The cumulative incidence function is widely reported in competing risks studies, with group differences assessed by an extension of the log‐rank test. However, simple, interpretable summaries of group differences are not available. An adaptation of the proportional hazards model to the cumulative incidence function is often employed, but the interpretation of the hazard ratio may be somewhat awkward, unlike the usual survival set‐up. We propose nonparametric inferences for general summary measures, which may be time‐varying, and for time‐averaged versions of the measures. Theoretical justification is provided using counting process techniques. A real data example illustrates the practical utility of the methods. Copyright © 2008 John Wiley & Sons, Ltd.