Counting Things that Didn't Happen

Got this question the other day:

I know how to report on the PRESENCE of a certain data element, but can I also report on its ABSENCE ? We're working with healthcare data and have a list of patients who have had certain diagnostic tests. From this data it's easy to find patients who have had a procedure (i.e., a mammogram), but can we use the same data to find patients who HAVEN'T had one?