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

A robust hazard ratio for general modeling of survival-times

Hazard ratios (HR) associated with the well-known proportional hazard Cox regression models are routinely used for measuring the impact of one factor of interest on a time-to-event outcome. However, if the underlying real model does not fit with the theoretical requirements, the interpretation of those HRs is not clear. We propose a new index, gHR, which generalizes the HR beyond the underlying survival model. We consider the case in which the study factor is a binary variable and we are interested in both the unadjusted and adjusted effect of this factor on a time-to-event variable, potentially, observed in a right-censored scenario. We propose non-parametric estimations for unadjusted gHR and semi-parametric regression-induced techniques for the adjusted case. The behavior of those estimators is studied in both large and finite sample situations. Monte Carlo simulations reveal that both estimators provide good approximations of their respective inferential targets. Data from the Health and Lifestyle Study are used for studying the relationship of the tobacco use and the age of death and illustrate the practical application of the proposed technique. gHR is a promising index which can help facilitate better understanding of the association of one study factor on a time-dependent outcome.

Learning the Treatment Impact on Time-to-Event Outcomes: The Transcarotid Artery Revascularization Simulated Cohort

Proportional hazard Cox regression models are overwhelmingly used for analyzing time-dependent outcomes. Despite their associated hazard ratio is a valuable index for the difference between populations, its strong dependency on the underlying assumptions makes it a source of misinterpretation. Recently, a number of works have dealt with the subtleties and limitations of this interpretation. Besides, a number of alternative indices and different Cox-type models have been proposed. In this work, we use synthetic data, motivated by a real-world problem, for showing the strengths and weaknesses of some of those methods in the analysis of time-dependent outcomes. We use the power of synthetic data for considering observable results but also utopian designs.

Estimating population-averaged hazard ratios in the presence of unmeasured confounding

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 papers. 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 from an instrumental variable-based procedure. 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 competitor (Wang et al.) 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.