SAVAE: Leveraging the variational Bayes autoencoder for survival analysis

In recent years, there has been a significant transformation in medical research methodologies towards the adoption of Deep Learning (DL) techniques for predicting critical events, such as disease development and patient mortality. Despite their potential to handle complex data, practical applications in this domain remain limited, with most studies still relying on traditional statistical methods. Survival Analysis (SA), or time-to-event analysis, is an essential tool for studying specific events in various disciplines, not only in medicine but also in fields such as recommendation systems [1], employee retention [2], market modeling [3], and financial risk assessment [4]. According to the existing literature, the Cox proportional hazards model (Cox-PH) [5] is the dominant SA method that offers a semiparametric regression solution to the non-parametric Kaplan-Meier estimator problem [6]. Unlike the Kaplan-Meier method, which uses a single covariate, Cox-PH incorporates multiple covariates to predict event times and assess their impact on the hazard rate at specific time points. However, it is crucial to acknowledge that the Cox-PH model is built on certain strong assumptions. One of these is the proportional hazards assumption, which posits that different individuals have hazard functions that remain constant over time. Furthermore, the model assumes a linear relation between the natural logarithm of the relative hazard (the ratio of the hazard at time t to the baseline hazard) and the covariates. Furthermore, it assumes the absence of interactions among these covariates.