When making Bayesian inferences we need to elicit an expert's opinion to set up the prior distribution. For applications in clinical trials, we study this problem with binary variables. A critical and often ignored issue in the process of eliciting priors in clinical trials is that medical investigators can seldom specify the prior quantities with precision. In this paper, we discuss several methods of eliciting beta priors from clinical information, and we use simulations to conduct sensitivity analyses of the effect of imprecise assessment of the prior information. These results provide useful guidance for choosing methods of eliciting the prior information in practice.