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. Kawasaki and Miyaoka [5] suggested a new Bayesian index  where  and  denote binomial random variables for trials  and  and parameters  and  respectively, and the non-inferiority margin is  They proposed two calculation methods which are an exact method and an approximate method. However, we cannot calculate the exact probability in a large sample case using SAS which is often using a pharmaceutical biostatistician. Also, the drawback of the approximate method is that it occasionally leads to a rough result in a small sample. In this paper, we propose a new calculation method using Markov Chain Monte Carlo (MCMC) method as a solution to these problems. We compare the approximate method and the MCMC method with the exact method for

non-inferiority test, binomial proportions, MCMC method.