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研究生:曾家誼
研究生(外文):Chia-Yi Tseng
論文名稱:比較多個處理之群序檢定方法
論文名稱(外文):Group Sequential Methods for Multi-Armed Trials
指導教授:陳怡如陳怡如引用關係
指導教授(外文):Yi-Ju Chen
學位類別:碩士
校院名稱:淡江大學
系所名稱:統計學系碩士班
學門:商業及管理學門
學類:會計學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:59
中文關鍵詞:顯著水準支配函數臨界值多個處理之臨床試驗多重比較
外文關鍵詞:Alpha spending functionboundariesmulti-armed trialsmultiple comparison
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針對臨床試驗的累積資料(accumulated data),常見的期中分析群序方法為Pocock (1977),
O''Brien 與Fleming (1979)以及Lan 與 DeMets (1983)等三種方法。
本文將探討Pocock方法 , O''Brien-Fleming方法與三個顯著水準支配函數
$alpha_{1}^{*}(t)=alpha{t}$ ,
$alpha_{2}^{*}(10,t)=alpha[(1-e^{-10t})/(1-e^{-10})]$ 及
$alpha_{3}^{*}(-10,t)=alpha[(1-e^{10t})/(1-e^{10})]$
所產生的臨界值之差異,並討論其所需的樣本數與固定樣本數之比較,
同時利用Pocock提出各階段名目顯著水準 $alpha''$
的概念,計算出不同階段下的群序卡方檢定和群序 $F$ 檢定之臨界值,
此計算過程比Jennison與Turnbull(1991)所提出的方法較為簡易並且其臨界值結果非常近似。
此外,本文著重討論 $J$ $(Jgeq3)$
個處理之群序檢定過程,以實例說明比較三種處理之群序檢定 ,
同時採用Bonferroni及LSD方法進行多重比較。



For accumulated data of clinical trials, three common group
sequential methods were proposed by Pocock (1977), O''Brien and
Fleming (1979), and Lan and DeMets (1983). The comparison of
boundaries among Pocock''s method, O''Brien-Fleming''s method and
three alpha spending functions: $alpha_{1}^{*}(t)=alpha{t}$,
$alpha_{2}^{*}(10,t)=alpha[(1-e^{-10t})/(1-e^{-10})]$ and
$alpha_{3}^{*}(-10,t)=alpha[(1-e^{10t})/(1-e^{10})]$ is
discussed. We adopt the concept of nominal significance level
$alpha''$ presented by Pocock to calculate the boundaries of group
sequential chi-squared test and group sequential $F$ test for
various of overall significance level $alpha$ and testing stages
$K$, which result in the similar critical values of chi-squared
test computed by Jennison and Turnbull (1991). The required
treatment sample size, maximun sample size and average sample size
for each method are compared with the fixed sample size.
Furthermore, the group sequential $F$ procedure for multi-armed
trials and the corresponding multiple comparisons are illustrated
by an example.

第一章~~緒論..1
1.1~~前言與文獻回顧..1
1.2~~研究動機..8
1.3~~本文架構..9
第二章~~群序檢定方法..10
2.1~~Pocock 方法..10
2.2~~O''Brien -Fleming方法..11
2.3~~Lan-DeMets方法..13
2.3.1~~顯著水準支配函數..13
2.3.2~~顯著水準支配函數的推廣..14
2.4~~顯著水準支配函數之樣本數比較..16
第三章~~比較多個處理之檢定過程..21
3.1~~總檢定過程..21
3.1.1~~群序卡方檢定..21
3.1.2~~群序 $F$ 檢定..24
3.2~~多重比較檢定..26
3.3~~實例探討..27
3.3.1~~Bonferroni 方法..28
3.3.2~~LSD方法..31
3.3.3~~總結..33
第四章~~結論與未來研究方向..34
參考文獻..36
附錄..38


DeMets, D. L. and Lan, K. K. G. (1994). Interim analysis: the alpha spending function approach,
Statistics in Medicine, 13, 1341-1352.

Follmann, D. A., Proschan, M. A. and Geller, N. L. (1994). Monitoring pairwise comparisons in multi-armed clinical trials,Biometrics, 50, 325-336.

Hwang, I. K. , Shih, W. J. and Decani, J. S. (1990). Group sequential designs using a family of type I error probability spending functions,Statistics in Medicine, 9, 1439-1445.

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 with applications to clinical trials, Chapman & Hall/CRC.

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.

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

Lui, K. J. (1993). A simple generalization of the O''Brien and Fleming group sequential test procedure to more than two treatment groups,Biometrics, 49, 1216-1219.

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, 1441-1452.

Sokal, R. R., and Rohlf, F. J. (1981).
Biometry, 2nd edition, San Francisco : W. H. Freeman.

Spiessens, B., Lesaffre, E., Verbeke, G., Kim, K. and DeMets, D. L. (2000).
An overview of group sequential methods in longitudinal clinical trials,Statistical Methods in Medical Research, 9, 497-515.

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