Inclusion Criteria

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