The appearance of The Doctors is based on that of normal doctors. They wear white medical scrubs stained with blood and guts. Their eyes are stitched shut and their surgical masks and hats are stitched to their bodies.
They are first seen in the elevator scene on the bottom right.
The second time they are in a glass cube on a computer monitor before Dana Polk releases them during the Purge. The last time they are seen is in a quick camera view preparing to perform surgery on a worker who is yelling "Please don't cut!" One of the doctors is seen holding up a bloody scalpel before the camera cuts away.
It is possible that surgical equipment summons them.
The Doctors were also among the monsters on display at Halloween Horror Nights 23 at Universal Studios Florida in 2013.
Cinema has a long history of using the "Evil Doctor" trope with notable examples being Dr. Jekyll or Dr. Frankenstein. However, the film clearly references more modern examples, such as Dr. Giggles, The Human Centipede, House On Haunted Hillor The Dead Pit, which share the common theme of featuring evil doctors who perform experiments on living people, having little to no supernatural or science fiction elements to them. There is also Professor Pyg from the Batman comics who is the very embodiment of the Evil Doctor/Surgeon.
The film Jacob's Ladder features eyeless doctors who perform mysterious, frightening surgeries as well.