The Use of Reference Priors and Bayes Factors in the Analysis of Clinical Trials

  • Dalene Stangl
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 116)


This paper was motivated by foundational issues that underlie the application of Bayesian methods. Advances in numerical methods and computation make applying Bayesian methods relatively easy, so now as a discipline we can step back and contemplate what these new tools will allow us to do with respect to the theoretical foundations of our work, and if desired, adjust our actions accordingly. The foundational issues that this paper will address are the use of reference priors and the use of Bayes factors in the analysis of clinical trials. The question that merges these two foundational issues is “Should data analysis and decision-making be approached as two separate tasks or should there be a seamless integration with each stage of the clinical trial being viewed as a subsequent step in a sequential decision-making problem?”


Prior Distribution Bayesian Method Bayesian Statistics Reference Prior Foundational Issue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Berger J.O., Robust Bayesian analysis: sensitivity to the prior, Journal of Statistical Planning and Inference, 25, 1990, pp. 303–328.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Berry D.A., Interim analysis in clinical trials: classical versus Bayesian approaches, Statistics in Medicine, 4, 1985, pp. 521–526.CrossRefGoogle Scholar
  3. [3]
    Berry, D.A., Interim analysis in clinical trials: The role of the likelihood principle, The American Statistician, 41, 1987, pp. 117–122.MathSciNetMATHGoogle Scholar
  4. [4]
    Berry, D.A., Interim analysis in clinical research, Cancer Invest., 5, (1988a), pp. 469–477.CrossRefGoogle Scholar
  5. [5]
    Berry, C.A., Multiple comparisons, multiple tests, and data dredging: A Bayesian perspective with discussion). In Bayesian Statistics 3, (eds. J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith), Oxford University Press, (1988b), pp. 79–94.Google Scholar
  6. [6]
    Berry, D.A., Monitoring accumulating data in a clinical trial, Biometrics, 45, 1989a, pp. 1197–1211.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Berry, D.A., Inferential aspects of adaptive allocation rules, Proceedings of the Pharmaceutical Section of the American Statistical Association, ASA, Washington DC, 1989c, pp. 1–8.Google Scholar
  8. [8]
    Berry D.A., Bayesian methodology in phase III trials, Drug Information Association Journal, 25, 1991, pp. 345–368.CrossRefGoogle Scholar
  9. [9]
    Berry DA, Experimental design for drug development: A Bayesian approach, Journal of Biopharmaceutical Statistics, 1, 1991, pp. 81–101.MATHCrossRefGoogle Scholar
  10. [10]
    Berry, D.A., A case for Bayesianism in clinical trials (with discussion), Statistics in Medicine, 12, 1993, pp. 1377–1404.CrossRefGoogle Scholar
  11. [11]
    Berry, D.A., Decision analysis and Bayesian methods in clinical trials, In Recent Advances in Clinical Trial Design and Analysis, (ed. P. Thall), Kluwer Press, New York, 1995, pp. 125–154.CrossRefGoogle Scholar
  12. [12]
    Berry D.A., and Fristedt, B., Bandit Problems: Sequential Allocation of Experiments, London: Chapman-Hall, 1985.MATHGoogle Scholar
  13. [13]
    Berry, D.A., and Hardwick, J., Using historical controls in clinical trials: Application to ECMO, Statistical Decision Theory and Related Topics V, New York: Springer-Verlag, (eds. Berger JO, Gupta S), 1993, pp. 141–156.Google Scholar
  14. [14]
    Berry, D.A., and Eick, S.G., Adaptive assignment versus balanced randomization in clinical trials: A decision analysis, Statistics in Medicine, 14, 1994, pp. 231–246.Google Scholar
  15. [15]
    Berry, D.A., and Ho, C.H., One-sided sequential stopping boundaries for clinical trials: A decision-theoretic approach, Biometrics, 44, 1988, pp. 219–227.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    Berry, D.A., Wolff, M.C., and Sack, D., Public health decision making: A sequential vaccine trial (with discussion), In Bayesian Statistics, (eds. Bernardo JM, Berger JO, Dawid AP, Smith AFM), Oxford, England: Oxford University Press, 1992, pp. 79–96.Google Scholar
  17. [17]
    Berry, D.A., Wolff, M.C., and Sack, D., Decision making during a phase III randomized controlled trial, Controlled Clinical Trials, 15, 1994, pp. 360–379.CrossRefGoogle Scholar
  18. [18]
    Breslow, N., Biostatistics and Bayes, Statistical Science, 5, 1990, pp. 269–284.MathSciNetMATHCrossRefGoogle Scholar
  19. [19]
    Brophy J.M., and Joseph, L., Placing trials in context using Bayesian analysis: Gusto revisited by Reverend Bayes, Journal of the American Medical Association, 273(11), 1995, pp. 871–875.CrossRefGoogle Scholar
  20. [20]
    Carlin, B.P., and Louis, T.A., Bayes and Empirical Bayes Methods for Data Analysis, Chapman and Hall, 1996.Google Scholar
  21. [21]
    Carlin, B.P., Chaloner, K. M., Louis, T.A., and Rhame, F.S., Elicitation, monitoring, and analysis for an AIDS clinical trial, In Case Studies in Bayesian Statistics: Volume II, (eds. C. Gatsonis, J. Hodges, R. Kass, and N. Singpur-walla), Springer, 1995, pp. 48–84.Google Scholar
  22. [22]
    Chaloner, K., Elicitation of Prior Distributions, In Bayesian Biostatistics, (eds. D.A. Berry and D.K. Stangl), Marcel Dekker, 1996, pp. 141–156.Google Scholar
  23. [23]
    Chaloner, K., Church, T., Matts, J.P., and Louis, T.A., Graphical elicitation of a prior distribution for an AIDS clinical trial, The Statistician, 42, 1993, pp. 341–353.CrossRefGoogle Scholar
  24. [24]
    Craig, P.S., Goldstein, M., Seheult, A.H., and Smith, J.A., Constructing partial prior specifications for models of complex physical systems, The Statistician, 47(1), 1998, pp. 37–53.Google Scholar
  25. [25]
    Gail, M., A discussion of: Bayesian approaches to randomized trials, J. Royal Statistical Soc. Ser. A, 157, 1995, pp. 357–416.Google Scholar
  26. [26]
    Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D. B., Bayesian Data Analysis, Chapman & Hall, London, 1995.Google Scholar
  27. [27]
    Greenhouse J.B., and Wasserman, L., A practical, robust method for Bayesian model selection: A case study in the analysis of clinical trials, Paper presented at the American Statistical Association Meetings, Carnegie-Mellon Technical Report #626, 1995a.Google Scholar
  28. [28]
    Greenhouse, J.B., and Wasserman, L., Robust Bayesian methods for monitoring clinical trials, Statistics in Medicine, 14, 1995b, pp. 1379–1391.CrossRefGoogle Scholar
  29. [29]
    Greenhouse, J.B., On some applications of Bayesian methods in cancer clinical trials, Statistics in Medicine, 11, 1992, pp. 37–53.Google Scholar
  30. [30]
    Hilden, J. and Habbema, J., The marriage of clinical trials and clinical decision science, Statistics in Medicine, 9, 1990, pp. 1243–1257.CrossRefGoogle Scholar
  31. [31]
    Hively, W., The mathematics of making up your mind, Discover, May 1996.Google Scholar
  32. [32]
    Kadane, J.B., and Wolfson, L. J., Priors for the design and analysis of clinical trials, In Bayesian Biostatistics, D. Berry and D. Stangl (eds.), Marcel Dekker, New York 1996.Google Scholar
  33. [33]
    Kadane, J.B., and Wolfson, L. J., Experiences in elicitation, The Statistician, 47(1), 1998, pp. 3–19.Google Scholar
  34. [34]
    Kadane, J.B., and Dickey, J.M., Bayesian decision theory and the simplification of models, In Evaluation of Econometric Models, (eds. J. Kmenta and J. Ramsey), Academic Press, 1980, pp. 245–268.Google Scholar
  35. [35]
    Lavine, M., and Schervish, M., Bayes factors: What they are and what they are not, The Statistician, 1999, to appear.Google Scholar
  36. [36]
    Lindley, D., A discussion of: Bayesian approaches to randomized trials, J. Royal Statistical Soc. Ser. A, 157, 1995, pp. 357–416Google Scholar
  37. [37]
    O’Hagan, A., Eliciting expert beliefs in substantial practical applications, The Statistician, 47(1), 1998, pp. 21–35.MathSciNetGoogle Scholar
  38. [38]
    Parmigiani, G., Ancukiewicz, M. and Matchar, D., Decision models in clinical recommendations development: The stroke prevention policy model, In Bayesian Biostatistics, ed. D.A. Berry and D.K. Stangl, Marcel Dekker, 1996, pp. 207–233.Google Scholar
  39. [39]
    Parmigiani, G. and Kamlet, M.S., A cost-utility analysis of alternative strategies in screening for breast cancer, In Case Studies in Bayesian Statistics, (eds. C. Gatsonis, J. Hodges, R. Kass, and N. Singpurwalla, Springer-Verlag, 1993, pp. 390–402.Google Scholar
  40. [40]
    Sargent, D. and Carlin, B.P., Robust Bayesian design and analysis of clinical trials via prior partitioning (with discussion), IMS Lecture Note Series: Second International Workshop on Bayesian Robustness, 1996.Google Scholar
  41. [41]
    Simes, R.J., Application of statistical decision theory to treatment choices: Implications for the design and analysis of clinical trials, Statistics in Medicine, 5, 1986, pp. 411–420.CrossRefGoogle Scholar
  42. [42]
    Spiegelhalter, D.J., Freedman, L.S., and Parmar, M.K., Bayesian approaches to randomized trials, J. Royal Statistical Soc. Ser. A, 157, 1994, pp. 357–416.MathSciNetMATHCrossRefGoogle Scholar
  43. [43]
    Stangl, D., Prediction and decision making using Bayesian hierarchical models, Statistics in Medicine, 14, 1995, pp. 2173–2190.CrossRefGoogle Scholar
  44. [44]
    The Gusto Investigators, An international randomized trial comparing four thrombolytic strategies for acute myocardial infarction, N. Engl. J. Med., 329, 1993, pp. 673–682.CrossRefGoogle Scholar
  45. [45]
    Wasserman, L., Recent methodological advances in robust Bayesian inference, In Bayesian Statistics IV, (eds. J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith), Oxford University Press, 1992, pp. 483–502.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Dalene Stangl
    • 1
  1. 1.Institute of Statistics and Decision SciencesDuke UniversityDurhamUSA

Personalised recommendations