A Study to Evaluate the Efficacy and Safety of Mabthera Alone and in Combination With Either Cyclophosphamide or Methotrexate in Patients With Rheumatoid Arthritis

Inclusion Criteria: * Participants with moderate to severe rheumatoid arthritis (RA) who have previously failed 1-5 DMARDS who currently have partial clinical response to treatment with methotrexate * Using methotrexate as a single DMARD for at least 16 weeks, of which the last 4 weeks prior to baseline on a stable oral dose greater than or equal to (\>=) 10 milligrams per week (mg/week) * \>=21 years of age * Swollen Joint Count (SJC) and Tender Joint Count (TJC) \>= 8 (out of 66 and 68 joints respectively) * At least 2 of the following parameters at Baseline: C- Reactive Protein \>= 15 mg/dL; Erythrocyte Sedimentation Rate \>= 30 millimeters per hour (mm/hr); Morning stiffness \>45 minutes * Rheumatoid factor titer \>=20 International units per milliliter (IU/mL) * Corticosteroid (less than or equal to \[=\<\] 12.5 milligrams per deciliter \[mg/d\] prednisone or equivalent) or Non-Steroidal Anti-Inflammatory Drugs (NSAIDs) are permitted if stable for at least 4 weeks prior to baseline Exclusion Criteria: * American Rheumatism Association (ARA) Class IV RA disease * Concurrent treatment with any DMARD (apart from randomized treatment) or anti-TNF-alpha therapy * Active infection or history of recurrent significant infection * Prior history of cancer including solid tumors and hematologic malignancies (except basal carcinoma of the skin that have been excised and cured) * Evidence of serious uncontrolled concomitant diseases such as cardiovascular disease, nervous system, pulmonary, renal, hepatic, endocrine or gastrointestinal disorders * Bone/joint surgery within 6 weeks prior to screening * Rheumatic Autoimmune disease other than RA * Active rheumatoid vasculitis * Prior history of gout * Chronic fatigue syndrome