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Many clinical studies (e.g., 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. We provide an overview of these methods, followed by an assessment of 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. A novel outcome-weighted approach for pairwise comparisons is described. Data from clinical trials are used as illustration.