Recurrent Event Analysis with Ordinary Differential Equations

TL;DR

This paper presents a novel framework for recurrent event analysis using ODEs, introducing a scalable estimation method that unifies various models and demonstrates strong theoretical and empirical performance.

Contribution

It develops a general ODE-based framework for recurrent event modeling and proposes a semi-parametric estimation method with proven statistical properties.

Findings

Method achieves semi-parametric efficiency when NHPP is valid.

Estimation procedure is scalable and easy to implement.

Numerical studies confirm effectiveness and applicability to real data.

Abstract

This paper introduces a general framework for analyzing recurrent event data by modeling the conditional mean function of the recurrent event process as the solution to an Ordinary Differential Equation (ODE). This approach not only accommodates a wide range of semi-parametric recurrent event models, including both non-homogeneous Poisson processes (NHPPs) and non-Poisson processes, but also is scalable and easy-to-implement. Based on this framework, we propose a Sieve Maximum Pseudo-Likelihood Estimation (SMPLE) method, employing the NHPP as a working model. We establish the consistency and asymptotic normality of the proposed estimator, demonstrating that it achieves semi-parametric efficiency when the NHPP working model is valid. Furthermore, we develop an efficient resampling procedure to estimate the asymptotic covariance matrix. To assess the statistical efficiency and computational scalability of the proposed method, we conduct extensive numerical studies, including simulations under various settings and an application to a real-world dataset analyzing risk factors associated with Intensive Care Unit (ICU) readmission frequency.