Many clinical trials involve the collection of data on the times to occurrence of different types of events, such as different fungal infections in AIDS research, or of recurrences of the same type, such as successive fits in epilepsy research. The multivariate proportional hazards model allows for analysis of this data and software for doing this is now widely available. In this paper, the approximate power of a clinical trial that aims to use such data for comparing two treatments is derived. Special attention is given to the bivariate case, both to show that the approximation works well and to illustrate how various design parameters affect the power of a trial. As with any multivariate data in clinical trials, there are many conceptual issues that should be considered during trial design; the paper closes with a discussion of some of these.