We proposed an extension of the Differences-in-Differences approach for more general setups, particularly Generalized Linear Models, to assess the impact of interventions/treatments on observational studies. We extend the usual causal effect identification procedures by presenting the necessary assumptions, and describing more appropriate causal measures, accordingly to the type of outcome and statistical model. We analyze novel data from three health issues in Brazil to illustrate the proposed methodology. The first application is related to the demographic impact of the Zika virus outbreak in 2015 on birth rates. The other two applications evaluate the impact of two distinct interventions in the primary health care on the hospitalization rates. Although several methods are currently available to tackle the complexities of data sampling and the dynamics of the interventions, the diff-in-diff approach is still relevant when estimating ATT and many studies can benefit from its generalization.