Two groups of patients were enrolled on this study. One group included those with high-risk hematologic malignancies and the second group included participants with refractory hematologic malignancies or undergoing a second transplant. The primary aim of the study was to estimate the relapse rate in the one group of research participants with refractory hematologic malignancies or those undergoing second allogeneic transplant. Both groups will be followed and analyzed separately in regards to the secondary objectives.