Patient description: A 16-year-old girl came to the clinic complaining of weight gain and abnormal menstrual cycles. Her BMI was 24, but she has gained 5 kg in the past few weeks. She gets tired more frequently and does not have energy to go dancing with her friends. Her lab results were remarkable for high TSH levels (15 mU/L) and low free T4 levels (0.18 ng/dl). Her anti-TPO levels were extremely high (136 IU/ml). She was diagnosed with Hashimoto disease. She does not smoke and she is not sexually active.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Thyroid Cancer Thyroid Cancer, Medullary Differentiated Thyroid Cancer Papillary Thyroid Cancer Follicular Thyroid Cancer Poorly Differentiated Thyroid Gland Carcinoma All histologically or cytologically confirmed diagnosis of thyroid cancer, other than anaplastic or stromal-cell derived cancers Participants with differentiated thyroid cancers (DTC) must have negative thyroglobulin antibodies Measurable disease meeting the following and confirmed by central radiographic review At least 1 lesion of ≥ 1.0 centimeter (cm) in the longest diameter for a non- lymph node or ≥ 1.5 cm in the short-axis diameter for a lymph node which is serially measurable according to Response Evaluation in Solid Tumors (RECIST) 1.1 using computerized tomography/magnetic resonance imaging (CT/MRI). If there is only one target lesion and it is a non-lymph node, it should have a longest diameter of ≥ 1.5 cm Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies such as radiofrequency (RF) ablation must show evidence of progressive disease (substantial size increase of ≥ 20%) within 12 months to be deemed a target lesion Participants must show evidence of disease progression comparing (a) scan in screening and (b) historical scan obtained within 12 months prior to signing informed consent, according to 1.1 assessed and confirmed by central radiographic review of CT and/or MRI scans Participants with DTC must not be eligible for possible curative surgery and must be radioiodine (RAI)-refractory / resistant as defined by at least one of the following One or more measurable lesions that do not demonstrate iodine uptake on any radioiodine scan One or more measurable lesions that has progressed by 1.1 within 12 months of RAI therapy, despite demonstration of radioiodine avidity at the time of that treatment by pre or post-treatment scanning  Participants who have received any anticancer treatment (including Chinese herbal medicine specified for the treatment of tumor) within 21 days or any investigational agent within 30 days prior to the first dose of study drug. This does not apply to the use of TSH-suppressive thyroid hormone therapy Major surgery within 21 days prior to the first dose of study drug Palliative radiation therapy within 14 days prior to the first dose of study drug Participants having > 30 mg/mL urine protein on urine dipstick testing (Participants with urine protein < 1 g/24 hour (h) will be eligible) Gastrointestinal malabsorption or any other condition that in the opinion of the investigator might affect the absorption of Lenvatinib, Sorafenib, Cabozantinib, or Vandetanib Significant cardiovascular impairment: history of (a) congestive heart failure greater than New York Heart association (NYHA) Class II, (b) unstable angina, (c) myocardial infarction, (d) stroke, or (e) cardiac arrhythmia associated with impairment within 6 months of the first dose of study drug Bleeding or thrombotic disorders (Treatment with low molecular weight heparin is allowed) Radiographic evidence of major blood vessel invasion/infiltration Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 21 days prior to the first dose of study drug Active infection (any infection requiring systemic treatment)