Registry data typically report incident cases within a certain calendar time interval. Such interval sampling induces double truncation on the incidence times, which may result in an observational bias. In this paper, we introduce nonparametric estimation for the cumulative incidences of competing risks when the incidence time is doubly truncated. Two different estimators are proposed depending on whether the truncation limits are independent of the competing events or not. The asymptotic properties of the estimators are established, and their finite sample performance is investigated through simulations. For illustration purposes, the estimators are applied to childhood cancer registry data, where the target population is peculiarly defined conditional on future cancer development. Then, in our application, the cumulative incidences inform on the distribution by age of the different types of cancer.