IV estimation of causal hazard ratio

TL;DR

This paper introduces a novel instrumental variable method for consistently estimating the causal hazard ratio in Cox models, addressing unmeasured confounding in survival analysis.

Contribution

It develops the first consistent estimator for the causal hazard ratio using an IV approach with a no-interaction assumption, including a closed-form version and asymptotic properties.

Findings

Estimator performs well in simulations

Method applied successfully to real data

Provides asymptotic distribution and variance estimation

Abstract

Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated using a Cox model is subject to unmeasured confounding bias. To address this, we propose a novel approach for the identification and estimation of the causal hazard ratio in the presence of unmeasured confounding factors. Our approach is based on a binary instrumental variable, and an additional no-interaction assumption in a first stage regression of the treatment on the IV and unmeasured confounders. We propose, to the best of our knowledge, the first consistent estimator of the (population) causal hazard ratio within an instrumental variable framework. A version of our estimator admits a closed-form representation. We derive the asymptotic distribution of our estimator, and provide a consistent estimator for its asymptotic variance. Our approach is illustrated via simulation studies and a data application.