title: A Bayesian non-inferiority test for two independent binomial proportions.
abstract: In drug development, non-inferiority tests are often employed to determine the difference between two independent binomial proportions. Many test statistics for non-inferiority are based on the frequentist framework. However, research on non-inferiority in the Bayesian framework is limited. In this paper, we suggest a new Bayesian index τ = P(π₁  > π₂-Δ₀|X₁, X₂), where X₁ and X₂ denote binomial random variables for trials n1 and n₂, and parameters π₁ and π₂ , respectively, and the non-inferiority margin is Δ₀> 0. We show two calculation methods for τ, an approximate method that uses normal approximation and an exact method that uses an exact posterior PDF. We compare the approximate probability with the exact probability for τ. Finally, we present the results of actual clinical trials to show the utility of index τ.
authors.affiliation: Biostatistics Section, Department of Clinical Research and Informatics, Clinical Science Center, National Center for Global Health and Medicine, Tokyo 162-8655, Japan. ykawasaki@hosp.ncgm.go.jp
authors.forename: Yohei
authors.initials: Y
authors.lastname: Kawasaki
authors.forename: Etsuo
authors.initials: E
authors.lastname: Miyaoka
mesh_terms: D001499:Bayes Theorem; D016010:Binomial Distribution; D002986:Clinical Trials as Topic / Q000379:methods*; D003627:Data Interpretation, Statistical; D015195:Drug Design; D006801:Humans; D011336:Probability
keywords: Bayesian inference; empirical Bayes method; exact probability; independent binomial proportions; non-inferiority