ICTSurF: Implicit Continuous-Time Survival Functions with Neural Networks

Survival analysis, also known as time-to-event analysis, aims at estimating the survival distributions of a specific event and time-of-interests. Typically, the estimation of survival probability involves modeling a relationship between covariates and time-to-event that is typically partially observed; e.g., it may not be possible to observe the event status of the same sample. This presents one of the key challenges in the field of survival analysis. The conventional approaches commonly employed in survival analysis include the Cox Proportional Hazards (CPH) model, as proposed by Cox [6]. Although the CPH model is widely used, it is burdened by a substantial assumption of a consistent proportional hazard throughout the entire lifespan and a predetermined relationship between covariates. Other conventional methods, such as Weibull or Log-Normal distribution, also model a relationship between time and covariates based on a strong parametric assumption. Recently, due to the success of DNN-based models, the majority of research in survival analysis has shifted towards models built on DNNs, demonstrating superior performance compared to traditional approaches. Recent studies have shown that the majority of the survival models are an extension of the conventional CPH model [28].