DISEASE CHARACTERISTICS:

• Histological evidence of hepatocellular carcinoma (HCC)

  • No evidence of residual or recurrent disease

• Received 1 of the following therapies:

  • Tumor resection between 4-8 weeks prior to study enrollment
  • Transarterial chemo-embolization between the past 4-8 weeks
  • Radiofrequency ablation and percutaneous ethanol injection (sequential or combinations thereof) between the past 2-8 weeks

• Meets 1 of the following high-risk features for recurrence:

  • History of resection of a single HCC > 5 cm
  • History of multifocal HCC (includes microsatellite disease found at time of resection)
  • History of vascular invasion (macro or micro)
  • History of poorly differentiated HCC
  • Underlying cirrhosis
• No Child-Pugh class C cirrhosis

PATIENT CHARACTERISTICS:

• Absolute neutrophil count > 1,500/mm^3
• Platelet count ≥ 75,000/mm^3
• Hemoglobin ≥ 9.0 g/dL
• Creatinine ≤ 2.0 mg/dL
• Bilirubin ≤ 2.0 mg/dL
• AST/ALT ≤ 3 times upper limit of normal (ULN)
• Alkaline phosphatase ≤ 3 times ULN
• INR ≤ 1.5 times ULN
• Albumin ≥ 2.5 g/dL
• ECOG performance status 0-2
• Life expectancy ≥ 2 years
• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception during and for at least 6 months after completion of study treatment
• No other malignancy within the past 5 years except nonmelanoma skin cancer
• Patients must agree not to wear contact lenses
• No history of ulcer disease or gastrointestinal bleeding
• No myocardial infarction within the past 18 months
• No cerebral vascular event within the past 18 months
• No history of aspirin or NSAID-induced asthma
• No history of Gilbert's syndrome
• No history of hypersensitivity reaction or allergy to sulfa drugs, aspirin, or other NSAIDs
• No liver transplantation candidates for phase I portion of the study
• No New York Heart Association class III or IV cardiac disease
• No interstitial lung disease
• No gastrointestinal disease prohibiting oral medication or requiring IV alimentation
• No active peptic ulcer disease
• No unstable angina pectoris
• No ongoing, active, or untreated infection
• No hypersensitivity to celecoxib
• No rising alpha-fetal protein (AFP) not attributable to hepatitis B or C virus
• No psychiatric illness or social situation that would preclude study compliance

PRIOR CONCURRENT THERAPY:

• No prior liver transplantation
• No prior chemotherapy or biologic therapy in the adjuvant setting
• No prior chest or mantle radiotherapy
• No concurrent aspirin or other nonsteroidal anti-inflammatory drug (NSAID)
• No concurrent interferon
• No concurrent oral steroids
• No concurrent anticoagulant therapy
• No concurrent CYP3A4 inducers or inhibitors
• No concurrent commercial or other investigational anticancer agents or therapies
• No concurrent selective cyclooxygenase-2 inhibitors
• No concurrent antineoplastic or antitumor agents, including chemotherapy, radiotherapy, immunotherapy, or hormonal anticancer therapy