A Study to Evaluate the Safety and Efficacy of ASP015K in Moderate to Severe Rheumatoid Arthritis Subjects Who Have Had an Inadequate Response to Methotrexate

Inclusion Criteria: * Subject has rheumatoid arthritis (RA) diagnosed according to the 1987 revised ACR criteria for at least 6 months prior to Screening * Subject has been treated with oral methotrexate (MTX) for a minimum of 90 days and at a stable dose for 28 days prior to the first dose of study drug * ≥6 tender/painful joints; ≥6 swollen joints * Subject meets the ACR 1991 Revised Criteria for Global Functional Status in RA Class I, II or III at Screening and Baseline * Subject's other medication taken for treatment of RA must be stable for at least 28 days prior to start of the study * Male and female subjects must be willing to comply with contraception requirements as well as restrictions regarding egg and sperm donation * Female subject must not be breastfeeding at Screening or during the study period, and for 60 days after the final study drug administration * Subject agrees not to participate in another interventional study while on treatment Exclusion Criteria: * Positive Mycobacterium tuberculosis (TB) test within 90 days of Screening * Abnormal chest x-ray indicative of an acute or chronic infectious process or malignancy * Receipt of live or live attenuated virus vaccination within 30 days prior to the first dose of study drug * Known history of positive test for hepatitis B surface antigen (HBsAg) or hepatitis C antibody or history of a positive test for human immunodeficiency virus (HIV) infection * History of any other autoimmune rheumatic disease, other than Sjogren's syndrome * Previous history of clinically significant infections or illness (requiring hospitalization or requiring parenteral therapy) within 90 days of the Baseline visit, or a history of any illness that would preclude participation in the study * History of any malignancy, except for successfully treated basal or squamous cell carcinoma of the skin or in-situ carcinoma of the cervix * Does not meet specified washout criteria for the following RA medications: gold, azathioprine, minocycline, penicillamine, etanercept, certolizumab, adalimumab, golimumab, infliximab, cyclophosphamide, and leflunomide * Subject has previously used a non anti-TNF biologic disease-modifying antirheumatic drug (DMARD) (e.g., anakinra, abatacept, rituximab, tocilizumab) * Previous intolerance to Janus kinase (JAK) inhibitors * Receipt of intra-articular or parenteral corticosteroid within 28 days prior to the first dose of study drug or is currently taking \> 30 mg oral morphine (or narcotic equivalent) per day * Absolute lymphocyte count (ALC) \< 750/mm3 * Receipt of plasma exchange therapy within 60 days prior to the start of study drug * Receipt of any investigational agent within 30 days or 5 half-lives, whichever is longer, prior to first dose of study drug * Receipt of medications that are CYP3A substrates with narrow therapeutic range within 14 days prior to first dose of study drug * History of heart failure, defined as New York Heart Association (NYHA) grade 3 or greater * History of long QT syndrome or prolonged QT interval * Any ongoing severe, progressive, or uncontrolled renal, hepatic, hematological, gastrointestinal, metabolic, endocrine, pulmonary, cardiac, neurological, or infectious disease, or any ongoing illness which would make the subject unsuitable for the study. This includes stomatitis, gastrointestinal ulcers, or any other condition that would preclude continued treatment with methotrexate * Subject has any condition possibly affecting oral absorption (e.g., gastrectomy, other malabsorption syndromes, or clinically significant diabetic gastroenteropathy)