We propose a new task for sound event detection (SED): sound event triage (SET). The goal of SET is to detect a high-priority event while allowing misdetections of low-priority events where the extent of priority is given for each event class. In conventional methods of SED for targeting a specific sound event class, only information on types of target sound can be treated. To flexibly control more wealth of information on the target event, the proposed SET exploits not only types of target sound but also the extent to which each target sound is detected with priority. To implement SET, we apply a method that allows the system input of the priority of sound events to be detected, which is based on the class-level loss-conditional training. Results of the experiment using the URBAN--SED dataset reveal that our SET scheme achieves reasonable detection performance in terms of frame-based and intersection-based F-scores. In particular, the proposed method of SET outperforms the conventional SED method by around 10 percentage points for some events.