We develop a simple statistic for comparing rates of rare adverse events between treatment groups in postmarketing safety studies where the events have uncertain status. In this setting, the statistic is asymptotically equivalent to the logrank statistic, but the limiting distribution has Poisson and binomial components instead of being Gaussian. We develop two new procedures for computing critical values: a Gaussian approximation and a parametric bootstrap. Both numerical and asymptotic properties of the procedures are studied. The test procedures are demonstrated on a postmarketing safety study of the RotaTeq vaccine. This vaccine was developed to reduce the incidence of severe diarrhea in infants.