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Epidemiologists often study the incidence density (ID; also known as incidence rate), which is the number of observed events divided by population-time at risk. Its computational simplicity makes it attractive in applications, but a common concern is that the ID is misleading if the underlying hazard is not constant in time. Another difficulty arises if competing events are present, which seems to have attracted less attention in the literature. However, there are situations in which the presence of competing events obscures the analysis more than nonconstant hazards do. The authors illustrate such a situation using data on infectious complications in patients receiving stem cell transplants, showing that a certain transplant type reduces the infection ID but eventually increases the cumulative infection probability because of its effect on the competing event. The authors investigate the extent to which IDs allow for a reasonable analysis of competing events. They suggest a simple multistate-type graphic based on IDs, which immediately displays the competing event situation. The authors also suggest a more formal summary analysis in terms of a best approximating effect on the cumulative event probability, considering another data example of US women infected with human immunodeficiency virus. Competing events and even more complex event patterns may be adequately addressed with the suggested methodology.