Selumetinib in Treating Patients With Papillary Thyroid Cancer That Did Not Respond to Radioactive Iodine

Inclusion Criteria:

* Histologically or cytologically confirmed papillary thyroid cancer or papillary thyroid cancer with follicular elements
* No longer amenable to radioactive iodine therapy or curative surgical resection

  * Tumor is no longer iodine avid
  * Tumor did not respond to the most recent radioactive iodine treatment
  * Patient is ineligible for further radioactive iodine therapy due to medical contraindications (e.g., lung toxicity)
* Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 20 mm with conventional techniques or as ≥ 10 mm with spiral CT scan
* Evidence of disease progression (objective growth of existing tumors)

  * New or enlarging measurable lesions within the past 12 months
  * If the most recent imaging study is older than 12 months, patients will still be eligible if objectively measurable disease progression is associated with clinical symptoms
* Archival tumor tissue available for mutational analysis
* No known brain metastases
* ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100%
* Life expectancy \> 12 weeks
* WBC ≥ 3,000/µL
* ANC ≥ 1,500/µL
* Platelet count ≥ 100,000/µL
* Total bilirubin normal
* AST and ALT \< 2.5 times upper limit of normal
* Creatinine normal OR creatinine clearance ≥ 60 mL/min
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception prior to, during, and for 4 weeks after completion of study treatment
* Able to understand and willing to sign a written informed consent document
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to selumetinib (AZD6244) or its excipient Captisol®
* QTc interval \> 450 msec or other factors that increase the risk of QT prolongation
* Arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome), including heart failure that meets NYHA class III and IV definition
* Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g., inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption
* Concurrent uncontrolled illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements
* At least 4 weeks since prior radiotherapy or chemotherapy (6 weeks for nitrosoureas or mitomycin C)
* Prior treatment with tyrosine kinase inhibitors that target RET or RAF
* Prior treatment with MEK inhibitors
* Concurrent combination antiretroviral therapy for HIV-positive patients
* Concurrent medication that can prolong the QT interval
* Other concurrent investigational agents