Dabrafenib With or Without Trametinib in Treating Patients With Advanced Differentiated Thyroid Cancer

PRIMARY OBJECTIVES: I. To screen two different regimens (GSK2118436 \[BRAFi\] \[dabrafenib\] as a single agent versus the combination regimen of GSK2118436 \[BRAFi\] and GSK1120212 \[MEKi\] \[trametinib\]) and identify which regimen is more promising for subsequent testing in a phase III trial in radioiodine refractory BRAF-mutated differentiated thyroid cancer (DTC) patients. SECONDARY OBJECTIVES: I. To understand duration of objective response, progression-free survival and overall survival for each treatment group. II. To assess tolerability and adverse events of GSK2118436 (BRAFi) as a single agent and the tolerability and adverse events of GSK2118436 (BRAFi) and GSK1120212 (MEKi) in combination, in patients with DTC. III. To evaluate impact of experimental drugs on serum tumor marker thyroglobulin and its correlation with overall response rate. IV. To understand pharmacokinetic, pharmacogenetics and pharmacodynamics of experimental drugs using serial tumor biopsies, tumor blocks and peripheral blood. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive dabrafenib orally (PO) twice daily (BID) on days 1-28. Patients with disease progression may cross-over to arm II. ARM II: Patients receive dabrafenib PO BID and trametinib PO once daily (QD) on days 1-28. In both arms, courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for 4 weeks.