Vandetanib to Treat Children and Adolescents With Medullary Thyroid Cancer

* INCLUSION CRITERIA: Age: Participants must be 5 to 18 years of age, inclusive. The first cohort of 3 to 6 participants enrolled on the trial will be at least 13 years of age. Diagnosis: Hereditary (Multiple endocrine neoplasia, type 2A (MEN 2A) or Multiple endocrine neoplasia, type 2B (MEN 2B) medullary thyroid carcinoma (histologically confirmed) that is unresectable, recurrent or metastatic. Participants must have previously had a characteristic germline mutation in the rearranged during transfection (RET) proto-oncogene documented. Results of the germline mutation testing will be obtained from the referring institution. Participants must have measurable disease as defined in Response Evaluation Criteria in Solid Tumors (RECIST) as the presence of at least one lesion that can be accurately measured in at least one dimension with longest diameter of at least 20 mm using conventional techniques or at least 10 mm with spiral computed tomography (CT) scan. Superficial (easily palpable) lymph nodes will be considered measurable. Participants must be able to take one of the oral formulations of vandetanib. Prior therapy: There are no standard chemotherapy regimens known to be effective for medullary thyroid carcinoma (MTC). Therefore, previously untreated participants are eligible if their tumor(s) are not surgically resectable. Participants must be at least 4 weeks from prior surgical procedures and surgical incisions must be healed. Participants must have had their last fraction of external beam radiation therapy at least 4 weeks prior to enrollment. Participants must have had their last dose of cytotoxic chemotherapy at least 28 days prior to enrollment, their last dose of biological therapy, such as biological response modifiers (e.g., cytokines), immunomodulatory agents, vaccines, differentiating agents, used to treat their cancer at least 7 days prior to enrollment, their last dose of a monoclonal antibody at least 30 days prior to enrollment, and their last dose of any investigational agent at least 30 days prior to enrollment. Participants must have received their last dose of short acting colony stimulating factor, such as filgrastim or sargramostim at least 72 hours prior to enrollment and their last dose of long-acting colony stimulating factors, such as polyethylene glycol (PEG)-filgrastim at least 7 days prior to enrollment. Participants must have recovered from the acute toxic effects of prior therapy to a grade 1 (Common Terminology Criteria for Adverse Events (CTCAE) v.3.0) level prior to enrollment. Performance Status: Lansky (for participants 10 years of age or younger) or Karnofsky (for participants older than 10 years) performance score greater than 50 Concomitant Medications: Participants who have previously had a thyroidectomy should be on thyroid hormone replacement therapy. Hematological Function: The peripheral absolute neutrophil count must be at least 1,500 micro liters and the platelet count must be at least 100,000 micro liters within 72 hours prior to enrollment. Coagulation: Prothrombin Time (PT) and Partial Thromboplastin Time (PTT) must not be more than 1.5 x ULN within 72 hours prior to enrollment. PT and PTT should drawn by venipuncture, rather than from a central venous catheter when feasible. Hepatic Function: Bilirubin must not be more than 1.5 x ULN and the aspartate aminotransferase (AST) and alanine aminotransferase (ALT) must not be more than 2.5 x ULN within 72 hours prior to enrollment. AST and ALT may be up to 5 x ULN within 72 hours prior to enrollment in participants with hepatic metastases. Renal Function: Participants must have an age-adjusted normal serum creatinine or a creatinine clearance of at least 60 ml/min/1.73 m\^2. Birth Control: Participants of child-bearing or child-fathering potential must be willing to use a medically effective form of birth control, which includes abstinence, while taking vandetanib and for 2 months after the last dose. Negative pregnancy test for women of childbearing potential. Informed Consent: Participants who are 18 years of age or legal guardians of participants who are younger than 18 years must sign an informed consent for the Pediatric Oncology Branch (POB) Screening Protocol prior to participating in studies required to determine eligibility for this trial. After confirmation of eligibility, participants or legal guardians of minor participants must sign an informed consent document for this trial, indicating that they are aware of the investigational nature of the proposed treatment, the risks and benefits of participating and the alternatives to participating. EXCLUSION CRITERIA: Pregnant or breast feeding females because the anti-angiogenic properties of vandetanib may be harmful to the developing fetus or nursing infant. Participants with pheochromocytoma as evidenced by elevated plasma free metanephrines. Electrolytes: Participants with a serum potassium less than 3.5 mmol/L or a serum calcium or magnesium below the lower limits of normal. Correction of these electrolyte abnormalities with supplements is allowed. Cardiac: Participants with a history of arrhythmia (multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia, uncontrolled atrial fibrillation, left bundle branch block) that is symptomatic or requires treatment (except for controlled atrial fibrillation) Participants with a history of congenitally prolonged Corrected QT Interval (QTc), a first degree relative with unexplained sudden death under 40 years of age, or a measured QTc (Bazett's correction) longer than 480 msec on electrocardiogram (ECG). ECGs should be performed after correction of electrolyte abnormalities. Participants with a prolonged QTc should have a repeat ECG at least 24 hour after the first, and the mean of the 2 QTcs should not exceed 480 msec. Participants who experienced QTc prolongation with other medications requiring discontinuation of that medication. Participants receiving a medication that has a known risk of QTc prolongation within 14 days (28 days for levomethadyl) of enrollment. Hypertension: Diastolic blood pressure above the 95% for age on at least 2 of 3 measurements with an appropriate-size cuff or patients who are currently taking anti-hypertensive therapy. Other clinically severe or uncontrolled systemic illness that could compromise the participants ability to tolerate vandetanib or could compromise study procedures or endpoints.