配對病例對照研究中羅吉斯迴歸模型的適合度檢定

Goodness-of-fit test of logistic regression model in matched case-control studies

曾靖茹(Ching-ju Tseng)

指導教授 ： 陳麗菁

淡江大學/管理學院/統計學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00813

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。

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

並列摘要

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.

並列關鍵字

matched case-control data ； two-sample semiparametric model ； logistic regression model ； condictional maximum likelihood estimator ； goodness-of-fit ； random effects model

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

[3] Arbogast, P.G. & Lin, D.Y. (2004). Goodness-of-fit methods for matched

regression model to individual matched sets of case-control data.