  Contrasting marginal counterfactual survival curves across treatment arms is
an effective and popular approach for inferring the causal effect of an
intervention on a right-censored time-to-event outcome. A key challenge to
drawing such inferences in observational settings is the possible existence of
unmeasured confounding, which may invalidate most commonly used methods that
assume no hidden confounding bias. In this paper, rather than making the
standard no unmeasured confounding assumption, we extend the recently proposed
proximal causal inference framework of Miao et al. (2018), Tchetgen et al.
(2020), Cui et al. (2020) to obtain nonparametric identification of a causal
survival contrast by leveraging observed covariates as imperfect proxies of
unmeasured confounders. Specifically, we develop a proximal inverse
probability-weighted (PIPW) estimator, the proximal analog of standard IPW,
which allows the observed data distribution for the time-to-event outcome to
remain completely unrestricted. PIPW estimation relies on a parametric model
for a so-called treatment confounding bridge function relating the treatment
process to confounding proxies. As a result, PIPW might be sensitive to model
misspecification. To improve robustness and efficiency, we also propose a
proximal doubly robust estimator and establish uniform consistency and
asymptotic normality of both estimators. We conduct extensive simulations to
examine the finite sample performance of our estimators, and proposed methods
are applied to a study evaluating the effectiveness of right heart
catheterization in the intensive care unit of critically ill patients.
