A Study of Selpercatinib (LY3527723) in Participants With RET-Mutant Medullary Thyroid Cancer

* At least 18 years of age (participants as young as 12 years of age will be allowed if permitted by local regulatory authorities). * Histologically or cytologically confirmed, unresectable, locally advanced and/or metastatic MTC and no prior history of treatment with kinase inhibitors for advanced/metastatic disease. * Radiographic progressive disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 at screening compared with a previous image taken within the prior 14 months as assessed by the BICR. Participants with measurable or non-measurable but evaluable disease are eligible; however, participants with non-measurable disease may not have disease limited to bone sites only. * A defined/acceptable RET gene alteration identified in a tumor, germline deoxyribonucleic acid (DNA) or blood sample. * Tumor tissue in sufficient quantity to allow for retrospective central analysis of RET mutation status * Eastern Cooperative Oncology Group performance status score of 0 to 2. * Adequate hematologic, hepatic, and renal function and electrolytes. * Men and women of childbearing potential must agree to use a highly effective contraceptive method during treatment with study drug and for 4 months following the last dose of study drug. * Ability to swallow capsules. Exclusion Criteria: * An additional validated oncogenic driver in MTC if known that could cause resistance to selpercatinib treatment. Examples include, but are not limited to RAS or BRAF gene mutations and NTRK gene fusions. * Symptomatic central nervous system (CNS) metastases, leptomeningeal carcinomatosis, or untreated spinal cord compression. * Clinically significant active cardiovascular disease or history of myocardial infarction within 6 months, history of Torsades de pointes, or prolongation of the QTcF \>470 milliseconds on more than one electrocardiogram (ECG) during screening. Participants who are intended to receive vandetanib if randomized to the control arm are ineligible if QTcF is \>450 milliseconds. * Active uncontrolled systemic bacterial, viral, or fungal infection or serious ongoing uncontrolled intercurrent illness. * Active hemorrhage or at significant risk for hemorrhage. * Other malignancy unless nonmelanoma skin cancer, carcinoma in situ or malignancy diagnosed ≥2 years previously and not currently active. Participants with multiple endocrine neoplasia type 2 (MEN2) associated pheochromocytoma may be eligible.