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.

Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal procedures, such as the doubly robust estimators, it is imperative to first extract important features from high or even ultra-high dimensional data. In this paper, we propose causal ball screening for confounder selection from modern ultra-high dimensional data sets. Unlike the familiar task of variable selection for prediction modeling, our confounder selection procedure aims to control for confounding while improving efficiency in the resulting causal effect estimate. Previous empirical and theoretical studies suggest excluding causes of the treatment that are not confounders. Motivated by these results, our goal is to keep all the predictors of the outcome in both the propensity score and outcome regression models. A distinctive feature of our proposal is that we use an outcome model-free procedure for propensity score model selection, thereby maintaining double robustness in the resulting causal effect estimator. Our theoretical analyses show that the proposed procedure enjoys a number of properties, including model selection consistency and pointwise normality. Synthetic and real data analysis show that our proposal performs favorably with existing methods in a range of realistic settings. Data used in preparation of this paper were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

In this paper, we respond to comments on our paper, “Instrumental variable estimation of the causal hazard ratio.”