Adjusting for bias introduced by instrumental variable estimation in the Cox Proportional Hazards Model

TL;DR

This paper identifies bias in instrumental variable methods within the Cox proportional hazards model and introduces a new approach that incorporates individual frailty to improve estimation accuracy.

Contribution

It proposes a novel 2SRI-frailty method that accounts for unmeasured confounders, enhancing bias correction in survival analysis.

Findings

2SRI-frailty reduces bias in treatment effect estimates

Method is consistent under certain conditions

Simulation studies validate improved performance

Abstract

Instrumental variable (IV) methods are widely used for estimating average treatment effects in the presence of unmeasured confounders. However, the capability of existing IV procedures, and most notably the two-stage residual inclusion (2SRI) procedure recommended for use in nonlinear contexts, to account for unmeasured confounders in the Cox proportional hazard model is unclear. We show that instrumenting an endogenous treatment induces an unmeasured covariate, referred to as an individual frailty in survival analysis parlance, which if not accounted for leads to bias. We propose a new procedure that augments 2SRI with an individual frailty and prove that it is consistent under certain conditions. The finite sample-size behavior is studied across a broad set of conditions via Monte Carlo simulations. Finally, the proposed methodology is used to estimate the average effect of carotid endarterectomy versus carotid artery stenting on the mortality of patients suffering from carotid artery disease. Results suggest that the 2SRI-frailty estimator generally reduces the bias of both point and interval estimators compared to traditional 2SRI.