In a small study comprising of just 8 people, the arthritis patients were asked to move their hands and visualise the same movement in mirror. Actually the reflection of the movement of patient was blocked and replaced by the movement of researcher’s healthy hand. What the subject visualised was the reflection of the movement of researcher’s healthy hand.  Perceiving the movement of healthy hand as own the patients brain believes that it is less stiff and painful.

UCSD neuroscientist Laura Case who presented the study narrated that “The subject, seeing only the researcher's hand in the mirror, saw a young, healthy hand performing movements fluidly and without pain or difficulty. And when asked about their hands' level of pain after the exercise, subjects rated their pain, on average, 1.5 points lower, on a scale of 1 to 10, than it had been at the outset. Some had a 3-point reduction in pain, added Case.

Regarding the reason  of feeling less pain Case said, it's not clear what trickery, exactly, made subjects feel less pain; it may have been the sight of "their" hand (actually, the researcher's) as a young, healthy hand with no arthritic deformities that made them feel better. It might have the appearance of the effortless movement that suggested a lack of pain. Then again, it may have been the exercise, which usually loosens pain's grip. Case and her colleagues are currently testing the mirror-based treatment on a larger population of patients with arthritic and other chronic pain.
Seeing the positive result of the study the researchers hope that using this safe, simple means may help millions of arthritis sufferers to get relief from chronic pain by enlisting the brain's willingness to see and feel a sick body as healthy.

Although the study comprise of less subjects, the result is promising. Let’s hope that, this illusion trick  turned out to be a safe and simple trick to reduce the pain as claimed.
However, here I would like to add that the complementary and alternative therapies have shown great results in treatment  as well as prevention of both type of arthritis(rheaumatoid and osteo arthritis). Instead of taking NSAIDs or painkillers; patient can switch to the other therapies such as Homoeopathy, Ayurveda- yoga, Acupressure, Hydrotherapy etc.

I also wonder if illusion or alter perception of brain can reduce the pain than  Hypnotherapy may have scope in such cases. I do not have more knowledge about it , however, fellow hypnotherapist can throw more light on it..

Know more:

Online consultation with complementary therapist

Complementary alternative therapy- medicine(CAM)

CAM tourism

Ref: Telegraph co.uk health news