A Trial of Lenvatinib (E7080) in Subjects With Iodine-131 Refractory Differentiated Thyroid Cancer to Evaluate Whether an Oral Starting Dose of 18 Milligram (mg) Daily Will Provide Comparable Efficacy to a 24 mg Starting Dose, But Have a Better Safety Profile
A Trial of Lenvatinib (E7080) in Subjects With Iodine-131 Refractory Differentiated Thyroid Cancer to Evaluate Whether an Oral Starting Dose of 18 Milligram (mg) Daily Will Provide Comparable Efficacy to a 24 mg Starting Dose, But Have a Better Safety Profile
This is a multicenter, randomized, double-blind study being conducted as a postmarketing
 requirement to the US Food and Drug Administration (FDA) to evaluate whether there is a lower
 starting dosage of lenvatinib 24 mg once daily (QD) that provides comparable efficacy but has
 a better safety profile in participants with radioiodine-refractory differentiated thyroid
 cancer RR-DTC with radiographic evidence of disease progression within the prior 12 months.
This study consists of 2 phases, the Prerandomization Phase and the Randomization Phase. The
 Prerandomization Phase will last no longer than 28 days and will include a Screening Period
 to establish protocol eligibility and a Baseline Period to confirm eligibility and establish
 disease characteristics prior to randomization and treatment.

 The Randomization Phase will consist of a Treatment Period and a Follow-up Period. It will
 begin at the time of randomization of the first participant and will consist of 28-day
 blinded study treatment cycles. The data cutoff for the primary analysis will occur at the
 end of the Randomization Phase, which is defined as when the last participant enrolled
 completes the Week 24 tumor assessments or discontinues study treatment if before Week 24.

 Participants on treatment at the time of data cutoff for the primary analysis will remain on
 blinded investigational product until the primary analysis has been completed, after which
 they will transition to commercial lenvatinib outside the study. The last participant's last
 assessment (Off-treatment visit) will be the End of Study.

 Participants will be randomly assigned to treatment with 1 of 2 blinded starting dosages of
 lenvatinib in a 1:1 ratio to receive lenvatinib 18 mg or 24 mg orally once daily (QD). Dose
 reductions will occur in succession based on the previous dose level (24, 20, 14, 10, and 8
 mg QD, or 18, 14, 10, 8, and 4 mg QD, respectively). Once the dose has been reduced, it may
 not be increased at a later date.
Inclusion Criteria:

 1. Participants must have histologically or cytologically confirmed diagnosis of one of
 the following differentiated thyroid cancer (DTC) subtypes:

 1. Papillary thyroid cancer (PTC)

 -  Follicular variant

 -  Variants (including but not limited to tall cell, columnar cell,
 cribriform-morular, solid, oxyphil, Warthin's-like, trabecular, tumor with
 nodular fasciitis-like stroma, Hürthle cell variant of papillary carcinoma,
 poorly differentiated)

 2. Follicular thyroid cancer (FTC)

 -  Hurthle cell

 -  Clear cell

 -  Insular

 2. Measurable disease meeting the following criteria and confirmed by central
 radiographic review:

 1. At least 1 lesion of greater than or equal to (>=)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 that is serially measurable according to Response Evaluation
 Criteria in Solid Tumors (RECIST 1.1) using computed tomography/magnetic
 resonance imaging (CT/MRI). If there is only 1 target lesion and it is a
 non-lymph node, it should have a longest diameter of >=1.5 cm.

 2. Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies
 such as radiofrequency (RF) ablation must show evidence of progressive disease
 based on RECIST 1.1 to be deemed a target lesion.

 3. Participants must show evidence of disease progression within 12 months (an additional
 month will be allowed to accommodate actual dates of performance of screening scans,
 that is, within less than or equal to <=13 months) prior to signing informed consent,
 according to RECIST 1.1 assessed and confirmed by central radiographic review of CT
 and/or MRI scans.

 4. Participants must be Iodine-131 refractory/resistant as defined by at least one of the
 following:

 1. One or more measurable lesions that do not demonstrate iodine uptake on any
 radioiodine scan.

 2. One or more measurable lesions that have progressed according to RECIST 1.1
 within 12 months (an additional month will be allowed to accommodate actual dates
 of performance of screening scans, ie, within ≤13 months) after Iodine-131
 therapy, despite demonstration of radioiodine avidity at the time of that
 treatment by pre- or posttreatment scanning. These participants must not be
 eligible for possible curative surgery.

 3. Cumulative activity of Iodine-131 of greater than (>) 600 millicurie (mCi) or 22
 gigabecquerels (GBq), with the last dose administered at least 6 months prior to
 study entry.

 5. Participants with known brain metastases who have completed whole brain radiotherapy,
 stereotactic radiosurgery or complete surgical resection, will be eligible if they
 have remained clinically stable, asymptomatic, and off steroids for one month.

 6. Participants must be receiving thyroxine suppression therapy and thyroid stimulating
 hormone (TSH) should not be elevated (TSH should be <=5.50 micro-international units
 per liter [mcIU/ML]). When tolerated by the participant, thyroxine dose should be
 changed to achieve TSH suppression (TSH <0.50 mcIU/ML) and this dose may be changed
 concurrently upon starting study drug treatment.

 7. All chemotherapy or radiation-related toxicities must have resolved to Grade <2
 severity per Common Terminology Criteria for Adverse Events (CTCAE v4.03), except
 alopecia and infertility.

 8. Participants must have an Eastern Cooperative Oncology Group (ECOG) Performance Status
 of 0, 1, or 2.

 9. Adequately controlled blood pressure (BP) with or without antihypertensive
 medications, defined as BP ≤150/90 mmHg at Screening and no change in antihypertensive
 medications within 1 week prior to Cycle 1/Day 1.

 10. Adequate renal function defined as calculated creatinine clearance >=30 mL/min per the
 Cockcroft and Gault formula.

 11. Adequate bone marrow function:

 1. Absolute neutrophil count (ANC) >=1500/mm^3 (>=1.5*10^3/uL)

 2. Platelets >=100,000/mm^3 (>=100*10^9/L)

 3. Hemoglobin >=9.0 g/dL

 12. Adequate blood coagulation function as evidenced by an International Normalized Ratio
 (INR) <=1.5.

 13. Adequate liver function:

 1. Bilirubin <=1.5*upper limit of normal (ULN) except for unconjugated
 hyperbilirubinemia or Gilbert's syndrome.

 2. Alkaline phosphatase, alanine aminotransferase (ALT), and aspartate
 aminotransferase (AST) <=3*ULN (<=5*ULN if participant has liver metastases). If
 alkaline phosphatase is >3*ULN (in absence of liver metastases) or >5*ULN (in
 presence of liver metastases) AND the participant also is known to have bone
 metastases, the liver-specific alkaline phosphatase must be separated from the
 total and used to assess the liver function instead of total alkaline
 phosphatase.

 14. Males or females age >=18 years at the time of informed consent.

 15. Females must not be lactating or pregnant at Screening or Baseline (as documented by a
 negative beta-human chorionic gonadotropin [B-hCG] test with a minimum sensitivity of
 25 IU/L or equivalent units of B-hCG. A separate baseline assessment is required if a
 negative screening pregnancy test was obtained more than 72 hours before the first
 dose of study drug.

 16. All females will be considered to be of childbearing potential unless they are
 postmenopausal (amenorrheic for at least 12 consecutive months, in the appropriate age
 group and without other known or suspected cause) or have been sterilized surgically
 (ie, bilateral tubal ligation, total hysterectomy or bilateral oophorectomy, all with
 surgery at least 1 month before dosing).

 17. Females of childbearing potential should avoid becoming pregnant and use highly
 effective contraception while on treatment with lenvatinib and for at least 1 month
 after finishing treatment. Females of childbearing potential must not have had
 unprotected sexual intercourse within 30 days before study entry and must agree to use
 a highly effective method of contraception (example, total abstinence, an intrauterine
 device, a contraceptive implant, an oral contraceptive, or have a vasectomized partner
 with confirmed azoospermia) throughout the entire study period and for 30 days after
 study drug discontinuation. Females who are using hormonal contraceptives must have
 been on a stable dose of the same hormonal contraceptive product for at least 4 weeks
 before dosing and must continue to use the same contraceptive during the study and for
 30 days after study drug discontinuation. Women using oral hormonal contraceptives
 should add a barrier method.

 18. Participants must voluntarily agree to provide written informed consent.

 19. Participants must be willing and able to comply with all aspects of the protocol.

 Exclusion Criteria:

 1. Anaplastic or medullary carcinoma of the thyroid.

 2. Diagnosed with meningeal carcinomatosis.

 3. Two or more prior vascular endothelial growth factor (VEGF)/vascular endothelial
 growth factor receptor (VEGFR)-targeted therapies or any ongoing treatment for RR-DTC
 other than TSH-suppressive thyroid hormone therapy.

 4. Prior treatment with lenvatinib.

 5. Participants who have received any anticancer treatment within 21 days or any
 investigational agent within 30 days (or 5 half-lives) prior to the first dose of
 study drug and should have recovered from any toxicity related to previous anticancer
 treatment. This does not apply to the use of TSH suppressive thyroid hormone therapy.

 6. Major surgery (example, laparotomy, thoracotomy or joint replacement) within 3 weeks
 prior to randomization or elective surgery scheduled to be performed during the study.

 7. Participants having >1+ proteinuria on urine dipstick testing will undergo 24-hour
 urine collection for quantitative assessment of proteinuria. Participants with urine
 protein >=1 g/24 h will be ineligible.

 8. Gastrointestinal malabsorption or any other condition that in the opinion of the
 investigator might affect the absorption of study drug.

 9. Significant cardiovascular impairment: history of congestive heart failure greater
 than New York Heart Association (NYHA) Class II, unstable angina, myocardial
 infarction or cerebral vascular accident within 6 months of the first dose of study
 drug, or cardiac arrhythmia associated with hemodynamic instability.

 10. Prolongation of corrected QT interval (QTc) to >480 ms as demonstrated by a repeated
 electrocardiogram (ECG) or a clinically significant ECG abnormality, including a
 marked prolonged QT/QTc interval (example, a repeated demonstration of a QTc interval
 >500 ms).

 11. Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to
 the first dose of study drug.

 12. Active infection (any infection requiring treatment).

 13. Active malignancy (except for DTC or definitively treated melanoma in-situ, basal or
 squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix) within the
 past 24 months.

 14. Bleeding or thrombotic disorders.

 15. Known intolerance to study drug (or any of the excipients).

 16. Any medical or other condition that in the opinion of the investigator(s) would
 preclude the participant's participation in a clinical study.

 17. Females who are pregnant or breastfeeding.