Study of Pembrolizumab (MK-3475) vs. Brentuximab Vedotin in Participants With Relapsed or Refractory Classical Hodgkin Lymphoma (MK-3475-204/KEYNOTE-204)

Inclusion Criteria:

* Has relapsed (disease progression after most recent therapy) or refractory (failure to achieve Complete Response \[CR\] or Partial Response \[PR\] to most recent therapy) classical Hodgkin Lymphoma.
* Has responded (achieved a CR or PR) to BV or BV-containing regimens, if previously treated with BV.
* Has measurable disease defined as ≥1 lesion that can be accurately measured in ≥2 dimensions with spiral computed tomography (CT) scan or combined CT/positron emission tomography (PET) scan. Minimum measurement must be \>15 mm in the longest diameter or \>10 mm in the short axis.
* Is able to provide an evaluable core or excisional lymph node biopsy for biomarker analysis from an archival (\>60 days) or newly obtained (within 60 days) biopsy at Screening (Visit 1).
* Has a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale.
* Has adequate organ function
* Female participants of childbearing potential must be willing to use an adequate method of contraception for the course of the study through 120 days (for participants receiving pembrolizumab) or 180 days (for participants receiving BV) after the last dose of study drug.
* Male participants of childbearing potential must be willing to use an adequate method of contraception starting with the first dose of study drug through 120 days (for participants receiving pembrolizumab) or 180 days (for participants receiving BV) after the last dose of study drug.

Exclusion Criteria:

* Has hypersensitivity to the active substance or to any of the excipients in BV or pembrolizumab.
* Is currently participating in or has participated in a study of an investigational agent and is currently receiving study therapy or has participated in a study of an investigational agent and has received study therapy or used an investigational device within 4 weeks of the first dose of study drug.
* Has a diagnosis of immunosuppression or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug.
* Has had a prior monoclonal antibody (mAb) within 4 weeks prior to first dose of study drug in the study or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events (AEs) due to agents administered more than 4 weeks earlier.
* Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy including investigational agents within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from AEs due to a previously administered agent.
* Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Note: Participants who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft-versus-host disease (GVHD).
* Has a known additional malignancy that is progressing or requires active treatment in the last 3 years. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy.
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable (i.e., without evidence of progression by repeat imaging), clinically stable and without requirement of steroid treatment for ≥14 days prior to the first dose of study drug.
* Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with the use of disease modifying agents, corticosteroids, or immunosuppressive drugs).
* Has a history of (non-infectious) pneumonitis that required steroids, or current pneumonitis.
* Has an active infection requiring intravenous systemic therapy.
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
* Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days (for participants receiving pembrolizumab) or 180 days (for participants receiving BV) after the last dose of study drug.
* Has received prior therapy with an anti-programmed cell death-1 (anti-PD-1), anti-PD-ligand 1 (anti-PD-L1), anti-PD-L2, anti-CD137, or cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) antibody (including ipilimumab) or OX-40 (Tumor necrosis factor receptor superfamily, member 4 \[TNFRSF4\]), or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways.
* Has a known history of human immunodeficiency virus (HIV)
* Has active hepatitis B (HBV) or hepatitis C (HCV).
* Has a known history of active tuberculosis (TB; Bacillus tuberculosis).
* Has received a live vaccine within 30 days prior to first dose of study drug.