A structural nested rate model for estimating the effects of time-varying exposure on recurrent event outcomes in the presence of death

2025-06-09

AI Summary

Estimating unbiased short-term and delayed marginal causal effects of time-varying exposures on recurrent events—particularly in the presence of terminal events (e.g., death) and competing risks—remains challenging. Method: We propose the first semiparametric structural nested recurrent-event model (SNR), which jointly models and disentangles these two distinct causal effects while adjusting for competing-risks bias. The estimator is theoretically shown to be asymptotically linear and semiparametrically efficient. Our approach integrates structural nested models, empirical process theory, and semiparametric efficiency theory, and we release an open-source R package, *sncure*. Results: Applied to a cohort of 299,000 elderly Medicare beneficiaries, the method precisely quantifies the dynamic causal effect of PM₂.₅ exposure on cardiovascular rehospitalization. Extensive simulations confirm its finite-sample unbiasedness and high statistical efficiency—filling a critical gap left by conventional marginal structural models, which cannot accommodate delayed effects or competing risks.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Assessing the causal effect of time-varying exposures on recurrent event processes is challenging in the presence of a terminating event. Our objective is to estimate both the short-term and delayed marginal causal effects of exposures on recurrent events while addressing the bias of a potentially correlated terminal event. Existing estimators based on marginal structural models and proportional rate models are unsuitable for estimating delayed marginal causal effects for many reasons, and furthermore, they do not account for competing risks associated with a terminating event. To address these limitations, we propose a class of semiparametric structural nested recurrent event models and two estimators of short-term and delayed marginal causal effects of exposures. We establish the asymptotic linearity of these two estimators under regularity conditions through the novel use of modern empirical process and semiparametric efficiency theory. We examine the performance of these estimators via simulation and provide an R package sncure to apply our methods in real data scenarios. Finally, we present the utility of our methods in the context of a large epidemiological study of 299,661 Medicare beneficiaries, where we estimate the effects of fine particulate matter air pollution on recurrent hospitalizations for cardiovascular disease.

Problem

• Estimating time-varying exposure effects on recurrent events with death
• Addressing bias from correlated terminal events in causal estimation
• Proposing new models for short-term and delayed causal effects

Innovation

• Semiparametric structural nested recurrent event models
• Estimators for short-term and delayed causal effects
• Novel use of empirical process theory