Study of Low Dose Chemotherapy Plus Sorafenib as Initial Therapy for Patients With Advanced Non-Squamous Cell NSCLC

Inclusion Criteria: * Pathologic-proven non-squamous cell-NSCLC * Advanced non-squamous-NSCLC: Stage IIIB with pleural effusion or stage IV, or recurrent disease * Eastern Cooperative Oncology Group (ECOG) Performance Status 2: In bed less than 50% of the time, unable to work, but able to care for self * Measurable or non-measurable disease as defined by solid tumor response criteria (RECIST) * No prior systemic chemotherapy or biologic therapy * Age greater than or equal to 19 years old (Note: State of Alabama requirement) * Adequate bone marrow and renal function as assessed by the following: * Hemoglobin greater than or equal to 9.0 g/dL * Absolute neutrophil count (ANC)greater than or equal to 1500/mm3 * Platelet count greater than or equal to 100,000/mm3 * Creatinine less than or equal to 1.5 times upper limit of normal (ULN) * Hepatic function requirements * Total bilirubin less than or equal to ULN * AST and ALT and alkaline phosphatase must be within the range allowing for eligibility. In determining eligibility the more abnormal of the two values (AST and ALT) should be used * Women of childbearing potential must have a negative serum pregnancy test performed within 72 hours prior to the start of treatment. Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Men should use adequate birth control for at least three months after the last administration of sorafenib. * Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study-specific procedures. * International normalized ratio (INR) less than or equal to 1.5 or a prothrombin time/partial prothrombin time (PT/PTT) within normal limits. Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable. Exclusion Criteria: * Predominant squamous cell histology will be excluded * Cardiac disease: Congestive heart failure greater than class II New York Heart Association (NYHA). Patents must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months. * Known brain metastasis. Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Uncontrolled hypertension defined as systolic blood pressure \>150 mmHg or diastolic pressure greater than 90 mmHg, despite optimal medical management. * Known human immunodeficiency virus (HIV) infection or chronic Hepatitis B or C. * Active clinically serious infection greater than Common Terminology Criteria for Adverse Events (CTCAE) Grade 2. * Thrombotic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months. * History of significant hemoptysis (defined as bright red blood of a ½ teaspoon or more). Patients with blood-tinged or blood-streaked sputum will be permitted on study if the hemoptysis amount to less than 5 mL of blood per episode and less than 10 mL of blood per 24 hour period. * Any other hemorrhage/bleeding event greater than or equal to CTCAE Grade 3 within 4 weeks of first dose of study drug. * Serious non-healing wound, ulcer or bone fracture. * Evidence or history of bleeding diathesis or coagulopathy. * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug. * Use of St. John's Wort or rifampin (rifampicin). * Known or suspected allergy to sorafenib or any agent given in the course of this trial. * Any condition that impairs patient's ability to swallow whole pills. * Any malabsorption problem. * History of severe hypersensitivity reaction to any drugs formulated with polysorbate 80. * Women who are breast-feeding.