Feed-Forward Panel Estimation for Discrete-time Survival Analysis of Recurrent Events with Frailty

Abstract: In recurrent survival analysis where the event of interest can occur multiple times for each subject, frailty models play a crucial role by capturing unobserved heterogeneity at the subject level within a population. Frailty models traditionally face challenges due to the lack of a closed-form solution for the maximum likelihood estimation that is unconditional on frailty. In this paper, we propose a novel method: Feed-Forward Panel estimation for discrete-time Survival Analysis (FFPSurv). Our model uses variational Bayesian inference to sequentially update the posterior distribution of frailty as recurrent events are observed, and derives a closed form for the panel likelihood, effectively addressing the limitation of existing frailty models. We demonstrate the efficacy of our method through extensive experiments on numerical examples and real-world recurrent survival data. Furthermore, we mathematically prove that our model is identifiable under minor assumptions.