比較多個處理之群序檢定方法

Group Sequential Methods for Multi-Armed Trials

曾家誼(Chia-Yi Tseng)

指導教授 ： 陳怡如

淡江大學/管理學院/統計學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00281

摘要

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。

關鍵字

顯著水準支配函數 ； 臨界值 ； 多個處理之臨床試驗 ； 多重比較

並列摘要

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.

並列關鍵字

Alpha spending function ； boundaries ； multi-armed trials ； multiple comparison

參考文獻

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,