Crude incidence curves display the cumulative number of failures of interest as a function of time. With competing causes of failure, they are distinct from cause-specific incidence curves that treat secondary types of failures as censored observations. After briefly reviewing their definition and estimation, we present five applications of crude incidence curves to show their utility in a broad range of studies. In some of these applications it is helpful to model survival-time distributions with use of two different time metameters, for example, time from diagnosis and age of the patient. We describe how one can incorporate published vital statistics into the models when secondary types of failure correspond to common causes of death.