I am no dentist - let me preface with that! Also let me add my opinions about childhood habits and "dependence" as well as my own experience really color this for me.
We had a thumbsucker I was worried about for a while. My daughter Sophie sucked her thumb until 4 1/2 (she's 6 now). On her first dentist appointment (at four) the dentist commented that it was pushing her teeth open ("open bite"). We explained the situation to Sophie (potential of orthodontia and all) and she tried to stop, but couldn't. I could see a potential bribe / bargaining / pressure situation getting set up (which was causing her to feel more "addicted" to the thumb) so I opted out of that.
She also would get a raw thumb now and then and we'd just tell her why. There isn't much you can do about the raw thumb IMO.
6 months later, after her next appointment and another talk with the dentist (who wasn't great with kids, but a nice enough guy), she gave it up on her own. No struggles, no "tricks". Her bite corrected very fast, I was shocked (the dentist said it likely would). I was also impressed and proud of her; considering it had been a life-long habit!
I am glad I didn't take much responsibility for the situation except to explain to her in a matter of fact way the reasons the dentist was concerned. I think it took the pressure off of her; and I know it took the pressure off of me!
15 months old sounds too young to understand why she should stop. If I had another child (my son who's 4 never took up any comfort habit) I know I'd follow suit for those first few years and let them have their habit.
Incidentally my daughter is an incredible self-soother when it comes to feelings. She is also extremely articulate about her wants and needs and responsibilities. I think of thumb-sucking as a potential positive trait in a child; it's them learning how to take care of themselves.
Good luck!