ANo. Synecdoche, New York is an original screenplay written by American film-maker Charles Kaufman, who also directed the movie.
AThe burning house is a bold and whimsical sign of Hazel's fate and, more generally, of everyone's inevitable death. Hazel is originally drawn to the house, but expresses fear over the danger of living in fire which could consume her at any moment. However, she puts these fears aside and purchases the house, accepting her fate. Contrast this with Caden, who is obsessed with death and fears his body is breaking down. His house contains plumbing which is failing much like Caden's own body. A water leak in the bathroom causes Caden's head to leak real blood. It represents a slow degradation which Caden is trying desperately to stop, while Hazel's house represents a sudden death which she is aware of yet accepts. These themes are repeated throughout the film in various forms. A related character-based interpretation is that Hazel is fire and Caden is water. She offers to smoke with him, but he refuses because it might turn him on sexually. Hazel is the only warm spot in Caden's life, but after sex with her he can only cry. One might find a correlation to this Tennessee Williams quote: "We all live in a house on fire, no fire department to call; no way out, just the upstairs window to look out of while the fire burns the house down with us trapped, locked in it."