Rachel Axelrod

The Hazard Ratio (HR) is often reported as the main effect when analyzing survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in selection bias in the HR as a parameter because similarly to the truncation by death problem, the HR conditions on post-treatment survival. While alternative approaches exist, the HR remains the most popular measure used by practitioners. Therefore, analysis approaches targeting directly the causal interpretation of the HR would have an immediate impact and contribute to research conducted worldwide.

A recently proposed alternative inspired by the Survivor Average Causal Effect (SACE) is the Causal-HR (C-HR), defined as the ratio between hazards across study groups among the study participants that would have survived regardless of the study group. Similar to the SACE, the assumptions underlying the identification of the C-HR from the data can be too strong in some scenarios. Therefore, we develop sensitivity analysis techniques coupled with a flexible non-parametric estimation of the hazard function at each treatment harm in this work.

First, we discuss the identification under censoring and estimation approaches for the C-HR in randomized controlled trials under a frailty model. We provide a flexible non-parametric estimation strategy based on improved boundary kernel estimators to estimate the C-HR without assuming the Cox proportional hazard (PH) regression model for the marginal distribution of the survival times. In this way, we allow the C-HR to change as a function of time and be valid in many real data examples, where the PH assumption is violated. We further extend our proposed sensitivity analysis approach to adjust for potential confounders using inverse probability of treatment weighting, making our method useful in analyzing observational studies.

Finally, to illustrate our framework, we apply it to two studies: estimating the effect of Atezolizumab in the treatment of cancer and survival time of kidney donation recipients as a function of expanded criteria donor type.