Abstract: Time-to-event modelling, known as survival analysis, differs from standard regression as it addresses censoring in patients who do not experience the event of interest. Despite competitive performances in tackling this problem, machine learning methods often ignore other competing risks that preclude the event of interest. This practice biases the survival estimation. Extensions to address this challenge often rely on parametric assumptions or numerical estimations leading to sub-optimal survival approximations. This paper leverages constrained monotonic neural networks to model each competing survival distribution. This modelling choice ensures the exact likelihood maximisation at a reduced computational cost by using automatic differentiation. The effectiveness of the solution is demonstrated on one synthetic and three medical datasets. Finally, we discuss the implications of considering competing risks when developing risk scores for medical practice.