An Instrumental Variable Procedure for Estimating Cox Models with Non-Proportional Hazards in the Presence Of Unmeasured Confounding

Abstract

Summary Two‐stage instrumental variable methods are commonly used for estimating average causal effects in the presence of an unmeasured confounder. In the context of the proportional hazard Cox regression models, this problem has recently received attention with several methods being proposed. Previously, we developed an improved estimator under the incumbent two‐stage residual inclusion procedure called ‘2SRI’ by adding a Gaussian frailty in the second stage. We now consider the more complex situation in which the treatment and the unmeasured confounders can have time varying effects, illustrating the method with the case of a step function with one prespecified change point. We prove that, in situations where the effects of the unmeasured confounder or the treatment change during the follow‐up, the first stage of the 2SRI algorithm induces a frailty with time varying coefficients in the second stage, which enables incumbent methods and our previously developed procedure to be improved on. A Monte Carlo simulation study demonstrates the superior performance of the proposed extension of 2SRI that we develop. We apply the new procedure to estimate the effect of endarterectomy versus carotid artery stenting on the time to death of patients suffering from carotid artery disease by using linked vascular quality initiative registry–Medicare data.

Time dependent hazard ratio estimation using instrumental variables without conditioning on an omitted covariate

“…We evaluated the behavior of the estimating equations we propose in (6) under two scenarios for the marginal timedependent hazard ratio; i) a three piece constant hazard ratio, and ii) a log linear time-dependent hazard ratio. In the first scenario, the estimation method is equivalent to applying the approach of MacKenzie et al [2] in early, middle and late follow-up settings, and that is how we implement and report the results.…”

“…Because Wang et al's approach is designed for a binary instrument, we dichotomize the continuous instrument of our simulations at the median. Second, we have evaluated the performance of the estimator of Martínez-Camblor et al [6] which estimates the hazard ratios of a Cox model for the multivariable effect of the treatment and the omitted covariate; that is, it conditions on the omitted covariate.…”

“…Martinussen et al [5] derived a consistent estimator for a structural Cox model. Martínez-Camblor et al [6] identified the role of frailties in estimation of the hazard ratio via the two-stage residual inclusion algorithm if the treatment and omitted covariate jointly satisfy a Cox model. Wang et al [7] derived an estimator of the marginal hazard ratio using a binary instrument.…”

Time Dependent Hazard Ratio Estimation Using Instrumental Variables Without Conditioning on an Omitted Covariate

“…We evaluated the behavior of the estimating equations we propose in (6) under two scenarios for the marginal time-dependent hazard ratio; iq a three piece constant hazard ratio, and…”

“…[5] derived a consistent estimator for a structural Cox model. Martínez-Camblor et al [6] identified the role of frailties in estimation of the hazard ratio via the two-stage residual inclusion algorithm if the treatment and omitted covariate jointly satisfy a Cox model. In this paper we extend IV based estimation of the HR beyond proportionality of hazards.…”