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

arXiv: https://arxiv.org/abs/2306.16571 · HTML: https://mlsanity.com/paper/2306.16571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 78 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 11 of 11)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Efficient nonparametric causal inference with missing exposure information](https://mlsanity.com/paper/1802.08952/) (2018)
- [Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes](https://mlsanity.com/paper/2105.02088/) (2021)
- [Nonparametric inverse probability weighted estimators based on the highly adaptive lasso](https://mlsanity.com/paper/2005.11303/) (2020)
- [Inference for treatment-specific survival curves using machine learning](https://mlsanity.com/paper/2106.06602/) (2021)
- [Insights into the "cross-world" independence assumption of causal mediation analysis](https://mlsanity.com/paper/2003.10341/) (2020)
- [Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation](https://mlsanity.com/paper/2106.11009/) (2021)
- [Improved Precision in the Analysis of Randomized Trials with Survival Outcomes, without Assuming Proportional Hazards](https://mlsanity.com/paper/1511.08404/) (2015)
- [Causal inference with recurrent and competing events](https://mlsanity.com/paper/2202.08500/) (2022)
- [Correcting an estimator of a multivariate monotone function with isotonic regression](https://mlsanity.com/paper/1810.09022/) (2018)
- [A Comparison of Different Methods to Adjust Survival Curves for Confounders](https://mlsanity.com/paper/2203.10002/) (2022)

## Abstract (arXiv)

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 PM2.5 on recurrent cardiovascular hospitalization.