Cord Blood Transplant With Dilanubicel for the Treatment of HIV Positive Hematologic Cancers

OUTLINE: Patients are assigned to 1 of 2 regimens. REGIMEN A: Patients receive fludarabine intravenously (IV) over 30 minutes on days -8 to -6, cyclophosphamide IV on days -7 to -6, and undergo total body irradiation (TBI) twice daily (BID) on days -4 to -1. Patients then undergo umbilical cord blood transplant on day 0. Between 4-24 hours after transplant completion, patients receive dilanubicel IV over 5-10 minutes in the absence of disease progression or unacceptable toxicity. REGIMEN B: Patients receive fludarabine IV over 30-60 minutes on days -6 to -2, cyclophosphamide IV on day -6, thiotepa IV over 4 hours on days -5 to -4, and undergo TBI once daily (QD) on days -2 to -1. Patients then undergo umbilical cord blood transplant on day 0. Between 4-24 hours after transplant completion, patients receive dilanubicel IV over 5-10 minutes in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 28, 80, and 180 days, and then at 1 and 2 years.