Identification of Most Aggressive Carcinoma Among Patients Diagnosed With Prostate Cancer Using Mathematical Modeling of Prostate-Specific Antigen Increases

Clin Genitourin Cancer. 2016 Jun;14(3):210-217.e1. doi: 10.1016/j.clgc.2015.12.006. Epub 2015 Dec 18.


Background: Tools for differentiating aggressive and indolent prostate carcinoma (PCa) are needed. Mathematical modeling is a promising approach for longitudinal analysis of tumor marker kinetics.

Patients and methods: The prostate-specific antigen (PSA) increases from patients with PCa and those with benign prostatic hyperplasia (BPH) were retrospectively analyzed using a mathematical model. Using the NONMEM program, individual PSA kinetics were fit to the following equation: [d(PSA)/dt = (PROD.K × exp [RHO1 × t]) × (1 - BPH) + PROD.NK × exp (RHO2 × t) - KELIM × (PSA)], where RHO1 is the PSA production increase rate by PCa cells (PROD.K), RHO2 is the PSA production increase rate by non-PCa cells (PROD.NK), and KELIM is the PSA elimination rate. The comparative value of the modeled kinetic parameters, estimated for each patient, for predicting the D'Amico score and relapse-free survival (RFS) were tested using logistic regression analysis and multivariate survival tests.

Results: The PSA kinetics from 62 patients with BPH and 149 patients with PCa before radical prostatectomy were successfully modeled. We identified statistically significant relationships between the PSA growth rate related to cancer cells (RHO1) and the probability of D'Amico high-risk group (less than the median RHO1 vs. at the median or greater: odds ratio, 2.15; 95% confidence interval [CI], 1.00-4.77; P = .05). RHO1 was also a significant prognostic factor for RFS on univariate analysis and against other reported prognostic factors using multivariate Cox tests. Three independent prognostic factors of RFS were found: RHO1 (hazard ratio [HR], 2.71; 95% CI, 1.25-5.84; P = .01), Gleason score (HR, 8.54; 95% CI, 4.19-17.40; P < .01), and positive surgical margins (HR, 2.04; 95% CI, 1.05-3.97; P = .03).

Conclusion: Using a few PSA time points analyzed with a mathematical model (easily manageable in routine practice), it could be possible to determine before surgery whether a patient has presented with aggressive PCa.

Keywords: Decision support techniques; Models; PSA kinetics; Prostrate neoplasms; Theoretical.

MeSH terms

  • Aged
  • Disease-Free Survival
  • Humans
  • Kallikreins / blood*
  • Kaplan-Meier Estimate
  • Male
  • Middle Aged
  • Proportional Hazards Models
  • Prostate / pathology
  • Prostate-Specific Antigen / blood*
  • Prostatic Neoplasms / diagnosis*
  • Prostatic Neoplasms / mortality
  • Retrospective Studies
  • Risk Assessment
  • Tumor Burden


  • KLK3 protein, human
  • Kallikreins
  • Prostate-Specific Antigen