Predicting the Duration of Sequential Survival Studies


Interim analyses are a common feature of clinical trial design, especially for large trials in high mortality conditions such as cancer or cardiovascular disease in which the primary endpoint is often the survival time from randomization to death. A plan for a series of interim analyses in which the criteria for stopping are specified in advance is known as a sequential design, and can be constructed to prevent patients from being randomized to an evidently inferior treatment and avoid continuation of a trial that is obviously futile.

In this paper, methods for predicting the final sample size and total duration of a sequential survival study are described, and the play-off between speed of recruitment and length of follow-up is examined. The use of interim analyses to review the event rate, recruitment period, and model assumptions is discussed and software for the implementation of the methods is described. The approach is illustrated in the context of a trial seeking to establish noninferiority.

This is a preview of subscription content, access via your institution.


  1. 1.

    Jones DR, Whitehead J. Sequential forms of the log rank and modified Wilcoxon tests for censored data. Biometrika. 1979;66:105–113. Correction. Biometrika. 1981;68:576.

    Article  Google Scholar 

  2. 2.

    Sellke T, Siegmund D. Sequential analysis of the proportional hazards model. Biometrika. 1983;70:315–326.

    Article  Google Scholar 

  3. 3.

    Tsiatis AA, Rosner GL, Tritchler DL. Group sequential tests with censored survival data adjusting for covariates. Biometrika. 1985;72:365–373.

    Article  Google Scholar 

  4. 4.

    Moss AJ, Hall WJ, Cannom DS, Daubert JP, Higgins SL, Klein H, Levine JH, Saksena S, Waldo A, Wilber D, Brown MW, Heo M. Improved survival with an implanted defibrillator in patients with coronary disease at high risk for ventricular arrythmia. New Engl J Med. 1996;335:1933–1940.

    CAS  Article  Google Scholar 

  5. 5.

    Boden WE, van Gilst WH, Scheldewaert RG, Starkey IR, Carlier MF, Julian DG, Whitehead A, Bertrand ME, Col JJ, Lederballe Pedersen O, Lie KI, Santoni J-P, Fox K. Diltiazem in acute myocardial infarction treated with thrombolytic agents: a randomised placebo-controlled trial. Lancet. 2000;355:1751–1756.

    CAS  Article  Google Scholar 

  6. 6.

    Arriagada R, Le Chevalier T, Pignon J-P, Rivière A, Monnet I, Chomy P, Tuchais C, Tarayre M, Rufflé P. Initial chemotherapeutic doses and survival in patients with limited small-cell lung cancer. New Engl J Med. 1993;329:1848–1852.

    CAS  Article  Google Scholar 

  7. 7.

    Medical Research Council Renal Cancer Collaborators. Interferon-α and survival in metastatic renal carcinoma: early results of a randomised controlled trial. Lancet. 1999;353:14–17.

    Article  Google Scholar 

  8. 8.

    Whitehead J. Monotherapy trials: Sequential design. Epilepsy Res. 2001;43:81–87.

    Article  Google Scholar 

  9. 9.

    MPS Research Unit. PEST 4: Operating Manual. Reading, UK: The University of Reading; 2000.

    Google Scholar 

  10. 10.

    Collett D. Modelling Survival Data in Medical Research. London: Chapman and Hall; 1994.

    Google Scholar 

  11. 11.

    Whitehead J. The Design and Analysis of Sequential Clinical Trials. Revised second ed. Chichester, England: Wiley; 1997.

    Google Scholar 

  12. 12.

    Sooriyarachchi MR, Whitehead J. The sequential analysis of survival data with non-proportional hazards. Biometrics. 1998;54:1072–1084.

    CAS  Article  Google Scholar 

  13. 13.

    Freedman LS. Tables of the numbers of patients required in clinical trials using the logrank test. Stat Med. 1982;1:121–129.

    CAS  Article  Google Scholar 

  14. 14.

    Machin D, Campbell MJ, Fayers PM, Pinol APY. Sample Size Tables for Clinical Studies. Second edition. Oxford: Blackwell Science Ltd.; 1997.

    Google Scholar 

  15. 15.

    Schoenfeld DA. Sample-size formula for the proportional-hazards regression model. Biometrics. 1983;39:499–503.

    CAS  Article  Google Scholar 

  16. 16.

    Whitehead J, Whitehead A, Todd S, Bolland K, Sooriyarachchi MR. Mid-trial design reviews for sequential clinical trials. Stat Med. 2001;20:165–176.

    CAS  Article  Google Scholar 

  17. 17.

    Wittes J, Brittain E. The role of internal pilot studies in increasing the efficiency of clinical trials. Stat Med. 1990;9:65–72.

    CAS  Article  Google Scholar 

  18. 18.

    Gould AL. Interim analyses for monitoring clinical trials that do not materially effect the type I error rate. Stat Med. 1992;11:55–66.

    CAS  Article  Google Scholar 

  19. 19.

    Gould AL. Planning and revising the sample size for a trial. Stat Med. 1995;14:1039–1051.

    CAS  Article  Google Scholar 

  20. 20.

    Gould AL, Shih WJ. Sample size re-estimation without unblinding for normally distributed data with unknown variance. Comm Stat—Theory Methods. 1992;21:2833–2853.

    Article  Google Scholar 

  21. 21.

    Whitehead. Sequential designs for equivalence studies. Stat Med. 1996;15:2703–2715.

    CAS  Article  Google Scholar 

  22. 22.

    Whitehead J. Overrunning and underrunning in sequential clinical trials. Control Clin Trials. 1992;13:106–121.

    CAS  Article  Google Scholar 

  23. 23.

    Gould AL, Shih WJ. Modifying the design of ongoing trials without unblinding. Stat Med. 1998;17:89–100.

    CAS  Article  Google Scholar 

  24. 24.

    Stallard N, Facey KM. Comparison of the spending function method and the Christmas tree correction for group sequential trials. J Biopharmaceutical Stat. 1996;6:361–373.

    CAS  Article  Google Scholar 

  25. 25.

    Fairbanks K, Madsen R. P values for tests using a repeated significance test design. Biometrika. 1982;69:69–74.

    Google Scholar 

  26. 26.

    Cytel Software Corporation. EaSt 2000: A Software Package for the Design and Interim Monitoring of Group Sequential Clinical Trials. Cambridge MA: Cytel; 2000.

    Google Scholar 

  27. 27.

    Gregory WM, Bolland KM, Whitehead J, Souhami RL. Cautionary tales of survival analysis: conflicting analyses from a clinical trial in breast cancer. Br J Cancer. 1997;76:551–558.

    CAS  Article  Google Scholar 

  28. 28.

    George SL, Desu MM. Planning the size and duration of a clinical trial studying the time to some critical event. J Chronic Dis. 1974;27:15–24.

    CAS  Article  Google Scholar 

  29. 29.

    Schoenfeld DA, Richter JR. Nomograms for calculating the number of patients needed for a clinical trial with survival as an endpoint. Biometrics. 1982;38:163–170.

    CAS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to John Whitehead PhD.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Whitehead, J. Predicting the Duration of Sequential Survival Studies. Ther Innov Regul Sci 35, 1387–1400 (2001).

Download citation

Key Words

  • Interim analysis
  • Noninferiority
  • Sequential analysis
  • Survival analysis