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