The study of time-to-event data is essential in fields such as biology and medicine, particularly for improving patient outcomes. For example it enables the evaluation of survival times in cancer patients or the duration until a relapse occurs. In liver transplantation, which is crucial for treating end-stage liver diseases, the increasing demand for grafts and the limited availability of donors have led to the use of extended criteria donors. This approach, while addressing the graft shortage, also increases the risk of graft failure. Traditional survival models are often insufficient for these high-risk scenarios and as a result, there is a critical need for highly advanced models that can reliably predict the success or failure of transplantations under these increasingly complex conditions. In parallel, a significant amount of data collected over recent years offers valuable insights into graft failures and patient survival. This wealth of data has generated numerous indicators, yet only a limited number are utilized in practice. Moreover, the diversity within the transplant patient population has introduced a significant heterogeneity in the data, which must be carefully managed to ensure accurate analysis and application. To effectively utilize this data, advanced statistical tools are needed. The Cox proportional hazards model, a well-established method in survival analysis, can be instrumental in this regard. This model and its extensions, such as mixture models or penalization techniques, provide robust frameworks for predicting patient outcomes and understanding the factors influencing survival. This article proposes a Deep Penalized Cox Mixture model (DPCM). The application of such a mixture of L1-penalized Cox model to liver transplant data will enable us to simultaneously establish patient subgroups with similar behavior and select the most relevant variables for determining survival time from the extensive data available today. This approach not only enhances our understanding of the factors contributing to graft failure but also improves the prediction of survival time for each patient within the entire population, ultimately leading to better outcomes in liver transplantation. Moreover, our model delivers better results compared to existing approaches that utilize only the mixture part or the penalty part, offering a more effective solution. This approach aims to enhance decision-making and improve patient care in the context of liver transplantation.