Instrumental variable estimation of the causal hazard ratio

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.

Automated summary

Cox‘s proportional hazards model is widely used in statistical analysis to evaluate the relationship between exposure and a censored failure time outcome. However, when confounding factors are not fully observed, the estimated hazard ratio can be biased due to unmeasured confounding. In this paper, we propose a novel approach using a binary instrumental variable to identify and estimate the causal hazard ratio, while accounting for unmeasured confounding. Our approach provides a consistent estimator for the causal hazard ratio, and we derive its asymptotic distribution and an estimator for its asymptotic variance. We demonstrate the effectiveness of our approach through simulation studies and a real data application.