Procedures with Equally Sized Stages

  • Gernot Wassmer
  • Werner Brannath
Chapter
First Online:
Part of the Springer Series in Pharmaceutical Statistics book series (SSPS)

Abstract

In this chapter, we describe group sequential test procedures that are designed for equal sample sizes per stage of the group sequential trial. The procedures that were originally developed in the literature (which we refer to as classical group sequential designs) make this assumption. In practice, the situation with equally sized stages often occurs. Namely, in all cases when there is no specific reason for assuming different stage sizes the sample sizes per stage should be the same.We introduce the designs due to O’Brien and Fleming (Biometrics 35:549–556, 1979), Pocock (Biometrika 64:191–199, 1977) and the power family of Wang and Tsiatis (Biometrics 43:193–199) and describe their basic properties. We also introduce the Pampallona and Tsiatis (Journal of Statistical Planning and Inference 42:19–35, 1994)symmetric design. The one-sided testing in group sequential designs is then described, together with a discussion of the stopping for futility issue in sequential designs. A note on two-sided tests in group sequential designs finalizes the chapter.

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References

  1. Anderson, K. M. (2007). Optimal spending functions for asymmetric group sequential designs. Biometrical Journal, 49, 337–345.MathSciNetCrossRefGoogle Scholar
  2. Barber, S., & Jennison, C. (2002). Optimal asymmetric one-sided group sequential tests. Biometrika, 89, 49–60.MathSciNetCrossRefMATHGoogle Scholar
  3. DeMets, D. L., & Ware, J. H. (1980). Group sequential methods for clinical trials with a one-sided hypothesis. Biometrika, 67, 651–660.MathSciNetCrossRefGoogle Scholar
  4. DeMets, D. L., & Ware, J. H. (1982). Asymmetric group sequential boundaries for monitoring clinical trials. Biometrika, 69, 661–663.CrossRefGoogle Scholar
  5. Eales, J. D., & Jennison, C. (1992). An improved method for deriving optimal one-sided group sequential tests. Biometrika, 79, 13–24.MathSciNetCrossRefMATHGoogle Scholar
  6. Emerson, S. S., & Fleming, T. R. (1989). Symmetric group sequential test designs. Biometrics, 45, 905–923.MathSciNetCrossRefMATHGoogle Scholar
  7. Gould, A. L., & Pecore, V. J. (1982). Group sequential methods for clinical trials allowing early acceptance of H0 and incorporating costs. Biometrika, 69, 75–80.Google Scholar
  8. Haybittle, J. L. (1971). Repeated assessments of results in clinical trials of cancer treatment. British Journal Radiology, 44, 793–797.CrossRefGoogle Scholar
  9. Jennison, C. (1987). Efficient group sequential tests with unpredictable group sizes. Biometrika, 74, 155–165.MathSciNetCrossRefMATHGoogle Scholar
  10. Jennison, C., & Turnbull, B. W. (2000). Group sequential methods with applications to clinical trials. Boca Raton: Chapman & Hall/CRC.MATHGoogle Scholar
  11. Köpcke, W. (1984). Zwischenauswertungen und vorzeitiger Abbruch von Therapiestudien. Berlin: Springer.CrossRefGoogle Scholar
  12. Köpcke, W. (1989). Analyses of group sequential clinical trials. Controlled Clinical Trials, 10, 222–230.CrossRefGoogle Scholar
  13. McPherson, K. (1982). On choosing the number of interim analyses in clinical trials. Statistics in Medicine, 1, 25–36.CrossRefGoogle Scholar
  14. O’Brien, P. C. (1998). Data and safety monitoring. In P. Armitage & T. Colton (Eds.), Encyclopedia of biostatistics (pp. 1058–1066). Chichester: Wiley.Google Scholar
  15. O’Brien, P. C., & Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics, 35, 549–556.CrossRefGoogle Scholar
  16. Pampallona, S., & Tsiatis, A. A. (1994). Group sequential designs for one-sided and two-sided hypothesis testing with provision for early stopping in favor of the null hypothesis. Journal of Statistical Planning and Inference, 42, 19–35.MathSciNetCrossRefMATHGoogle Scholar
  17. Peto, R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J., & Smith, P. G. (1976). Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design. British Journal of Cancer, 34, 585–612.CrossRefGoogle Scholar
  18. Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika, 64, 191–199.CrossRefGoogle Scholar
  19. Pocock, S. J. (1982). Interim analyses for randomized clinical trials: The group sequential approach. Biometrics, 38, 153–162.CrossRefGoogle Scholar
  20. Proschan, M. A. (1999). Properties of spending function boundaries. Biometrika, 86, 466–473.MathSciNetCrossRefMATHGoogle Scholar
  21. Wald, A. (1947). Sequential analysis. New York: Wiley.MATHGoogle Scholar
  22. Wang, S. K., & Tsiatis, A. A. (1987). Approximately optimal one-parameter boundaries for group sequential trials. Biometrics, 43, 193–199.MathSciNetCrossRefMATHGoogle Scholar
  23. Wassmer, G. (1999c). Statistische Testverfahren für gruppensequentielle und adaptive Pläne in klinischen Studien. Theoretische Konzepte und deren praktische Umsetzung mit SAS. Köln: Verlag Alexander Mönch.Google Scholar
  24. Wassmer, G., & Bock, W. (1999). Tables of Δ-class boundaries for group sequential trials. Informatik, Biometrie und Epidemiologie in Medizin und Biologie, 30, 190–194.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gernot Wassmer
    • 1
  • Werner Brannath
    • 2
  1. 1.University of CologneCologneGermany
  2. 2.University of BremenBremenGermany

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