Allocation Rules for Sequential Clinical Trials

  • D. Siegmund
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 20)

Abstract

Consider the following simplified model of a clincial trial. Patients arrive sequentially at a treatment center and receive one of two treatments: A or B. The (immediate response of the ith patient to receive treatment A is xi, i = l,2,..., that of the jth patient to receive treatment B is yj, j = 1,2,.... At any stage of the process, having observed x1,...,xm, y1,...,yn, the experimenter can stop the experiment and declare (1) A is the better treatment, (2) B is better, or (3) there is essentially no difference between A and B; or he can continue the experiment and assign the next patient to treatment A or B according to some allocation rule. In this paper we shall be primarily interested in the experimenter’s allocation rule, which should be selected insofar as possible (i) to permit valid inferences upon termination of the experiment and (ii) to minimize in some sense the number of patients receiving the inferior treatment during the course of the experiment.

Keywords

Stratification Allo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bather, J. A. (1980). Randomized allocation of treatments in sequential trials, Adv. Appl. Probab. 12, 174–182.MathSciNetMATHCrossRefGoogle Scholar
  2. Bather, J. A. (1981). Randomized allocation of treatments in sequential experiments, Jour. Roy. Statist. Soc. B, 43.Google Scholar
  3. Blackwell, D. and Hodges, J. L. (1957). Design for the control of selection bias, Ann. Math. Statist. 28, 449–460.MathSciNetMATHCrossRefGoogle Scholar
  4. Flehinger, B., Louis, T. A., Robbins, H., and Singer, B. (1972). Reducing the number of inferior treatments in clinical trials. Proc. Nat. Acad. Sci. USA 69, 2993–2994.MathSciNetMATHCrossRefGoogle Scholar
  5. Hayre, L. S. (1979). Two population sequential tests with three hypotheses, Biometrika, 66, 465–474.MathSciNetMATHCrossRefGoogle Scholar
  6. Jennison, C. Johnstone, I. M., and Turnbull, B. W. (1981). Asymptotically optimal procedures for sequential adaptive selection of the best of several normal means, Proceedings of the Third Purdue Symposium on Statistical Decision Theory and Related Topics, S. S. Gupta and J. Berger, Eds.Google Scholar
  7. Louis, T. A. (1975). Optimal allocation in sequential tests comparing the means of two Gaussian populations, Biometrika, 62, 359–369.MathSciNetMATHCrossRefGoogle Scholar
  8. Robbins, H. (1974). A sequential test for two binomial populations, Proc. Nat. Acad. Sci. USA, 71, 4435–4436.MathSciNetMATHCrossRefGoogle Scholar
  9. Robbins, H. and Siegmund, D. (1974). Sequential tests for involving two populations, J. Amer. Statist. Assoc. 69, 132–139.MathSciNetMATHCrossRefGoogle Scholar
  10. Siegmund, D. (1979). Corrected diffusion approximations in certain random walk problems, Adv. Appl. Probab. 11, 701–719.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • D. Siegmund
    • 1
  1. 1.Stanford UniversityStanfordUSA

Personalised recommendations