本文考慮以配對病例對照鑑取抽樣 (matched case-control proband sampling) 來探討疾病的「家族聚集性 (familial aggregation) 」現象。當沒有共變量資訊時，我們推廣 Datta & Satten (2005) 群集資料的秩和檢定 (rank-sum test for clustered data)，以無母數統計法檢視疾病是否存在家族聚集性。當進一步蒐集到共變量資料時,我們推廣 Liang & Pulver (1996) 的方法，透過模型的建立，以解析家族聚集性的起因：遺傳因素或是環境因素。針對推廣後的新方法，我們亦進行有限樣本的模擬研究。最後就阻塞型睡眠呼吸中止症候群 (Obstructive sleep apnea, OSA) 的虛擬資料進行實例分析。

In this paper, some methods are proposed for the analysis of matched case-control proband data arising from familial aggregation studies. When there is no covariate information, we generalized the rank-sum test for clustered data (Datta & Satten, 2005) to detect 
familial aggregation. If there are some cavariate informations, we apply the generalized method of Liang & Pulver (1996) to analyze the cause of familial aggregation : genetic or environmental factors. We apply the proposed methods to obstructive sleep apnea pseudodata.
Some simulation studies with finite sample demonstrate the usefulness of our approach.

目錄 
第一章 緒論...1 
第二章 配對病例對照鑑取抽樣下之秩和檢定...6 
第一節 檢定統計量...6 
第二節 模擬研究...11 
第三章 配對病例對照鑑取抽樣下之廣義估計方程式...14 
第一節 廣義估計方程式...14 
第二節 模擬研究...18 
第四章 虛擬實例分析...30 
第五章 結論...35 
參考文獻...37 
附錄一 定理1 證明...40 
附錄二 虛擬資料...43 

圖目錄
1 五組配對家庭之參數估計量 δ 與估計量變異數 Var(δ)比較圖... 22
2 五組配對家庭下 δ 的變異數與變異數估計量比較圖...23
3 五組配對家庭之參數估計量 β 與估計量變異數 Var(β)比較圖...24
4 五組配對家庭下 β 的變異數與變異數估計量比較圖...25
5 十組組配對家庭之參數估計量 δ 與估計量變異數 Var(δ)比較圖...26
6 十組配對家庭下 δ 的變異數與變異數估計量比較圖...27
7 十組配對家庭之參數估計量 β 與估計量變異數 Var(β)比較圖...28
8 十組配對家庭下 β 的變異數與變異數估計量比較圖...29

表目錄
1 兩種秩和檢定統計量之名目顯著水準...13
2 推廣的Datta-Satten 群集資料秩和檢定統計量之近似檢定力...13
3 Liang & Pulver (1996) 及新方法之GEE 分析結果...34

英文部分:

1. Agresti, A. (2002), Categorical Data Analyasis, 2nd. New York: John Wiley.
2. Breslow, N.E. (1996), Statistics in Epidemiology: The Case-Control Study. Journal of the American Statistical Association, 91, 14-28.
3. Breslow, N.E., and Day, N.E. (1980), Statistical Methods in Cancer Research, 1, The Analysis of Case-Control Studies, Lyon: IARC.
4. Datta, S., and Satten, G.A. (2005), Rank-sum tests for clustered data. Journal of the American Statistical Association, 100, 908-915.
5. Liang, K.Y., and Beaty, T.H. (2000), Statistical designs for familial aggregation. Statistical Methods in Medical Research, 9, 543-562.
6. Liang, K.Y., and Pulver, A.E. (1996), Analysis of case-control/family sampling design. Genetic Epidemiology, 13, 253-270.
7. Liang, K.Y., and Zeger, S.L. (1986), Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
8. Mantel, N., and Haenszel, W. (1959), Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute, 22, 719-748.
9. Mathur, R., and Douglas, N.J. (1995), Family studies in patients with the sleep apnea-hypopnea syndrome. Annals of Internal Medicine, 122, 174-178.
10. Pillar, G., and Lavie, P. (1995), Assessment of the role of inheritance in sleep apnea syndrome. American Journal of Respiratory and Critical Care Medicine, 151, 688-691.
11. Prentice, R.L., and Pyke, R. (1979), Logistic disease incidence models and case-control studies. Biometrika, 66, 403-411.
12. Redline, S., Tishler, P.V., Tosteson, T.D., Williamson, J., Kump, K., Browner, I., Ferrette, V., and Krejci, P. (1995), The familial aggregation of obstructive sleep apnea. American Journal of Respiratory and Critical Care Medicine, 151, 682-687.
13. Serfling, R.J. (1980), Approximation Theorems of Mathematical Statistics, New York: Wiley.
14. Wang, M., Williamson, J.M., and Redline, S. (2004), A Semiparametric Method for Analyzing Matched Case-Control Family Studies with a Continuous Outcome and Proband Sampling. Biometrics, 60, 573-844.
15. Wedderburn, R.W.M. (1974), Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439-447.
16. Wilcoxon, F. (1945), Individual comparisons by ranking methods. Biometrics, 1, 80-83.
17. Williamson, J., Tosteson, T., Redline, S., Liu, X., and Dawson, D. (1996), Familial aggregation studies with matched proband sampling. Human Heredity, 46, 76-84.
18. Woodward, M. (2004), Epidemiology: Study Design and Data Analysis, 2nd , Florida: Chapman & Hall/CRC.

中文部分:

1. 戴政, 2002 年, 遺傳流行病學-基因定位之遺傳設計與分析方法, 藝軒圖書出版社。
2. 戴政與江淑瓊, 2004 年, 生物醫學統計概論, 第三版, 翰蘆圖書出版社。