Causal Proportional Hazards Estimation with a Binary Instrumental Variable

TL;DR

This paper introduces a new causal hazard ratio estimator within a proportional hazards model using instrumental variables, effectively addressing unmeasured confounding in survival analysis with right-censored data.

Contribution

It develops a simple, robust IV-based estimator for survival data that can handle complex features like truncation and competing risks, with proven asymptotic properties.

Findings

Estimator performs well in simulations

Applied to cancer screening data to estimate causal effects

Method is implementable with standard software

Abstract

Instrumental variables (IV) are a useful tool for estimating causal effects in the presence of unmeasured confounding. IV methods are well developed for uncensored outcomes, particularly for structural linear equation models, where simple two-stage estimation schemes are available. The extension of these methods to survival settings is challenging, partly because of the nonlinearity of the popular survival regression models and partly because of the complications associated with right censoring or other survival features. We develop a simple causal hazard ratio estimator in a proportional hazards model with right censored data. The method exploits a special characterization of IV which enables the use of an intuitive inverse weighting scheme that is generally applicable to more complex survival settings with left truncation, competing risks, or recurrent events. We rigorously establish the asymptotic properties of the estimators, and provide plug-in variance estimators. The proposed method can be implemented in standard software, and is evaluated through extensive simulation studies. We apply the proposed IV method to a data set from the Prostate, Lung, Colorectal and Ovarian cancer screening trial to delineate the causal effect of flexible sigmoidoscopy screening on colorectal cancer survival which may be confounded by informative noncompliance with the assigned screening regimen.