Estimating populational-average hazard ratios in the presence of unmeasured confounding

TL;DR

This paper investigates the properties and estimation of population-average hazard ratios in Cox models when unmeasured confounding is present, proposing a robust estimator and illustrating its application with real data.

Contribution

It introduces a consistent estimation method for marginal Cox models with non-binary treatments under unmeasured confounding, supported by simulations and real data analysis.

Findings

Estimator is more robust with weak instruments

Finite sample performance is adequate

Method applied successfully to real registry data

Abstract

The Cox regression model and its associated hazard ratio (HR) are frequently used for summarizing the effect of treatments on time to event outcomes. However, the HR's interpretation strongly depends on the assumed underlying survival model. The challenge of interpreting the HR has been the focus of a number of recent works. Besides, several alternative measures have been proposed in order to deal with these concerns. The marginal Cox regression models include an identifiable hazard ratio without individual but populational causal interpretation. In this work, we study the properties of one particular marginal Cox regression model and consider its estimation in the presence of omitted confounder. We prove the large sample consistency of an estimation score which allows non-binary treatments. Our Monte Carlo simulations suggest that finite sample behavior of the procedure is adequate. The studied estimator is more robust than its competitors for weak instruments although it is slightly more biased for large effects of the treatment. The practical use of the presented techniques is illustrated through a real practical example using data from the vascular quality initiative registry. The used R code is provided as Supplementary Material.