Juan Alvarez, who prefers to be addressed as Alvie, is a Puerto Rican patient at Mayfield Psychiatric Hospital who meets House in the episode Broken. He was House's roommate, and suffers from bipolar disorder (as a result, Alvie is a chatterbox, and raps at every opportunity). He was portrayed by Tony-Award-winning composer and lyricist Lin-Manuel Miranda,
Alvie is at Mayfield because he refuses to take medication to even out his manic and depressive episodes. As is common with people with bipolar, they enjoy when they are in a manic state as they feel they can accomplish a great deal. However, also like many patients, the manic state makes Alvie overestimate his abilities (in this case, his ability to rap spontaneously without recording or rehearsing his raps).
Alvie bonds easily with people and immediately takes a liking to House, although he just as quickly rubs House the wrong way. Alvie introduces House to the routine of Ward 6 and quickly agrees to become embroiled in House's various schemes to get out of the hospital without actually taking any treatment (a goal Alvie shares). At one point, he even agrees to let House beat him up in order to get haldol to bribe Hal Connor for phone privileges.
However, as House's schemes go awry, House eventually agrees to take medication and accept therapy. Alvie gets very upset at this course of events, and House lashes back telling Alvie to stop worshipping him and go back to his loser life. However, they reconcile during the talent show when Alvie cannot complete his spontaneous unrehearsed raps and House steps in to fill in the gaps.
After House is discharged, Alvie agrees to take medication.
Alvie returns in Baggage. When House returns to 221B Baker Street (after finally being allowed to leave Wilson's care), he finds Alvie there, hiding from the U.S. Immigration Service. Immigration won't believe Alvie is Puerto Rican, and Alvie's mania won't let him get focused long enough to complete the necessary documentation. Alvie has painted House's apartment, but to do so, he sold some of House's possessions, including an antique medical text written by Cuddy's great-grandfather. With Alvie's help, House finds out the identity of a Jane Doe patient and recovers the text from the man who bought it from the pawn shop.
House returns the favor by faking DNA evidence showing Alvie's relationship to his mother, who was known to be an American Citizen. No longer being chased by authorities, Alvie leaves to join his cousin in Arizona.