Beyond the Cox Hazard Ratio: A Targeted Learning Approach to Survival Analysis in a Cardiovascular Outcome Trial Application

Abstract

The Hazard Ratio (HR) is a well-established treatment effect measure in randomized trials involving right-censored time-to-events, and the Cardiovascular Outcome Trials (CVOTs) conducted since the FDA’s 2008 guidance have indeed largely evaluated excess risk by estimating a Cox HR. On the other hand, the limitations of the Cox model and of the HR as a causal estimand are well known, and the FDA’s updated 2020 CVOT guidance invites us to reassess this default approach to survival analyses. We highlight the shortcomings of Cox HR-based analyses and present an alternative following the causal roadmap—moving in a principled way from a counterfactual causal question to identifying a statistical estimand, and finally to targeted estimation in a large statistical model. We show in simulations the robustness of Targeted Maximum Likelihood Estimation (TMLE) to informative censoring and model misspecification and demonstrate a targeted learning analogue of the original Cox HR-based analysis of the Liraglutide Effect and Action in Diabetes: Evaluation of Cardiovascular Outcome Results (LEADER) trial. We discuss the potential reliability, interpretability, and efficiency gains to be had by updating our survival methods to incorporate the recent decades of advancements in formal causal frameworks and efficient nonparametricestimation.