Violence against women (VaW) is difficult to quantify as it is typically a largely underrated phenomenon. Clearly, gender-based violence could be more effectively contrasted if policies were informed by up-to-date and comprehensive evidence. Sample surveys are acknowledged to be the most reliable and established method to estimate the prevalence of violence and its characteristics, but when recent specialized survey data are not available (the last survey in Italy dates back to 2014), administrative data sources such as police registers can be considered as a possible source of information, though affected by large underreporting. We propose to model these data by a Poisson regression, explicitly accounting for the under-reporting, using the so-called Pogit model. To inform our model we include the available information on both the reporting process and the event intensity obtained from additional data sources such as the 1522 helpline number database and the BES system of indicators.