In Chapter 2 we assumed that only one event, such as breast cancer recurrence, could occur, apart from independent censoring. If deaths from other causes occurred, they were treated as independent censoring. Now we consider the possibility that any of M events can occur, apart from censoring. If the occurrence of one of these events precludes any subsequent event, the M events are called competing risks. Often the focus is on a particular risk, or a subset of risks. For example, in a long term study of a new treatment for women diagnosed with breast cancer, the main outcome of interest might be death from breast cancer. However, some women will die of causes other than breast cancer, and either of these two types of death precludes the other. One therefore needs to account for the competing effects of death from other causes to appropriately assess the impact of treatment on breast cancer mortality (Figure 3.1). The chance of dying from breast cancer may be reduced either because treatment forestalls breast cancer death or, possibly, because it increases risk of mortality from other causes.