Journal Article10.1111/J.1541-0420.2012.01806.X
Bayesian hypothesis testing in two-arm trials with dichotomous outcomes.
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TL;DR: The article addresses the study of one-sided superiority and noninferiority Bayesian tests in terms of the posterior probability that the null hypothesis is true for the binomial distribution and in termsof one- sided credible limits.
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Abstract: Summary
This article is motivated by an interest in comparing inferences made when using a Bayesian or frequentist statistical approach. The article addresses the study of one-sided superiority and noninferiority Bayesian tests. These tests are stated in terms of the posterior probability that the null hypothesis is true for the binomial distribution and in terms of one-sided credible limits. We restrict our considerations to conjugate beta priors with integer parameters. Under this assumption, the posterior probabilities of tested hypotheses can be transformed into the frequentist probabilities of Bernoulli trials with an adjusted number of events and population sizes. The method resembles a standard frequentist problem formulation. By using an appropriate choice of prior parameters, the posterior probabilities of the null hypothesis can be made smaller or larger than the p-values of frequentist tests.
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References
Testing Statistical Hypotheses
George Casella,Ingram Olkin,Stephen E. Fienberg +2 more
- 01 Jan 2005
TL;DR: This classic textbook, now available from Springer, summarizes developments in the field of hypotheses testing and indicates that optimality considerations continue to provide the organizing principle, but they are now tempered by a much stronger emphasis on the robustness properties of the resulting procedures.
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The Interplay of Bayesian and Frequentist Analysis
Maria J. Bayarri,James O. Berger +1 more
TL;DR: In this article, the authors embark upon a rather idiosyncratic walk through some of the fundamental philosophical and pedagogical issues at stake in the Bayesian or frequentist paradigm. But they also recognize that each approach has a great deal to contribute to statistical practice and each is essential for full development of the other approach.
Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem
George Casella,Roger L. Berger +1 more
TL;DR: For the one-sided hypothesis testing problem, it is shown in this article that the infimum of the Bayesian posterior probability of H 0 is equal to the p value, while for some classes of prior distributions the infum is less than or equal to p value.
Bayesian methods in health technology assessment: a review.
TL;DR: A full structured review of applications of Bayesian methods to randomised controlled trials, observational studies, and the synthesis of evidence, in a form which should be reasonably straightforward to update is provided.