The prediction of university dropout is a complex problem, given the number and diversity of variables involved. Therefore, different strategies are applied to understand this educational phenomenon, although the most outstanding derive from the joint application of statistical approaches and computational techniques based on machine learning. Student Dropout Prediction (SDP) is a challenging problem that can be addressed following various strategies. On the one hand, machine learning approaches formulate it as a classification task whose objective is to compute the probability of belonging to a class based on a specific feature vector that will help us to predict who will drop out. Alternatively, survival analysis techniques are applied in a time-varying context to predict when abandonment will occur. This work considered analytical mechanisms for supporting the decision-making process on higher education dropout. We evaluated different computational methods from both approaches for predicting who and when the dropout occurs and sought those with the most-consistent results. Moreover, our research employed a longitudinal dataset including demographic, socioeconomic, and academic information from six academic departments of a Latin American university over thirteen years. Finally, this study carried out an in-depth analysis, discusses how such variables influence estimating the level of risk of dropping out, and questions whether it occurs at the same magnitude or not according to the academic department, gender, socioeconomic group, and other variables.