Statistical considerations when using a composite endpoint for comparing treatment groups

When comparing two treatment groups in a time-to-event analysis, it is common to use a composite event consisting of two or more distinct outcomes. The goal of this paper is to develop a statistical methodology to derive efficiency guidelines for deciding whether to expand a study primary endpoint from E1 (for example, non-fatal myocardial infarction and cardiovascular death) to the composite of E1 and E2 (for example, non-fatal myocardial infarction, cardiovascular death or revascularisation). We investigate this problem by considering the asymptotic relative efficiency of a log-rank test for comparing treatment groups with respect to a primary relevant endpoint E1 versus the composite primary endpoint, say E, of E1 and E2, where E2 is some additional endpoint.