Patients in large clinical trials and in studies employing large observational databases report many different adverse events, most of which will not have been anticipated at the outset. Conventional hypothesis testing of between group differences for each adverse event can be problematic: Lack of significance does not mean lack of risk, the tests usually are not adjusted for multiplicity, and the data determine which hypotheses are tested. This article describes a Bayesian screening approach suitable for clinical trials and large observational databases that do not test hypotheses, are self‐adjusting for multiplicity, provide a direct assessment of the likelihood of no material drug‐event association, and quantify the strength of the observed association. Clinical and/or regulatory considerations define the criteria for assessing drug‐event associations. The diagnostic properties of this new approach can be evaluated analytically. The result of comparison of the results from the method relative to current methods when applied to a commonly used data set indicates that the findings are largely similar, but with some interesting differences that may be relevant in application. Applying the method to a large vaccine trial reduces the number of adverse events that might require further investigation substantially.