Flexible Doubly Robust Proximal Causal Inference for Censored Outcomes

Estimating causal effects on right-censored time-to-event outcomes is challenging under unmeasured confounding. Proximal causal inference addresses unmeasured confounding through proxy variables, but existing proximal survival methods rely largely on restrictive parametric bridge models. We introduce Proximal Survival Bridge learning (PSB), a flexible doubly robust proximal framework for censored outcomes. Building on existing proximal identification of treatment-specific survival curves, the framework yields outcome-bridge (OB), treatment-bridge (TB), and doubly robust (DR) estimators, with two flexible bridge learners: PSB-K, a kernel estimator with a low-rank time decomposition, and PSB-N, a neural estimator trained by a projected maximum-moment-restriction loss. Unlike existing flexible proximal learners for scalar outcomes, PSB directly handles censoring and survival-curve targets. On a standard SEM benchmark, a proximal semi-synthetic ACTG study, and the real-world Framingham study, PSB-K performs strongest on SEM and ACTG, whereas PSB-N is the most stable on Framingham. Additional results with modern causal survival baselines, weakened or invalid proxies, and heavier censoring assess robustness across challenging settings.