系統識別號 | U0002-2206200922464700 |
---|---|
DOI | 10.6846/TKU.2009.00807 |
論文名稱(中文) | 比較多種處理具有多項趨勢線性混合模式之群序檢定 |
論文名稱(英文) | Group Sequential Comparison for Linear Mixed Models with Polynomial Trend in Multi-Armed Trials |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 統計學系碩士班 |
系所名稱(英文) | Department of Statistics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 97 |
學期 | 2 |
出版年 | 98 |
研究生(中文) | 黃世溥 |
研究生(英文) | Shih-Pu Huang |
學號 | 695650209 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
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 |
關鍵字(中) |
群序檢定 多項處理試驗 多變量卡方分配 多項式趨勢 |
關鍵字(英) |
Group sequential test multi-armed trial multivariate chi-squared distribution polynomial trend |
第三語言關鍵字 | |
學科別分類 | |
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. |
第三語言摘要 | |
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 |
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