The purpose of this study, in patients with rheumatoid arthritis who have had an incomplete response to etanercept and methotrexate (MTX), are to evaluate: safety and evidence of therapeutic benefit of infliximab and methotrexate, the levels (pharmacokinetics) of etanercept and infliximab and antibodies (immunogenicity) to etanercept and infliximab in patients blood, whether switching from etanercept to infliximab changes progression of structural damage over the study period, and whether specific markers in the blood (pharmacodynamics) correlate with therapeutic response or benefit.