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系統識別號 U0002-2206200922464700
中文論文名稱 比較多種處理具有多項趨勢線性混合模式之群序檢定
英文論文名稱 Group Sequential Comparison for Linear Mixed Models with Polynomial Trend in Multi-Armed Trials
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 97
學期 2
出版年 98
研究生中文姓名 黃世溥
研究生英文姓名 Shih-Pu Huang
學號 695650209
學位類別 碩士
語文別 英文
口試日期 2009-06-05
論文頁數 28頁
口試委員 指導教授-陳怡如
委員-林國欽
委員-鄧文舜
中文關鍵字 群序檢定  多項處理試驗  多變量卡方分配  多項式趨勢 
英文關鍵字 Group sequential test  multi-armed trial  multivariate chi-squared distribution  polynomial trend 
學科別分類 學科別自然科學統計
中文摘要 在臨床實驗中,基於成本與管理的考量,常使用群序檢定以有機會提早結束試驗。當資料為橫斷面(cross-sectional data)型態,且欲檢定兩處理平均數之差異時,常使用的群序檢定方法有Pocock(1977)、O’Brien與Fleming(1979)以及Lan與DeMets(1983)等方法。Lee與DeMet(1991)提出在長期追蹤資料(longitudinal data)中,利用線性混合模式檢定兩處理之線性趨勢。本文延伸Lee與DeMets之方法,推廣其線性混合模式至多項式趨勢型態,提出在多種處理下之群序檢定方法。各階段檢定統計量之聯合分配為多變量卡方分配,文中使用Pocock及O’Brien與Fleming概念,提出二階段與三階段檢定之臨界值,並使用實例說明此檢定程序。
英文摘要 For ethical, economical and administrative considerations, group sequential methods are frequently applied for possibly early determination clinical trials. For cross-sectional data, three common group sequential methods for comparing means between two treatments are proposed by Pocock (1977), O'Brien and Fleming (1979) and Lan and DeMets (1983). For longitudinal data, Lee and DeMets (1991) proposed a sequential comparison for testing the rates of change with linear trend between two treatments.
In this article, a group sequential method for multi-armed trials is proposed, which is a generalization of Lee and DeMets' method, for testing responses changes with time in polynomial trend. The asymptotic joint distribution of proposed test statistics is a multivariate chi-squared distribution. Boundaries of the proposed methods based on Pocock-type and O'Brien and Fleming-type are provided for practical use. The proposed testing procedure is illustrated by a clinical example.
論文目次 Contents
1 Introduction 1
2 Historical Review 4
2.1 Classical Group Sequential Method 4
2.1.1 Pocock Procedure 5
2.1.2 O’Brien and Fleming Procedure 6
2.1.3 Lan and DeMets Procedure 7
2.2 Group Sequential Tests for Multi-Armed Trials 7
2.3 Multivariate Chi-Squared Distribution 9
3 Test For Polynomial Trend 14
3.1 Lee and DeMets Procedure 14
3.2 Proposed Test 16
3.3 Numerical Study 18
3.4 An Example 19
4 Conclusions and Remarks 21

List of Figures
1 Plots of bivariate chi-squared distributions with various degrees of freedom and correlations, (a)nu=2, rho=0.1 (b)nu=2, rho=0.5 (c)nu=6,rho=0.5 (d)nu=6,rho=0.9 11
2 Plot of Empirical Density Values against Ordered Values of
f(q1, q2) 19

List of Tables
1 Boundaries of Pocock-type and O’Brien-Fleming-type repeated chi^2 test for two stages 23
2 Boundaries of Pocock-type and O’Brien-Fleming-type repeated chi^2 test for three stages and the correlations ((rho_1,rho_2,rho_3)=(0.7,0.5,0.3) 26
參考文獻 Follmann, D. A., Proschan, M. A. and Geller, N. L. (1994). Monitoring pairwise comparisons in multi-armed clinical trials, Biometrics, 50: 325–336.
Hewett, J. E. and Tsutakawa, R. K. (1972). Two-stage chi-square goodness-of-fit test, Journal of the American Statistical Association, 67: 395–401.
Jennison, C. and Turnbull, B. W. (1991). Exact calculations for sequential t, chi^2 and F tests, Biometrika, 78: 133–141.
Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods: Applications to Clinical Trials, Chapman & Hall/CRC, Boca Raton.
Jenson, D. R. (1970). The joint distribution of quadratic forms and related distributions, Australian Journal of Statistics, 12: 13–22.
Kibble, W. F. (1941). A two-variate gamma type distribution, Sankhya,5: 137–150.
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: 149–154.
Krishnamoorthy, A. S. and Parthasarathy, M. (1951). A multivariate gammatype distribution, The Annals of Mathematical Statistics, 4: 549–557.
Lan, K. K. G. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials, Biometrika, 70: 659–663.
Lee, J. W. and DeMets, D. L. (1991). Sequential comparison of changes with repeated measurement data, Journal of the American Statistical Association, 86: 757–762.
Miliken, G. A. and Johnson, D. E. (1993). Analysis of Messy Data, Vol. 1: Designed Experiments, Chapman & Hall/CRC, Boca Raton.
O’Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials, Biometrics, 35: 549–556.
Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials, Biometrika, 64: 191–199.
Proschan, M. A., Follmann, D. A. and Geller, N. L. (1994). Monitoring multi-armed trials, Statistics in Medicine, 13: 1411–1452.
Royen, T. (1991). Expansions for the multiviriate chi-square distribution, Journal of Multivariate Analysis, 38: 213–232.
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