Sorafenib Tosylate in Treating Patients With Locally Advanced, Metastatic, or Locally Recurrent Thyroid Cancer

Inclusion Criteria: Histologically confirmed diagnosis of 1 of the following: Papillary thyroid cancer (stratum I) Papillary, follicular, Hurthle cell, insular, or anaplastic thyroid cancer (stratum II) Mixed histology, poorly differentiated, or tall-cell variants allowed Metastatic, locally advanced, or locally recurrent disease At least 1 unidimensionally measurable lesion >= 20 mm by conventional techniques OR >= 10 mm by spiral CT scan The following are considered non-measurable disease: Tumors in a previously irradiated area Bone lesions Leptomeningeal disease Ascites Pleural/pericardial effusion Lymphangitis cutis/pulmonis Abdominal masses not confirmed and followed by imaging techniques Cystic lesions Archival tumor tissue block OR material collected before study entry available (stratum I) Biopsy-accessible disease (stratum I) Performance status - ECOG 0-1 At least 6 months WBC >= 3,000/mm^3 Absolute neutrophil count >= 1,500/mm^3 Platelet count >= 100,000/mm^3 No bleeding diathesis Bilirubin =< 1.5 times upper limit of normal (ULN) AST and ALT =< 1.5 times ULN Creatinine =< 1.5 times ULN No uncontrolled hypertension Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception Willing to undergo 2 tumor biopsies during study participation (stratum I) No history of allergic reaction attributed to compounds of similar chemical or biologic composition to sorafenib No ongoing or active infection No psychiatric illness or social situation that would preclude study compliance No other uncontrolled illness No other concurrent malignancy except nonmetastatic nonmelanoma skin cancer or carcinoma in situ of the cervix No prior systemic chemotherapy for thyroid cancer (stratum I) Prior systemic chemotherapy used to treat a second primary cancer with curative intent allowed provided the primary cancer was treated more than 5 years before study entry No more than 3 prior systemic chemotherapy regimens for thyroid cancer (stratum II) More than 6 weeks since prior systemic chemotherapy (stratum II) No prior external beam radiotherapy to the sole site of measurable disease (except for patients with anaplastic thyroid cancer) More than 6 weeks since prior external beam radiotherapy More than 24 weeks since prior iodine I 131 Recovered from all prior therapy No prior sorafenib More than 6 weeks since prior investigational tumor-specific therapy Concurrent oral or IV bisphosphonates for bony metastases allowed at the discretion of the investigator No other concurrent tumor-specific or investigational therapy No concurrent combination antiretroviral therapy for HIV-positive patients No concurrent therapeutic anticoagulation Concurrent prophylactic anticoagulation (e.g., low-dose warfarin) for venous or arterial access devices allowed provided PT, INR, or PTT are normal