Abatacept for Kidney Transplant Recipients

Inclusion Criteria: Observational Study: 1. Subject must be able to understand and provide informed consent 2. Received (within 14 days) or candidate for an ABO-compatible kidney transplant, including A2 to B 3. Panel Reactive Antibody \<=60% as determined by local site 4. Virtual cross-match negative as determined by local site or Donor Specific Antibody (DSA) negative by central lab within 14 days post-transplant 5. Female subjects of childbearing potential must have a negative pregnancy test upon study entry 6. All subjects with reproductive potential must agree to use highly effective contraception for the duration of the study (http://www.fda.gov/birthcontrol) 7. Hepatitis C Virus Ab positive subjects with negative Hepatitis C Virus polymerase chain reaction (HCV PCR) are eligible if they have spontaneously cleared infection or are in sustained virologic remission 8. Vaccines up to date as per Division of Allergy, Immunology, and Transplantation (DAIT) guidance for patients in transplant trials (Refer to Manual of Procedures). 9. Triple Immunosuppression - Calcineurin Inhibitor/Mycophenolic Acid/Steroid (CNI/MPA/steroid) 1. CNI (Tacrolimus (TAC), target trough \[C0\] level: 0-3 mo, 8-12 ng/mL; 4-6 mo, 6-10 ng/mL; \>6 mo, 5-8 ng/mL\]) 2. MPA \[target dose: mycophenolate mofetil \>=500 mg bid or mycophenolate sodium \>=360 mg bid\]); and 3. Glucocorticoid, with a minimum dose equivalent to 5mg of prednisone per day Nested Randomized Control Trial (RCT): 1. Subject must be able to understand and provide informed consent 2. A 6-month protocol biopsy free of Biopsy Proven Acute Rejection (BPAR)(by Central Pathology Core) 3. Negative 6-month serum test for DSA (by Central HLA Core) 4. eGFRCKD-EPI 30-90 ml/min/1.73m\^2 at 6 months 5. Has a verified negative purified protein derivative (PPD) or negative testing for tuberculosis using an approved IGRA blood test, such as QuantiFERON Gold TB or T-SPOT-TB assay OR has completed treatment for latent tuberculosis and has a negative chest x-ray. PPD or IGRA testing must occur within 52 weeks prior to randomization. These requirements apply as well to prior recipients of Bacille Calmette-Gurin (BCG) vaccination 6. Minimum Mycophenolate mofetil (MPA) dose (MPA 500 mg po bid, or Mycophenolate sodium 360 mg po bid) 7. Minimum Prednisone dose of 5mg per day 8. Hepatitis C Virus Ab positive subjects with negative HCV PCR are eligible if they have spontaneously cleared infection or are in sustained virologic remission 9. Hepatitis C Virus negative recipients of a Hepatitis C Virus positive organ are eligible if they have undergone treatment and are in sustained virologic remission 10. Female subjects of childbearing potential must have a negative pregnancy test upon study entry 11. All subjects with reproductive potential, must agree to use highly effective contraception the duration of the study-specific methods may be listed, if applicable Exclusion Criteria: Observational Study: 1. Inability or unwillingness of a participant to give written informed consent or comply with study protocol including a mandated 6-mo kidney transplant biopsy 2. Non-Kidney Transplant (KTx) (pre-existing or concurrent) 3. Current use of immunomodulatory agents (including but not limited to: Rituximab, anti-Tumor necrosis factor(TNF) Monoclonal antibodies (mAb), or Belatacept, abatacept, Janus kinase inhibitors) 4. Transplant in which the kidney donor is the recipient's Identical twin 5. Epstein-Barr virus (EBV) sero-negative KTx recipient 6. Chronic obstructive pulmonary disease (COPD) 7. Untreated Latent Tuberculosis (TB) 8. Human immunodeficiency virus (HIV) infection 9. Active Hepatitis B infection (HBsAg+ or anti-HBcore +) 10. Enrollment in another investigational trial 11. Current, diagnosed, mental illness or current, diagnosed or self-reported drug or alcohol abuse that, in the opinion of the investigator, would interfere with the participant's ability to comply with study requirements 12. Recent recipient of any licensed or investigational live attenuated vaccine(s) within 4 weeks of enrollment 13. Use of investigational drugs within 8 weeks of participation 14. Past or current medical problems or findings from physical examination or laboratory testing that are not listed above, which, in the opinion of the investigator, may pose additional risks from participation in the study, may interfere with the participant's ability to comply with study requirements or that may impact the quality or interpretation of the data obtained from the study 15. Use of Campath(R) Nested Randomized Control Trial (RCT): 1. Inability or unwillingness of a participant to give written informed consent or comply with study protocol 2. Biopsy Proven Acute Rejection (BPAR) or treated clinically-diagnosed rejection in the 6 months following enrollment in the Observational Study 3. Positive for a Donor Specific Antibody (DSA) 0-6 months post-kidney transplant 4. Acute Banff interstitial (i) score \>0 on a 6-month protocol biopsy as determined by core pathology read 5. Presence of recurrent on de novo glomerulonephropathy 0-6 months post-kidney transplant 6. Presence of active infection including BK virus (BKV), Cytomegalovirus (CMV) or EBV viremia by Polymerase chain reaction (PCR) analysis 7. Unable or unwilling to undergo protocol biopsies 8. Not on Tacrolimus/Mycophenolic Acid (MPA)/Pred 9. Unable to administer therapy s.c. 10. Thrombocytopenia (\<50,000/mm\^3) 11. Pregnant, or unwilling to practice highly effective birth control 12. Use of immunomodulatory agents (including but not limited to Rituximab, anti-TNF mAb, or Belatacept, abatacept, Janus kinase inhibitors) \* since enrollment, other than cytolytic agents (i.e., Thymoglobulin(R)or Campath(R) or Basiliximab(R) used for induction therapy at the time of transplant 13. Use of investigational drugs since transplant 14. Past or current medical problems or findings from physical examination or laboratory testing that are not listed above, which, in the opinion of the investigator, may pose additional risks from participation in the study, may interfere with the participant's ability to comply with study requirements or that may impact the quality or interpretation of the data obtained from the study