Because of the high cost and time constraints for clinical trials, researchers often need to
determine the smallest sample size that provides accurate inferences for a parameter of
interest. Although most experimenters have employed frequentist sample-size determination
methods, the Bayesian paradigm offers a wide variety of sample-size determination
methodologies. Bayesian sample-size determination methods are becoming increasingly
more popular in clinical trials because of their flexibility and easy interpretation inferences.
Recently, Bayesian approaches have been used to determine the sample size of a single
Poisson rate parameter in a clinical trial setting. In this paper, we extend these results to
the comparison of two Poisson rates and develop methods for sample-size determination
for hypothesis testing in a Bayesian context. We have created functions in R to determine
the parameters for the conjugate gamma prior and calculate the sample size for the average
length criterion and average power methods. We also provide two examples that implement
our sample-size determination methods using clinical data.