Vertical modelling (VM) offers an alternative approach to competing risks models, particularly when relaxing the proportional assumption or when facing missing causes of failure. It focuses on the joint probability, denoted as P(T, D), of the time to failure T and the cause of failure D, which is decomposed into \(P(D|T)\) and \(P(T)\) . Both components rely on observable quantities: the total hazard and the relative cause-specific hazard, which can be easily estimated using multinomial regression and Cox proportional hazard models adding for covariates. This paper introduces a novel approach by incorporating a random component in each part of the model to address unobserved heterogeneity in the presence of clusters. Data from the EMergenze-URgenze database, comprising Emergency Department (ED) access records from 63 Sicilian EDs in 2019, are utilized to analyze the risk of hospitalization or discharge during the length of stay once admitted to the hospital in a multi-center setting. The Cumulative Incidence Function (CIF) estimated from the vertical mixed model (VMM) is compared with that of the traditional competing risks frailty model. The VMM with independent random effects represents the first attempt to extend VM and can be viewed as an alternative to the frailty competing risks model when computational time for estimation methods is prohibitive or when exploring different aspects of the data is desired.