In nested case-control studies, incidence density sampling is the time-dependent matching procedure to approximate hazard ratios. The cumulative incidence function can also be estimated if information from the full cohort is used. In the presence of competing events, however, the cumulative incidence function depends on the hazard of the disease of interest and on the competing events hazard. Using hospital-acquired infection as an example (full cohort), we propose a sampling method for nested case-control studies to estimate subdistribution hazard ratios. With further information on the full cohort, the cumulative incidence function for the event of interest can then be estimated as well.