Odds are this premise will sound familiar to you.
An enigmatic homicidal psychopath makes a daring, impossible escape from a mental hospital. His sole objective is to hunt down and murder a female family member. Along the way to his goal he murders a number of other people who get in his way and proves to be all but unstoppable, and there are vague allusions to him even being supernatural.
Playing “spot the similarities” between two works of fiction is often a mug’s game; paint the picture broadly enough and any story can be made similar to any other, but the details will usually belie the notion that the stories genuinely mirror one another. Nonetheless, if you’re a horror fan who likes movies as much as literature, then that description in the first paragraph probably brought John Carpenter’s Halloween to mind. It’s also an apt (albeit broad) description of the plot to John Farris’s novel Nightfall.