The Annals of Applied Statistics

Incorporating external information in analyses of clinical trials with binary outcomes

Minge Xie, Regina Y. Liu, C. V. Damaraju, and William H. Olson

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External information, such as prior information or expert opinions, can play an important role in the design, analysis and interpretation of clinical trials. However, little attention has been devoted thus far to incorporating external information in clinical trials with binary outcomes, perhaps due to the perception that binary outcomes can be treated as normally-distributed outcomes by using normal approximations. In this paper we show that these two types of clinical trials could behave differently, and that special care is needed for the analysis of clinical trials with binary outcomes. In particular, we first examine a simple but commonly used univariate Bayesian approach and observe a technical flaw. We then study the full Bayesian approach using different beta priors and a new frequentist approach based on the notion of confidence distribution (CD). These approaches are illustrated and compared using data from clinical studies and simulations. The full Bayesian approach is theoretically sound, but surprisingly, under skewed prior distributions, the estimate derived from the marginal posterior distribution may not fall between those from the marginal prior and the likelihood of clinical trial data. This counterintuitive phenomenon, which we call the “discrepant posterior phenomenon,” does not occur in the CD approach. The CD approach is also computationally simpler and can be applied directly to any prior distribution, symmetric or skewed.

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Ann. Appl. Stat., Volume 7, Number 1 (2013), 342-368.

First available in Project Euclid: 9 April 2013

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Bayesian method combining information confidence distribution expert opinion requentist method discrepant posterior prior distribution


Xie, Minge; Liu, Regina Y.; Damaraju, C. V.; Olson, William H. Incorporating external information in analyses of clinical trials with binary outcomes. Ann. Appl. Stat. 7 (2013), no. 1, 342--368. doi:10.1214/12-AOAS585.

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Supplemental materials

  • Supplementary material: Appendix: MCMC algorithm and CD examples. Appendix I contains a Metropolis–Hastings algorithm used in Section 2. Appendix II presents two CD examples that are relevant to the exposition of this paper.