Can a B-Cell drug stop antibodies from attacking a new kidney?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Stage 1 Inclusion Criteria for All Participants: * Willing to provide informed consent * Previously diagnosed end stage renal disease (ESRD) * Received kidney transplant within 3 and 36 months of study entry * Willing to comply with the study protocol * Willing to use acceptable forms of contraception during the study and for 12 months following rituximab/placebo therapy * Willing to refrain from breastfeeding during the study and for 12 months following rituximab therapy Stage 1 Inclusion Criteria for Pediatric Participants (\<\\=18 Years of Age): * Parent or guardian willing to provide informed consent * Have received all childhood vaccinations prior to study entry Stage 2 Inclusion Criteria for Pilot Treatment Study: * Three to 39 months post-transplant * Developed new antibodies detected at two time points within 1 month between 3 to 36 months post-transplant * Negative pregnancy test Stage 1 Exclusion Criteria for All Participants: * Recipient of a kidney from a donor older than 70 years of age * Multi-organ transplant * History of organ transplantation other than current kidney transplantation * Previous treatment with rituximab * History of severe allergic reactions to monoclonal antibodies * History of allergic reaction to iodine glomerular filtration rate (GFR) assay * Lack of intravenous (IV) access * Sensitized to greater than 5% Panel Reactive Antibody (PRA) within 12 weeks prior to transplant * History of recurrent bacterial or other significant infections * Known active bacterial, viral, fungal, mycobacterial, or other infection (including tuberculosis \[TB\] or atypical mycobacterial disease) or any major episode of infection requiring hospitalization or treatment with IV antibiotics within 4 weeks of study entry. Patients with fungal infections of nail beds are not excluded. * HIV infected * Surface antigen positive for hepatitis B virus (HBV) * Antibody positive for hepatitis C virus (HCV) * History of drug, alcohol, or chemical abuse within 6 months prior to study entry * History of cancer. Patients with adequately treated in situ cervical carcinoma or adequately treated basal or squamous cell carcinoma of the skin are not excluded. * Clinically significant cardiovascular or pulmonary disease * Evidence of urinary tract obstruction causing decreased kidney function, unless corrected by study entry * Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that would contraindicate use of an investigational drug, may affect interpretation of study results, or put the patient at high risk for treatment complications * History of psychiatric disorder that may interfere with participation in the study * History of nonadherence to prescribed regimens * Use of other investigational drugs within 4 weeks of study entry * Received any licensed or investigational live attenuated vaccine within 2 months of study entry. Stage 2 Exclusion Criteria for All Participants: * Previous treatment with rituximab * Immunoglobulin Levels \<500mg/dL (Combined IgM, IgG, IgA, IgE, IgD) * History of severe allergic reactions to monoclonal antibodies * History of cancer. Patients with adequately treated in situ cervical carcinoma or adequately treated basal or squamous cell carcinoma of the skin are not excluded. * Active systemic infection at the time of entry into Stage 2 * Recurrent or de novo glomerular disease or Banff Grade III chronic rejection other than chronic humoral rejection (CHR) indicated in baseline kidney biopsy post-transplant * History of post-transplant lymphoproliferative disease (PTLD) * Serum creatinine of 3.0 mg/dl or greater OR GFR less than 25 ml/min at the time of entry into Stage 2 * Hemoglobin less than 8.5 g/dl * Platelets less than 80,000 cells/mm\^3 * White blood cell count less than 3,000 cells/mm\^3 * AST or ALT 2.5 times the upper limit of normal at study entry * Pregnant or breast-feeding * Absolute neutrophil count less than 1000/mm\^3 Stage 2 Exclusion Criteria for Pediatric Participants (\<\\=18 Years of Age): * Positive test for parvovirus (B19) by PCR in the blood.