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中文論文名稱 不完整長期追蹤順序型資料之群序檢定分析方法
英文論文名稱 Group Sequential Methods for Analysis of Longitudinal Ordinal Data with Dropouts
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 96
學期 2
出版年 97
研究生中文姓名 黃怡樺
研究生英文姓名 Yi-Hua Huang
學號 695650076
學位類別 碩士
語文別 中文
口試日期 2008-06-05
論文頁數 43頁
口試委員 指導教授-陳怡如
委員-林國欽
委員-張春桃
中文關鍵字 廣義線性混合模式  廣義估計方程式模式  長期追蹤研究  遺失資料  順序型反應變數 
英文關鍵字 Generalized estimating equations model  Generalized linear mixed model  Longitudinal study  Missing data  Ordinal response 
學科別分類 學科別自然科學統計
中文摘要 不完整長期追蹤資料常見於臨床實驗中,Fitzmaurice et
al.(2001)針對不完整二元資料,考慮遺失型態為MAR(missing
at random)時,比較不同形式GEE參數估計值之影響,其結果顯示
Liang and Zeger(1986)所提出一般GEE方法隨著遺失比率增加會產
生較大偏誤。此外,Spiessens et al.(2003)模擬結果指出,不完
整長期追蹤二元資料且當遺失型態為MAR之群序檢定方法時,邏輯
斯隨機效果模式的型I誤差機率估計值較GEE模式更接近所設定的顯
著水準,而且邏輯斯隨機效果模式比廣義估計方程式模式具有較高的檢定力。

本文著重在討論不同遺失型態為MCAR(missing completely
at random)與MAR之情況下,應用廣義線性混合模式和廣義估計
方程式模式於不完整長期追蹤順序型資料,並以模擬研究來比較在不完整資料下,此兩種模式之型I誤差機率和檢定力之差異。
英文摘要 Longitudinal studies with dropouts are commonly occurred in clinical trials. For the incomplete binary data, Fitzmaurice et al. (2001) discussed the impact on bias of direrent estimating equation methods where missing data follow a MAR (missing at random) process. They pointed out that generalization estimating equations (GEE) proposed by Liang and Zeger (1986) has manifest bias as the MAR dropout rate increases. Spiessens et al. (2003) conducted the group sequential tests for analyzing longitudinal binary data with MAR and MCAR (missing completely at random) dropouts, and compared the performance of logistic random exect models and GEE models in terms of type I error rate and power. The simulation studies indicated that logistic random exect models have noticeably larger power than GEE models for MAR dropouts data.

In this article, we consider the group sequential tests based on GLMM (generalized linear mixed model) and GEE models for incomplete longitudinal ordinal data, and compare the two methods with respect to type I
error rate and power for various dropout rates by simulation studies.
論文目次 目錄
1 緒論 1
1.1 文獻回顧 2
1.2 研究動機與目的 5
1.3 研究架構 7
2 不完整長期追蹤資料之分析方法 8
2.1 完整個案分析 9
2.2 加權法 10
2.3 插補法 11
2.4 模式建構法 13
3 GLMM與GEE模式之比較 16
3.1 廣義線性混合模式 18
3.2 廣義估計方程式模式 19
3.3 實例分析 22
3.4 模擬研究 25
4 結論 38
參考文獻 41
表格目錄
表1 在alpha=0.01、不同alpha支配函數與遺失比率下,GLMM和GEE模式之型I誤差估計值 28
表2 在alpha=0.05、不同alpha支配函數與遺失比率下,GLMM和GEE模式之型I誤差估計值 29
表3 在alpha=0.1、不同alpha支配函數與遺失比率下,GLMM和GEE模式之型I誤差估計值 30
表4 在alpha=0.05、不同alpha支配函數與參數beta3下,GLMM之檢定力 31
表5 在alpha=0.05、不同alpha支配函數與參數beta3下,GEE之檢定力 32
表6 在alpha=0.01、GLMM模擬架構下、不同alpha支配函數與遺失比率下,GLMM和GEE模式之型I誤差估計值 33
表7 在alpha=0.05、GLMM模擬架構下、不同alpha支配函數與遺失比率下,GLMM和GEE模式之型I誤差估計值 34
表8 在alpha=0.1、GLMM模擬架構下、不同alpha支配函數與遺失比率下,GLMM和GEE模式之型I誤差估計值 35
表9 在alpha=0.05、GLMM模擬架構下、不同alpha支配函數與參數beta3下,GLMM之檢定力 36
表10 在alpha=0.05、GLMM模擬架構下、不同alpha支配函數與參數beta3下,GEE之檢定力 37
參考文獻 [1] Agresti, A. (2002). Categorical Data Analysis (2nd ed.). New York: Wiley.

[2] Fitzmaurice, G. M., Lipsitz, S. R., Molenberghs, G., and Ibrahim, J. G. (2001). Bias in estimating association parameter for longitudinal binary responses with drop-outs. Biometrics. 57: 15-21.

[3] O'Hara Hines. R. J. (1997). Analysis of clustered polytomous data using generalized estimating equations and working covariance structures. Biometrics. 53: 1552-1556.

[4] O'Hara Hines. R. J. (1998). Comparison of two covariance structures in the analysis of clustered polytomous data using generalized
estimating equations. Biometrics. 54: 312-316.

[5] O'Hara Hines, R. J. and Hines, W. G. S. (2005). An approach of methods for the analysis of longitudinal categorical data with MAR drop-outs. Statistics in Medicine. 24: 3549-3563.

[6] Kaslow, R. A., Ostrow, D. G. and Detels, R. (1987). The multicenter AIDS cohort study: rationale, organization and selected characteristics of the participants. American Journal of Epidemiology. 126:310-318.

[7] Laird, N. M. and Ware, J. H. (1982). Random-exects models for longitudinal data. Biometrics. 38: 963-974.

[8] Lan, K. K. G. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika. 70: 659-663.

[9] Lee, J. W. and DeMets, D. L. (1991). Sequential comparison of changes with repeated measurements data. Journal of American Statistical Association. 86: 757-762.

[10] Lee, S. J. Kim, K. and Tsiatis, A. A. (1996). Repeated signi‾cance testing in longitudinal clinical trials. Statistics in Medicine. 11: 779-789.

[11] Li, X., Mehrotra, D. V. and Barnard J. (2006). Analysis of incomplete longitudinal binary data using multiple imputation. Statistics in Medicine. 25: 2107-2124.

[12] Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika. 73: 13-22.

[13] Lipsitz, S. R., Kim, K. and Zhao, L. (1994). Analysis of repeated categorical data using generalized equations. Statistics in Medicine. 73: 13-22.

[14] Lipsitz, S. R., Molenberghs, G., Fitzmaurice, G. M. and Ibrahim, J. (2000). Gee with Gaussian estimation of the correlations when data are incomplete. Biometrics. 56: 528-536.

[15] Little, R. J. A. and Rubin, B. R. (2002). Statistical Analysis with Missing Data (2nd ed.), New York: Wiley.

[16] O'Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics. 35: 549-556.

[17] Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika. 64: 191-199.

[18] Rubin, D. B. (1978). Bayesian inference for causal exects: the role of randomization. Annals of Statistics. 7: 34-58.

[19] Sommer, A. (1982). Nutritional Blindness. New York: Oxford University Press.

[20] Spiessens, B., Lesaxre, E. and Verbeke, G. (2003). A comparison of group sequential methods for binary longitudinal data. Statistics in Medicine. 22: 501-515.

[21] Scharfstein, D. O. , Tsiatis, A. A. and Robins, J. M. (1997). Semiparametric e±ciency and its implication on the design and analysis of group-sequential studies. Journal of the American Statistical Association. 92: 1342-1350.

[22] Stanish, W. M. , Gillings, D. B. and Koch, G. G. (1978). An application of multivariate ratio methods for the analysis of a longitudinal clinical trial with missing data. Biometrics. 34: 305-317.

[23] Stirarelli, R. and Laird, N. and Ware, J. H. (1984). Random-exects models for serial observations with binary response. Biometrics. 40: 961-971.

[24] Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika. 61: 439-447.

[25]林鍵志(民95)。順序型長期追蹤資料之群序檢定方法。淡江大學統計學系應用統計碩士班碩士論文。
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