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

TL;DR

This paper introduces a sensitivity analysis method for estimating the causal hazard ratio in survival studies, addressing interpretability issues and bias in traditional hazard ratio measures, with extensions for confounder adjustment and practical estimation.

Contribution

It proposes a novel sensitivity analysis framework for the causal hazard ratio, including a Cox-based and non-parametric estimator, applicable to randomized and observational studies.

Findings

The proposed method effectively adjusts for bias in causal hazard ratio estimation.

Simulation studies demonstrate good finite-sample properties of the estimators.

Real-data applications show practical utility of the framework.

Abstract

The Hazard Ratio (HR) is often reported as the main causal effect when studying 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, because similarly to the truncation by death problem, the HR conditions on post-treatment survival. A recently proposed alternative, inspired by the Survivor Average Causal Effect (SACE), is the causal HR, defined as the ratio between hazards across treatment groups among the study participants that would have survived regardless of their treatment assignment. We discuss the challenge in identifying the causal HR and present a sensitivity analysis identification approach in randomized controlled trials utilizing a working frailty model. We further extend our framework to adjust for potential confounders using inverse probability of treatment weighting. We present a Cox-based and a flexible non-parametric kernel-based estimation under right censoring. We study the finite-sample properties of the proposed estimation method through simulations. We illustrate the utility of our framework using two real-data examples.