Balstilimab Versus Investigator Choice Chemotherapy in Patients With Recurrent Cervical Cancer (BRAVA)

Inclusion Criteria: 1. Voluntarily agree to participate by giving written informed consent. 2. ≥ 18 years of age. 3. Diagnosis and prior systemic treatment: 1. Has recurrent or metastatic cervical cancer (SCC, AC, or ASC histology) and has experienced disease progression during or after treatment with a standard platinum based therapy with or without bevacizumab. 2. Has received at least 1 prior systemic therapy regimen for recurrent, persistent, and/or metastatic cervical cancer. Note: Chemotherapy administered in the adjuvant or neoadjuvant setting, or in combination with radiation therapy, should not be counted as a prior systemic therapy regimen for recurrent, persistent, and/or metastatic cervical cancer. 4. Measurable disease - based on Investigator assessment. a. Radiological evidence of measurable disease on imaging based on RECIST v1.1 Note: Patients must have at least 1 "target lesion" to be used to assess response, as defined by RECIST v1.1. Tumors within a previously irradiated field will be designated as "non target" lesions unless progression is documented, or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy. 5. Has a life expectancy of at least 3 months and an ECOG performance status of 0 or 1. 6. Patients must have sufficient and adequate formalin-fixed tumor tissue sample available that is not older than 3 years; otherwise, a fresh biopsy is required. Archival tissue or fresh biopsy must be from a site not previously irradiated. 7. Has adequate organ function as indicated by the following laboratory values: 1. Adequate hematological function defined by absolute neutrophil count ≥ 1.5 × 109/L, platelet count ≥ 100 × 109/L, and stable hemoglobin ≥ 8 g/dL (without transfusions within 1 week before first dose). 2. Adequate hepatic function based by a total bilirubin level ≤ 1.5 × the upper limit of normal (ULN), aspartate aminotransferase (AST) level ≤ 2.5 × ULN, alanine aminotransferase (ALT) level ≤ 2.5 × ULN, alkaline phosphatase (ALP) ≤ 2.5 × ULN, and albumin ≥ 3.0 mg/dL. In the case of hepatic metastases, \< 5 × ULN for AST/ALT and ALP. 3. Adequate renal function defined as calculated creatinine clearance \> 40 mL/min or a serum creatinine \< 1.5 × ULN, per institutional standards (creatinine clearance should be calculated per institutional standards). 4. Adequate coagulation defined by international normalized ratio or prothrombin time ≤ 1.5 × institutional upper limit of normal IULN unless the patient is receiving anticoagulant therapy) and activated partial thromboplastin time ≤ 1.5 × IULN (unless the patient is receiving anticoagulant therapy). 5. Normal thyroid function (thyroid stimulating hormone) whether or not the patient is on supplemental thyroid hormone. 8. Has no history of another primary malignancy except: 1. Malignancy treated with curative intent and with no known active disease ≥ 5 years before the first dose of study drug and of low potential risk for recurrence. 2. Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. 3. Adequately treated carcinoma in situ without evidence of disease. 9. Women of childbearing potential (WOCP) must have a negative serum pregnancy test at Screening (within 72 hours before first dose of study drug). Non-childbearing potential is defined as (by other than medical reasons): 1. ≥ 45 years of age and has not menstruated for greater than 1 year. 2. Definitive pelvic radiation for the treatment of cervical cancer. 3. Whose status is post hysterectomy, bilateral oophorectomy, or tubal ligation. 4. WOCP must be willing to use 2 highly effective methods of contraception (defined in the informed consent form) throughout the trial, starting with the Screening Visit through 90 days after the last dose of study drug Note: Abstinence is acceptable if this is the established and preferred contraception for the patient. 10. Is willing and able to comply with the requirements of the protocol. Exclusion Criteria: 1. Is currently participating and receiving study therapy or has participated in a trial of an investigational agent and received study therapy or used an investigational device within 4 weeks before the first dose of treatment. 2. Has an inadequate period of time prior to first dose of study treatment that is defined as: 1. Received systemic cytotoxic chemotherapy or biological therapy within 28 days before initiation of study treatment 2. Received radiation therapy within 28 days before initiation of study treatment, except for palliative bone therapy, which can be received 2 weeks prior to initiation of study treatment 3. Had major surgery within 4 weeks before initiation of study treatment 3. Has received prior therapy with: a. Any antibody/drug targeting T-cell co-regulatory proteins (immune checkpoints) such as anti-programmed cell death protein 1 and anti-PD-L1 antibodies. 4. Has persisting toxicity related to prior therapy of NCI-CTCAE v5.0 Grade ≥ 1 severity, with the exceptions noted below: 1. Peripheral neuropathy Grade ≤ 2. 2. Alopecia Grade ≤ 2. 5. Is expected to require any other form of systemic or localized antineoplastic therapy while on trial (including maintenance therapy with another agent, radiation therapy, and/or surgical resection). 6. Has known severe hypersensitivity reactions to fully human monoclonal antibodies (NCI CTCAE v5.0 Grade ≥ 3), any history of anaphylaxis, or uncontrolled asthma. 7. Is receiving systemic corticosteroids ≤ 7 days prior to the first dose of trial treatment or receiving any other form of systemic immunosuppressive medication (corticosteroid use on trial for management of immune-related adverse events and/or as a premedication for intravenous \[IV\] contrast allergies/reactions is allowed). Patients who are receiving daily corticosteroid replacement therapy are an exception to this rule. Examples of permitted therapy are daily prednisone at doses of 5 to 7.5 mg or equivalent hydrocortisone dose and steroid therapy administered by topical, intraocular, intranasal, and/or inhalation routes. 8. History of central nervous system tumor, metastasis(es), and/or carcinomatous meningitis identified either on the baseline brain imaging obtained during the Screening period or identified prior to consent. Note: Patients with a history of brain metastases that have been treated may participate provided they show evidence of stable supra-tentorial lesions at screening (based on 2 sets of brain images, performed ≥ 4 weeks apart, and obtained after the brain metastases treatment). In addition, any neurologic symptoms that developed either as a result of the brain metastases or their treatment must have resolved or be minimal and be expected as sequelae from treated lesions. For individuals who received steroids as part of brain metastases treatment, steroids must be discontinued ≥ 7 days prior to the first dose of study drug. 9. Has active or history of autoimmune disease that requires systemic treatment within 2 years of the start of study drug (ie, with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs) Note: Patients with autoimmune conditions requiring hormone replacement therapy or topical treatments are eligible. 10. Has had an allogeneic tissue/solid organ transplant requiring ongoing immunosuppressive treatment. 11. Has or had known drug-induced interstitial lung disease, not fully resolved, or has had a history of pneumonitis that has required oral or IV corticosteroids. 12. Has an active infection requiring IV systemic treatment. 13. Has known history of HIV (HIV 1/2 antibodies). 14. Has known untreated hepatitis B/hepatitis C virus (HBV/HCV) or tuberculosis. Active HBV is defined as a known positive hepatitis B surface antigen result. Active HCV is defined as a known positive hepatitis C antibody result and known quantitative HCV RNA results greater than the lower limits of detection of the assay. 15. Has clinically significant (ie, active) cardiovascular disease: cerebral vascular accident/stroke or myocardial infarction within 6 months before enrollment, unstable angina, congestive heart failure (New York Heart Association Class ≥ II), or serious uncontrolled cardiac arrhythmia requiring medication. 16. Has other systemic conditions or organ abnormalities that in the opinion of the Investigator may interfere with the conduct and/or interpretation of the current trial. 17. Has known psychiatric or substance use disorders that would interfere with cooperation or compromise participation with the requirements of the trial. 18. Is legally incapacitated or has limited legal capacity. 19. Is pregnant or breastfeeding. 20. Has received a live/attenuated vaccine within 14 days of first dose of study treatment and other vaccines within 48 hours of first dose of study treatment.