Dealing With Nonproportional Hazards in Coronary Revascularisation Studies

The Cox proportional hazards model is one of the most popular statistical tools to model time to event outcomes without the need for specifying the hazards or survival time distributions. The Cox model requires that the ratio of the hazards of the occurrence of the outcome for any 2 individuals remains constant during the entire follow-up. Studies comparing coronary revascularisation strategies, however, might be prone to violations of proportionality by the crossing of the hazard functions over time. Early increases in the risk of cardiovascular outcomes are commonly observed when comparing coronary artery bypass grafting vs percutaneous coronary intervention, whereas decreased risk might be observed later during the follow-up. The same is valid for comparisons between invasive vs conservative coronary revascularisation strategies. In these situations, the statistical power of the Cox model is reduced, and hazard ratios might not be an informative summary measure of treatment effect. In this article, we discuss methods to identify and account for nonproportionality. We illustrate the use of these methods in a case study based on reconstructed data from a coronary revascularisation clinical trial. And finally, we review the cardiovascular literature to estimate how the proportionality assumption has been reported in coronary revascularisation studies recently.