Testing Pembrolizumab Versus Observation in Patients With Merkel Cell Carcinoma After Surgery, STAMP Trial

Inclusion Criteria: * Patient must be \>= 18 years of age * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status: 0, 1, or 2 (However, those patients with a performance state of 3 because they are wheel chair bound due to congenital or traumatic events more than one year before the diagnosis of Merkel cell carcinoma are eligible). * Patient must not be pregnant or breast-feeding due to the unknown effects of the study drug in this setting. All patients of childbearing potential must have a blood test or urine study within 2 weeks prior to randomization to rule out pregnancy. A patient of childbearing potential is anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * Patients on Arm A pembrolizumab (MK-3475) must not conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse from the time of registration, while on study treatment, and continue for 120 days after the last dose of study treatment. For patients on Arm B only receiving radiation therapy, contraception use should be pe…