We discuss the construction of asymptotic simultaneous upper or lower confidence limits that jointly bound relative risks formed by comparing several treatments to control. Motivated by a vaccine efficacy study, we investigate the performance of several methods under such settings. Inverting the minimum of score statistics, together with estimating the correlation matrix of these statistics under the null hypotheses gives simultaneous coverage rate closest to the nominal level. In typical settings of vaccine studies, this method also proves to be the most powerful of the ones considered.