The problem of under-reporting in count data has led to many statistical developments. Our work is driven by the need to estimate the true number of cases of violence against women in Italy. A key methodological aspect is the integration of multiple data sources, achieved through a hierarchical Bayesian approach that combines individual-level and aggregated data. The aggregated-level data provide only a quantification that underestimates the true number of events. Introducing an additional hierarchical layer that captures the relationship between covariates and both the occurrence of events and the probability of reporting, individual-level data are thus used to define the prior distributions for the aggregated model. The final model is able to provide correction for the under-reporting count data on the aggregated level.