The aim of survival analysis in healthcare is to estimate the probability of occurrence of an event, such as a patient's death in an intensive care unit (ICU). Recent developments in deep neural networks (DNNs) for survival analysis show the superiority of these models in comparison with other well-known models in survival analysis applications. Ensuring the reliability and explainability of deep survival models deployed in healthcare is a necessity. Since DNN models often behave like a black box, their predictions might not be easily trusted by clinicians, especially when predictions are contrary to a physician's opinion. A deep survival model that explains and justifies its decision-making process could potentially gain the trust of clinicians. In this research, we propose the reverse survival model (RSM) framework that provides detailed insights into the decision-making process of survival models. For each patient of interest, RSM can extract similar patients from a dataset and rank them based on the most relevant features that deep survival models rely on for their predictions.