PROSTATE-SPECIFIC ANTIGEN KINETICS AFTER EXTERNAL-BEAM IRRADIATION FOR CARCINOMA OF THE PROSTATE

Purpose: A mathematical model that describes the kinetics of prostate-specific antigen measured in patients who received therapeutic doses of radiation therapy is presented. The clinical implications of the model are also investigated. Methods and Materials: Data from 122 patients treated at Stanford University between December 1985 and December 1990 were used. The general form of the model contains five parameters, two associated with a decreasing exponential, two with a rising exponential and one additional constant. A nonlinear steepest-descent procedure that minimized chi-squared was used to determine the parameters producing the best fit to a patient's data. The correlation of the model parameters with clinical findings was investigated using standard statistical techniques including multivariate life-table and logistic regression. Results: The data for all patients could be fit with either a decreasing exponential with or without the additional constant (nonrelapsing pattern with two or three parameters) or with a decreasing plus rising exponential (relapsing pattern with three or four parameters). In no instance were all five parameters of the general model required to describe a patient's data. Three of 61 patients with nonrelapsing patterns experienced clinical relapse, whereas 36 of 61 patients with relapsing patterns did. The logarithm of the initial prostate-specific antigen level and the corresponding model parameter correlated with T-stage and Gleason score. Among the patients with relapsing patterns, the nadir in antigen level occurred within 2 years of the start of treatment and the time to nadir, as calculated from the model parameters, was associated with the probability of clinical relapse. In no instance was the rate of initial decline ever exceeded by the rate of subsequent rise. Conclusion: The model is capable of describing the kinetics of prostate-specific antigen levels found in patients after receiving radiation therapy. The parameters derived from the model are strong correlates with clinical findings and patient outcome.