Student dropout is a major concern in studies investigating higher education retention strategies. However, studies investigating the optimal time to identify students who are at risk of withdrawal and the type of data to be used are scarce. Our study consists of a withdrawal prediction analysis based on classification trees using both sociodemographic and academic data from 935 first-year students at an engineering school in Spain. We build prediction models using information collected at three different moments throughout the first semester of the students' first university year. Our results echo those of previous studies supporting the need for an early first-year intervention to prevent non-completion. In addition, academic performance data serve as a good predictor. Finally, academic monitoring throughout the first semester improves the prediction accuracy, challenging the demand for 'as soon as possible' identification of students who are at risk of dropout.