A data-driven method to identify frequent sets of course failures that students should avoid in order to minimize the likelihood of their dropping out from their university training is proposed. The overall probability distribution of the dropout is determined by survival analysis. This result can only describe the mean dropout rate of the undergraduates. However, due to the failure of different courses, the chances of dropout can be highly varied, so the traditional survival model should be extended with event analysis. The study paths of students are represented as events in relation to the lack of completing the required subjects for every semester. Frequent patterns of backlogs are discovered by the mining of frequent sets of these events. The prediction of dropout is personalised by classifying the success of the transitions between the semesters. Based on the explored frequent item sets and classifiers, association rules are formed providing the estimates of the success of the continuation of the studies in the form of confidence metrics. The results can be used to identify critical study paths and courses. Furthermore, based on the patterns of individual uncompleted subjects, it is suitable to predict the chance of continuation in every semester. The analysis of the critical study paths can be used to design personalised actions minimizing the risk of dropout, or to redesign the curriculum aiming the reduction in the dropout rate. The applicability of the method is demonstrated based on the analysis of the progress of chemical engineering students at the University of Pannonia in Hungary. The method is suitable for the examination of more general problems assuming the occurrence of a set of events whose combinations may trigger a set of critical events.