Proximal Causal Inference for Censored Data with an Application to Right Heart Catheterization Data

In observational causal inference studies, unmeasured confounding remains a critical threat to the validity of effect estimates. While proximal causal inference (PCI) has emerged as a powerful framework for mitigating such bias through proxy variables, existing PCI methods cannot directly handle censored data. This article develops a unified proximal causal inference framework that simultaneously addresses unmeasured confounding and right-censoring challenges, extending the proximal causal inference literature. Our key contributions are twofold: (i) We propose novel identification strategies and develop two distinct estimators for the censored-outcome bridge function and treatment confounding bridge function, resolving the fundamental challenge of unobserved outcomes; (ii) To improve robustness against model misspecification, we construct a robust proximal estimator and establish uniform consistency for all proposed estimators under mild regularity conditions. Through comprehensive simulations, we demonstrate the finite-sample performance of our methods, followed by an empirical application evaluating right heart catheterization effectiveness in critically ill ICU patients.