Many have observed poor correlations between serum prostate-specific antigen (PSA) and tumor volume, and this noise undoubtedly reduces the diagnostic specificity of PSA.

To explore this phenomenon, we addressed the problem from a theoretical viewpoint. Specifically, we used a compartmental model and first-order kinetics to develop the mathematics necessary to relate serum PSA to tumor volume. We found that the resulting model fit well the observed kinetic data of PSA measured after biopsy or prostatectomy. The model also predicted a linear relationship between PSA and the sum of volumes of benign and malignant tissues, but the coefficients for this linear equation are more complex than previously thought. They reflect not only how much PSA may be present in each tissue but also 3 rate parameters and the volume of serum. Much of the noise in the linkage between PSA and tumor volume is due to individual patient differences in the 3 rate parameters and in serum volume. Our model predicts that without ways to directly measure the several involved rate parameters, we will not be able to accurately predict tumor volume from PSA. Nevertheless, surrogates for the missing parameters may exist and could lead to statistical models that could improve the prediction of tumor volume.