Eribulin Mesylate Administered in Combination With Pemetrexed Versus Pemetrexed Alone as Second Line Therapy in Patients With Stage IIIB or IV Nonsquamous Non Small Cell Lung Cancer

Inclusion Criteria: Patients may be entered in the study only if they meet all of the following criteria: 1. Male or female patient greater than or equal to 18 years of age; 2. Histologically or cytologically confirmed nonsquamous NSCLC stage IIIB with malignant pleural effusion or stage IV disease not amenable to curative therapy. Patients with history of stage III disease that have relapsed after chemo- and radiotherapy are also eligible; 3. Have at least 1 site of measurable disease by the Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST) criteria; 4. Have failed 1 prior platinum-doublet containing chemotherapy regimen for stage IIIB with malignant pleural effusion or stage IV nonsquamous NSCLC. One additional cytotoxic regimen is allowed for neoadjuvant, adjuvant, or neoadjuvant plus adjuvant therapy for Phase II patients. For patients enrolled in the Phase Ib portion, a maximum of three total prior regimens is allowed. Definition of a Chemotherapy Regimen: Any platinum-doublet containing chemotherapy, that may also include biological or targeted agents, and/or humanized antibodies, given concomitantly, sequentially, or both, is considered 1 regimen. If, due to toxicity, the dosing of 1 or more of the components must be reduced, or 1 or more of the components of the regimen must be omitted, or 1 of the components must be replaced with another similar drug, the changed version of the original regimen is not considered a new regimen. However, if a new component, dissimilar to any of the original components, is added to the regimen, the new combination is considered a new regimen. If the treatment is interrupted for surgery or radiotherapy, and then continues with an unchanged schedule and components, that treatment is considered as one regimen despite the interruption. 5. Life expectancy of greater than 3 months; 6. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) less than 1; 7. Patients must have adequate renal function as evidenced by calculated creatinine clearance greater than 45 mL/min per the Cockcroft and Gault formula; 8. Patients receiving daily treatment with non-steroidal anti-inflammatory agents (NSAIDS) are eligible. Patients with creatinine clearance 45-79 ml/min must be able to interrupt NSAIDS 2 days before (5 days for long-acting NSAIDs), the day of, and 2 days following administration of pemetrexed; 9. Patients must have adequate bone marrow function as evidenced by absolute neutrophil count (ANC) greater than 1.5 x 10\^9/L, hemoglobin greater than 9.0 g/dL (a hemoglobin less than 9.0 g/dL at Screening is acceptable if it is corrected to greater than 9 g/dL by growth factor or transfusion prior to first dose), and platelet count greater than 100 x 10\^9/L; 10. Patients must have adequate liver function as evidenced by bilirubin less than 1.5 times the upper limit of the normal range (ULN), and alkaline phosphatase, alanine aminotransferase (ALT) and aspartate aminotransferase (AST) less than 3 x ULN (in the case of liver metastases, less than 5 x ULN). If there are bone metastases, liver-specific alkaline phosphatase may be separated from the total and used to assess liver function instead of total alkaline phosphatase; 11. Male or female patients of child-producing potential must agree to use double barrier contraception, oral contraceptives, or avoidance of pregnancy measures during the study and for 90 days after the last day of treatment; 12. Females of childbearing potential must have a negative serum pregnancy test; 13. Females may not be breastfeeding; and 14. Ability to understand and willingness to sign a written informed consent. Exclusion Criteria: Patients may be entered in the study only if they meet all of the following criteria: 1. Prior treatment with pemetrexed, epothilone, ixabepilone, patupilone, halichondrin B or halichondrin B-like compounds; 2. Received chemotherapy, targeted therapy, radiotherapy, surgery, or immunotherapy within the 30 days prior to commencing study treatment or have not recovered from all treatment-related toxicities to Grade less than 1, except for alopecia; 3. History of other malignancies except: (1) adequately treated basal or squamous cell carcinoma of the skin; (2) curatively treated, a) in situ carcinoma of the uterine cervix, b) prostate cancer, or c) superficial bladder cancer; or (3) other curatively treated solid tumor with no evidence of disease for greater than 5 years; 4. Presence of brain metastases, unless the patient has received adequate treatment at least 4 weeks prior to randomization, and is stable, asymptomatic, and off steroids for at least 4 weeks prior to randomization; 5. Received treatment in another clinical study within the 30 days prior to commencing study treatment or patients who have not recovered from side effects of an investigational drug to Grade less than 1, except for alopecia; 6. Are currently receiving any other treatment, including palliative radiotherapy for the tumor aside from control of symptoms; 7. Common Toxicity Criteria (CTC) greater than Grade 3 peripheral neuropathy; 8. Require therapeutic doses of vitamin K antagonists; 9. Uncontrolled pleural effusions, ascites, or other third space fluid collections; 10. Uncontrolled diabetes mellitus Type 1 or 2; Significant cardiovascular impairment (history of congestive heart failure greater than New York Heart Association (NYHA) Grade II, unstable angina or myocardial infarction within the past 6 months, or serious cardiac arrhythmia); 11. Patients with organ allografts requiring immunosuppression; 12. Known positive human immunodeficiency virus (HIV), known hepatitis B surface antigen, or hepatitis C positive; 13. Hypersensitivity to halichondrin B and/or halichondrin B chemical derivative; or Have any medical condition that would interfere with the conduct of the study.