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研究生:賴信宇
研究生(外文):Lai, Shin-Yu
論文名稱:家族發病時間資料之統計推論 - 文獻回顧
論文名稱(外文):Statistical Inference based on Familial Age-onset Data - A Literature Review
指導教授:王維菁王維菁引用關係
指導教授(外文):Wang, Wei-Jing
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:34
中文關鍵詞:存活時間發病時間關聯模式
外文關鍵詞:Failure timesAge-at-onsetCopula model
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在本論文中,我們回顧有關分析家族發病時間的統計文獻。我們以統整的架構,說明如何探討變數間的關聯性,與建立聯合分佈的方法。討論也包含如何將解釋變數納入分析中的方法。在介紹完模式之理論意義與性質之後,我們討論幾個文獻的實例,了解統計推論所牽涉到的問題與解決的方法。
In the thesis, we review literature on statistical analysis of familial age-onset data. A unified framework is provided to illustrate how statistical methods are applied to investigate interesting scientific phenomenon. We discuss some important association measures and several approaches to handling correlated failure time variables. The extension to include the effect of covariates is also introduced. Finally we discuss applications of these theoretical models to biomedical data.
Chapter 1 Introduction 1
1.1 Motivation and Background 1
1.2 Outline of the Thesis 1
Chapter 2 Association Measures and Models 2
2.1 Association Measures 2
2.1.1 Pearson’s correlation 2
2.1.2 Kendall’s tau 2
2.1.3 The odds ratio function 3
2.2 Model Construction 3
2.2.1 Random effect approach 4
2.2.2 Conditional approach 6
2.2.3 Copula modeling 8
Chapter 3 Mixed-effect Analysis for Familial Age-onset Data 12
3.1 Model for the Familial Study by Li and Thompson 12
3.2 EM Algorithm for the Familial Study 14
3.3 Analysis for Breast Cancer Data 16
3.4 Model for the Twin Study by Do et al. 16
3.5 Bayesian Inference for the Twin Study 19
3.6 Data Analysis for the Twin Study 21
Chapter 4 Copula Analysis for Familial Age-onset Data 23
4.1 Copula Model for the Familial Study by Andersen 23
4.2 Likelihood Analysis 24
4.3 Marginal Estimation 26
4.3.1 Likelihood-based approach 26
4.3.2 Martingale-based approach 27
4.4 Association Estimation 28
4.5 Data Analysis for Mortality in Twins 29
Chapter 5 Concluding Remarks 31
Reference 32


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[2] Aalen, O. O. (1994). Effects of Frailty in Survival Analysis. Statistical Methods in Medical Research. 3, 227-243.
[3] Andersen, E. W. (2005). Two-Stage Estimation in Copula Models Used in Family Studies. Lifetime Data Analysis. 11, 333-350.
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[5] Clayton, D. G. (1978). A Model for Association in Bivariate Life Tables and its Application in Epidemiological Studies of Familial Tendency in Chronic Disease Incidence. Biomeirika. 65, 141-151.
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[8] Eaves, L. J., Last, K., Young, P. A. & Martin, N. G. (1978). Model-fitting approaches to the analysis of human behavior. Heredity. 41, 249-320.
[9] Genest, C. & MacKay J. (1986). The Joy of Copulas: Bivariate Distributions with Uniform Marginals. The American Statistician. 40, 280-283.
[10] Genest, C. & Rivest, L.-P. (1993). Statistical Inference Procedures for Bivariate Archimedean Copulas. Journal of the American Statistical Association. 88, 1034-1043.
[11] Hsu, L. & Zhao, L. P. (1996). Assessing Familial Aggregation of Age at Onset, by Using Estimating Equations, with Application to Breast Cancer. Am. J. Hum. Genet. 58, 1057-1071.
[12] Li, H. & Thompson, E. (1997). Semiparametric Estimation of Major Gene and Family-Specific Random Effects for Age of Onset. Biometrics. 53, 282-293.
[13] Malkin, D., Li, F. P., Strong, L. C., Fraumeni, J. F., Jr., Nelson, C. E., Kim, D. H., Kassel, J., Gryka, M. A., Bischoff, F. Z., Tainsky, M. A. & Friend S. H. (1990). Germ line p53 mutations in a familial syndrome of breast cancer, sarcomas, and other neoplasms. Science. 250, 1233–1238.
[14] Miki, Y., Swensen, J., Shattuck-Eidens, D., Futreal, P. A., Harshman, K., Tavtigian, S., Liu, Q., Cochran, C., Bennett, L. M., Ding, W., Bell, R., Rosenthal, J., Hussey, C., Tran, T., McClure, M., Frye, C., Hattier, T., Phelps, R., Haugen-Strano, A., Katcher, H., Yakumo, K., Gholami, Z., Shaffer, D., Stone, S., Bayer, S., Wray, C., Bogden, R., Dayananth, P., Ward, J., Tonin, P., Narod, S., Bristow, P. K., Norris, F. H., Helvering, L., Morrison, P., Rosteck, P., Lai, M., Barrett, J. C., Lewis, C., Neuhausen, S., Cannon-Albright, L., Goldgar, D., Wiseman, R., Kamb, A. & Skolnick, M. H. (1994). A strong candidate for the breast and ovarian cancer susceptibility gene BRCA1. Science 266, 66–71.
[15] Oakes, D. (1989). Bivariate Survival Models Induced by Frailties. Journal of the American Statistical Association. 84, 487-493.
[16] Shih, J. H. and Louis, T. A. (1995). Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics, 51, 1384-1399.
[17] Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris. 8, 229-231.
[18] Wang, W. & Wells, M. T. (2000). Estimation of Kendall’s tau Under Censoring. Statistica Sinica. 10, 1199-1215.
[19] Wooster, R., Bignell, G., Lancaster, J., Swift, S., Seal, S., Mangion, J., Collins, N., Gregory, S., Gumbs, C., Micklem, G., Barfoot, R., Hamoudi, R., Patel, S., Rice, C., Biggs, P., Hashim, Y., Smith, A., Connor, F., Arason, A., Gudmundsson, J., Ficenec, D., Kelsell, D., Ford, D., Tonin, P., Bishop, D. T., Spurr, N. K., Ponder, B.A.J., Eeles, R., Peto, J., Devilee, P., Cornelisse, C., Lynch, H., Narod, S., Lenoir, G., Eglisson, V., Barkadottir, R. B., Easton, D. F., Bentley, D. R., Futreal, P. A., Ashworth, A., Stratton, M. R. (1995). Identification of the breast cancer susceptibility gene BRAC2. Nature. 378, 789-792.

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