Modeling postradiation prostate specific antigen level kinetics

BACKGROUND The goals of this study are twofold: 1) to describe the postradiation kinetics of nonrecurring prostate carcinoma based on prostate specific antigen (PSA) levels in men who remain biochemically free of disease; and 2) to determine predictors of all three components of the resulting piecewise exponential model based on pretreatment and treatment characteristics. METHODS Between March 1988 and May 1994, 153 patients with T1‐T3 nonmetastatic prostate carcinoma were treated definitively with radiation therapy and at last follow‐up had not failed biochemically (PSA rising on 2 consecutive occasions to a level > 1.0 ng/mL or 3 consecutive elevations). All patients were required to have at least 6 posttreatment PSA determinations and a minimum follow‐up of 36 months. The median follow‐up was 53 months (range, 36‐94 months). A piecewise exponential model was used to describe the mean PSA levels because 1) the kinetics of postradiation PSA levels appear to follow first‐order rate processes, and 2) there is evidence that PSA levels may rise slightly several years after treatment. Nonlinear mixed effects modeling was used in this situation because of the aforementioned nonlinearity and because variability between patients and within patients (PSA variation) must be taken into account. In addition, this methodology allows for modeling parameters as a function of patient and treatment characteristics. RESULTS The random effects model based on the entire patient population demonstrated that PSA levels do not continue to drop 3 years after treatment, and that in fact the levels begin to rise slowly between 2‐3 years after treatment. Pretreatment PSA was the only independent predictor of baseline PSA at time zero (end of radiation therapy). Gleason score was the only independent predictor of the rate of PSA decline after treatment, in which tumors with Gleason scores 7‐10 drop at a slower rate than do tumors with Gleason scores 2‐6. Finally, pretreatment prostate volume was the only independent predictor of the postnadir rise in PSA level, in which larger volumes translate to a steeper slope. CONCLUSIONS The fact that pretreatment PSA level is the only independent predictor of the baseline PSA at time zero is not surprising. The observation that patients with tumors with higher Gleason scores have a slower rate of decline is in agreement with previous reports that these tumors contribute less PSA per unit volume than do tumors with moderate to well differentiation. Finally, the fact that no tumor‐related characteristic (only pretreatment prostate volume) was predictive independently of the observed postnadir rise in PSA level suggests that these patients were cured. Cancer 1998;83:130‐134. © 1998 American Cancer Society.