The purpose of this study is to use long-term administration of a low molecular weight heparin (tinzaparin) for primary treatment and secondary prophylaxis of venous thromboembolism in patients with cancer. We will determine the efficacy (recurrent VTE) and safety (major hemorrhage) of this approach. Secondarily, we will analyze the outcome of patients in terms of survival and response to therapy versus matched controls. We will also determine baseline levels of markers of hemostasis, fibrinolysis, and angiogenesis and will follow changes with treatment as well as correlate levels of these plasma markers with outcomes, including recurrent venous thromboembolism, major hemorrhage,and survival.