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A Bayesian non‐inferiority test for two independent binomial proportions
Author(s) -
Kawasaki Yohei,
Miyaoka Etsuo
Publication year - 2013
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.1571
Subject(s) - frequentist inference , statistics , mathematics , bayesian probability , binomial (polynomial) , continuity correction , binomial distribution , margin (machine learning) , econometrics , bayesian inference , negative binomial distribution , beta binomial distribution , computer science , machine learning , poisson distribution
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 ( π 1 > π 2 − Δ 0 | X 1 , X 2 ), where X 1 and X 2 denote binomial random variables for trials n 1 and n 2 , and parameters π 1 and π 2 , respectively, and the non‐inferiority margin is Δ 0 > 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 . Copyright © 2013 John Wiley & Sons, Ltd.