Causal inference for the expected number of recurrent events in the presence of a terminal event

TL;DR

This paper introduces a multiply robust estimation framework for causal inference on recurrent events with a terminal event, applicable under general censoring conditions, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It develops a novel multiply robust estimator for causal effects in recurrent event data with a terminal event, relaxing traditional assumptions and broadening applicability.

Findings

Estimator performs well in small samples in simulations

Framework successfully applied to Medicare data on PM2.5 effects

Provides influence functions under general censoring without absolute continuity

Abstract

While recurrent event analyses have been extensively studied, limited attention has been given to causal inference within the framework of recurrent event analysis. We develop a multiply robust estimation framework for causal inference in recurrent event data with a terminal failure event. We define our estimand as the vector comprising both the expected number of recurrent events and the failure survival function evaluated along a sequence of landmark times. We show that the estimand can be identified under a weaker condition than conditionally independent censoring and derive the associated class of influence functions under general censoring and failure distributions (i.e., without assuming absolute continuity). We propose a particular estimator within this class for further study, conduct comprehensive simulation studies to evaluate the small-sample performance of our estimator, and illustrate the proposed estimator using a large Medicare dataset to assess the causal effect of PM$_{2.5}$ on recurrent cardiovascular hospitalization.