配對病例對照研究下羅吉斯模型的動差形式適合度檢定的檢定函數的選擇

The choice of testing function in the moment-type goodness-of-fit test of the logistic model for matched case-control studies

江欣芳(Hsin-Fang Jiang)

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.2014.00268

摘要

病例對照研究被廣泛地使用在探討稀有疾病的研究中。當干擾變數難以量化時，實務上採用配對設計控制干擾變數，以調整因干擾作用產生的偏差。在配對病例對照研究中，常使用羅吉斯迴歸模型推論風險因子和二元反應變數的關係。由於模型包含大量的層效應參數，Breslow & Day (1980)提出條件概似法來消除過多的截距項參數。Chen & Wang (2013) 針對模型的適合度檢定提出動差形式檢定統計量，該檢定統計量是由任意的可測函數的條件最大概似估計量和無母數最大概似估計量的差建構而來。Chen & Wang (2013)採用的可測函數為共變量的平方，本文考慮可測函數為多項式函數、指標函數、對數函數，進一步以模擬研究評估不同的可測函數在動差形式適合度檢定的表現，最後透過實際資料說明新方法的操作。

關鍵字

條件最大概似估計量 ； 適合度檢定 ； 羅吉斯模型 ； 配對病例對照研究

並列摘要

Case-control studies have been widely applied to investigate rare diseases. When confounding variables are difficult to be quantified, matching designs are used to adjust the confounding effects to reduce the bias in practice. Matched case-control studies often use the logistic regression model to fit the relationship between the risk factors and binary response variable. As a result of highly stratum-effect parameters, Breslow & Day (1980) adopted the conditional approach to eliminate the intercepts. Chen & Wang (2013) proposed a moment-type goodness-of-fit test. This test statistic was constructed based on the discrepancy between the conditional maximum likelihood estimator and nonparametric maximum likelihood estimator of any measurable function. Chen & Wang (2013) set the measurable function as the square of the covariates. This study considers the measurable function to be the polynomial function, indicator function and logarithmic function. Further, the performances of the different testing functions of the moment-type goodness-of-fit test are assessed through simulation studies. Finally, a real dataset is used to illustrate the implement of the proposed method.

並列關鍵字

Conditional maximum likelihood estimator ； Goodness-of-fit ； Logistic regression model ； Matched case-control study

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.

Chen, L. C. & 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.