My DD is 2 yrs 9 mos. and I've been seriously trying to get her to stop for about three months. My main concern is not just buck teeth, but her jaw is accomodating the thumb, and her teeth are pulled forward on the uppers and the lower teeth look caved in so her thumb can fit right in there. Kinda scary when you notice that. I'm really trying because my older DD is 5 1/2, and she has always sucked her thumb also. She has only sucked her thumb in her sleep for the last 2 years or so, but the way her upper teeth look , I don't want my little one's teeth to look like that if I can help it! She has a hard time trying to keep her lips over her teeth, and usually has her upper teeth hanging out, just out of habit.
Here are some of the things I've tried:
I tried the "thumb guard"(look it up online, by Med et. al) on my 2 3/4 y.o., but she was able to yank it up and off of her thumb, then was able to put it back on her thumb most of the time. I only figured that out towards the end of the 30 day trial period, fortunately. I sent it back and got my $$ back. But I'm sure it works for some, but they would probably tell you that 15 mos. is too young.
I also tried the nail polish like stuff which has a bitter taste, mine is called "Thum". That also didn't work, and when I tried it recently, she actually liked it.
Right now the bribe is a trip to Chuck E. Cheese's and a pizza there. For whatever reason that is something she really wants and when I tell her "no Chuck e. Cheese's then" she pulls her thumb right out and says, "pizza too?" Hey whatever works! Of course the thumb goes right back in pretty quickly, but she does understand NOW that she has a bad habit. It did take 3 months to get to this point, and she's much older than yours, so I suggest you not worry about it for at least another year. HTH!