This paper investigates the student dropout phenomenon in a technical Italian university from a time-to-event perspective. Shared frailty Cox time-dependent models are applied to analyse the careers of students enrolled in different engineering programs with the aim of identifying the determinants of student dropout through time, predicting the time to dropout as soon as possible and to observe how the dropout phenomenon varies across time and degree programs. The innovative contributions of this work are methodological and managerial. First, the adoption of shared frailty Cox models with time-varying covariates is relatively new to the student dropout literature and it allows to consider the student career evolution and the heterogeneity across degree programs. Second, understanding the dropout pattern over time and identifying the earliest moment for obtaining its accurate prediction allow policy makers to set timely interventions for students at risk of dropout.