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

TL;DR

This paper introduces a new semiparametric structural nested rate model to accurately estimate the causal effects of time-varying exposures on recurrent events, accounting for competing risks like death, with proven asymptotic properties and practical implementation.

Contribution

It develops novel estimators for short-term and delayed causal effects in recurrent event data with competing risks, addressing limitations of existing models.

Findings

Estimators perform well in simulations.

Application to Medicare data reveals pollution effects on hospitalizations.

Provides an R package for practical use.

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.