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RATIONALE: Celecoxib may stop the growth of cancer by stopping blood flow to the tumor and by blocking the enzymes necessary for tumor cell growth. PURPOSE: Phase II trial to study the effectiveness of celecoxib in treating patients who have relapsed prostate cancer following radiation therapy or radical prostatectomy. OBJECTIVES: * Determine the effect of celecoxib on prostate-specific antigen (PSA) levels in patients with prostate cancer in biochemical relapse after prior definitive radiotherapy or radical prostatectomy. * Compare the PSA doubling times in patients treated with this drug vs historical controls. * Compare the PSA doubling times in patients treated with this drug vs pretreatment PSA values. * Determine the time to clinical recurrence in patients treated with this drug. OUTLINE: Patients receive oral celecoxib twice daily. Treatment continues for 5 years in the absence of disease progression. Patients may continue treatment beyond 5 years at the discretion of the treating physician. PROJECTED ACCRUAL: A total of 100 patients will be accrued for this study.
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