Research studies have shown a strong association between cancer and blood clots in the veins (also known as deep vein thrombosis). These blood clots can flow to the lungs (pulmonary embolism) which in severe cases may be life threatening. The purpose of this research study is to see if enoxaparin is effective in preventing blood clots in the veins in participants who have cancer of the pancreas, colorectal, non-small cell lung, ovary, or gastric and also have high levels of tissue factor bearing microparticles in their blood (TFMP). TFMP are small particles that are generated from different types of blood cells in the body. In people who have cancer, TFMP are thought to be generated from cancer cells and may represent a risk factor for deep vein thrombosis. Enoxaparin has been used to prevent formation of blood clots in patients after abdominal or orthopedic surgery and in patients who suffer from a severe medical illness. Based on these studies, we are investigating to see if it prevents thrombosis in people with certain types of cancer.