The competing risks model encompasses the situation where a subject or unit is exposed to multiple causes of failures and a failure can be caused by one of the multiple risks. When a failure occurs, procedures are exploited in an attempt to attain a definitive cause of failure. However, if the cause of failure for a subject or unit is not precisely defined, it can be narrowed down to a subset of the potential risks and this phenomenon is called masking. In the context of biomedical applications, statistical inferences and methods for the competing risks with and without masking are discussed.