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

An information matrix goodness-of-fit test of the conditional logistic model for matched case-control studies

蔡靜雯(Ching-Wen Tsai)

指導教授 ： 陳麗菁

淡江大學/商管學院/統計學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00409

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。

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

並列摘要

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.

並列關鍵字

goodness-of-fit ； information matrix ； logistic model ； matched case-control data

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.

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.