Combination Pembrolizumab, Chemotherapy and Bevacizumab in Patients With Cervical Cancer

Inclusion Criteria: 1. Patients must have histologically confirmed recurrent, persistent or metastatic (primary stage IVB) squamous cell carcinoma, adenosquamous carcinoma or adenocarcinoma of the cervix that is not amenable to curative treatment with surgery and/or radiation therapy. 2. All patients must have measurable disease as defined by Response Evaluation Criteria In Solid Tumors (RECIST) 1.1. 3. Patients must have recovered from effects of recent surgery or radiotherapy or chemoradiotherapy. 4. Patients should be free of active infections requiring antibiotics (with the exception of uncomplicated urinary tract infection). 5. Tissue from an archival sample or newly obtained core or excisional biopsy of a tumor lesion within 6 weeks confirming diagnosis. 6. Age ≥ 18 years 7. Life expectancy \> 3 months 8. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1 9. Patients must have normal organ and marrow function as defined below: * Absolute neutrophil count (ANC) ≥1,500 /microliter (mcL) * Platelets ≥ 100,000 / mcL * Hemoglobin ≥ 8 g/dL or ≥ 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency * Serum creatinine ≤ 1.5 X upper limit of normal (ULN) OR Measured or calculated a creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≥ 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN. Creatinine clearance should be calculated per institutional standard. * Serum total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate transaminase (AST) (SGOT) and alanine transaminase (ALT) (SGPT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases * Albumin ≥ 2.5 mg/dL * International Normalized Ratio (INR) or Prothrombin Time (PT) ≤ 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Activated Partial Thromboplastin Time (aPTT) ≤ 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. 10. Negative urine or serum pregnancy ≤72 hours (i.e. 3 days) prior to receiving the first dose of study medication if not surgically sterilized. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 11. Female subjects of childbearing potential (i.e., have not been surgically sterilized or have not been without menses for \>1 year) should be willing to use 2 methods of birth control at the same time, be surgically sterile, or abstain from heterosexual activity for the course of the study and at least 120 days after the last study dose. 12. Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 1. Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer, are ineligible if there is any evidence of other malignancy being present within the last 5 years. 2. Patients who have had prior chemotherapy except when used concurrently with radiation therapy. 3. Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis other than for the treatment of cervical cancer within the last 5 years are excluded. Prior radiation for localized cancer of the breast, head and neck, or skin is permitted provided that it was completed more than 3 years prior to registration, and the patient remains free of recurrent or metastatic disease. 4. Patients with an ECOG performance status of 2, 3 or 4. 5. Has received prior therapy with an anti-programmed cell death protein 1 (PD-1), anti-PD-L1, or anti-PD-L2 agent. 6. Patients with known active central nervous system (CNS) metastases and/or carcinomatous meningitis. 7. Patients with a known history of human immunodeficiency virus (HIV) or active bacillus tuberculosis (TB). 8. Known psychiatric or substance abuse disorders that would interfere with cooperation with requirements of the study 9. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (i.e., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 10. History of non-infectious pneumonitis that required steroids, evidence of interstitial lung disease or active, non-infectious pneumonitis, or history of pneumonitis requiring treatment. 11. Is pregnant, breastfeeding or expecting to conceive within the projected duration of the study, starting with the pre-screening or screening visit through 120 days after the last dose of study treatment. 12. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (HCV) (defined as HCV RNA \[qualitative\] is detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. 13. Received live vaccine within 30 days prior to the first dose of study treatment. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however. intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines and are not allowed. 14. Patient with known hypersensitivity to Pembrolizumab or any of its excipients (active ingredients). 15. Patient receiving concurrent additional biologic therapy. 16. Patients who are adults and unable to consent, who are not yet adults, pregnant and nursing women, and prisoners are ineligible. 17. Has an active infection requiring systemic therapy. 18. Thromboembolism (either arterial or venous) within 6 weeks of initiation of treatment. 19. Has significant cardiovascular disease, such as New York Heart Association cardiac disease classification of Class II or greater, myocardial infarction, or cerebrovascular accident within 3 months prior to initiation of study treatment, unstable arrhythmias, or unstable angina. Patients with known coronary artery disease, congestive heart failure not meeting the above criteria, or left ventricular ejection fraction \<50% must be on a stable medical regimen that is optimized in the opinion of the treating physician in consultation with a cardiologist if appropriate. 20. Has undergone major surgical procedure within 28 days prior to first Bevacizumab dose or anticipation of the need for a major surgical procedure during the course of the study. 21. Has proteinuria, as demonstrated by urine dipstick or \>2.0 g of protein in a urine protein-to creatinine ratio and/or 24 hour (hr) urine collection. All patients with ≥ 2+ protein on dipstick urinalysis at baseline must undergo a urine-to-protein ratio and/or 24 hr urine collection and demonstrate \< 2.0 g of protein.