Recurrent Event Analysis with Ordinary Differential Equations

2025-07-27

AI Summary

This paper addresses modeling the conditional mean function for recurrent event data. We propose a general semiparametric framework grounded in ordinary differential equations (ODEs), wherein the conditional mean function is characterized as the solution to an ODE, with a nonhomogeneous Poisson process (NHPP) serving as the working model. To estimate the unknown components, we develop a sieve-based maximum pseudo-likelihood estimator. Our method achieves both semiparametric efficiency and computational scalability: theoretically, the estimator is consistent and asymptotically normal, attaining the semiparametric efficiency bound under the NHPP assumption; additionally, we design an efficient resampling procedure to estimate the asymptotic covariance matrix. Extensive numerical simulations and application to ICU readmission data demonstrate the method’s statistical accuracy, robustness to model misspecification, and practical utility in real-world settings.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Model recurrent event data using ODE-based conditional mean function
• Propose scalable Sieve Maximum Pseudo-Likelihood Estimation method
• Assess method efficiency via simulations and ICU readmission analysis

Innovation

• ODE-based recurrent event analysis framework
• Sieve Maximum Pseudo-Likelihood Estimation method
• Efficient resampling for covariance estimation