On Sample Size Determination Based on a Bayesian Index of Non-inferiority for Two Independent Binomial Proportions

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. In this paper, we propose a method for the determination of sample sizes using the index ( ) , , 2 1 0 2 1 X X P ∆ − π > π = τ where 1 X and 2 X denote binomial random variables for trials 1 n and , 2 n and parameters 1 π and , 2 π respectively, and the non-inferiority margin is . 0 0 > ∆ In this paper, we propose a new method of calculation, by which we determine in advance the estimated difference between the posterior proportions and the value to be derived at the end of the test to obtain the necessary sample size. We provide the lists of necessary sample sizes with various assumptions. YOHEI KAWASAKI and HIROSHI YAMADA 196