Celecoxib in Treating Patients With Relapsed Prostate Cancer Following Radiation Therapy or Radical Prostatectomy

DISEASE CHARACTERISTICS: * Diagnosis of clinically localized adenocarcinoma of the prostate * T1 or T2 disease * Received prior primary treatment with definitive radiotherapy (at least 5,500 cGy) OR radical prostatectomy * Biochemical relapse within 5 years after prior primary therapy, defined as 1 of the following: * Detectable and rising prostate-specific antigen (PSA) after surgery (at least 2 values above the residual cancer detection limit of the assay) * PSA at least 2 values above 1 ng/mL OR at least 3 rising values at any level after radiotherapy * PSA no greater than 10 ng/mL PATIENT CHARACTERISTICS: Age * Not specified Performance status * ECOG 0-2 Life expectancy * Not specified Hematopoietic * Not specified Hepatic * ALT no greater than 2.5 times upper limit of normal Renal * Creatinine normal Other * No allergy to cyclooxygenase-2 inhibitors, aspirin, nonsteroidal anti-inflammatory drugs, or sulfa drugs * No untreated peptic ulcer disease PRIOR CONCURRENT THERAPY: Biologic therapy * Not specified Chemotherapy * No prior chemotherapy Endocrine therapy * More than 6 months since prior adjuvant or neoadjuvant hormonal therapy * Duration of prior adjuvant or neoadjuvant hormonal therapy must have been no more than 6 months Radiotherapy * See Disease Characteristics * Prior salvage radiotherapy after prostatectomy allowed Surgery * See Disease Characteristics