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The Hazard Ratio (HR) is often reported as the main causal effect whenstudying survival data. Despite its popularity, the HR suffers from an unclearcausal interpretation. As already pointed out in the literature, there is abuilt-in selection bias in the HR, because similarly to the truncation by deathproblem, the HR conditions on post-treatment survival. A recently proposedalternative, inspired by the Survivor Average Causal Effect (SACE), is thecausal HR, defined as the ratio between hazards across treatment groups amongthe study participants that would have survived regardless of their treatmentassignment. We discuss the challenge in identifying the causal HR and present asensitivity analysis identification approach in randomized controlled trialsutilizing a working frailty model. We further extend our framework to adjustfor potential confounders using inverse probability of treatment weighting. Wepresent a Cox-based and a flexible non-parametric kernel-based estimation underright censoring. We study the finite-sample properties of the proposedestimation method through simulations. We illustrate the utility of ourframework using two real-data examples.

A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies