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Group sequential extensions of a standard bioequivalence testing procedure

  • A. Lawrence Gould
Article

Abstract

Bioequivalence trials compare the relative bioavailability of different formulations of a drug. Regulatory requirements for demonstrating average bioequivalence of two formulations generally include showing that a (say) 90% confidence interval for the ratio of expected pharmacologic end point values of the formulations lies between specified end points, e.g., 0.8–1.25. The likelihood of demonstrating bioequivalence when the formulations truly are equivalent depends on the sample size and on the variability of the pharmacologic end point. Group sequential bioequivalence testing provides a statistically valid way to accommodate misspecification of the variability in designing the trial by allowing for additional observations if a clear decision to accept or reject bioequivalence cannot be reached with the initial set of observations. This paper describes group sequential bioequivalence designs applicable in most practical situations that allow a decision to be reached with fewer observations than fixed-sample designs about 60% of the time at approximately the same average cost. The designs can be used in trials where the formulations are expected to have equal bioavailability and in trials where the formulations are expected to differ slightly. Data analyses are carried out exactly as for fixed-sample designs. Providing the capability of sequential decisions modestly affects the nominal significance levels, e.g., the required confidence level may be 93–94% instead of 90%.

Key Words

trial design sample size interim analysis bioavailability group sequential 

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References

  1. 1.
    S. Durrleman and R. Simon. Planning and monitoring of equivalence trials.Biometrics 46:329–336 (1990).PubMedCrossRefGoogle Scholar
  2. 2.
    D. J. Schuirmann. On hypothesis testing to determine if the mean of a normal distribution is contained in a known interval.Biometrics 37:617 (1981).Google Scholar
  3. 3.
    D. J. Schuirmann. A comparison of the two one-sided test procedure and the power approach for assessing the equivalence of average bioavailability.J. Pharmacokin. Biopharm. 15:657–680 (1987).CrossRefGoogle Scholar
  4. 4.
    W. J. Westlake. Use of confidence intervals in analyses of comparative bioavailability trials.J. Pharm. Sci. 61:1340–1341 (1972).PubMedCrossRefGoogle Scholar
  5. 5.
    W. J. Westlake. Symmetrical confidence intervals for bioequivalence trials.Biometrics 32:741–744 (1976).PubMedCrossRefGoogle Scholar
  6. 6.
    W. J. Westlake. Statistical aspects of comparative bioavailability trials.Biometrics 35:273–280 (1979).PubMedCrossRefGoogle Scholar
  7. 7.
    D. Mandallaz and J. Mau. Comparison of different methods for decision-making in bioequivalence assessment.Biometrics 37:213–222 (1981).PubMedCrossRefGoogle Scholar
  8. 8.
    A. Racine-Poon, A. Grieve, H. Fluehler, and A. F. M. Smith. A two-stage procedure for bioequivalence studies.Biometrics 43:847–856 (1987).PubMedCrossRefGoogle Scholar
  9. 9.
    B. E. Rodda and R. L. Davis. Determining the probability of an important difference in bioavailability.Clin. Pharmacol. Ther. 28:247–252 (1980).PubMedCrossRefGoogle Scholar
  10. 10.
    R. Srinivasan and P. Langenberg. A two-stage procedure with controlled error probabilities for testing bioequivalence.Biomet. J. 28:825–833 (1986).CrossRefGoogle Scholar
  11. 11.
    C. Jennison and B. W. Turnbull. Sequential equivalence testing and repeated confidence intervals, with applications to normal and binary responses.Biometrics 49:31–43 (1993).PubMedCrossRefGoogle Scholar
  12. 12.
    D. M. Rocke. On testing for bioequivalence.Biometrics 40:225–230 (1984).PubMedCrossRefGoogle Scholar
  13. 13.
    S. Chow and J. P. Liu.Design and Analysis of Bioavailability and Bioequivalence Studies, Marcel Dekker, New York, 1992.Google Scholar
  14. 14.
    M. Hills and P. Armitage. The two period cross-over clinical trial.Br. J. Clin. Pharmacol. 8:7–20 (1979).PubMedCentralPubMedCrossRefGoogle Scholar
  15. 15.
    B. Jones and M. G. Kenward.Design and Analysis of Cross-Over Trials, Chapman and Hall, London, 1989.Google Scholar
  16. 16.
    D. J. Schuirmann. Design of bioavailability/bioequivalence studies.Drug Inform. J. 24:315–323 (1990).Google Scholar
  17. 17.
    J. Liu and S. Chow. Sample size determination for the two one-sided tests procedure in bioequivalence.J. Pharmacokin. Biopharm. 20:101–104 (1992).CrossRefGoogle Scholar
  18. 18.
    C. Jennison and B. W. Turnbull. Interim analysis: the repeated confidence interval approach (with discussion).J. Roy. Statis. Soc. SeriesB 51:305–361 (1989).Google Scholar
  19. 19.
    C. Jennison and B. W. Turnbull. Exact calculations for sequentialt, X 2 andF tests.Biometrika 78:133–141 (1991).Google Scholar
  20. 20.
    E. V. Slud and L. J. Wei. Two-sample repeated significance tests based on the modified Wilcoxon statistic.J. Am. Statist. Assoc. 77:855–861 (1982).CrossRefGoogle Scholar
  21. 21.
    K. Kim and D. L. Demets. Design and analysis of group sequential tests based on the Type I error spending rate function.Biometrika 74:149–154 (1987).CrossRefGoogle Scholar
  22. 22.
    A. L. Gould and V. J. Pecore. Group sequential methods for clinical trials allowing early acceptance ofH o and incorporating costs.Biometrika 69:75–80 (1982).Google Scholar
  23. 23.
    A. L. Gould. Planning and revising the sample size for a trial.Statist. Med. 14:1039–1051 (1995).CrossRefGoogle Scholar
  24. 24.
    E. J. Dudewicz. Confidence intervals for power, with special reference to medical trials.Aust. J. Stat. 14:211–216 (1972).CrossRefGoogle Scholar
  25. 25.
    E. Diletti, D. Hauschke, and V. W. Steinijans. Sample size determination for bioequivalence assessment by means of confidence intervals.Int. J. Clin. Pharmacol. Ther. Toxicol. 29:1–8 (1991).PubMedGoogle Scholar
  26. 26.
    D. Hauschke, V. W. Steinijans, E. Diletti, and M. Burke. Sample size determination for bioequivalence assessment using a multiplicative model.J. Pharmacokin. Biopharm. 20:557–561 (1992).CrossRefGoogle Scholar
  27. 27.
    S. Emerson and T. R. Fleming. Parameter estimation following group sequential hypothesis testing.Biometrika 77:875–892 (1990).CrossRefGoogle Scholar
  28. 28.
    W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling.Numerical Recipes in Pascal, Cambridge University Press, Cambridge, 1989.Google Scholar
  29. 29.
    S. Anderson and W. W. Hauck. Consideration of individual bioequivalence.J. Pharmacokin. Biopharm. 18:259–273 (1990).CrossRefGoogle Scholar
  30. 30.
    G. Ekbohm and H. Melander. The subject-by-formulation interaction as a criterion of interchangeability of drugs.Biometrics 45:1249–1254 (1989).CrossRefGoogle Scholar
  31. 31.
    D. J. Holder and F. Hsuan. Moment-based criteria for determining bioequivalence.Biometrika 80:835–846 (1993).CrossRefGoogle Scholar
  32. 32.
    S. Hwang, P. B. Huber, M. Hesney, and K. C. Kwan. Bioequivalence and interchangeability.J. Pharm. Sci. 67:IV (1978).PubMedCrossRefGoogle Scholar
  33. 33.
    M. H. Gail, D. L. Demets, and E. V. Slud, in R. Johnson and J. Crowley (eds.),Survival Analysis, Monograph Series 2, IMS Lecture Notes, Hayward, CA, 1981. p. 287–301.Google Scholar
  34. 34.
    E. V. Slud. Sequential linear rank tests for two-sample censored survival data.Ann. Statist. 12:551–571 (1984).CrossRefGoogle Scholar
  35. 35.
    D. Demets and M. H. Gail. Use of logrank tests and group sequential methods at fixed calendar times.Biometrics 41:1039–1044 (1985).PubMedCrossRefGoogle Scholar
  36. 36.
    K. K. G. Lan and D. L. Demets. Discrete sequential boundaries for clinical trials.Biometrika 70:659–663 (1983).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. Lawrence Gould
    • 1
  1. 1.Merck Research LaboratoriesWest Point

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