When Steven is at the school for the parent teacher conference, the principal tells him that Kim wrote a paper on Iphigenia for which she got an A, and that was read aloud to the class. Iphigenia, in Greek mythology, is the daughter of Agamemnon. She who was to be sacrificed for the sins of her father.
Nicole Kidman and Colin Farrell began working together on The Beguiled (2017). Only a few weeks later they wrapped filming on this film. Both films would go on to be in competition for the Palme d'Or at the 2017 Cannes Film Festival and both would win awards in the official competition ("The Beguiled" won the Directing award for Sofia Coppola while "The Killing of a Sacred Deer" shared the Screenplay award with Lynne Ramsay's You Were Never Really Here (2017)).
Martin's favorite movie is Groundhog Day (1993), which is famous for not explaining how the lead character ends up in a time loop, much like this film never explains how Martin sickens Steven's family.
Bob is the only member of the Murphy family that doesn't smoke a cigarette during the film. Furthermore, when Martin asks if he can light a cigarette in Kim's room, Bob responds with "You'd better not."