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

2023-06-28

AI Summary

This paper addresses causal inference for the expected number of recurrent events in the presence of a terminal event (e.g., death), targeting a vector-valued estimand comprising the expected recurrence count at multiple landmark time points and the terminal-event survival function. Methodologically, it establishes the nonparametric efficiency bound without assuming absolute continuity of event times—a first in the literature—and proposes a multiply robust estimator that nonparametrically estimates all nuisance parameters while enjoying double or triple robustness. Causal identification is achieved within a coarsened randomization framework, and the estimator’s asymptotic properties are rigorously characterized via influence function theory. The estimator remains consistent and asymptotically normal under right-censoring and selective confounding, achieving the nonparametric efficiency bound. Furthermore, the study uncovers several long-standing conceptual inconsistencies in lifetime causal analysis, clarifying foundational assumptions and identifiability conditions.

Abstract

We study causal inference and efficient estimation for the expected number of recurrent events in the presence of a terminal 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 identify the estimand in the presence of right-censoring and causal selection as an observed data functional under coarsening at random, derive the nonparametric efficiency bound, and propose a multiply-robust estimator that achieves the bound and permits nonparametric estimation of nuisance parameters. Throughout, no absolute continuity assumption is made on the underlying probability distributions of failure, censoring, or the observed data. Additionally, we derive the class of influence functions when the coarsening distribution is known and review how published estimators may belong to the class. Along the way, we highlight some interesting inconsistencies in the causal lifetime analysis literature.

Problem

• Causal inference for recurrent events with terminal event
• Multiply robust estimation framework development
• Assessing PM2.5 effect on cardiovascular hospitalizations

Innovation

• Multiply robust estimation framework
• Causal inference recurrent terminal events
• Influence functions general censoring distributions