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 o f radiation therapy is presented. The clinical implications of the mod el are also investigated. Methods and Materials: Data from 122 patient s treated at Stanford University between December 1985 and December 19 90 were used. The general form of the model contains five parameters, two associated with a decreasing exponential, two with a rising expone ntial and one additional constant. A nonlinear steepest-descent proced ure that minimized chi-squared was used to determine the parameters pr oducing the best fit to a patient's data. The correlation of the model parameters with clinical findings was investigated using standard sta tistical techniques including multivariate life-table and logistic reg ression. Results: The data for all patients could be fit with either a decreasing exponential with or without the additional constant (nonre lapsing pattern with two or three parameters) or with a decreasing plu s rising exponential (relapsing pattern with three or four parameters) . In no instance were all five parameters of the general model require d 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-specifi c 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 tr eatment and the time to nadir, as calculated from the model parameters , was associated with the probability of clinical relapse. In no insta nce was the rate of initial decline ever exceeded by the rate of subse quent rise. Conclusion: The model is capable of describing the kinetic s of prostate-specific antigen levels found in patients after receivin g radiation therapy. The parameters derived from the model are strong correlates with clinical findings and patient outcome.