A Study of the Effectiveness and Safety of Ustekinumab (STELARA) and CNTO 1959 Administered Under the Skin of Patients With Active Rheumatoid Arthritis, Despite Existing Methotrexate Therapy

Inclusion Criteria: * Have had RA for at least 6 months prior to screening * Have a diagnosis of RA according to the revised 1987 criteria of the American Rheumatism Association - Be positive for either anti-cyclic citrullinated peptide antibody or rheumatoid factor in serum at screening * Have been treated with and tolerated MTX for at least 6 months prior to screening, and have a MTX dose of \>= 10 mg and \<= 25 mg per week and stable for at least 12 weeks prior to first administration of study agent * Have active RA, defined as persistent disease activity with both of the following criteria: at least 6 swollen and 6 tender joints at the time of screening and baseline; serum C-reactive protein (CRP) \>= 0.80 mg/dL at screening. The investigator may consider the patient eligible if the CRP value is at least 0.80 mg/dL in a single repeat testing during the screening period * If using oral corticosteroids, must be on a stable dose of \<= 10 mg/day of prednisone or an equipotent dose of another oral corticosteroid for at least 2 weeks prior to the first administration of study agent. If not using corticosteroids at Week 0, the patient must not have received oral corticosteroids for at least 2 weeks prior to the first administration of study agent * If using nonsteroidal anti-inflammatory drugs (NSAIDs) or other analgesics regularly for RA, the patient must have been on a stable dose for at least 2 weeks prior to the first administration of study agent. If not using NSAIDs or other analgesics for RA at Week 0, the patient must have not received NSAIDs or other analgesics for RA for at least 2 weeks prior to the first administration of study agent Exclusion Criteria: * Has other inflammatory diseases, including but not limited to psoriatic arthritis, ankylosing spondylitis (AS), systemic lupus erythematosus, or Lyme disease, that might confound the evaluation of the benefit of study agent therapy * Has current signs or symptoms of liver insufficiency or cardiac, vascular, pulmonary, gastrointestinal, endocrine, neurologic, hematologic, psychiatric, or metabolic disturbances that are severe, progressive, or uncontrolled * Has any known malignancy or history of malignancy (with the exception of basal cell carcinoma, squamous cell carcinoma in situ of the skin, or cervical carcinoma in situ that has been treated with no evidence of recurrence, or squamous cell carcinoma of the skin that has been treated with no evidence of recurrence within 5 years prior to the first administration of study agent) * Has a history of lymphoproliferative disease, including lymphoma, or signs suggestive of possible lymphoproliferative disease such as lymphadenopathy of unusual size or location, or clinically significant splenomegaly * Has known allergies, hypersensitivity, or intolerance to ustekinumab or CNTO 1959 or its inactive ingredients * Has ever received any approved or investigational biologic agent