Proximal Causal Inference for Marginal Counterfactual Survival Curves

TL;DR

This paper extends proximal causal inference methods to estimate marginal survival treatment effects in observational studies with unmeasured confounding, using proxies and developing robust estimators.

Contribution

It introduces a proximal inverse probability-weighted estimator and a proximal doubly robust estimator for causal survival analysis under unmeasured confounding.

Findings

Proposed estimators are consistent and asymptotically normal.

Simulation studies show good finite sample performance.

Applied methods to ICU data on right heart catheterization.

Abstract

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.