We use exact methods and Bayesian methodology. Our sample size estimations are based on power calculations under the one-sided alternative hypothesis that a new treatment is better than a control by a clinically important margin. The method resembles a standard frequentist problem formulation and, in the case of conjugate prior distributions with integer parameters, is similar to the frequentist approach. We evaluate type I and II errors through the use of credible limits in Bayesian models and through the use of confidence limits in frequentist models. Particularly, for conjugate priors with integer parameters, credible limits are identical to frequentist confidence limits with adjusted numbers of events and sample sizes. We consider conditions under which the minimal Bayesian sample size is less than the frequentist one and vice versa.