Celecoxib in Treating Patients With Progressive Metastatic Differentiated Thyroid Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed thyroid carcinoma, including 1 of the following subtypes: * Papillary * Follicular * Hurthle cell * Insular * Assessable disease, defined by at least 1 of the following: * Metastatic (including neck lymph nodes) measurable disease * At least 20 mm by conventional techniques or at least 10 mm by spiral CT scan * The following are not considered measurable disease: * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Tumor lesions within a previously irradiated area * Elevated serum thyroglobulin levels indicating the presence of metastatic disease * Must have negative thyroglobulin antibodies * Must have progressive disease within the past year, defined by at least 1 of the following: * At least 20% increase in serum thyroglobulin levels * At least 20% increase in the sum of the longest diameter of measurable lesions * Appearance of at least 1 new lesion * Failed or ineligible for standard therapy with iodine I 131 and/or surgery PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-2 Life expectancy * At least 1 year Hematopoietic * Absolute neutrophil count at least 1,000/mm\^3 * Platelet count at least 75,000/mm\^3 Hepatic * Bilirubin no greater than 2.0 mg/dL * AST/ALT no greater than 2 times upper limit of normal Renal * Creatinine no greater than 2.0 mg/dL Cardiovascular * No symptomatic congestive heart failure * No unstable angina pectoris * No uncontrolled cardiac arrhythmia Gastrointestinal * No prior symptomatic or complicated peptic ulcer disease by endoscopy within the past 6 months, defined by any of the following conditions: * Active gastric or duodenal ulcer * Gastric or duodenal perforation * Upper gastrointestinal bleeding Other * Not pregnant or nursing * Negative pregnancy test * No prior allergic reaction to celecoxib or sulfonamides * No prior urticaria, asthma, or allergic reaction to aspirin or other nonsteroidal anti-inflammatory agents * No ongoing or active infection * No psychiatric illness or social situation that would preclude study compliance * No other uncontrolled concurrent illness that would preclude study participation PRIOR CONCURRENT THERAPY: Biologic therapy * Not specified Chemotherapy * More than 1 month since prior systemic chemotherapy Endocrine therapy * Not specified Radiotherapy * See Disease Characteristics * More than 3 months since prior external beam radiotherapy (unless an indicator lesion is outside the radiation field) * More than 6 months since prior iodine I 131 therapy Surgery * See Disease Characteristics * More than 1 month since prior surgery Other * More than 2 weeks since prior conventional doses of celecoxib or rofecoxib for osteoarthritis, rheumatoid arthritis, or dysmenorrhea * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No concurrent chronic (more than 1 week of therapy) fluconazole therapy * Concurrent oral or IV bisphosphonates for bony metastases are allowed * Concurrent low-dose aspirin (no greater than 325 mg/day) for cardiovascular disease is allowed