Properties of composite time to first event versus joint marginal analyses of multiple outcomes

Many clinical studies (eg, cardiovascular outcome trials) investigate the effect of an intervention on multiple event time outcomes. The most common method of analysis is a so-called "composite" analysis of a composite outcome defined as the time to the first component event. Other approaches have been proposed, including the win ratio (or win difference) for ordered outcomes and the application of the Wei-Lachin test. Herein, we assess the influence of the marginal and joint distributions of the component events, and their correlation structures, on the operating characteristics of these methods for the analysis of multiple events. The operating characteristics are investigated using a bivariate exponential model with a shared frailty, under which these properties are obtained in closed form. While the composite time-to-first-event analysis provides an unbiased test of the hypothesis of equality of the distribution of the time to first event, we show that it can provide a biased test of the joint null hypothesis of equal marginal hazards when the correlation of event times differs between groups. The same applies to the win ratio. However, the operating characteristics of the Wei-Lachin or other tests of the joint equality of the marginal hazards are unaffected. Furthermore, when the correlations are equal, the Wei-Lachin test is more powerful to detect a difference in marginal hazards than the composite analysis test. Careful consideration of the properties of the various methods for analysis of composite outcome measures are in order before adopting one as primary analysis in a clinical study.