Prostate Cancer Biology Analytics

Abstract

Prostate-specific antigen (PSA) time series exhibit both systematic trends and irregular fluctuations, complicating their interpretation in clinical contexts such as prostate cancer progression. In this study, we frame longitudinal PSA measurements within a stochastic dynamical systems perspective, drawing on the Fokker-Planck equation to decompose observed dynamics into directional (drift) and stochastic (diffusion) components. The drift term captures the underlying progression of disease activity, while the diffusion term represents measurement variability and biological noise. Using a multi-year PSA dataset, we estimate a positive but slow drift (≈0.8 units/year) and moderate diffusion, corresponding to a PSA doubling time of approximately 4.4 years. To further refine interpretation, we introduce a latent state formulation in which the observed PSA values are modeled as noisy realizations of an unobserved disease process. This state-space approach enables separation of signal from noise, yielding a smoothed trajectory that reflects underlying biological activity without assuming direct equivalence between PSA levels and disease stage. Importantly, while the latent state reduces the impact of stochastic fluctuations, it does not eliminate uncertainty and cannot uniquely distinguish between benign conditions, localized cancer, or metastatic disease. Our results highlight that PSA dynamics are best understood as a combination of deterministic progression and stochastic variability. Although drift-diffusion and latent-state models provide a principled framework for analyzing PSA trajectories, they remain insufficient for definitive clinical diagnosis in isolation. Integration with imaging, histopathology, and other clinical indicators is essential for accurate assessment of disease status. The analysis was performed on 25 longitudinal PSA measurements collected from a single prostate cancer patient during approximately five years of post-treatment follow-up.