一般的群序檢定方法中，每位受測者僅有單一觀察值，所以各階段檢定統計量之間具有IIS(independent increments structure)性質。
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。然而在長期追蹤資料(longitudinal data)下，每位受測者有重覆測量值，而且這些測量值彼此間具有相關性，因此各階段檢定統計量之間不再具有IIS性質。針對分析重覆測量值或者多重反應變數之資料型態，Armitage等人(1985)，Geary(1988)，Tang等人(1989)以及Lee與DeMets(1991)分別提出不同的方法。本文將以Lee-DeMets方法為基礎，推廣其線性混合模式概念至多項式趨勢型態，應用二次式檢定統計量進行群序檢定。此外，藉由模擬研究討論各階段檢定統計量之邊際抽樣分配和所有檢定統計量之聯合分配，並使用實例說明其檢定程序。

關鍵字:IIS性質，線性混合模式，長期追蹤資料。

Classical group sequential methods are based on the assumption of independent increments structure (IIS) between the interim test statistics. Three common classical group sequential methods are proposed by Pocock(1977), O'Brien and
Fleming(1979), and Lan and DeMets(1983). However, for longitudinal data the IIS assumption between the interim test statistics does not hold because of the correlation between the measurements from the same subject. Several parametric methods of group sequential test for analyzing the data with repeated measurements or multiple observations have been developed by Armitage et al.(1985), Geary(1988), Tang et al.(1989) and Lee and DeMets(1991). The proposed quadratic form test statistic
is a generalization of Lee and DeMets' statistic to polynomial setting. The sampling distributions of the proposed test statistic at each stage as well as the joint
distribution are discussed by simulation studies. The proposed testing procedure is
illustrated by a clinical example.

目錄

第一章 緒論...........1
  1.1 研究背景和動機.....1
  1.2 文獻探討 .....4
  1.3 研究架構...7
第二章 長期追蹤資料之群序檢定方法....9
  2.1 Armitage-Stratton-Worthington方法..10
  2.2 Geary方法...14
  2.3 Tang-Gnecco-Geller方法....16
  2.4 Lee-DeMets方法.....18
第三章 多項式線性混合模式...24
  3.1 線性混合模式..25
  3.2 多項式線性混合模式...27
  3.3 模擬研究....29
  3.4 實例探討.....36
     3.4.1 線性資料型態...37
     3.4.2 多項式資料型態...39
第四章 結論與未來研究方向...40
  4.1 結論..40
  4.2 未來研究方向...41
參考文獻....43

         圖目錄
圖1  Pocock和O'Brien-Fleming方法之資料結構....4
圖2  各類型alpha支配函數...6
圖3  Armitage等人方法之資料結構..13
圖4  Tang等人方法之資料結構....17
圖5  Lan與DeMets方法之資料結構...19
圖6  p=2，K=2時，各階段檢定統計量之抽樣分配。...29
圖7  p=2，K=3時，各階段檢定統計量之抽樣分配。...31
圖8  p=3，K=2時，各階段檢定統計量之抽樣分配。...32
圖9  p=3，K=3時，各階段檢定統計量之抽樣分配。...33
圖10 前10位實驗組和對照組受測者之資料分佈...36

       表目錄

表1 p=2時，各階段檢定統計量之邊際與聯合分配的拒絕率與
    chi分配的顯著水準比較。.....30
表2 p=3時，各階段檢定統計量之邊際與聯合分配的拒絕率與
    chi分配的顯著水準比較。.....34
  
表3 當隨機效果bi之共變異數矩陣不為單位矩陣時，各階段檢定統
    計量之邊際與聯合分配的拒絕率。....35
表4 K=2時，各支配函數之臨界值。....38

1. Armitage, P., Stratton, I. M. and Worthington, H.   (1985). Repeated significance tests for clinical trials   with a fixed number of patients and variable follow-up, Biometrics, 41, pp.353-359.

2. Cox, D. R. and Hinkley, D. V. (1979). Theoretical statistics, Chapman & Hall, London.

3. Fitzmaurice, G. M., Laird, N. M. and Ware J. H. (2004).
Applied longitudinal analysis, Wiley, New Jersey.

4. Geary, D. N. (1988). Sequential testing in clinical trials with repeated measurements, Biometrika, 75, pp.311-318.

5. Halperin, M., DeMets, D. L., and Ware, J. H. (1990). Early methodological developments for clinical trials at the national heart, lung and blood institute, Statistics in Medicine, 9, pp.881-892.

6. Jennison, C. and Turnbull, B. W. (1991). Exact calculations for sequential t , chi and F tests, Biometrika, 78, pp.133-141.

7. Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data, Biometrics, 38, pp.963-974.

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

9. Lee, J., W. and DeMets, D. L. (1991). Sequential comparison of changes with repeated measurements data, Journal of the American Statistical Association, 86, pp.757-762.

10. Lee, J. W. (1994). Group Sequential testing in clinical trials with multivariate observations: a review, Statistics in Medicine, 13, pp.101-111.

11. Lee, J. W. and DeMets, D. L.(1995). Group sequential comparison of changes: ad-hoc versus more exact method, Biometrics, 51 , pp.21-30.

12. O'Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials, Biometrics, 35, pp.549-556.

13. O'Brien, P. C. (1984). Procedures for comparing samples
with multiple endpoints, Biometrics, 40, pp.1079-1087.

14. Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials, Biometrika, 64, pp.191-199.

15. Tang, D. I., Gnecco, C. and Geller N. L. (1989). Design of group sequential clinical trials with multiple endpoints, Journal of the American Statistical Association, 84, pp.776-779.

16. Scharfstein, D. O., Tsiatis, A. A. and Robins, J. M. (1997). Semiparametric efficiency and its implication on the design and analysis of group-sequential studies, Journal of the American Statistical Association, 92, pp.1342-1350.

17. 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, pp.497-515.