University dropout is a serious problem in higher education that is increasingly gaining importance, as it is essential to understand its causes and search for public and institutional policies that can help reduce it. This research uses conventional and extended Cox survival models to analyze the factors behind dropout rates at a co-financed higher education institution (HEI) in Ecuador. The latter allows us to model specific components, such as time-dependent and independent variables, and unobserved heterogeneity. The results show that certain student-related, family-related, or background characteristics are relevant for the ecuadorian context. However, the most influential factors affecting the dropout risk are institutional and academic. These findings provide valuable insights into the actions and policies that HEI can implement to mitigate dropout rates through internal measures that public policies can complement.