Sample-size determination for two independent binomial experiments

Sample size determination is commonly encountered in modern medical studies for two independent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.