Dealing With Nonproportional Hazards in Coronary Revascularisation Studies

The Cox proportional hazards model is one of the most popular sta-tistical 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.

Automated summary

The Cox proportional hazards model is a popular statistical tool for modeling time to event outcomes. However, in studies comparing coronary revascularization strategies, violations of proportionality can occur due to crossing hazard functions over time. This article discusses methods for identifying and accounting for nonproportionality and provides an example case study. It also reviews recent literature on how the proportionality assumption has been reported in coronary revascularization studies.