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

TL;DR

This paper introduces FFPSurv, a novel variational Bayesian method for discrete-time recurrent survival analysis that efficiently estimates frailty models with a closed-form likelihood, improving upon traditional approaches.

Contribution

The paper presents a new feed-forward panel estimation technique using variational inference for recurrent survival data with frailty, providing a closed-form likelihood and proof of identifiability.

Findings

Effective estimation of frailty models demonstrated on real data.

Closed-form panel likelihood derived, enabling efficient computation.

Model proven to be identifiable under mild conditions.

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.