In a phase II trial, high risk hospitalized cancer patients will be enrolled and randomized to standard dose enoxaparin versus intermediate dose (weight adjusted) enoxaparin thromboprophylaxis. Study subjects will be administered enoxaparin during hospitalization in a double-blinded manner. Following completion of 14 days, the study arms will be unblinded and lower extremity ultrasound performed on the standard dose enoxaparin arm in order to more accurately determine the overall cumulative incidence of thrombosis in this group.