Meta-analysis allows researchers to combine evidence from multiple studies, making it a powerful tool for synthesizing information on the safety profiles of new medical interventions. There is a critical need to identify subgroups at high risk of experiencing treatment-related toxicities. However, this remains quite challenging from a statistical perspective as there are a variety of clinical risk factors that may be relevant for different types of adverse events, and adverse events of interest may be rare or incompletely reported. We frame this challenge as a variable selection problem and propose a Bayesian hierarchical model which incorporates a horseshoe prior on the interaction terms to identify high-risk groups. Our proposed model is motivated by a meta-analysis of adverse events in cancer immunotherapy, and our results uncover key factors driving the risk of specific types of treatment-related adverse events.