I think you are asking for the frequency of coexistence of true rheumatoid arthritis with psoriasis, rather than psoriatic arthropathy? There may be literature on this but the problem is that ascertaining the existence of true RA in the presence of psoriasis is not straightforward. Rheumatoid factors and ACPA occur in a small percentage of normals so could occur alongside psoriatic arthropathy.
The only time I have been convinced that I knew that an arthritis was true RA in the presence of psoriasis was in a case with typical rheumatoid nodulosis and RF. I only saw the one case in thirty odd years.
In practical terms relating to hydroxychloroquine, I think you are entitled to go on probabilities. If an inflammatory arthritis is associated with RF and or ACPA and does not have DIP involvement then if you feel hydroxychloroquine is a reasonable choice for RA (I was never very convinced) then it is probably still reasonable if the patient also has psoriasis. Without autoantibodies or nodules the chances must be that you are dealing with psoriatic arthropathy and I know of no theoretical or practical evidence for hydroxychloroquine being useful there.
I'am Physical Medicine and Rehabilitation specialist almost 30 year, and I have made the Thesis in Psoriatic Arthritis 2014 in 400 patients, 260 were affected by psoriatic arthritis, 140 by psoriasis and 100 relatives. The answer to Your question is1-3 %. Please see the 52. page in the book Psoriatic Arthritis, of Dafna Gladman, Cheril Rosen and Vinod Chandran, ORL Oxford, Rheumatology Library, Oxford University Press 2014. It is very important because of differential diagnosis between RA and rheumatoid like PsA, in therapy (not to use corticosteroids in PsA per os, except locally Depot Triamcinolon), prognostic in clinical outcome (Psa iz much more milder than RA in invalidity).
The radiological pictures are different in true RA and in psoriatic arthropathy.
The presence of ACPA high-levels in a patient with psoriatic arthropathy give to me an important question : is it possible that my patient has RA associated with psoriasis (without psoriatic arthrtitis) ? In the elderly patients, the presence of rheumatoid factors is very high and so this presence is not useful for my clinical practice in absence of typical erosions . Instead ACPA positivity is not age-related.
Rheumatoid nodulosis is very rare in my experience and so it cannot be an useful element in the differential diagnosis. Besides, rheumatoid nodulosis is characteristic of severe and/or long-lasting RA.
In my experience, I have treated 4 patients with RA + psoriasis , always with methotrexate having very good results for dermatological and for rheumatological aspects.
And again : what is your opinion about RA in relatives of patients with psoriasis (true RA or arthritis in psoriatic context ?