Akkam’s Razor

According to this MeFi thread, the similarities may not be coincidental.  From Wikipedia:

House is victim to an infarction in his right leg, which was misdiagnosed by his doctors and resulted in muscle deterioration prior to the events of the series. House is in near-constant pain and walks with a severe limp, carrying a trademark cane in the series. He develops an addiction to Vicodin through the course of the series. His colleagues frequently suggest that his physical pain affects his medical judgment and exacerbates his irritable personality.

One of House's distinctive traits is his low tolerance for boredom, which results in his unusual role in the series' hospital. When unoccupied or thinking, he has been seen juggling, listening to music, watching soap operas, constructing an elaborate contraption from objects in his office, and most frequently twirling his cane with one hand. In many episodes House can be seen playing a Nintendo DS portable gaming device while he is waiting.

In spite of this apparent frivolity and impatience (with a "nine to three" job), House is nevertheless dedicated once a problem takes his attention. Many of the critical diagnoses in the show come at the end of a long night's study, and at one point he enacts an elaborate plot and learns Hindi in order to avenge a slight from decades previous.

House also shares a number of personality quirks with the fictional detective Sherlock Holmes. The show's creator, David Shore, has said in an interview ^[4] that the character of Dr. House is indeed partly inspired by Holmes. This comes full circle as Arthur Conan Doyle modeled Holmes on the brilliant medical diagnostician Dr. Joseph Bell.

Among the characteristics the two characters share are their ability to come to rapid conclusions after the briefest examination of a client/patient, their drug use (cocaine for Holmes and Vicodin for House), and the fact that each character has only one real friend (Dr. Wilson being a direct reference to Dr. Watson) who connects the cerebral hero to human concerns. (The drug Vicodin is often distributed by Watson Laboratories, Inc., with Watson written on the backside of each pill.) In addition, both House and Holmes play a musical instrument (House plays the piano and Holmes plays the violin). Also, in one episode House's apartment number is revealed to be 221B, Sherlock Holmes's Baker Street address. On the pilot episode, the main patient is named Rebecca Adler, possibly after Irene Adler, a well known female character from a Sherlock Holmes story. Another patient, whom House failed to diagnose twelve years ago, has the name Esther Doyle which evokes Sir Arthur Conan Doyle—the author of the Sherlock Holmes stories. The patient who shot House in the second-season finale was named (at least in House's subconscious) Jack Moriarty, i.e., Holmes' nemesis Professor James Moriarty. Perhaps most tellingly, the characters' names (Holmes and House) are homophonically-related synonyms.