Regression-based Proximal Causal Inference for Right-censored Time-to-event Data

Unmeasured confounding is a major concern in obtaining credible inferences about causal effects from observational data. Proximal causal inference is an emerging methodological framework to detect and potentially account for confounding bias by carefully leveraging a pair of negative control exposure and outcome variables, also known as treatment and outcome confounding proxies. Although regression-based proximal causal inference is well-developed for binary and continuous outcomes, analogous proximal causal inference regression methods for right-censored time-to-event outcomes are currently lacking. In this paper, we propose a novel two-stage regression proximal causal inference approach for right-censored survival data under an additive hazard structural model. We provide theoretical justification for the proposed approach tailored to different types of negative control outcomes, including continuous, count, and right-censored time-to-event variables. We illustrate the approach with an evaluation of the effectiveness of right heart catheterization among critically ill patients using data from the SUPPORT study. Our method is implemented in the open-access R package "pci2s."