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中文論文名稱 順序型長期追蹤資料之群序檢定方法
英文論文名稱 Group Sequential Methods for Longitudinal Data with Ordinal Responses
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 95
學期 2
出版年 96
研究生中文姓名 林鍵志
研究生英文姓名 Jian-Jhih Lin
學號 694460352
學位類別 碩士
語文別 中文
口試日期 2007-06-08
論文頁數 48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 廣義估計方程式模式  廣義線性混合模式  獨立增量結構  長期追蹤研究  順序型資料 
英文關鍵字 Generalized estimating equations model  Generalized linear mixed model  Independent increment structure  Longitudinal study  Ordinal data. 
學科別分類 學科別自然科學統計
中文摘要 基於醫學倫理道德與經濟成本考量,期中分析常應用群序檢定方法於臨床實驗中, 以有機會提早結束實驗。常見的群序檢定方法有Pocock (1977)、O'Brien與Fleming (1979)以及Lan與DeMets (1983)等三種方法。
傳統的群序檢定方法應用於橫斷面資料,即每位受測者僅有單一觀察值,所以各階段檢定統計量具有獨立增量結構(independent
increment structure; IIS )性質。但在長期追蹤資料 (longitudinal data)下,同一受測者的重複觀測值彼此間具有相關性,IIS性質則無法適用。
本論文中,我們根據廣義線性混合模式和廣義估計方程式模式,提出兩種群序檢定方法以分析順序型長期追蹤資料,並以模擬研究來比較此兩種分析模式之型I誤差機率和檢定力。 此外,藉用臨床實例來闡述我們所提出的檢定方法。 有鑑於此,Scharfstein等人 (1997)指出若能使用有效的檢定統計量,像是Wald、Score統計量,則IIS性質乃可沿用於 長期追蹤資料方面。

本論文中,我們根據廣義線性混合模式和廣義估計方程式模式,提出兩種 群序檢定方法以分析順序型長期追蹤資料,並以模擬研究來比較此兩種分析模式之型I誤差機率和檢定力。 此外,藉用臨床實例來闡述我們所提出的檢定方法。
英文摘要 For ethical, economical and administrative considerations, interim analyses are often conducted to allow for possibly early termination of a clinical trial. Group sequential methods are essentially used for a correct application of interim analyses. Three common group sequential methods are
proposed by Pocock (1977), O'Brien and Fleming (1979) and Lan and DeMets (1983).
Those classical group sequential methods are applied
for cross-sequential data as well as based on the assumption of independent increment structure (IIS) between the successive test statistics. For longitudinal data, the IIS assumption between the successive test statistics is violated due to the correlation between the measurements from the same subject. However, Scharfstein{et al}. (1997) prove that the IIS holds in parametric and semi-parametric models when efficient test statistics are employed.
In the article, we propose group sequential
methods based on GLMM (generalized linear mixed model) and GEE (generalized estimating equations)
model for analysing ordinal longitudinal data. These two methods are compared with respect to the probability of type I error and power by simulation studies. The testing procedures are illustrated by a clinical trial for ordinal responses.

論文目次 第一章~~緒論..1
1.1~~研究動機..3
1.2~~文獻探討..5
1.3~~研究架構..8
第二章~~比例勝算模式,GLMM與GEE模式..10
2.1~~比例勝算模式..11
2.2~~GLMM..14
2.3~~GEE模式..16
第三章~~長期追蹤資料之群序檢定方法..20
3.1~~二元長期追蹤資料之模式..22
3.1.1~~邏輯斯隨機效果模式..22
3.1.2~~GEE模式..24
3.2~~順序型長期追蹤資料之模式..26
3.1.1~~比例勝算型GLMM..27
3.1.2~~比例勝算型GEE模式..27
3.3~~模擬研究..29
3.4~~實例探討..33
3.4.1~~GLMM..33
3.4.2~~GEE模式..34
第四章~~結論與未來研究方向..36
4.1~~結論..37
4.2~~未來研究方向..37
參考文獻..39
參考文獻 [1] Agresti, A. (2002). Categorical Data Analysis, second edition.
[2] Fitzmaurice, G. M. ,Laird, N. M. and Ware, J. H. (2004). Applied Longitudinal Analysis .
[3] Kim, K. and DeMets, D. L. (1987). Design and analysis of group sequential tests based on the type I error spending rate function, Biometrika, 74 , 1, pp. 149-154.
[4] Laird, N. M. and Ware, J. H. (1982). Random-e®ects models for longitudinal data, Biometrics, 38, pp. 963-974.
[5] Little, R. J. A. and Rubin, B. R. (2002). Statistical Analysis with Missing Data, second edition.
[6] Lan, K. K. G. and DeMets, D. L. (1983). Discrete sequential bound-aries for clinical trials, Biometrika, 70, pp. 659-663.
[7] Lee, J. W. and DeMets, D. L. (1991). Sequential comparison of changes with repeated measurements data, Journal of American Statistical Association, 86, pp. 757-762.
[8] Lee, S. J. Kim, K. and Tsiatis, A. A. (1996). Repeated significance testing in longitudinal clinical trials, Statistics in Medicine, 11, pp.779-789.
[9] Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models, Biometrika, 73, pp. 13-22.
[10] O'Brien, P. C. and Fleming, T. r. (1979). A multiple testing procedure for clinical trials, Biometrics, 35, pp. 549-556.
[11] Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials, Biometrika, 64, pp. 191-199.
[12] Spiessens, B. ,Lesa®re, E. ,Verbeke, G. Kim, K. and DeMets,D. L. (2000). An overview of group sequential methods in longi-
tudinal clinical trials, Statistical Methods in Medical Research, 9,pp. 497-515.
[13] Spiessens, B. ,Lesa®re, E. and Verbeke, G. (2003). A comparison of group sequential methods for binary longitudinal data, Statistics in Medicine, 22, pp. 501-515.
[14] Scharfstein, D. O. ,Tsiatis, A. A. and Robins, J. M. (1997). Semi-parametric e±ciency and its implication on the design and analysis of group-sequential studies, Journal of the American Statistical As-
sociation, 92, pp. 1342-1350.
[15] 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, pp.305-317.
[16] Stirarelli, R. and Laird, N. and Ware, J. H. (1984). Random-effects models for serial observations with binary response, Biometrics, 40,pp. 961-971.
[17] Ware, J. H. (1985). Linear models for the analysis of longitudinal studies, The American Statistician, 39, pp. 95-101.
[18] Zeger, S. L. and Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes, Biometrics, 42, pp. 121-130.
[19] Zeger, S. L. and Liang, K. Y. (1992). An overview of methods for the analysis of longitudinal data, Statistics in Medicine, 11, pp.1825-1839.
[20]{任志中}任志中~(民94)。依據多項式模式用於分析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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