Bayesian Methods and Applications

  • Mark Chang
Part of the Statistics for Biology and Health book series (SBH)


This introductory section will provide some key elements in the Bayesian paradigm and a quick review of basic Bayesian methods. It is intended mainly for those who are new to Bayesianism or Bayesian applications in biostatistics.


Posterior Distribution Markov Chain Monte Carlo Inclusion Probability Bayesian Credible Interval Bayesian Paradigm 
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.

Further Readings and References

  1. Berger, J.: Statistical Decision Theory and Bayesian Analysis. Springer, New York (1985)zbMATHGoogle Scholar
  2. Berger, J.: Bayesian Adjustment for Multiplicity. Subjective Bayes 2009. Duke University Statistical and Applied Mathematical Sciences Institute. December 14–16 (2009)Google Scholar
  3. Berry, S.M., Berry, D.A.: Accounting for multiplicities in assessing drug safety: A three-level hierarchical mixture model. Biometrics 60, 418–426 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  4. Braun, T.M.: The bivariate continual reassessment method: Extending the CRM to phase I trials of two competing outcomes. Control. Clin. Trials 23, 240–256 (2002)CrossRefGoogle Scholar
  5. Braun, T.M., Thall, P.F., Nguyen, H., de Lima, M.: Simultaneously optimizing dose and schedule of a new cytotoxic agent. Clin. Trials 4, 113–124 (2007)CrossRefGoogle Scholar
  6. Chang, M.: Adaptive Design Theory and Implementation Using SAS and R. Chapman and Hall/CRC, Boca Raton (2007a)Google Scholar
  7. Chang, M.: Multiple-arm superiority and noninferiority designs with various endpoints. Pharm. Stat. 6, 43–52 (2007b)CrossRefGoogle Scholar
  8. Chang, M.: Classical and Adaptive Designs Using ExpDesign Studio. Wiley, New York (2008)CrossRefGoogle Scholar
  9. Chang, M.: Monte Carlo Simulation for the Pharmaceutical Industry. Chapman and Hall/CRC, Boca Raton (2010)CrossRefGoogle Scholar
  10. Chang, M., Boral, A.: Current opinion: ABC of Bayesian approach for clinical trials. J. Pharm. Med. 22(3), 141–150 (2008)Google Scholar
  11. Chang, M., Chow, S.C.: A hybrid Bayesian adaptive design for dose response trials. J. Biopharm. Stat. 15, 667–691 (2005)CrossRefGoogle Scholar
  12. Chang, M., Chow, S.C.: Power and sample size for dose response studies. In: Ting, N. (ed.) Dose Finding in Drug Development. Springer, New York (2006)Google Scholar
  13. Chen, M.H., Shao, Q.M., Ibrahim, J.G.: Monte Carlo Methods in Bayesian Computation. Springer, New York (2000)zbMATHCrossRefGoogle Scholar
  14. Chi, G., Hung, H.M.J., O’Neill, R.: Some comments on “Adaptive Trials and Bayesian Statistics in Drug Development” by Don Berry. Pharm. Rep. 9, 1–11 (2002)Google Scholar
  15. Carvalho, C.M., Scott, J.G.: Objective Bayesian model selection in Gaussian graphical models. Biometrika 96(3), 497–512 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  16. Gelman, A., Carlin, B.J., Stern, H.S., Rubin, D.B.: Bayesain Data Analysis, 2nd edn. Chapman and Hall/CRC, Boca Raton (2004)Google Scholar
  17. Ghosh, G.K., Delampady, M., Samanta, T.: An Introduction to Bayesian Analysis: Theory and Methods. Springer, New York (2006)zbMATHGoogle Scholar
  18. Lehmann, E.L.: The Theory of Point Estimation. Wiley, New York (1983)Google Scholar
  19. Liu, J.P., Hsueh, H., Hsiao, C.F.: A Bayesian noninferiority approach to evaluation of bridging studies. J. Biopharm. Stat. 14, 291–300 (2004)CrossRefMathSciNetGoogle Scholar
  20. Mehrotra, D.V., Heyse, J.F.: Multiplicity considerations in clinical safety analyses. Stat. Meth. Med. Res. 13, 227–238 (2004)zbMATHMathSciNetGoogle Scholar
  21. Nelsen, R.B.: An Introduction to Copulas. Springer, New York (1999)zbMATHGoogle Scholar
  22. Robert, C.P.: The Bayesian Choice. Springer, New York (1997)Google Scholar
  23. Scott, J.G., Berger, J.O.: Bayes and Empirical-Bayes multiplicity adjustment in the variable-selection problem. Ann. Stat. 38, 2587–2619 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  24. Simon, R.: Bayesian design and analysis of active control trials. Biometrics 55, 484–487 (1999)zbMATHCrossRefGoogle Scholar
  25. Spiegelhalter, D.J., Abrams, K.R., Myles, K.J.: Bayesian Approaches to Clinical Trials and Health-Care Evaluation. Wiley, Southern Chichester (2004)Google Scholar
  26. Thall, P.F., Cook, J.: Dose-finding based on toxicity-efficacy trade-offs. Biometrics 60, 684–693 (2004)zbMATHMathSciNetGoogle Scholar
  27. Thall, P.F., Millikan, R.E., MÄuller, P., Lee, S.-J.: Dose-finding with two agents in phase I oncology trials. Biometrics 59, 487–496 (2003)Google Scholar
  28. Wang, K., Ivanova, A.: Two-dimensional dose-finding in discrete dose space. Biometrics 61, 217–222 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  29. Yuan, Z., Chappell, R., Bailey, H.: The continual reassessment method for multiple toxicity grades: A Bayesian quasi-likelihood approach. Biometrics 63, 173–179 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  30. Yin, G., Li, Y., Ji, Y.: Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios. Biometrics 62, 777–784 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  31. Yin, G., Yuan, Y.: Bayesian model averaging continual reassessment method in phase I clinical trials. J. Am. Stat. Assoc. 104, 954–968 (2009a)CrossRefMathSciNetGoogle Scholar
  32. Yin, G., Yuan, Y.: Bayesian dose–finding in oncology for drug combinations by copula regression. J. R. Stat. Soc. C 58, 211–224 (2009b)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Mark Chang
    • 1
  1. 1.BiometricsAMAG Pharmaceuticals, Inc.LexingtonUSA

Personalised recommendations