Behaviour of the Hazard ratio in Composite endpoints

The assessment of treatment efficacy in time-to-event confirmatory clinical trials is commonlybased on the hazard ratio (HR) of the primary endpoint. When designing a study, the propor-tionality of the hazard ratios to determine sample size is usually assumed. However, when theprimary endpoint consists of a combination of several components, i.e. a composite endpointE∗, the hazard ratio ofE∗ is, in general, not constant, even if the hazard ratios of the marginalcomponents are.We show that the shape of the combined HR over time mainly depends on the marginal hazardratio values, the probability of observing each marginal component, and the correlation betweenthe components.Furthermore, we explore the different patterns that the combined HR can follow under realis-tic clinical trial scenarios. Special consideration is given to the evaluation of the departure frombeing constant and to the parameters which play the main role. The online platform CompARE,initially developed as a tool to choose the primary endpoint by means of the ARE method, isextended to accommodate the computation of the hazard ratios in different scenarios and is usedto derive some relevant conclusions by means of illustrative plots. References1 Gómez G. Some theoretical thoughts when using a composite endpoint to prove the efficacyof a treatment (2011). International Workshop on Statistical Modelling. Proceedings of the 26thInternational Workshop on Statistical Modelling, 14–21.2 Gómez-Mateu M and Gómez G. http://composite.upc.edu/CompARE (Last date of access: Oc-tober 23, 2015).3 Gómez G and Lagakos SW (2013). Statistical considerations when using a composite endpointfor comparing treatment groups. Statistics in Medicine, 32, 719–738.