In 1935 Cardozo was awarded a two-year fellowship in pediatrics at Children's Memorial Hospital and Provident Hospital in Chicago. With the aid of a grant from Alpha Phi Alpha , he pioneered research on sickle cell anemia. In October 1937 he published "Immunologic Studies in Sickle Cell Anemia" in the Archives of Internal Medicine.
Cardozo concluded that sickle cell anemia was found almost exclusively among people of African descent; that it was inherited following Mendel's laws; that not all people having sickle cells were anemic; that not all patients died of sickle cell disease per se; and that no successful treatment had been found. Today his findings are still valid.
In addition to his work on sickle cell anemia, Cardozo studied gastrointestinal disorders in children and published works on Hodgkin's disease, and on early growth and development of black children.