型的適合度檢定...........................10
   第三節 Arbogast & Lin 統計量與Hosmer-Lemeshow統計量...22
第三章 模擬研究..........................................28
   第一節 模擬研究.......................................28
   第二節 實例分析.......................................31
第四章 結論..............................................33
參考文獻.................................................34

表目錄
1 不同的beta2及樣本數下以X=(X1,X1^2)模擬顯著水準,以X=X1模擬檢定力...................................................30

2 不同風險因子下的病例組與對照組之邊際和.................32

參考文獻
[1] Arbogast, P. G. and Lin, D. Y. (2005). Model-checking techniques for strati¯ed case-control studies. Statistics in medicine, 24, 229-247.
[2] Breslow, N. E. and Day, N. E. (1980). Statistical Methods in Cancer Research I: The Analysis of Case-Control Studies. Lyon: International Agency for Research on Cancer.
[3] Cheng, K. F. and Chen, L. C. (2005). Testing goodness-of-fit of a logistic regression model with case-control data. Journal of statistical planning and inference, 124, 409-422.
[4] Hosmer, D. W. and Lemeshow, S. (1989). Applied logistic regression, New York: Wiley.
[5] Erik, P. and Timothy, J. R. (2002). Two goodness-of-fit tests for logistic regression models with continuous covariates. Statistics in medicine, 21, 79-93.
[6] Prentice, R. L. Pyke, R. (1979). Logistic disease incidence models and case-control studies. Biometrika, 66(3), 403-11.
[7] Qin, J. and Zhang, B. (1997). A goodness-of-fit test for logistic regression models based on case-control data. Biometrika, 84(3), 609-618.
[8] Qin, J. (1998). Inferences for case-control and semiparametric two-sample density ratio models. Biometrika, 85(3), 619-630.
[9] Scott A. J. and Wild C. J. (1991). Fitting logistic regression models in stratified case-control studies. Biometrics, 47(2), 497-510.
[10] White, J. E. (1982). A two stage design for the study of the relationship between a rare exposure and a rare disease. American Journal of Epidemiology, 115(1), 119-28.
[11] Zhang, B. (1999). A chi-squared goodnes-of-fit test for logistic regression models based on case-control data. Biometrika, 86(3), 531-839.
[12] Zhang, B. (2001). An information matrix test for logistic regression models based on case-control data. Biometrika, 88(4), 921-932.
[13] 梁正憲(2008)。分層病例對照資料下羅吉斯迴歸模型的適合度檢定。[碩士論文]台北:淡江大學統計學系應用統計研究所。