The purpose of this study is to compare the usual treatment to using duvelisib or CC-486 plus the usual treatment for patients with CD30 negative peripheral T-Cell lymphoma that has not been previously treated. The addition of duvelisib or CC-486 (azacitidine) to the usual treatment may or may not increase the chance of the cancer going into remission.   

The usual approach for patients who are not in a study is treatment with the U.S. Food and Drug Administration (FDA) approved chemotherapy regimens (CHOP or CHOEP). The drugs in CHOP and CHOEP (cycloposhamide, doxorubicin, and vincristine) are administered through a vein in the arm. The drug etoposide in CHOEP will either be given through a vein in the arm or by mouth as a pill. The prednisone pills with both regimens are taken by mouth. 

Duvelisib and CC-486 (azacitidine) are not yet approved by the FDA and are taken by mouth.
   
Participants will be randomized into one of 3 study groups. There is an equal chance of being assigned to any of the groups. 

Group A will receive the study drug duvelisib plus CHOP or CHOEP. Group B will receive the study drug CC-486 (azacitidine) plus CHOP or CHOEP. Group C will receive CHOP or CHOEP alone without either of the study drugs. All groups will receive treatment for six 21-day cycles and the study doctor will determine which chemotherapy regimen each participant will receive.

Participants will come into the clinic to receive study treatment and will also visit the clinic  every 3 months for 2 years after completing study treatment, then every 6 months until 5 years have passed since completing study treatment.